question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
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<p>In class I got given a diagram like this: (albeit without the Electrostatic force line)</p>
<p><img src="http://www.boredofstudies.org/wiki/images/b/bb/Sci_phys_quanta_strong_force.png" alt=""></p>
<p>However the teacher told us the nucleons are typically separated when the force is zero. So as the string force crosses the x axis. (as does our textbook)</p>
<p>However initially this did not make sense to me because electrostatic force will still be repelling (in the case of a proton-proton "bond"/interaction) and so surely the separation distance must be on the positive side to counteract the electrostatic force?</p> | g13412 | [
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<p>Consider a cube of mass M resting on a rough surface such that the coefficient of friction between the cube and the surface is K. So in order to just slide the cube I need to apply a minimum force of KMg, g= acceleration due to gravity.
Now IF I apply a force, F which is very small as compared to KMg in magnitude then the body will not slide because the surface will exert an equal amount of friction force on the body.
Now consider a sphere of same mass resting on the same surface having the same coefficient of friction. Now when I apply a force very very small in magnitude as compared to KMg, then an equal amount of frictional force will be exerted by the surface on the sphere at the point of contact. This frictional force will cause the sphere to rotate as it exerts a torque about the center of the sphere. Now as the sphere rotates the point of contact slides and hence now frictional force of magnitude KMg acts on it, pushes it forward and slowly sets the sphere on rolling motion. But This certainly constructs a perpetual motion machine and hence violates conservation of energy.
May I know where was I wrong, where is the flaw in this so called perpetual motion machine?</p> | g13413 | [
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<p>I see that many papers written on fundamentals of thermodynamics(theory) nowadays are by some old professors somewhere(there may be exceptions). Most active young faculty don't seem to be seriously interested in reinterpreting thermodynamics like nonequlibrium thermodynamics i.e. continuing the work of Ilya Prigogine etc. So is this worth while for a graduate student starting his research career to work in this area? Any open problems a fresh graduate student can aim to solve theoretically?</p> | g13414 | [
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<p>At least if $\vec v$ is really only a one dimensional parameter, measuring all the moments $\langle v^n \rangle_f$ seems to give me all the information to compute $\langle A \rangle_f$ with $A(v)$ being a function of $v$. So integer powers of the generator of the function algebra $v$ are special functions. </p>
<p>I wonder if there are other special functions whos expectation are equally useful and if so, how they depend of the system you consider. For example, let $\langle \dots \rangle_f$ be some prescrition to calculate a mean or expectation and</p>
<p>$$\langle A \rangle_f:=\int_\Gamma A(\vec v)\ f(\vec v)\ \text d \vec v,$$</p>
<p>then is there e.g. a statistical significance to $\langle f \rangle_f$?</p>
<p>Maybe this question has a "trivial" yes as answer, because there are more options than taylor series to give a basis for some function algebra of elements $f(v_1,v_2,\dots)$. However, I don't know how this changes if one considers noncomutative generators $[v_1,v_2]\ne0$.</p>
<p>The question comes in part because I'm intimidated by relations like</p>
<p>$$\langle T^n\rangle \equiv \int_0^\infty E^{n-1}\, e^{ - \left( {E /T } \right)^C }{\rm d}E\ = \tfrac{\Gamma \left(\tfrac{n }{ C }\right)}{C} \cdot T^n,$$</p>
<p>i.e. $\langle A(E) \rangle$ expectation values are apprearently trivial to compute for weights which are polynomial in functions $f_{\ T,C}(E)=e^{ - \left( {E /T } \right)^C}$.</p> | g13415 | [
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<blockquote>
<p>Question: Find the relationship between angles $\theta$ and $\phi$
using the equations of equilibrium and solve for $\theta$.</p>
<p>Express your equation for $\theta$ in terms of $\phi$.</p>
<p><em>Hint: To derive the relationship between angles $\theta$ and $\phi$,
you first must write the equations of equilibrium for the pulley. Once
you have the equations of equilibrium, you then can isolate the angles
and solve the two equations</em>.</p>
</blockquote>
<p>I know that $T_D\cos\theta=T_C\cos\phi$.
I also know that $T_D\sin\theta=T_C+T_C\sin\phi$. </p>
<p>I tried solving these equations for $\theta$ in terms of $\phi$, I get keep getting stuck.</p>
<p><img src="http://i.stack.imgur.com/G78kL.jpg" alt="Diagram"></p> | g13416 | [
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<p>I'd like to numerically simulate the magnetic field due to a cylindrical rare earth magnet of known dimensions at a bunch of points $\vec{r}=(x,y,z)$ from its origin. My goal is to be as accurate as possible up to some global normalization which ultimately doesn't matter for my application.</p>
<p>My approach is to simply assume the magnet is made of a continuum of dipoles and do the relevant integral:</p>
<p>$$
\frac{\mu_0 m}{4\pi}\int\int\int \frac{3\left(\hat{m}\cdot\frac{\vec{r}-\vec{r}'}{||\vec{r}-\vec{r}'||}\right)\frac{\vec{r}-\vec{r}'}{||\vec{r}-\vec{r}'||}-\hat{m}}{||\vec{r}-\vec{r}'||^3}d\vec{r}'
$$</p>
<p>where the dipole moment norm $m=||\vec{m}||$ is the aforementioned global normalization.</p>
<p>Performing this integral is easy and it works etc., my question is about the physics: am I leaving anything out? Will a commercial solver include any physics that I haven't? In general, what will be my biggest source of error (except that I don't know $m$)?</p>
<p>Thanks!</p> | g13417 | [
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<p>Why do wave functions spread out over time? Where in the math does quantum mechanics state this? As far as I've seen, the waves are not required to spread, and what does this mean if they do?</p> | g13418 | [
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<p>Suppose that two masses with different mass are connected by a string in horizontal frictionless table. Then when there is equal acceleration for two masses, string force would extend in some direction. My question here, why don't two boxes create canceling effect for string's stretching? (Often, in we just calculate one box's force opposite to the direction of acceleration and equals to kx, which solves the problem. But why?)</p> | g13419 | [
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<p>My book is incredibly scarce on insulator based Gauss law questions. Conductors seem to handle themselves pretty simply.</p>
<p>Here's a question I'm working on that isn't part of my book.
<img src="http://i.imgur.com/y2cDZdl.png" alt="question">
where the radii are $a,b,c,d$ from smallest to largest and gray regions are insulating spherical shells with charge distributions.</p>
<blockquote>
<p>Given $a,b,c,d,q$ Find:-<br>
1)$E(r)$ for all the different positions<br>
2)Graph $E(r)$<br>
3)Find volume charge densities</p>
</blockquote>
<ul>
<li>I've never done "partial" shaped insulators, my thought process is that since $\Phi = \frac{q_i}{\epsilon_0}$ and $q_i$ is relative to how much of the volume is enclosed by whatever gaussian surface with radius r we make:</li>
</ul>
<p>$\rho = \frac{q}{V}$</p>
<p>$\rho \cdot V_i = q_i$</p>
<p>$\int^r_a \rho 4 \pi r^2 dr = q_i$</p>
<p>is this the right process?</p>
<ul>
<li>Conductors are conveniently discontinuous and easy to handle in separate "radius chunks", but for insulators shouldn't they scramble each other? when I'm dealing with between the outer shell, or beyond the outer shell, how do i handle the fully enclosed inner shell? My gut says it's additive and could be treated as a point charge, but I have no way of being sure.</li>
</ul>
<p>Thanks for any help.</p> | g13420 | [
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<p>I was often told by my professor, using the following example, to demonstrate the relationship of conservation of energy and <a href="http://en.wikipedia.org/wiki/Lenz%27s_law" rel="nofollow">Lenz's Law</a>.</p>
<p>If you push a conductor into a constant magnetic field. By <a href="http://simple.wikipedia.org/wiki/Lenz%27s_law" rel="nofollow">Lenz's Law</a>, voltage will be induced to oppose the "cause" which then resists the conductor from moving quicker which would be a violation of conservation of energy. In other words, if you push the rod very slightly, and the induced force turns out to push it even further, you generate infinite energy which then contradicts the conservation of energy law.</p>
<p>However, I wasn't happy enough by this answer, even though the fact is that you won't get infinite energy. I was thinking, whether it is something to do with the things happening on the atomic scale. Considering a more trivial example, a magnet moving towards a current loop, </p>
<p>so why would it produce a opposite pole to resist the change? </p>
<p>Is it something to do with the cutting flux of the magenetic field? </p>
<p>Why must a field be created to cancel the effect? </p>
<p>Why can't nothing happen? </p>
<p>Or is it just a matter of fact in nature? </p>
<p>I am finding this hard to understand how this really works. Is it a virtual particle?</p>
<p>Please explain the above phenomena without relating it to energy conservation law.</p>
<p><img src="https://encrypted-tbn2.gstatic.com/images?q=tbn%3aANd9GcQDqLDM2ItVWprRaOhuwQLfirdc2Rwgh0r15ONevI9yT0ZiEMQB-g" alt="MOVING conductor in a magnetic field"></p> | g13421 | [
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<p>If there were extra compact dimensions,and at the big bang all dimensions were compact,my question is why the big bang failed to expand those presumed extra dimensions like it did with the 3 spatial classical dimensions and time?Moreover the expansion is still ongoing so why the presumed extra dimensions are fixed in size?Does this have anything to do with the initial energy available at the big bang?Would this validate the many world hypothesis so that the number of the expanded dimensions and the still compact ones are random?or would this help to "dismiss" the whole idea of extra dimensions?</p> | g418 | [
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<p>Looking at the <a href="http://en.wikipedia.org/wiki/Nakajima-Zwanzig_equation" rel="nofollow">Nakajima-Zwanzig equation</a>, wich gives the time evolution of a projection $\cal {P} \rho$ of a full density matrix $\rho$, I am wondering if the trace of $\cal P \rho$ is preserved under time evolution.</p>
<p>The terms like $LX \stackrel{def}= \dfrac{i}{\hbar} [X,H]$ have a null trace, but it seems there is no reason why terms like $\mathcal {P} L X$ necessarily have a null trace, so it seems that the trace of the projected density matrix is not necessarily conserved.</p>
<p>Is it correct ?</p> | g13422 | [
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<p>I have a conceputal question regarding the following problem:</p>
<p>A round massive stone disk with diameter $0.600 m$ has a mass of $50.0 kg$. The stone rotates at an angular velocity of $115.2 rad/s$, around an axis located at the center of the disk. An axe pressed against the disk applies a tangential frictional force, $F_f$ at $50.0 N$. Assume that we turn off the rotating power of the disk, so that the frictional force is the only force acting on the disk. What is the magnitude of the angular acceleration, $\alpha$, of the disk?</p>
<p>OK, so I have calculated the torque ($-15 Nm$), and the moment of inertia ($I = 2.25 kg \cdot m^2$). By using the formula:</p>
<p>$$\tau = I \alpha$$</p>
<p>It is easy to show that $\alpha = -6.67 rad/s^2$, which is also the correct answer.</p>
<p>However, say I want to try to solve this in another way, without using the torque and moment of inertia. Since the frictional force is the only force acting on the disk, I would assume that we would have:</p>
<p>$$F_f = ma_T$$</p>
<p>$$-50 = ma_T$$</p>
<p>$$-50 = 50 \cdot a_T$$</p>
<p>$$a_T = - 1 m/s^2$$</p>
<p>And since we have:</p>
<p>$$a_T = r \alpha$$</p>
<p>This gives:</p>
<p>$$\alpha = \frac{-1}{0.3} = -3.33 rad/s^2$$</p>
<p>Which is not the same answer. So why doesn't this second approach work? If anyone can explain this to me, I would really appreciate it!</p> | g13423 | [
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<p>Does anyone have a (semi-)intuitive explanation of why momentum is the Fourier transform variable of position?</p>
<p>(By semi-intuitive I mean, I already have intuition on Fourier transform between time/frequency domains in general, but I don't see why momentum would be the Fourier transform variable of position. E.g. I'd expect it to be a derivative instead.)</p> | g8 | [
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<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/24548/is-the-portal-feasible-in-real-life">Is the Portal feasible in real life?</a> </p>
</blockquote>
<p>I'm designing a plausible faster-than-light (FTL) drive for a SF universe. Here's what I have so far. I'm aware of existing attempts, e.g., Alcubierre's warp drive. I'm taking a different approach, and would appreciate comments from physicists on where I am (too) implausible.</p>
<p>The drive is what I call a "space-skip" drive. You have a drive and an matter/anti-matter battery attached to it (typically half-full.) When you activate the drive, you instantaneously change your spatial coordinates only; any change in your gravitational potential energy is added to or taken away from the battery. Your momentum doesn't change. You do end up interpenetrating whatever matter there is at your destination so it's a good idea to skip into high vacuum areas (e.g, into the wake of a planetoid.)</p>
<p>Since you're changing only your coordinates, your kinetic energy does not change. Infinite energy isn't needed, nor do you need immense shielding to protect against .999c particles or radiation hitting your ship.</p>
<p>A skip conserves energy, linear momentum, angular momentum, charge, etc. Did I miss anything?</p>
<p>If you need to match velocity vectors with your destination, a simple way is to skip near a sun and simply fall for a bit (with the falling vector's direction matching the velocity change vector you need.) You'll deplete the battery somewhat when you do that, of course.</p>
<p>The universe "cooperates" with the drive to preserve causality. Specifically, you can not skip to any coordinate until your resulting light cone will not violate causality. </p>
<p>Note that special relativity (as I understand it) does in fact allow superluminal travel as long as causality isn't violated; if I skipped to Pluto, was careful not to change my velocity, and skipped back to Earth, I believe I don't actually break anything.</p>
<p>If two ships are involved, say A and B, and A skips from Earth to Pluto, and B at Pluto has a non-zero velocity with respect to A, then "censorship" occurs and B will find that the drive refuses to work in any attempts to travel back to Earth until enough time passes in B's frame that causality is preserved.</p>
<p>So what do you think? Anything obviously impossible here (assuming you can actually make stuff skip?)</p> | g419 | [
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<p>When some smooth surface (like that of a steel or glass plate) is brought in contact with steam (over e.g. boiling milk) then water is usually seen to condense on that surface not uniformly but as droplets. What are the equations which govern the formation and growth of these droplets ? In particular what role does the geometry of the surface plays in it? Also it is possible to prepare experimental conditions where no droplets are formed but water condenses uniformly ? </p> | g13424 | [
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<p>Or, why is QFT "better" than QM?</p>
<p>There may be many answers.</p>
<p>For one example of an answer to a parallel question, GR is better than Newtonian gravity (NG) because it gets the perihelion advance of Mercury right.</p>
<p>You could also say that GR predicts a better black hole than NG, but that's a harder sale.</p>
<p>For QFT versus QM, I've heard of the Lamb shift, but what else makes QFT superior?</p> | g13425 | [
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<p>I need to show that Green Function:</p>
<p>$\displaystyle G(\vec{r},t;\vec{r}^{\prime},t^{\prime}) = \frac{\delta(t-t^{\prime}\pm |\vec{r}-\vec{r}^{\prime}|\,/c)}{|\vec{r}-\vec{r}^{\prime}|}$</p>
<p>Obeys</p>
<p>$\displaystyle \nabla^2 G -\frac{1}{c^2}\frac{\partial^2 G}{\partial t^2} = -4\pi \delta(\vec{r}-\vec{r}^{\prime})\delta(t-t^{\prime})$</p>
<p>I tried to use the identity for Laplacian :</p>
<p>$\displaystyle \nabla^2 (\psi\phi) = \phi\nabla^2\psi + \psi\nabla^2\phi + 2\vec{\nabla}\phi\cdot\vec{\nabla}\psi $</p>
<p>As follows:</p>
<p><img src="http://i.stack.imgur.com/9DJKa.jpg" alt="My work"></p>
<p>But I couldn't get nice results. Any suggestions?</p> | g13426 | [
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<p>In the image, it looks like the tangential direction is always 45 degrees away from the string, not 90 degrees. Is it not the circular path that the solution is talking about?</p>
<p><img src="http://i.stack.imgur.com/dyjFb.png" alt="enter image description here"></p> | g13427 | [
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... |
<p>Consider a zero-temperature, one-dimensional crystal with allowed electron momenta $k_n = \frac{2\pi n}{L}$.</p>
<p><strong>Question:</strong> Which is the more correct way to think about the Fermi sea? </p>
<ol>
<li><p>Sharp plane waves --</p>
<p>$$ \prod_{\epsilon_k<\epsilon_f} c_{k\uparrow}^\dagger c_{k\downarrow}^\dagger \lvert 0\rangle$$</p>
<p>or</p></li>
<li><p>Wave packets that are very narrow in momentum space --</p>
<p>$$ \prod_{\epsilon_{k_1}<\epsilon_f, \epsilon_{k_2}<\epsilon_f} \alpha_{k_1\uparrow}^\dagger(x_{k_1}) \alpha_{k_2\downarrow}^\dagger(x_{k_2}) \lvert 0\rangle,$$</p>
<p>where</p>
<p>$$\alpha_{k\uparrow}^\dagger(x_k) = \sum_q \exp\biggl[-\frac{1}{2}\biggl(\frac{q-k}{\delta}\biggr)^2 + i q x_k\biggr]\ c_{q\uparrow}^\dagger,$$</p>
<p>with a small width $\delta$ and randomly distributed positions $x_{k_1},x_{k_2}$.</p></li>
</ol>
<p>Also, if (2) is more correct, what determines the width $\delta$?</p>
<p><strong>Discussion:</strong>
I expected sharp plane waves. But wave packets seem necessary to make sense of the semiclassical equation of motion:</p>
<p>$$\frac{d}{dt}k = -e E\tag{3}$$</p>
<p>which, as I understand it, applies to the center $k$ of a given wave packet.</p>
<p>For a definite example where wave packets seem necessary, consider <a href="http://en.wikipedia.org/wiki/Bloch_oscillations" rel="nofollow">Bloch oscillations</a>. One solves for the positions $x_k$ as a function of time using (3).</p> | g13428 | [
0.0038506798446178436,
0.056462373584508896,
-0.009253794327378273,
-0.015773985534906387,
0.065181203186512,
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0.02659456804394722,
0.05249309912323952,
-0.017232820391654968,
0.0645... |
<p>This regards the following problem:</p>
<p>A ray of light is traveling in glass and strikes a glass/liquid interface. The angle of incidence is $58.0^\circ$ and the index of refraction of the glass is $n = 1.50$. What is the largest index of refraction that the liquid can have, such that none of the light is transmitted into the liquid and all of it is reflected back into the glass?</p>
<p>My solution: We have $n_1 \sin \theta_1 = n_2 \sin \theta_2$. We wish to maximize $n_2$ provided $90^\circ \leq \theta \leq 180^\circ$. Plugging in our givens, we have $(1.50)(\sin 58^\circ) = n_2 \sin \theta_2 \rightarrow n_2 = \frac{(1.50)(\sin 58^\circ)}{\sin \theta_2}$. Since we wsh to maximize $n_2$, we should minimize $\sin \theta_2$, which can be any value in $(0, 1]$ so there is no theoretical limit on the size of $n_2$ (according to this math)</p>
<p>However, the textbook says the correct maximum is $1.27$, which is taking $\theta_2 = 90^\circ$. I don't think this is right at all, since if anything that is the <em>minimum</em>. Consider $1 < n_2 < 1.27$. Then $1.27 > \sin \theta_2 > 1$, which is impossible given the range of the sine function over the reals.</p>
<p>Who is right?</p> | g13429 | [
-0.0013908211840316653,
0.012887978926301003,
-0.007787042297422886,
0.003706490620970726,
-0.015588820911943913,
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-0.005082535557448864,
0.04891484975814819,
0.10104802250862122,
-0.014829976484179497,
... |
<p>The following is the solution to the 1D diffusion equation with diffusion coefficient D, initial particle position $x_0$, and a perfectly absorbing boundary at $x=0$ (s.t. $P(x=0)=0$).</p>
<p>$$
P(x;t)=\frac{1}{\sqrt{4 \pi D t}}e^{-\frac{(x-x_0)^2}{4 D t}} - \frac{1}{\sqrt{4 \pi D t}}e^{-\frac{(x+x_0)^2}{4 D t}}
$$</p>
<p>If I understand correctly, for an $x_0>0$.</p>
<p>$$
P(\text{no collision at time $t$})=\int_0^\infty P(x;t) dx
$$</p>
<p>In other words, the total probability in allowed space at time $t$ is exactly the probability that the particle <em>never</em> contacted the absorbing boundary at $x=0$ up to time $t$. What I want to compute is the rate of probability loss $k(t)$. From above, it seems that would be:</p>
<p>$$
k(t) = \frac{d}{dt} \int_0^\infty P(x;t) dx
$$</p>
<p>evaluating with mathematica reveals:
$$
k(t)=-\frac{D x_0}{2 \sqrt{\pi}} \left(\frac{1}{D t}\right)^{3/2} e^{-\frac{x_0^2}{4 D t}}
$$</p>
<p>which seems reasonable. </p>
<p>It seems that there should be a way to compute $k(t)$ <em>without</em> computing the spatial integration across $x$, perhaps some computation involving only the boundary. I thought since all the loss occurs at $x=0$, the time derivative of $P(x;t)$ evaluated at $x=0$ should be k(t). However, the result of that calculation is 0.</p>
<p><em>Question: is there a way to compute k(t) without computing the spatial integral over the $x$ domain?</em></p> | g13430 | [
0.05409390106797218,
-0.02283034473657608,
-0.000010178368938795757,
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0.020692795515060425,
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0.08660255372524261,
0.06920439749956131,
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0.0064628529362380505,
0.0030293790623545647,
0.03489101305603981,
0.07187825441360474,
0.... |
<p>I'm learning about the 2D ferromagnetic Ising model in zero field and trying to verify what I know by calculating the ground-state energy for the state with all 'up' spins in a 3x3 lattice.</p>
<p>$$H = -J\sum_{<i,j>}s_{i}s_{j}$$</p>
<p>where the sum is over nearest neighbors.</p>
<p>My question is, how do you include the energy values for each spin? Do you just calculate the hamiltonian for each site and then add the sites together?</p>
<p>In that case, I get, assuming fixed boundaries, -4J for the central spin, -2J for each of the four spins on the corners (two nearest neighbors), and -3J for each of the four spins in the middle of the edge rows and columns (three nearest neighbors).</p>
<p>Adding it all together, I get H = -24J for the entire lattice.</p>
<p>In Chandler's stat mech book, he says that the lowest energy of the Ising model on a square lattice is given by -2NJ, where N is the number of spins. He doesn't specify what the boundary conditions are, but I assume he means fixed boundaries. Here, that means the lowest energy should be -18J. What am I doing wrong?</p> | g13431 | [
0.03288187459111214,
-0.002984919585287571,
-0.009255719371140003,
-0.014450544491410255,
-0.013294760137796402,
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0.08751804381608963,
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-0.01982850767672062,
-0.02479470707476139,
0.029630620032548904,
-0.009073607623577118,
... |
<p>Let's make the question easier by considering two-level atoms(with spin states, i.e. spin up $|\uparrow\rangle$ and spin down $|\downarrow\rangle$). An article I recently read claims that atoms do not have dipole moments when they are in energy eigenstates (i.e. when you put it into a magnetic field in z direction).</p>
<p>I was thinking if it's an eigenstate, since the spin cannot be pointing in z direction (remember it's actually pointing in a cone area), how could it not have a dipole moment?</p> | g13432 | [
-0.07115232944488525,
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-0.016141055151820183,
-0.03171413019299507,
-0.020546335726976395,
0.018990524113178253,
-0.064... |
<p>As the title says, does a particle lose its location wavefunction if its location is measured exactly (I know this would be impossible in reality)?</p>
<p>Also, in reality, if one measures a particle, does the wavefunction of a particle become something different from original afterwards?</p> | g13433 | [
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0.001759611419402063,
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0.06707555055618286,
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0.01387729961425066,
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... |
<p>I was always curious how scientists achieve a particle with particular wavefunction (of location and spins etc.) </p>
<p>So how do they achieve it? Or is this impossible?</p> | g13434 | [
-0.024480514228343964,
-0.02414967678487301,
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-0.013367364183068275,
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0.016389358788728714,
0.07080631703138351,
-0... |
<p>The relation</p>
<p>$$\psi=Ce^{i/\hbar(Et-\mathbf{p}\cdot\mathbf{x})}\tag{1}$$</p>
<p>satisfies the Klein Gordon equation on the mass shell, i.e. for $E^2=p^2+m^2$.</p>
<p>Now let's think in the reverse direction.
Relation (1) should satisfy the PDE:</p>
<p>$$\frac{\partial^2 \psi}{\partial E^2}-\frac{\partial^2 \psi}{\partial p_x^2}-\frac{\partial^2 \psi}{\partial p_y^2}-\frac{\partial^2 \psi}{\partial p_z^2}=0\tag{2}$$ </p>
<p>on the "coordinate shell":
$$ t^2-x^2-y^2-z^2=0 $$
Could relation (2) be related to a gravitational wave?</p>
<p>[You may assume that observation is being made from a Local Inertial Frame(your lab). Alternatively you may think of upgraded forms of the given equations in the curved spacetime context]</p>
<p>Allied issue: Going "off the mass shell" has produced interesting results in particle physics?What about the prospects of going "off the coordinate shell"? </p> | g13435 | [
0.043550413101911545,
0.020285962149500847,
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-0.010226602666079998,
0.029717586934566498,
0.009351402521133423,
0.04173741117119789,
0.0... |
<p>I was solving a practice Physics GRE and there was a question about springs connected in series and parallel. I was too lazy to derive the way the spring constants add in each case. But I knew how capacitances and resistances add when they are connected in series/parallel. So I reasoned that spring constants should behave as capcitances because both springs and capacitors store energy.</p>
<p>This line reasoning did give me the correct answer for how spring constants add, but I was just curious if this analogy makes sense, and if it does, how far one can take it. That is, knowing just that two things store energy, what all can you say will be similar for the two things.</p> | g13436 | [
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0.007331793196499348,
0.013827876187860966,
0... |
<p><strong>PART 1</strong>:<br>
I was reading the article <a href="http://en.wikipedia.org/wiki/Relativity_of_simultaneity" rel="nofollow">Relativity of simultaneity</a> Wikipedia. I couldn't understand this line: </p>
<blockquote>
<p>"if the two events are causally connected ("event A causes event B"), the causal order is preserved (i.e., "event A precedes event B") in all frames of reference." </p>
</blockquote>
<p>Is this an assumption or a consequence of STR? Please explain. </p>
<hr>
<p>Note: My question consists of 2 parts this is the 2nd part.<br>
Below is a genral version of my previous question question:<a href="http://physics.stackexchange.com/questions/98489/breaking-the-simultaneity">Breaking the simultaneity</a>. </p>
<p><strong>PART 2:</strong><br>
Let there be three events $A$,$B$ and $C$ s.t: $C$ is the result of Simultaneous occurrence of $A$ and $B$. In other words $C$ occurs <em>iff</em> $A$ and $B$ are simultaneous.<br>
Now as we know in STR any two events separated in space are not simultaneous in different frames. So In some frames $C$ will occur and in some $C$ will not occur which will cause paradox.<br>
I tried many thought experiments to make such a paradox but i failed. In all the experiments that i thought i could not break the causality even by breaking the simultaneity because everytime the fact: "all signals move slower than light" preserved the causality. </p>
<p>So why causlity remains preserved always? Is it due to the fact that nothing can move faster than light?</p> | g13437 | [
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-0.05638482794165611,
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0.00837715808302164,
0.03... |
<p>I was wondering if it is possible to move the atom nucleus and leave behind the electrons? I can imagine that the electrons will follow the nucleus. But what if the speed of the nucleus is almost the same as the speed of the electrons or faster. where will the electrons go?</p>
<p>If it is not possible, do we have a theory I can read to explain what could happen?</p>
<p><br>
<em>(Edit: as of the comments, "core" actually refers to "nucleus" -changed)</em></p> | g13438 | [
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0.05086210370063782,
0.009437669068574905,
-0... |
<p>I have completely no idea and I am inquiring about this as it is an interesting question that popped in my head while doing physics homework.</p> | g13439 | [
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0.06341125071048737,
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0.005510146263986826,
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0.001201152103021741,
-0.036805201321840286,
-0.... |
<ol>
<li><p>If I wanted to solve the <a href="http://en.wikipedia.org/wiki/Einstein_field_equations" rel="nofollow">Einstein equations</a> for the solar system, which choice of $g_{\mu\nu}$ and $T_{\mu\nu}$ is more suitable? </p></li>
<li><p>I thought about using a <a href="http://en.wikipedia.org/wiki/Schwarzschild_metric" rel="nofollow">Schwarzschild metric</a> near each planet, but how to connect them?</p></li>
</ol> | g13440 | [
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0.05828256160020828,
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0.05314645916223526,
-0.... |
<p>In a conformal field theory, is it possible to construct a machine that shrinks or expands objects?</p> | g13441 | [
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0.05677180364727974,
0.... |
<p>I heard from my lecturer that electron has dual nature. For that instance in young's double slit experiment electron exhibits as a particle at ends but it acts as a wave in between the ends. It under goes diffraction and bends. But we don't see a rise in energy. It has to produce 500kev of energy (please correct if my approximation is wrong) according to <a href="http://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence">mass energy equivalence relation</a>. But wave is a form of pure energy and doesn't show properties of having mass as of experimental diffraction. So where is the mass gone?</p> | g13442 | [
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0.018009118735790253,
0.009202520363032818,
0.0141... |
<p>I have been reading Young's book called: <em>University physics with modern physics</em> and on page 1284 author states that we can derive Lorenz time transformation by eliminating two equations for Lorentz space transformation along the vector of relative speed $u$. First we eliminate them for $x$ and then for $x'$.</p>
<p>The equations to eliminate are:</p>
<p>\begin{equation}
x=\gamma(x'+ut')
\end{equation}</p>
<p>\begin{equation}
x'=\gamma(x+ut)
\end{equation}</p>
<p>After elimination we are supposed to get the following Lorentz transformations:</p>
<p>\begin{equation}
t'=\gamma(t+ux/c^2)
\end{equation}</p>
<p>\begin{equation}
t =\gamma(t-ux/c^2)
\end{equation}</p>
<p>There is also an article about this <a href="http://arxiv.org/pdf/physics/0606103v4.pdf" rel="nofollow">here</a>. But neither in this article, neither in the Young's book the solution is shown. I have been trying to derive it myself, but failed and am now puting it as a topic on this forum. </p> | g13443 | [
0.0254360381513834,
0.001105526345781982,
0.005914408713579178,
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0.07152209430932999,
0.015670105814933777,
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0.03901379182934761,
-0.00908774882555008,
0.028314774855971336,
-0.008041064254939556,
0.0... |
<p>Relative to the following</p>
<blockquote>
<p>Indeed, the modern point of view is that the operator of electric charge is the generator of a U(1) group. The charge quantization condition arises in models of unification if the electromagnetic subgroup is embedded into a semi-simple non-Abelian gauge group of higher rank. In this case, the electric charge generator forms nontrivial commutation relations with all other generators of the gauge group. </p>
</blockquote>
<p>I have a few questions:</p>
<p>Could someone explain me why it is important that the gauge group $U(1)$ embedded in the a large gauge group should have non-trivial commutation relations to guarantee charge quantization. Isn't it enough that it should be compactly embedded?</p>
<p>Why does the group has to be semi-simple? Aren't the main Grand Unified Theories that are now considered <em>simple</em> group, like $SO(5)$ or $SO(10)$ ?</p>
<p>And finally: the group has to be non-abelian to embed the groups $SU(2)$ and $SU(3)$ describing the other forces?</p>
<p>'Magnetic Monopoles', Yakov M. Shnir
Googlebooks: <a href="http://books.google.be/books/about/Magnetic_Monopoles.html?id=g3L8SWx8ulkC&redir_esc=y" rel="nofollow">http://books.google.be/books/about/Magnetic_Monopoles.html?id=g3L8SWx8ulkC&redir_esc=y</a></p> | g13444 | [
-0.07422631233930588,
0.0397908017039299,
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0.06585650146007538,
0.04090586304664612,
0.027125200256705284,
0.04990013316273689,
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0.02005661092698574,
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0.02460... |
<p>Let's say that we have two canister first bigger (metal canister 2l) with 1l of water at 100C, and second smaller (metal canister 1l) with 1l of ice. And we want to cool down boiled water to 50C. So we will insert ice (only ice not hole canister) into boiled water and after some time get wanted water (50C). </p>
<p><strong>But what if we insert into boiled canister - small canister (hole canister with ice inside), should boiled water be cooled down faster?</strong> (cause smaller canister with <strong>metal</strong> surface <strong>have bigger thermal conductivity than pure water</strong>) </p> | g13445 | [
0.04465905949473381,
0.037495438009500504,
0.007588845677673817,
0.02430087886750698,
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0.010125084780156612,
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-0.028329461812973022,
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0.06982023268938065,
0.0043951296247541904,
0.... |
<p>I've been told that an electron is somewhere within the space of $10^{-10}m$ and am supposed to find the uncertainty in its velocity.</p>
<p>Simply applying $m\Delta x \Delta v \geq \frac{h}{4\pi}$ results in $\Delta v \geq 5.79\times10^{10} m/s$. Now, this velocity is not approaching the speed of light, but I wanted to know if I could use the Lorentz factor to make this calculation more accurate (of course in this situation it would not make much of a difference.</p>
<p>So I redefined momentum uncertainty as $\Delta p = \gamma m_0 \Delta v$ and solved the inequality... but my final answer states $\Delta v \leq 3\times10^8$... this relation is obvious... but why has it popped out of this?</p>
<p>What if the space was even smaller when special relativistic effects actually would come into play, how would I then tackle the question?</p> | g13446 | [
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0.03830341622233391,
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-0.04403609037399292,
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0.04789179563522339,
-0.015016352757811546,
0.001811... |
<p>Please can someone provided me with academic literature (Journals/Books, titles & links) which discuss the current view on space time i.e. that there is not Infinitely many points of space-time? </p> | g13447 | [
0.006941033061593771,
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0.034925639629364014,
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0.04499302804470062,
0.007... |
<p>I have ground-level radiation data of solar incoming radiation from a radiometer (cosine collector) measured along the day. In the following plot you can see PAR irradiance (ie visible light) in Watts per square meter versus time of day (local time). AS usual for this type of sensor, radiation intensity varies with the Sun's angle with respect to the ground level.</p>
<p><img src="http://i.stack.imgur.com/ivFcD.jpg" alt="PAR vs local time"></p>
<p>As you can see it doesn't look perfectly smooth, rather it has some 'chopped' sections (most notably after maximum at noon) due to the presence of transient, passing-by clouds. I would like to use these data points to fit a model and obtain the ideal radiation curve as if it was a clear-sky day, ie perfect, continuous curve. </p>
<p>As you can see it is not a gaussian curve... I've heard before that the appropriate model is the Rayleigh distribution, but I'm not sure... </p>
<p>What do you think? is that the correct one or should I use another distribution? I don't want just to fit any equation, rather I want to use the <em>appropriate</em> one which is suitable for investigating ant testing the <em>corresponding parameters</em>. Thanks!</p> | g13448 | [
0.03836718946695328,
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<p>Classical mechanics is a good approximation to special relativity, which is a good approximation to general relativity etc. I have heard that if <a href="http://en.wikipedia.org/wiki/String_theory" rel="nofollow">string theory</a>/<a href="http://en.wikipedia.org/wiki/M-theory" rel="nofollow">M-theory</a> is right, then it is not just an approximation to a more accurate theory, but represents the end of the line as a TOE, why is this so? Can this be proved in string theory/M-theory?</p> | g13449 | [
0.05414441227912903,
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0.02616199105978012,... |
<p>I am reading Griffiths QM textbook and I got confused by the following identity:</p>
<p>How to prove from $$\frac{\partial \Psi}{\partial t} = \frac{i\hbar}{2m} \frac{\partial^2 \Psi}{\partial x^2} - \frac{i}{\hbar}V\Psi$$ to $$\frac{\partial \Psi^*}{\partial t} = -\frac{i\hbar}{2m} \frac{\partial^2 \Psi^*}{\partial x^2} + \frac{i}{\hbar}V\Psi^*.$$</p>
<p>Can anyone give me a mathematical proof of this complex conjugate identity?</p> | g13450 | [
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<p>Is there the formula (if someone already has discovered it) or what is the algorithm (if a particular formula was not deduced), to calculate the critical pressure of thick-walled spherical shell $−$ the pressure which provokes buckling?</p> | g13451 | [
0.06614130735397339,
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<p>The Yang-Mills action are usually given by $$S= \int\text{d}^{10}\sigma\,\text{Tr}\left(-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}-\theta^{T}\gamma^{\mu}D_{\mu}\theta\right)$$</p>
<p>with the field strength defined as $F_{\mu\nu}=\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu}-ig\left[A_{\mu},A_{\nu}\right]$
, $A_{\mu}$
being a U(N)
Hermitian gauge field in the adjoint representation, $\theta$
being a $16\times1$
Majorana-Weyl spinor of $SO(9)$
in the adjoint representation and $\mu=0,\dots,9$
. The covariant derivative is given by $D_{\mu}\theta=\partial_{t}\theta-ig\left[A_{\mu},\theta\right]$. We are using a metric with mostly positive signs.<br><br></p>
<p>We re-scale the fields by $A_{\mu}\to\frac{i}{g}A_{\mu}$
and let $g^{2}\to\lambda$
which gives us $$S=\int\text{d}^{10}\sigma\,\text{Tr}\left(\frac{1}{4\lambda}F_{\mu\nu}F^{\mu\nu}-\theta^{T}\gamma^{\mu}D_{\mu}\theta\right)$$
with the field strength defined as $F_{\mu\nu}=\partial_{\mu}A_{\nu}-\partial_{\nu}A_{\mu}+\left[A_{\mu},A_{\nu}\right]$
and the covariant derivative $D_{\mu}\theta=\partial_{t}\theta+\left[A_{\mu},\theta\right]$.
<br><br>
Now we perform a dimensional reduction from $9+1$
to $0+1$
, so that all the fields only depend on time, thous all spatial derivatives vanish i.e. $\partial_{a}(\text{Anything})=0$
. The $10$
-dimensional vector field decomposes into $9$
scalar fields $A_{a}$
which we rename $X^{a}$
and one gauge field $A_{0}$
which we rename $A$
. This gives (note that $\gamma^{t}=\mathbb{I}$ and that $\gamma^{a}=\gamma_{a}$. $$F_{0a}= \partial_{t}X^{a}+\left[A,X^{a}\right],\quad F_{ab}=+\left[X^{a},X^{b}\right]
\gamma^{t}D_{t}\theta= \partial_{t}\theta+\left[A,\theta\right],\quad\gamma^{a}D_{a}\theta=\gamma_{a}\left[X^{a},\theta\right]$$</p>
<p>The action for this theory is then
$$S=\int\text{d}t\,\text{Tr}\left(\frac{1}{2\lambda}\bigg\{-\left(D_{t}X^{a}\right)^{2}+\frac{1}{2}\left[X^{a},X^{b}\right]^{2}\bigg\}-\theta^{T}D_{t}\theta-\theta^{T}\gamma_{a}\left[X^{a},\theta\right]\right)$$
with the covariant derivative defined as $D_{t}X^{a}=\partial_{t}X^{a}+\left[A,X^{a}\right]$
and $D_{t}\theta=\partial_{t}\theta+\left[A,\theta\right]$
<br><br>
Now to the question. I need the potential energy $V=+\frac{1}{2}\left[X^{a},X^{b}\right]^{2}$ to be negative, not positive.
<br><br>
Taylor has a discussion on this in his paper "Lectures on D-branes, Gauge Theory and M(atrices)" (<a href="http://arxiv.org/abs/hep-th/9801182" rel="nofollow">http://arxiv.org/abs/hep-th/9801182</a>) on page 10, where he writes:<br>
"Because the metric we are using has a mostly positive signature,
the kinetic terms have a single raised 0 index corresponding to a change of
sign, so the kinetic terms indeed have the correct sign. The commutator term $\left[X^{a},X^{b}\right]^{2}$ which acts as a potential term is actually negative definite. This follows from the fact that $\left[X^{a},X^{b}\right]^{\dagger}=\left[X^{b},X^{a}\right]=-\left[X^{a},X^{b}\right]$. Thus, as expected,
kinetic terms in the action are positive while potential terms are negative."
<br><br>
But I don't understand where the Hermitian conjugate $^\dagger$ comes from, to me this term is just: $$\left[X^{a},X^{b}\right]^{2}=\left[X^{a},X^{b}\right]\left[X_{a},X_{b}\right]$$
<br><br>
Note that Taylor uses a little different conventions when he re-scales, instead of $A_{\mu}\to\frac{i}{g}A_{\mu}$ he uses $A_{\mu}\to\frac{1}{g}A_{\mu}$ and $\theta \to\frac{1}{g}\theta$. But this should not cause any troubles I think.</p> | g13452 | [
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<p>Let us consider the following <a href="http://en.wikipedia.org/wiki/Thought_experiment">Gedankenexperiment</a>:</p>
<p>A cylinder <strong>rotates</strong> symmetric around the $z$ axis with <a href="http://en.wikipedia.org/wiki/Angular_velocity">angular velocity</a> $\Omega$ and a plane wave with $\mathbf{E}\text{, }\mathbf{B} \propto e^{\mathrm{i}\left(kx - \omega t \right)} $ gets scattered by it.</p>
<p>We assume to know the <em>isotropic</em> <a href="http://en.wikipedia.org/wiki/Permittivity">permittivity</a> $\epsilon(\omega)$ and <a href="http://en.wikipedia.org/wiki/Permeability_%28electromagnetism%29">permeability</a> $\mu(\omega)$ of the cylinder's material <em>at rest</em>. Furthermore, the cylinder is infinitely long in $z$-direction.</p>
<p>The static problem ($\Omega = 0$) can be treated in terms of <a href="http://en.wikipedia.org/wiki/Mie_theory">Mie Theory</a> - here, however, one will need a <strong>covariant</strong> description of the system for very fast rotations (which are assumed to be possible) causing nontrivial transformations of $\epsilon$ and $\mu$.</p>
<p>Hence my question:</p>
<blockquote>
<h3>What is the scattering response to a plane wave on a fastly rotating cylinder?</h3>
</blockquote>
<p><img src="http://www.personal.uni-jena.de/~p3firo/PhysicsSE/RotatingDisc.png" alt="RotatingDisc"></p>
<p>Thank you in advance </p> | g13453 | [
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-0.02... |
<p>I haven't seen any reference which explains these things and I am not sure of all the steps of the argument or the equations. I am trying to reproduce here a sequence of arguments that I have mostly picked up from discussions and I would like to know of references for the background details and explanations. </p>
<ul>
<li><p>It seems that in general the Witten Index (${\cal I}$) can be written as $ Tr (-1)^F \prod_i x_{i}^{C_i}$ where $x_is$ are like the fugacities of the conserved quantity $C_is$ and $C_is$ form a complete set of simultaneously measurable operators. </p>
<p>I would like to know the motivation for the above and especially about calling the above an ``index" even if it depends on the fugacities which doesn't seem to be specified by the Lagrangian of the theory or by the underlying manifold? Even with this dependence does it reproduce some intrinsic property of either the underlying manifold or the theory? </p></li>
<li><p>Say $\phi$ and $\psi$ are the bosonic and fermionic component fields of a superfield and ${\cal D}$ be the superderivative. Now when the above tracing is done over operators of the kind $Tr({\cal D}^n\phi)$ and $Tr({\cal D}^n\psi)$ it is probably called a "single trace letter partition function (STLP)" and when it also includes things like products of the above kind of stuff it is called a ``multi-trace letter partition function (MTLP)" </p></li>
</ul>
<p>I would like to know about the exact/general definitions/references for the above terminologies and the motivations behind them.</p>
<ul>
<li><p>Probably for adjoint fields, if $f(x)$ is a STLP then apparently in some limit ("large N"?) one has, MTLP = $\prod _{n=1} ^{\infty} \frac{1}{1-f(x^n)}$ </p></li>
<li><p>One also defines something called the ``full STLP (FSTLP)" where one probably includes terms also of the kind $Tr({\cal D}^n \phi ^m {\cal D}^p \psi ^q)$ and then the MTLP can be gotten from that as MTLP = $exp [ \sum _{m=1} ^ {\infty} \frac{1}{m} FSTLP]$</p></li>
<li><p>The upshot all this is probably to show that MTLP is the same as Witten Index (in some limit?). </p></li>
</ul>
<p>I don't understand most of the above argument and I would be happy to know of explanations and expository references which explain the above concepts (hopefully beginner friendly!). </p>
<p>(I see these most often come up in the context of superconformal theories and hence references along that might be helpful especially about the representations of the superconformal group.) </p> | g13454 | [
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0... |
<p>Dirac once said that he was mainly guided by mathematical beauty more than anything else in his discovery of the famous Dirac equation. Most of the deepest equations of physics are also the most beautiful ones e.g. Maxwell's equations of classical electrodynamics, Einstein's equations of general relativity. Beauty is always considered as an important guide in physics. My question is, can/should anyone trust mathematical aesthetics so much that even without experimental verification, one can be fairly confident of its validity? (Like Einstein once believed to have said - when asked what could have been his reaction if experiments showed GR was wrong - Then I would have felt sorry for the dear Lord)</p> | g13455 | [
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<p>In page 32 of Peskin & Schroeder, it is written: </p>
<blockquote>
<p>But if $j(x)$ is turned on for only a finite time, it is easiest to solve the problem using the field equation directly.</p>
</blockquote>
<p>I am wondering:</p>
<ol>
<li>How is it possible to "solve" the field equation at all? I thought that <em>once we make the quantization</em>, the field equation is meaningless. It is only classically that it gives a field varying in time and space and quantum mechanically it would be what exactly? A differential equation for an operator?</li>
<li>If I insisted to find the spectrum of the system using the methods used before, how would I go about it? I tried to compute the Hamiltonian by the definition:
$$ H=\int d^3x[\pi(x)\partial_0\phi(x)-\mathcal{L(\phi)}] $$
where $\pi(x)=\partial^0\phi(x)$ and $\mathcal{L}=\frac{1}{2}\partial_\mu\phi\partial^\mu\phi-\frac{1}{2}m^2\phi^2+j\phi$. Thus: $$ H=\int d^3x[\frac{1}{2}\pi^2+\frac{1}{2}(\nabla\phi)^2+\frac{1}{2}m^2\phi^2-j\phi] $$ If we denote by $H_0$ the free Hamiltonian, then we get: $$ H = H_0 -\int d^3xj(x)\int \frac{d^3p}{(2\pi)^3}\frac{1}{\sqrt{2E_p}}(a_p e^{-i p_\alpha x^\alpha} +a_p^\dagger e^{i p_\alpha x^\alpha})$$ which clearly does not lead to the same expression between equations 2.64 and 2.65 (for one, the integration over $x$ is only 3-dimensional and we would need a 4-dimensional integral to get to $\tilde{j}(p)$.)</li>
</ol> | g13456 | [
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0... |
<p>The Hamiltonian for m(atrix) theory is given by
$$H=\frac{1}{2\lambda}\text{Tr}\left(P^{a}P_{a}+\frac{1}{2}\left[X^{a},X^{b}\right]^{2}+\theta^{T}\gamma_{a}\left[X^{a},\theta\right]\right).$$
Where $X^a$ are the $9$ bosonic $N\times N$ matrices and $\theta$ are a $16$-component matrix-valued spinor of $SO(9)$. (Given by Taylor on page 8 in "M(atrix) Theory: Matrix Quantum Mechanics as a Fundamental Theory" at <a href="http://arxiv.org/abs/hep-th/0101126" rel="nofollow">http://arxiv.org/abs/hep-th/0101126</a>).
This can be derived from an action looking like
$$S=\frac{1}{2\lambda}\int\text{d}t\,\text{Tr}\left(\partial_{t}X^{a}\partial_{t}X_{a}-\frac{1}{2}\left[X^{a},X^{b}\right]^{2}+i\theta^{T}\partial_{t}\theta-\theta^{T}\gamma_{a}\left[X^{a},\theta\right]\right)$$.
<br><br>
Since this is a super-symmetric theory the bosonic and fermionic degrees of freedom must match. The equations of motion for the fermions halves the it's degrees if freedom and we are left with only 8. But what about the bosonic degrees, we should have 8 not 9. There is however also a Gauss-constraint given by $\left\{ \partial_{0}X^{I},X_{I}\right\} +\left\{ \theta^{T},\theta\right\} =0$ (which we must impose if we are to have a gauge invariant theory, here the usual gauge field $A$ has been put to zero $A=0$), but this involves both the fermions and bosons and can not only restrict a degree of freedom for the bosonic matrices? <br>
How do I get the bosonic and fermionic degrees of freedom to match?</p> | g13457 | [
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0.0068648033775389194,
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0.021060340106487274,
-0.031200764700770378,
-... |
<p>Apologies in advance for what may be a stupid question from a layman. In reading recently about <a href="http://en.wikipedia.org/wiki/Quantum_entanglement" rel="nofollow">quantum entanglement</a>, I understood there to be a direct link between entangled particles, even at arbitrarily large distances. I'm wondering how time plays into all of this. </p>
<ol>
<li><p>Is there any data on how variable passage of time impacts this linkage? </p></li>
<li><p>For example, if one entangled particle is in a large gravitational field, while another is not (making the passage of time different for the two), is the link the same? </p></li>
<li><p>If spin or position is one of the observable traits of these entangled particles, do these traits operate on any measurable cycle? </p></li>
<li><p>If so, would these cycles be necessarily synched in order for the observed linkage to be present? </p></li>
<li><p>And if so, would asynchronous passage of time ever be able to break the synchronization and/or entanglement? </p></li>
</ol>
<p>I feel like this unleashes a whole host of related questions, but hopefully you see where I'm going. </p> | g13458 | [
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<p>As I have been studying electromagnetic theory, I have always been lead to confusion when trying to visualise the fields. Fortunately, the electric and magnetic fields are vector fields and also along the propagation direction they provide a 3-Dimensional Coordinate system. </p>
<p>However, in general to visualise a N-dimensional field (I mean field depending on N coordinates), N+1 dimensions are necessary. For instance, in the case of 1D field $\phi(x)$, we can plot a graph $x$ vs $\phi(x)$. </p>
<p>But I am wondering if it is also possible to describe the fields using contours. To elaborate, if I have 2D field $\lambda(x,y)$ will it possible to visualise the field in 2D itself using contours (without actually plotting the variation of $\lambda(x,y)$ vs $x$ and $y$).</p> | g13459 | [
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0.0439729169011116,
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0.015... |
<p>Why should two sub-atomic (or elementary particle) - say electrons need to have identical static properties - identical mass, identical charge? Why can't they differ between each other by a very slight degree? Is there a theory which proves that?</p>
<p>Imagine an alien of size of order of Milky-way galaxy examining our solar system with a probe of size of 10's of solar system dimension and concludes that all planets are identical.</p> | g13460 | [
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<p>Firstly, sorry for any silly mistakes or improper use of this website - this is my first time using it! </p>
<p>I am trying to use Excel to model the flight of the Apollo 11 Saturn V rocket using the real values from the mission evaluation report.
However, I can't seem to get the right acceleration. It is always too low. My initial acceleration at t=0.1s is 2.06 m/s^2 while the values in the evaluation report show the acceleration to be close to 10 m/s^2. My final goal is to calculate the acceleration at the S-IC OECO event (at t=161s). My spreadsheet showed 28m/s^2 while the real value is 39m/s^2. Obviously I have done something terribly wrong since the difference between the values is quite large, but I've been looking over my spreadsheet for days now and I just can't find my problem. </p>
<p>What <em>should</em> the columns be? </p>
<p>This is what I have so far: </p>
<ul>
<li>Range time (s) - in increments of 0.1s down the column</li>
<li>Mass (kg) - the mass at that time calculated by previous mass - mass flow rate*0.1s</li>
<li>g (m/s^2) - the acceleration due to gravity at that altitude</li>
<li>Weight (N) - mass*g</li>
<li>Thrust (N) - the thrust at that time using real values from the graphs in the evaluation report</li>
<li>Drag (N) - using the drag equation and estimated coefficients </li>
<li>Total force (N) - weight + thrust + drag </li>
<li>Acceleration (m/s^2) - using F=ma so I did total force/mass </li>
<li>Velocity (m/s) - previous velocity + acceleration*0.1s </li>
<li>Altitude (m) - previous altitude + velocity*0.1s</li>
</ul>
<p>I've taken into account changing thrust, mass flow rate, acceleration due to gravity and drag as well. </p>
<p>The values in the report are given as 'inertial acceleration' but I haven't learnt this yet (still in high school). So is inertial acceleration different to the acceleration I have calculated using F=ma? Have I misused Newton's second law? Was I wrong to consider the weight of the propellants in this case? </p>
<p>I'll appreciate any and all helpful feedback and I can provide more information if needed. Thank you so much! :)</p> | g13461 | [
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<p>In a dc circuit work done by battery=QV while energy stored in capacitor =(QV)/2 loss in energy=(QV)/2
While a capacitor in ac circuit has a no power loss.why is it so? Shouldn't heat be lost in ac circuit capacitor too while charging.</p> | g13462 | [
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0.037280257791280746,
0.019559351727366447,
0.0... |
<p>This just blew my mind away! I was watching a video about imagining the fourth dimension and the narrator said that little line. Can some people elaborate on this. Also please keep it simple not too complicated. Thank you!</p> | g420 | [
0.009266636334359646,
0.06006891652941704,
-0.02408183179795742,
-0.023383093997836113,
-0.006535979453474283,
0.05884186178445816,
0.004056681413203478,
-0.0011957903625443578,
-0.06779851019382477,
-0.03548233211040497,
-0.02900487743318081,
0.017038602381944656,
0.006221710238605738,
-0... |
<p>How can I find the magnetic interference a stationary 35000 kg block of 100% pure iron would have on a magnetic compass and what the drop off rate of the interference would be. </p>
<p>So if said 35000 kg block of iron was 1 meter away from the compass, 100 meters away, or 1000 kilometers way I would like to calculate the rate of drop off of the interference.</p>
<hr>
<p>This may seem absurd, but it is very important for a conceptual project I am working on.</p>
<p>For the context of this question, assume everything is perfect, and that we are basically operating in a vacuum and there is no interference from anything else and that all instruments are 100% accurate and infinitely precise. And that I have only a very very basic understanding of physics, mathematics and magnetism.</p> | g13463 | [
0.019935019314289093,
0.01706242933869362,
0.020056577399373055,
0.0062901778146624565,
0.0077150482684373856,
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0.014579415321350098,
0.06303444504737854,
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0.019202936440706253,
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0.028479622676968575,
-0.005660112015902996,
-0.... |
<p>If we have a Hilbert space of $\mathbb{C}^3$ so that a wave function is a 3-component column vector
$$\psi_t=(\psi_1(t),\psi_2(t),\psi_3(t))$$
With Hamiltonian $H$ given by
$$H=\hbar\omega
\begin{pmatrix}
1 & 2 & 0 \\
2 & 0 & 2 \\
0 & 2 & -1
\end{pmatrix}$$
With
$$\psi_t(0)=(1,0,0)^T$$
So I proceeded to find the stationary states of $H$ by finding it's eigenvectors and eigenvalues. $H$ has eigenvalues and eigenvectors:
$$3\hbar\omega,0,-3\hbar\omega$$
$$\psi_+=\frac{1}{3}(2,2,1)^T,\psi_0=\frac{1}{3}(2,-1,-2)^T,\psi_-=\frac{1}{3}(1,-2,2)^T$$
Respectively.</p>
<p>Could anyone explain to me how to go from this to a general time dependent solution, and compute probabilities of location? I have only ever encountered $\Psi=\Psi(x,y,z,t)$ before, so I am extremely confused by this matrix format.</p>
<p>I would be extremely grateful for any help!</p> | g13464 | [
-0.0022491354029625654,
-0.04442073404788971,
-0.03117970936000347,
-0.03792008012533188,
0.012029875069856644,
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0.11236059665679932,
0.02667648158967495,
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0.013684763573110104,
0.0005351220024749637,
-0.001966924639418721,
-0.01770862191915512,
... |
<p><strong>BACKGROUND</strong></p>
<p>So far I understood that the <a href="http://en.wikipedia.org/wiki/Hierarchy_problem" rel="nofollow">hierarchy problem</a> was the large difference between the gravitational scale, $M_{pl}\sim 10^{18}\; [GeV]$, compared with the electroweak scale, $M_{ew}\sim 10^3\;[GeV]$.</p>
<p>However, I heard that the hierarchy problem is due to the existence of quadratic divergences in the scalar sector of the Standard Model.</p>
<p><strong>QUESTION</strong></p>
<p>Can someone explain with ease the hierarchy problem? </p>
<p>Additionally, Is it possible to relate both of the above points of view?</p> | g13465 | [
0.06831173598766327,
0.09812470525503159,
-0.016723306849598885,
-0.06370862573385239,
0.06084222346544266,
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0.01945941522717476,
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0.010392392985522747,
-0.0631769597530365,
0.014820861630141735,
0.012038356624543667,
0.0373704... |
<p>A massless rod of length $L$ attached to mass $m$ and with axle to cart of mass $M$. The cart has a shape of equilateral triangle (edge $L$). the cart is at rest and its center of mass is above $x=0$ and a rod is perpendicular to the ground. the cart is free to move without friction. at time t=0 the mass $m$ is released and starts to fall to the left. at time $t=\tau$ the rod is parallel to the ground. Where is the center of mass at $x$ axis at time $t=\tau$ of the cart? <img src="http://i.stack.imgur.com/8WWPf.jpg" alt="enter image description here">
Why does the answer say: $mx_m+Mx_M=m(x_M-L)+Mx_M=0$? How does $x_m=x_M-L$? And isn't $x_M=mL/(M+m)$ is the center of mass of the cart with the mass $m$ and not just the cart as the question asks?</p> | g13466 | [
0.027463003993034363,
0.013295041397213936,
0.02553124725818634,
-0.039473965764045715,
0.07463119924068451,
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0.0006167091778479517,
-0.012545904144644737,
-0.006860090885311365,
0.06377444416284561,
-0.... |
<p>In <em>M. Veltman's Diagrammatica</em>, appendix E, one can find the full Standard Model lagrangian. Some sectors (e.g fermion-Higgs and weak sectors) contain so-called Higgs ghosts $\phi^+,\phi^-$ and $\phi^0$. </p>
<blockquote>
<p>Are Higgs ghosts Faddeev-Popov ghosts? </p>
</blockquote>
<p>If so, </p>
<blockquote>
<p>why does the Higgs field, not being a gauge field, yield Faddeev-Popov ghosts? </p>
</blockquote>
<p>If not, </p>
<blockquote>
<p>in which sense are they <em>ghosts</em>?</p>
</blockquote> | g13467 | [
0.07016488909721375,
-0.00513189984485507,
0.008977008052170277,
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-0.018846429884433746,
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-0.02240658551454544,
0.0030112024396657944,
0.067... |
<p>Suppose a projectile is launched from the Earth's surface with initial velocity $v_0$ well below speed of light and initial angle $\theta_0$ with respect to the vertical line perpendicular to the Earth's surface. Omitting Earth's rotation, but knowing that Earth is not flat (as in the real world), what is the maximum height of the projectile with respect to center of the Earth? (Suppose air resistance is negligible.)</p>
<p>Is it possible to solve this problem using only the material in the first $8$ chapters of Fundamentals of Physics; D. Holliday, R. Resnick & J. Walker? I'm eager to see a various number of solutions!</p> | g13468 | [
0.06371280550956726,
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0.0657082125544548,
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0.01831643469631672,
-0.029877478256821632,
0.004936533514410257,
0.05292818695306778,
-0.0... |
<p>This is the problem from our Physics textbook : </p>
<blockquote>
<p><em>A player throws a ball upwards with an initial speed of 29.4 m s–1.
(a) Choose the x = 0 m and t = 0 s to be the location and time of the ball at its highest point, vertically downward direction to be the positive direction of
x-axis, and give the signs of position, velocity and acceleration of the ball
during its upward, and downward motion.</em></p>
</blockquote>
<p>Answer is : </p>
<blockquote>
<p><em>x > 0 (upward and downward motion); v < 0 (upward), v > 0 (downward), a > 0
throughout;</em></p>
</blockquote>
<p>a > 0 is what is bothering me and I have done hours of searching and trying to understand.</p>
<p>Kindly explain all the parts of the answer.
Thanks in advance.</p> | g13469 | [
0.04641801863908768,
0.02610184997320175,
0.013826349750161171,
0.02061663195490837,
0.019203459843993187,
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0.1253650188446045,
0.02467598393559456,
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0.013853248208761215,
-0.036733102053403854,
0.055539123713970184,
0.02732219360768795,
-0.0298339... |
<p>From this <a href="http://physics.stackexchange.com/questions/19632/how-much-electric-charge-do-electromagnetic-waves-carry"><strong>question</strong></a>, I've noted that an electromagnetic field carries <em>no electric charge</em> but it has two components:</p>
<ul>
<li>Electric field</li>
<li>Magnetic field</li>
</ul>
<p>Now what I failed to understand is how does the receiving antenna get an induced small voltage. Is it due to the electric or the magnetic field component of EMF? and How?</p> | g13470 | [
0.031225508078932762,
0.016285935416817665,
-0.02724180743098259,
-0.016050077974796295,
0.0916886031627655,
0.07171962410211563,
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0.029500987380743027,
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-0.03572072833776474,
-0.08130946010351181,
0.039405420422554016,
0.0019432841800153255,
-... |
<p>I have been learning gauss's law in capacitor recently, recently I come up with this problem that I couldn't solve myself. If we have a capacitor,and a dielectric medium with half the volume between the plates, the permittivity of the dielectric is epsilon.Find the electric field inside the dielectric.
The second one is when the dielectric only covers half the area.
First picture (Symbols are E1,E2,Epsilon for clarification)
Again,What is the Electric field in the dielectric?Express In terms of Q A(area) epsilon0 and epsilon . How do we go about solving this problem?Is there anything to do with boundary conditions?</p>
<p><img src="http://i.stack.imgur.com/IX0Vu.png" alt="a"></p>
<p><img src="http://i.stack.imgur.com/KJmls.png" alt="enter image description here"></p> | g13471 | [
0.054685212671756744,
0.013813615776598454,
-0.0066057355143129826,
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0.003003291552886367,
0.022802041843533516,
0.01199760939925909,
0.003492980729788542,
-0.014721793122589588,
-0.046313848346471786,
0.033398229628801346,
-0.00408917386084795,
... |
<p>To the best of my knowledge thermal fluctuations are responsible for washing out any effective magnetization, once the external field is switched off. Since thermal fluctuations need some time to drive the system back to random orientation, what would be the time scale for this process? Is it of the order of 200 ps? </p> | g13472 | [
0.02168477512896061,
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0.023536479100584984,
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0.00935034267604351,
-0.05414646491408348,
0.07771723717451096,
0.04731346294283867,
-0.034... |
<p>I was discussing with my colleagues why it feels easier to walk up an escalator when it is moving. My natural assumption was that the movement of the escalator imparts some extra acceleration on the rider that helps to move up the stairs. But my colleagues insisted that this was nonsense, and that the affect is purely psychological (i.e. it just <em>seems</em> easier).</p>
<p>We actually came up with three contradictory hypotheses, and I'm not sure which is right:
1. The escalator is constantly accelerating the rider since without constant acceleration the body wouldn't be able to counteract the force of gravity (i.e. my theory).
2. The rider is not accelerating since no acceleration is needed to maintain a constant velocity.
3. The acceleration of the escalator actually makes it harder to get to the next step since it pushes the rider against the current step.</p>
<p>Which of these is correct?</p> | g13473 | [
0.05820535495877266,
0.1007326990365982,
0.006687250453978777,
0.0914396196603775,
0.024921195581555367,
0.042277686297893524,
0.06397335976362228,
0.0265408493578434,
-0.05555129423737526,
-0.01488802582025528,
0.02156844362616539,
-0.020389962941408157,
-0.03377489745616913,
0.0513514466... |
<p>If you balance a pencil of length $d$ on its tip, and let it fall, how do you compute the final velocity of its other end just before it touches the ground?</p>
<p>(Assume the pencil is a uniform one dimensional rod)</p> | g13474 | [
0.07184115797281265,
0.008292526006698608,
-0.01610223390161991,
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0.07044440507888794,
0.0009912451496347785,
0.07014910131692886,
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0.0041773514822125435,
-0.028220435604453087,
0.0003900453739333898,
-0.0062516797333955765,
... |
<p>When I learned classical Markov process, I noticed some similarity of quantum process and Markov process, and the only difference of them is between probability and probability amplitude whose modulus square represents a probability.</p>
<p>I show the some similarity here. The Schordinger's equation gives us the relationship between present state and next state.$$\frac{d}{dt}\lvert\psi\rangle=\hat{H}\lvert\psi\rangle$$</p>
<p>Here, we ignore the complex number and Planck constant.Its discrete time version is
$$\lvert\psi\rangle_{n+1}-\lvert\psi\rangle_{n}=\hat{H}\lvert\psi\rangle_{n}$$</p>
<p>I found it very similar to Markov process which express as $V_{n+1}=MV_{n}$ or
$$V_{n+1}-V_{n}=(M-1)V_{n}$$
where $V$ is the vector in the state space.</p>
<p>If we ingore the difference between probability and probability amplitude, the matrix $(M-1)$ is something very like Hamiltonian.</p>
<p>In the Schordinger picture, the similarity is more obviously.
$$\lvert\psi(t)\rangle=\hat{O}(t,t_0)\lvert\psi(t_0)\rangle$$</p>
<p>Actually, my question is about Markov process. I want to know how to deal with a Markov process whose state space has infinite dimensions. I think maybe quantum mechanics could give me some help.</p>
<p>Can I treat a quantum process as a Markov process? Is it true that the difference between them is just the difference between probability and probability amplitude?</p>
<p>How to deal with the case of infinite dimensions? Can I introduce some thing like probability amplitude to help me solve this question?</p> | g13475 | [
0.009466120041906834,
-0.03439649939537048,
0.012635624036192894,
-0.023686137050390244,
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0.010117375291883945,
0.00611542584374547,
0.059072982519865036,
0.00926539208739996,
-0.02525394596159458,
0.0206693597137928,
0.010647335089743137,
0.028964875265955925,
0.04875... |
<p>Suppose I put a pendulum of metal ball and very thin rope in highest achievable vacuum. What would keep it from not swinging forever?</p> | g301 | [
0.07415933907032013,
0.005359019618481398,
0.00030400705873034894,
-0.016637859866023064,
0.029521502554416656,
0.10330911725759506,
0.013594431802630424,
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0.003220554906874895,
-0.06079588085412979,
-0.049627162516117096,
-0.0002767724508885294,
-0.03712880611419678,
... |
<p>I have just started learning optics at school and my teacher derived the lens and mirror formulas. While doing so, she applied the sign convention for u,v and f and arrived at the final expression. However, while solving problems using the mirror formula why do we again apply sign convention for the given values of u,v or f?</p> | g702 | [
-0.061515845358371735,
-0.03762420266866684,
0.012535820715129375,
-0.02962299808859825,
0.02047117054462433,
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0.06685631722211838,
0.09105703979730606,
0.012024110183119774,
-0.0214556735008955,
-0.02589862421154976,
0.04463767632842064,
0.06889229267835617,
0.049712... |
<p>With respect to waves traveling through a diffraction grating, we have an equation like this one: $$d_s\sin(\theta) = m\lambda.$$</p>
<p>Where $d_s$ is the distance between slits in the grating, $\theta$ is an approximate angle at which the waves bend through each slit of the grating, $\lambda$ is the wavelength of the waves passing through the gradient, and $m$ is the number of wavelengths by which distances traveled by one wave from one slit differ from an adjacent slit. $d_s$ and $m$ are usually given a remain constant in the scenarios I'm working with.</p>
<p>My physics book says that the <em>differential of the above mentioned equation</em> is $$d_s \cos(\theta)d\theta = md\lambda$$ (without confusing the single $d_s$ (distance) with the ones in $d\theta$ and $d\lambda$).</p>
<p>What does it mean to call the second equation the "differential" of the first? I am trying to understand the concept behind the differentials more so that I may later make sense of the physics.</p>
<p>EDIT: In <a href="http://math.stackexchange.com/questions/21199/is-dy-dx-not-a-ratio">user6786's question</a>, user6786 states that "according to the formula $dy=f'(x)dx$ we are able to plug in values for $dx$ and calculate a $dy$ (differential)". I'm trying to see how that works.</p> | g13476 | [
0.025073038414120674,
-0.043755680322647095,
-0.03293071687221527,
-0.02104264125227928,
0.05991409718990326,
0.017845002934336662,
0.04575621709227562,
0.004215736407786608,
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-0.04502168297767639,
-0.01712544448673725,
0.049430958926677704,
0.057123180478811264,
-0.00... |
<p>The real question was: <strong>A proton is trapped in an infinitely deep well of 1*10^-14m.</strong> I suppose that is unimportant as that should only help us decided the limits of our integration. What I'm worried about is the second part of the question. <strong>"The proton is in the first excited state."</strong> Does "The proton being in the first excited state" have some effect on the wavefunction or the question? Or for any probability required should I just find the integral of the wavefunction of a free particle over what ever limits they ask for? For examples.
<strong>Calculate the probability of finding the proton within 0.25*10^-14m of the left hand wall.</strong> Which would give us an integral between say (0... and 0.25*...) or to be more specific (0.25*... and 1*10...).
The question also asked for the wavelength of the photon emitted if the proton returns to the ground state.
[<strong>these are past paper questions</strong> I'm working on in preparation for a final <strong>so I have no solutions or help *<em>:(</em>*</strong>]</p>
<ul>
<li>]</li>
</ul> | g13477 | [
-0.026358503848314285,
0.04613199830055237,
0.0010558681096881628,
-0.024610240012407303,
0.04407525435090065,
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0.04193005710840225,
0.0810256078839302,
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-0.030169405043125153,
-0.06436385959386826,
0.06941093504428864,
-0.04081185162067413,
0.01786... |
<p>It is given that the angular size of the Sun as viewed from Earth is $0.533^\circ$, the distance of the Moon from Earth at perigee is $3.633\times 10^5$ km, and the mean radius of the Moon is $1737.1$ km. </p>
<p>Suppose that the perigee of the Moon is receding from Earth at a uniform rate of $4$ cm/year. Estimate how long it will take to reach "final totality" (i.e. when we can no longer observe total solar eclipse on Earth).</p> | g13478 | [
0.047305524349212646,
0.06995394080877304,
0.018384123221039772,
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0.06429196149110794,
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0.019246967509388924,
0.011398132890462875,
0.03906204178929329,
0.040499478578567505,
-0.03... |
<p>That I could create as a classical mechanics class project? Other than the classical examples that we see in textbooks (catenary, brachistochrone, Fermat, etc..)</p> | g13479 | [
0.04311586171388626,
0.0241167563945055,
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0.03429363667964935,
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0.003536310512572527,
0.014647259376943111,
-0... |
<p>I am wondering whether the five$^1$ units of the natural unit system really is dictated by nature, or invented to satisfy the limited mind of man?
Is the number of linearly independent units a property of the nature, or can we use any number we like? If it truly is a property of nature, what is the number? -five? can we prove that there not is more?</p>
<p>In the answers please do not consider cgs units, as extensions really is needed to cover all phenomenon. - or atomic units where units only disappear out of convenience. - or SI units where e.g. the mole for substance amount is just as crazy as say some invented unit to measure amount of money.</p>
<p>--</p>
<p>$^1$length, time, mass, electric charge, and temperature (or/and other linear independent units spanning the same space).</p> | g13480 | [
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0.07323947548866272,
0.0076354495249688625,
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0.017757995054125786,
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-0.008832263760268688,
0.008253277279436588,
-0.010685198940336704,
-0.007190675940364599,
... |
<p>I fail to understand the true difference between EMR and electric and magnetic fields. When current flows, there is an electric field due to the electron flow and a magnetic field, however no EMR (Save blackbody radiation from the wire) is emitted. Then how can radio broadcasts function if magnetic fields only are emitted from wires? Obviously I am missing something major here.</p> | g13481 | [
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0.05149730667471886,
0.004486536141484976,
... |
<p>How are Monte Carlo simulations used in experimental high energy physics? Particularly in studying detectors limitations (efficiencies?) and data analysis.</p>
<p>I will appreciate giving a simple example to clarify how MC is used if the question is too technical to have a simplified answer</p> | g13482 | [
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0.03475131094455719,
0.027... |
<p>I believe that no real objects are actually (<em>exactly</em>) 1 meter long, since for something to be 1.00000000... meters long, we would have to have the ability to measure with infinite precision. Obviously, this can be extended to any units of measurement. Am I wrong?</p> | g13483 | [
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-0.008607546798884869,
-0.021014036610722542,
-0.040760286152362823,
-0.0018710874719545245,... |
<p>The Rayleigh-Lamb equations:</p>
<p>$$\frac{\tan (pd)}{\tan (qd)}=-\left[\frac{4k^2pq}{\left(k^2-q^2\right)^2}\right]^{\pm 1}$$</p>
<p>(two equations, one with the +1 exponent and the other with the -1 exponent) where</p>
<p>$$p^2=\frac{\omega ^2}{c_L^2}-k^2$$
and
$$q^2=\frac{\omega ^2}{c_T^2}-k^2$$</p>
<p>show up in physical considerations of the elastic oscillations of solid plates. Here, $d$ is the thickness of a elastic plate, $c_L$ the velocity of longitudinal waves, and $c_T$ the velocity of transverse waves. These equations determine for each positive value of $\omega$ a discrete set of real "eigenvalues" for $k$. My problem is the numerical computation of these eigenvalues and, in particular, to obtain curves displaying these eigenvalues. What sort of numerical method can I use with this problem? Thanks.</p>
<p>Edit: Using the numerical values $d=1$, $c_L=1.98$, $c_T=1$, the plots should look something like this (black curves correspond to the -1 exponent, blue curves to the +1 exponent; the horizontal axis is $\omega$ and the vertical axis is $k$):</p>
<p><img src="http://i.stack.imgur.com/zIRvb.png" alt="The curves are supposed to look like this."></p> | g13484 | [
0.06476181000471115,
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0.004893828649073839,
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0.005294695030897856,
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-0.018032288178801537,
0.016211628913879395,
0.013794259168207645,
0.014081411063671112,
0.0... |
<p>in the formula </p>
<p>$$dB = \frac{\mu_0l ~|dl \times r|}{4 \pi r^3} $$</p>
<p>and the image<br>
<img src="http://i.stack.imgur.com/NVNYK.png" alt="enter image description here"></p>
<p>where dl is in y-z plane and dB is in x-y plane. the ring conductor is in y-z plane carrying current I in direction as mentioned<br>
<strong>EDIT</strong>: also point p can move in the circular ring</p>
<p><strong>EDIT 2</strong>:To clear the confusion...The dl vector is having (L alphabet) and current is I (i alphabet). </p>
<p>I want to know that is the angle between dl and r is 'Theta' ? how?</p> | g13485 | [
0.007045117672532797,
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0.004259602166712284,
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0.06304171681404114,
-0.025858823210000992,
... |
<p>Question:</p>
<blockquote>
<p>A wheel starts is spinning at $27\text{ rad/s}$ but is slowing with an angular
acceleration that has a magnitude given by $\alpha(t) = (3.0\;\mathrm{rad/s^4})t^2$. It stops in a time of: $\qquad$ ?</p>
</blockquote>
<p>I happened to guess $3.0\text{ s}$ and it turned out to be right. But I want to understand why.</p>
<p>I tried using a kinematics equation and plugging $a$ in for $\alpha$, but it gave me the wrong answer. Am I missing something simple here?</p> | g13486 | [
0.06175149977207184,
0.037702515721321106,
0.014319547452032566,
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0.03147458657622337,
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0.010887963697314262,
-0.01865062303841114,
0.02728593349456787,
0.05216926708817482,
0.0101960... |
<p>In dimensional regularization, we must shift the dimensionless coupling $g$ by the renormalization scale $\mu$ (which has unit mass dimension):
\begin{equation}
g \rightarrow \mu^{4-d} g \tag{1}
\end{equation}
This is done to ensure that the action will have the correct dimensions.</p>
<p>Apparently, $\mu$ will not affect any observables. But I don't understand how this can be proven.</p>
<p>Edit: I am aware that we do not want to "true" theories to depends on the cut-off $\Lambda \rightarrow \infty$ or $\epsilon=4-d \rightarrow 0$, but this doesn't tell me what will happen with $\mu$.</p>
<p>Edit 2: Ok, maybe I understand it. We introduce the renormalization scale $\mu$ and this is an <em>unphysical</em> parameter. Therefore, we <em>demand</em> that that physical observable are not dependent on $\mu$. This procedure results in the renormalization group equations. Is this correct?</p> | g13487 | [
0.0072297765873372555,
0.0317695252597332,
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0.019014457240700722,
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-0.031191183254122734,
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0.01155521348118782,
-0.05943769961595535,
0.... |
<p>The smallest particles of the universe (or the smallest part of the smallest particles of the universe) must have infinity density. But if it have infinity density, you can calculate mass of one of these particles as infinity - so if any thing would composed of these particles, would it have infinity mass. How is it possible?</p> | g13488 | [
0.02355324849486351,
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0.009911841712892056,
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0.005060174036771059,
-0.0... |
<p>We are told that they can only terminate on surfaces, grain boundaries or other dislocations but we are not told why they can't terminate inside the crystal.</p> | g13489 | [
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0.023759735748171806,
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-0.... |
<p>I'm trying to follow the Feynman lectures and I'm stuck on a particular piece. Let me frame it for you before I ask my question. Nobody does it better than the author himself,</p>
<blockquote>
<p>we must find out how a particular particle moves when the angular velocity is such and such. To do this, let us take a certain particle which is located at a distance $r$ from the axis and say it is in a certain location $P(x,y)$ at a given instant, in the usual manner. If at a moment $\Delta t$ later the angle of the whole object has turned through $\Delta \theta$, then this particle is carried with it. It is at the same radius away from $O$ as it was before, but is carried to $Q$. The first thing we would like to know is how much the distance $x$ changes and how much the distance $y$ changes. If $OP$ is called $r$, then the length $PQ$ is $r \Delta \theta$, because of the way angles are defined. The change in $x$, then, is simply the projection of $r \Delta \theta$ in the $x$-direction:
$$\Delta x = -PQ \sin \theta = -r \Delta \theta \dot (y/r) = -y \Delta \theta$$
Similarly, $$\Delta y = +x \Delta \theta$$</p>
</blockquote>
<p><img src="http://i.stack.imgur.com/cXuy7.png" alt="Angular velocity problem"></p>
<p><em>Source: Feynman Lecturs on Physics</em></p>
<p>Now I will try to reproduce this in a way I find logically consistent:
we can imagine an isosceles triangle formed by $ABC$ where the angle $ACB$ is $\gamma$ and the line segment $AC$ is $b$, the line segment $CB$ is $a$ and the line segment of $AB$ is $c$. The law of cosines says that, $c^2 = a^2 + b^2 - 2ab$. In the case of an isosceles triangle we can simplify this by saying $a=b=r$ ($r$ because that is what we have in our example), therefore our law simplifies to: $c^2 = r^2 + r^2 - 2r^2 \cos \gamma = 2r^2(1 - \cos \Delta \theta)$.</p>
<p>If we suppose that $c$ is the length of the line segment $PQ$ then it should be:
$$c = \sqrt{ 2r^2(1 - cos \Delta \theta)}$$ Instead, Feynman says that this should be $r\Delta \theta$. Okay, maybe it is only an implicit approximation for infinitesimal angles, so we can look and see that $\cos \Delta \theta \approx 1$ for very small angles which immediately implies that $c \approx 0$. So why and how does Feynman find $c=r \Delta \theta$? Where did I go wrong?</p> | g13490 | [
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0.0791931301355362,
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0.01984081231057644,
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0.06408938765525818,
0.024372193962335587,
-0.02... |
<p>If Electricity and magnetism are the same viewed from a different reference frame (they are the same force as unified by maxwell) then is electricity medium dependant? I came to this question when trying some experiment with two wires close to each other where I place between them non-conductor mediums such as: paper, wood, plastic... And I see some difference. So is the electrostatic force medium dependant? That is, if I have a charge Q1, and Q2, they will attract/repulse each other (F=k.Q1.Q2/r²) based on the medium where they are separated? If so, does it have to do with density, what is the general formula? </p> | g13491 | [
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0.007289366330951452,
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0.016067277640104294,
0.007786785252392292,
-0.027047717943787575,
-0.0439373254776001,
-0.0... |
<p>Or can they just be used as an interpolation points and use some other "transported property" which are just evolved and propagated from boundary conditions like for eg. heat conduction through a solid metal bar. It seems to be possible, but isn't clearly elaborated. The force computation step is always used for fluid flow to move particles forward according to Newton's laws, but what if heat is transported purely by conduction in a solid? Here, nothing moves but still, heat flows and destroys temperature gradients. What equations are to be considered here (apart from the heat diffusion equation) to adapt this problem for this kind of discretization?</p> | g13492 | [
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0.019096296280622482,
0.019214343279600143,
0.0... |
<ol>
<li><p>What is the <a href="http://en.wikipedia.org/wiki/Moduli_%28physics%29" rel="nofollow">moduli space</a> of a QFT? </p></li>
<li><p>What does it mean exactly that there are different inequivalent vacua? </p></li>
<li><p>Can someone give a precise definition of the moduli space, and some easy examples? </p></li>
<li><p>And why is it so important and studied nowadays?</p></li>
</ol> | g13493 | [
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-0.03729260340332985,
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0.... |
<p>I've just answered <a href="http://physics.stackexchange.com/questions/81896/dipping-a-dyson-ring-below-the-event-horizon">Dipping a Dyson Ring below the event horizon</a>, and while I'm confident my answer is correct I'm less certain about the exact consequences. To simplify the situation consider a diatomic molecule falling into a Schwarzschild black hole with its long axis in a radial direction.</p>
<p><img src="http://i.stack.imgur.com/KZea4.gif" alt="Molecule"></p>
<p>The inner atom cannot interact with the outer atom because no radially outwards motion is possible, not even for electromagnetic fields travelling at the speed of light. However I find I'm uncertain exactly what the outer atom would experience.</p>
<p>We know that the outer atom feels the gravitational force of the black hole even though gravitational waves cannot propagate outwards from the singularity. That's because it's experiencing the curvature <em>left behind</em> as the black hole collapsed. Would the same be true for the interaction of the outer atom with the inner atom? Would it still feel an electromagnetic interaction with the inner atom because it's interacting with the field (or virtual photons if that's a better description) left behind by the inner atom? Or would the inner atom effectively have disappeared?</p>
<p>If the latter, presumably the fanciful accounts of observers falling into the black hole (large enough to avoid tidal destruction) are indeed fancy since it's hard to see how any large scale organisation could persist inside the event horizon.</p>
<p><strong>Later:</strong></p>
<p>I realise I didn't ask what I originally intended to. In the above question my molecule is freely falling and the question arose from a situation where the object within the event horizon is attempting to resist the inwards motion. I'll have to go away and re-think my question, but thanks to Dmitry for answering what I asked even if it wasn't what I meant :-)</p> | g13494 | [
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-0... |
<p><strong>Update.</strong> As my previous figure had conceptual mistakes I decided to change the picture to another, more instructive.</p>
<p>After a long time I came back to try to understand an article on the Ising model.
The review article is <a href="http://arxiv.org/pdf/math/9907186.pdf" rel="nofollow">Percolation and number of phases in the 2D Ising
model</a> by Hans-Otto Georgii and Yasunari Higuchi (published in 2000 in the <strong>Journal of Mathematical Physics</strong> as <em>Percolation and number of phases in the two-dimensional Ising model</em>).</p>
<p>I confess that since after the first half of the statement of the first theme got lost. For an expert my doubts about the second half of the proof of the lemma below is certainly primitive.</p>
<p>I reproduce below the statement of the lemma and its proof together as some figures to illustrate what I did the first half of the demonstration of the lemma.</p>
<blockquote>
<p><em><strong>Lema 2.1(Existence of infinite clusters)</strong>
If $\mu\in\mathcal{G}$ is different from $\mu^-$, there exists with
positive probability an infinite $+$cluster.
That is, $\mu(E^+)>0$ when $\mu\ne\mu^-$.</em></p>
</blockquote>
<p>[Here, $\mathcal{G}$ is the set of Gibbs measures of the Ising model of first neighbors in the net $\mathbb{Z}^2$. And $\mu^-$ is the extremal Gibbs measure, which is obtained by
thermodynamic limit of finite volume measures whit borders fixed in negative sign.
$E^+$ denotes the event que there exists an infinite cluster of spins in state $+$.]</p>
<p><em><strong>Proof.</strong>
Suppose that $\mu(E^+)=0$. Then any given square
$\Delta$ is almost surely surrounded by a $-*$circuit, and with
probability close to $1$ such a circuit can already be found within a
square $\Lambda\supset\Delta$ provided $\Lambda$ is large enough. If this
occurs, we let $\Gamma$ be
the largest random subset of $\Lambda$ which is the
interior of such a $-*$circuit. (A largest such set exists because
the union of such sets is again the interior of a $-*$circuit.)
In the alternative case we set $\Gamma=\emptyset$. By
maximality, $\Gamma$ is determined from outside [ see figure below].</em></p>
<p><img src="http://i.stack.imgur.com/qos6X.png" alt="enter image description here"></p>
<p>So far I understand the argument. And in any section of this theorem repeats this argument in several demonstrations. But what comes next does not seem intelligible to a non specialist. I have no idea how the properties below to get the desired equality through the instruction below:</p>
<p><em><strong>Continuation of proof:</strong> The <strong>strong Markov
property</strong> together with the <strong>stochastic monotonicity</strong>
$\mu^-_\Gamma\preceq \mu^-$ therefore implies (in the limit $\Lambda\uparrow\mathbb{Z}^2$)
that $\mu\preceq\mu^-$ on $\mathcal{F}_\Delta$.
Since $\Delta$ was arbitrary and $\mu^-$ is minimal we find that
$\mu=\mu^-$, and the lemma is proved.</em> $\Box$</p>
<p><strong>Question:</strong> How to use the strong Markov property and the stochastic monotonicity to finish the proof of lemma? Below the properties used as set out in Article.</p>
<blockquote>
<p>$\bullet$
the <strong>strong Markov property</strong> of Gibbs measures,
stating that
$\mu(\cdot\,|\mathcal{F}_{\Gamma^c})(\omega) =\mu_{\Gamma(\omega)}^\omega$ for
$\mu$-almost
all $\omega$ when $\Gamma$ is
any finite random subset of $\mathbb{Z}^2$ which is determined from
outside, in that
$\{\Gamma=\Lambda\}\in\mathcal{F}_{\Lambda^c}$ for all finite $\Lambda$, and
$\mathcal{F}_{\Gamma^c}$ is the $\sigma$-algebra of all events $A$ outside
$\Gamma$, in the sense that
$A\cap \{\Gamma=\Lambda\}\in\mathcal{F}_{\Lambda^c}$ for all finite $\Lambda$. (Using the
conventions $\mu_{\emptyset}^\omega=\delta_\omega$ and $\mathcal{F}_{\emptyset^c}=\mathcal{F}$
we can in fact allow that $\Gamma$ takes the value $\emptyset$.)
For a proof<br>
one simply splits $\Omega$ into the disjoint sets $\{\Gamma=\Lambda\}$ for
finite $\Lambda$.</p>
<p>$\bullet$
the <strong>stochastic monotonicity (or FKG order)</strong> of Gibbs
distributions; writing $\mu\preceq\nu$ when
$\mu(f)\leq\nu(f)$ for all increasing local (or, equivalently,
all increasing bounded measurable) real functions $f$ on $\Omega$,
we have $\mu_{\Lambda}^\omega\preceq\mu_{\Lambda}^{\omega'}$ when $\omega\leq\omega'$, and<br>
$\mu_{\Lambda}^\omega\preceq\mu_{\Delta}^\omega$ when $\Delta\subset\Lambda$ and $\omega\equiv
+1$ on $\Lambda\setminus\Delta$ (the opposite relation holds when $\omega\equiv
-1$ on $\Lambda\setminus\Delta$).</p>
</blockquote> | g13495 | [
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-0.027977177873253822,
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0.0805811807513237,
0.008592839352786541,
0... |
<p>So I need to find the possible energies and the probabilities of these using the eigenvalues of a Hamiltonian.</p>
<p>Once I obtain the eigenvalues, are those the energies E_n in and of themselves?
Or do they simply give me the n values, i.e. n = 1, 2, 3, that I would then plug in to the equation</p>
<p><img src="http://i.stack.imgur.com/4QNC5.gif" alt="Equation for finding energies"></p>
<p>Or is it both? Do they both yield the same answer? (I am still waiting on the installation of the computer program to use to find the eigenvalues)</p>
<p>Finally, I am completely at a loss as to how to go on to find the probabilities of the energies. I am not given a traditional wavefunction to normalize, so how do I find the probability without the normalization constant?</p>
<p>EDIT: I normally don't like to put problem specifics from my homework on here, but I suppose it's hard to understand what I mean by "I am not given a traditional wave function." As such, the exact problem is stated:</p>
<blockquote>
<p>Models describing electrons on a crystal lattice are very important to
understanding various phenomena in solids. Here we consider a model in
which an electron lives on a one-dimensional lattice of N sites. The
sites are labeled by i=1,2, ....,N. The system looks like</p>
<pre><code> o----o----o-- .... --o----o
1 2 3 N-1 N
</code></pre>
<p>The state of the electron is then a vector of dimension N. The
Hamiltonian is given by an N by N matrix whose elements are:</p>
<pre><code> / - 1, if i and j are near-neighbors;
H_{ij} = |
\ 0 , otherwise.
</code></pre>
<p>Physically, the electron can be thought of as hopping from site to
site through a near-neighbor hopping. As you see, the Hamiltonian
resembles the one we obtained in class when we discretized the problem
of a particle in a box. Suppose we prepare the electron in a state
|a> with equal amplitude for all N sites, i.e., a(1)=a(2)=....=a(N).
To be specific, let's consider N=5.</p>
<pre><code>What is the lowest value we can find if we measure the energy of the electron? With what probability?
List all the possible (i.e., with non-zero probability) energy values that we could find in such a measurement.
</code></pre>
</blockquote>
<p>So I used Maple to obtain eigenvalues for N=5, and thus have the energies.</p>
<p>So I suppose the root of my question is: if I am only given this information, how do I know what state the electron is in? Is it as simple as the corresponding eigenvector for each eigenvalue? Can I assume anything about the wave function (i.e. follows particle in a box method)? </p>
<p>Thank you.</p> | g13496 | [
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... |
<p>I have heard that the Morse potential equation</p>
<p>$$\tag{1} -\frac{\hbar ^{2}}{2m} \frac{d^{2}}{dx^{2}}y(x)+ae^{bx}y(x)-E_{n}y(x)=0 $$ </p>
<p>is related to the two dimensional equation on the Poincare half plane with a constant magnetic field</p>
<p>$$\tag{2} -\frac{y^{2}}{2m}( \partial _{x}^{2}+\partial _{y}^{2})f(x,y)+B\partial_{y}f(x,y) = 0$$ </p>
<p>by means of a substitution that turns (2) into (1) but i do not know where to find some free avaliable info.</p> | g13497 | [
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<p>At my university the second half of a year long sequence in basic calculus based physics focuses on electrodynamics and magnetism. I am wondering what is the significance of these topics to physics in general? How does it relate/prepare you to study the more advanced subjects like quantum mechanics and the like? </p> | g13498 | [
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<p>Application of mechanical stress to a piezo crystal generates a charge. </p>
<p>Quoting from wikipedia, a 1 cm3 cube of quartz with 2 kN (500 lbf) of correctly applied force can produce a voltage of 12500 V.</p>
<p>What happens when the crystal is exposed to a vacuum? Is the converse true? If the structural deformation occurs as a result of exposure to vacuum, is a voltage still generated? </p> | g13499 | [
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-0.0... |
<p><a href="https://en.wikipedia.org/wiki/Collision_frequency">Collision frequency</a> for particles in gases is well known, and <a href="https://en.wikipedia.org/wiki/Collision_theory">collision theory</a> is used to derive chemical reaction rates in gases, (and particles in liquid solutions as well). Using the mean velocity as a function of temperature, one arrives at
$Z = N_A \sigma_{AB}\sqrt{\frac{8k_BT}{\pi\mu_{AB}}}$.</p>
<p>I need something similar where the collisions/interactions can only occur at the surface between two areas. I understand phenomenologically the collision frequency will be proportional to the area, but I am looking for something a little more rigorous. I have two types of particles, A and B. They occupy separate volumes of space and do not mix. One can assume no mixing because the time window I am interested in is too small compared to the average velocities or because of surface tension. I haven't thought it out completely yet.</p>
<p>The only thing I've thought of yet is to define some sort of mixing depth, and then just use the traditional collision frequency, multiplying by the mixing depth to arrive at collision frequency per unit surface area. But then the mixing depth should itself be derived from the average velocities of the particles and it should not really have sharp boundaries.</p>
<p>What is the canonical kind of model used for similar problems, such as reactions on liquid/liquid or liquid/gas boundaries?</p> | g13500 | [
0.057520706206560135,
-0.00635143555700779,
-0.007502682972699404,
-0.02120693400502205,
0.025749560445547104,
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0.0014673966215923429,
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-0... |
<p>If we have a harmonic oscillator and look at it on small scale the energy is quantized and we can calculate the different eigenstates. In general the energy eigenvalues are given by $$E_n = \left(\frac{1}{2}+n\right) \hbar \omega$$</p>
<p>Even if we can bring this system at $T=0$ into it's ground state, there will be zero point motion or quantum fluctuations remaining. Now if we heat a system, depending on its excitations we need Maxwell–Boltzmann, Bose-Einstein or Fermi statistics to calculate the occupation of each state. The resulting spectra are due to thermal excitations from the ground state. </p>
<p>Now if we remain at about absolute zero the system still has quantum fluctuations. From Heisenberg's principle the energy is uncertain but that does not tell me which is the current energy or eigenstate. How can one calculate the 'quantum' spectrum of an harmonic oscillator, or bluntly, how can one calculate the probabilities for observing the system at the state $n=1,2,...$ at $T=0$ if we prepare the system to be in $n=0$? </p> | g13501 | [
-0.016108166426420212,
0.02449186146259308,
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0.00994076393544674,
0.024445468559861183,
0.017467599362134933,
0.057... |
<p>What's the state of <a href="http://en.wikipedia.org/wiki/Star" rel="nofollow">stars</a>? I'm not pretty sure whether the stars are stationary or rotating. For instance, if they are not rotating what makes them to be stable?</p> | g13502 | [
-0.08695504069328308,
0.017631327733397484,
-0.020102379843592644,
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-0.04823824018239975,
-0.009647893719375134,
0.04636986181139946,
-0.023405883461236954,
-... |
<p>Say I build a perfect rectangle. Side lengths $l_1$ and $l_2$ and perfect right angles. I am on earth and the metric is given by the Schwarzschild metric. Setting $dt=0$ leads to the spatial Riemannian metric
$$\mathrm{d}s^2=\left(1-\frac{r_s}{r}\right)^{-1}\mathrm{d}r^2+r^2\left(\mathrm{d}\theta^2+\sin^2\theta \,\mathrm{d}\varphi^2 \right)$$</p>
<p>Now I would like to write down the set points of my perfect rectangle. But I need some help. Although I asked about the <a href="http://physics.stackexchange.com/q/108359/42950">notion of angles in curved space</a> I still feel unsure to find the set points of the rectangle. Of course the position of the rectangle shall be such that it is easy to solve the problem.</p> | g13503 | [
0.03449607267975807,
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0.022067055106163025,
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0.033488545566797256,
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0.01020895130932331,
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-0.00020614732056856155,
0.038551732897758484,
-... |
<p>How could one charge a spherical capacitor with a battery or any other emf source?</p> | g13504 | [
0.03167208656668663,
0.008678937330842018,
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0.008553053252398968,
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0.002... |
<p>I know that there are two different ways to write the Bragg condition namely
$k^2=(k+G)^2$ and $n\lambda=2d\sin \theta$ where $G$ is a reciprocal lattice vector, $\lambda$ is the wavelength and $d$ is the distance between planes. I am also familiar with the equivalence of both and the intuitive derivation of the second form. But is there an intuitive understanding of the condition using reciprocal lattice vectors?</p> | g13505 | [
0.0213471669703722,
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0.012991986237466335,
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0.0730520486831665,
-0.03591114655137062,
... |
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