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Work done by an external force on a system equal and opposite to a conservative force is stored as potential energy within the system.
We choose an arbitrary location x and define the potential energy at a point y to be the potential energy required to move an object from x to y.
Am I missing something? or is this the ... |
There are examples of topological "terms" causing spontaneous symmetry breaking. One that comes to mind is the $\theta$ term in $4d$ $SU(N)$ Yang-Mills, which at $\theta=\pi$ spontaneously breaks time reversal symmetry.
I am curious of a purely topological field theory's ability to spontaneously break a symmetry. My un... |
what exactly is the difference between a skyrmion and a skyrmion bubble? Thanks.
|
Is the potential at each point on a circuit same,if so why?
I have read that in order for current to flow through any kind of resistance,the potential of charges reaching resistance is higher than those exiting it. ie. all the charges before it are at same potential and the charges exiting it are at some low but same p... |
Electric potential at a point is defined as the amount of work done in bringing a test charge from infinity to that point..my question is that if we don't know where this point of infinity lies then how can we calculate the potential at a point in influence of electric field and if we do know where it lies can you tell... |
Is a measurement of the current flowing through some material a measurement of the momentum of the electrons? Does their wavefunction collapse to an (approximate?) wavefunction of momentum?
|
A phototube1 (or "photoemissive cell") is a simple vacuum tube device that works by the photoelectric effect; it produces a current when light strikes the photocathode.
For it to work, a potential difference is generally applied between the cathode and the anode of 15V, I only need to know the current to calculate the ... |
Regarding the function theorem: W (non-conservative force) = △ K, this formula I once derived, it is also acceptable, but I saw W = △ K + △ U in the reference book a few days ago, I don't understand this, how can there be △ U? And how to derive it?
|
The area of a black hole is an important parameter in the thermodynamic description of a black hole. In particular, reading popular literature, everyone knows that the entropy of a black hole is proportional to its area as discovered by Stephen Hawking. Can someone explain with a diagram which is really the area of a b... |
Well, suppose then Schwarschild black holes. Following the $[1]$, we have the redshift factor:
$$d\tau = \sqrt{1-\frac{2M}{r}}dt. \tag{1}$$
This factor have an physical interpretation to be the time a given observer
measures on her own clock, i.e., for a stationary observer the proper time relates to the time as meas... |
This Wikipedia article gives a table of certain constants in different systems of units. I noticed that in Gaussian and electrostatic CGS the value of $\epsilon_0$ equals the dimensionless $1$.
I wondered whether anyone could provide justification for this? I was under the impression that $\epsilon_0$ is not even neces... |
I’m working through Special Relativity by V. Faraoni, and am puzzled by something in his chapters on tensors. He tells us that the partial derivative of a tensor field, e.g. $T_{\alpha, \gamma}$, is not a tensor, because
\begin{align*}\frac{\partial T_{\alpha'}}{\partial x^{\gamma'}} &= \frac{\partial x^{\delta}}{\part... |
Send white light through a vertical polarizer and then through a second horizontal gap that is just wide enough to let all the light through. Now slowly close the second gap until it becomes a slit. All the photons hitting the second slit are vertically polarized and should not make it through but as the slit slowly cl... |
So as we all know for a system that has translational symmetry Noether's Theorem states that momentum is conserved, more precisely the theorem states that the quantity:
$$\frac{\partial L}{\partial \dot{q}}$$
so the generalized momentum is conserved. Here i have a problem: suppose i want to show that classical momentu... |
So the energy given to the charge (assume it to be positive) in unit time is completely consumed when it crosses the resistor, why does the charge still flows towards the battery.
|
i know this is a silly question, but i couldn't manage to wrap my head around it. I am kinda new to electronics.
My home's outlets provide 220V. Upon doing some (a lot) research, the current that this voltage can supply is enough to kill me. However, when i try to do the maths myself, i can't seem to get the correct an... |
This plot gives the amount of the seemingly 10000 brightest stars.
Can someone help me to explain why there's a minimum at number 3, I know how to explain 1 (there are less
big stars) and 2 (small stars are not bright enough)
|
In ultrashort laser physics, frequency-resolved optical gating (FROG) has been a standard method since a few decades to measure the temporal profile of an unknown pulse's electric field $E(t)$ via a spectrally resolved nonlinear autocorrelation. The simplest and most popular FROG is second-harmonic FROG where the two d... |
There is something I do not understand and its bothering me. If I have a twin and we are both in our 20's.
Now let's assume I take a trip to space close to the speed of light, when I will come back I will be younger according to my twin (from the perspective of my twin in earth), but will I myself feel like an old man?... |
Why do things(it may include positive charges or just water kept at height etc) move from Higher potential level to lower potential level
Is that a law or there is some special reason behind it...or probably it is just the behaviour of nature
|
When a drop of liquid splits into a number of drops, each drop tries to minimize its area but the overall surface area of drops increases. How does the overall surface area of the drops increase????
|
I was learning about the Inflaton model and by quantizing it ,I can derive a $1/k^3$ power spectra , which is the Fourier transform of the fluctuation correlation function. But that doesn't give a Gaussian. I must have some wrong understanding.
|
My textbook says the following:
Suppose we put $+Q$ and $-Q$ charges at the two ends of a copper wire. The electrons will be accelerated due to an electric field towards $+Q$. They will thus neutralize the charges. There will be current for a very short time and no current thereafter. But if we continuously supply fre... |
I have problems understanding how transformations of Lorentz or Poincaré groups act on fields.
We can think about two ways of transformation of a field $\phi_r(x)$:
$$\phi_r(x) \rightarrow \phi^{'}_r(x^{'})=\phi_r(x)+\delta\phi$$
$$\phi_r(x) \rightarrow \phi^{'}_r(x)=\phi_r(x)+\delta\phi_0$$
in other words
$$\delta\phi... |
In quantum electrodynamics "photons don't have positions". The physical relevance and consequences of this fact has been discussed on this site 1. (Further relevant questions about the concept of photon position: 2, 3, 4, 5). The answer to 1 says that this is a consequence of the Reeh-Schlieder theorem (see e.g. arXiv:... |
Consider a uniform cylindrical rod mounted on a horizontal frictionless axle through its
center. The axle is carried on a turntable revolving with constant angular velocity Ω, with the
center of the rod over the axis of the turntable. Let θ be the angle the rod makes with horizontal
as shown in the sketch. Us... |
I'm tring to understand some symbols in physics formula
for example in Ehrenfest’s theorem
$$\frac{\partial}{\partial t}\langle \hat Q \rangle = \left\langle \frac{\partial \hat Q}{\partial t} \right\rangle +\frac{i}{\hbar}\langle[\hat H,\hat Q]\rangle $$
I think Q and H with hat represent operator, but what's the symb... |
This question may sound like a no-brainer, but I'm getting confused after watching this lecture (cf. the slide at minute 5:07).
The context is to motivate the quantization of a field which, for the sake of simplicity, is taken to be a classical, one-dimensional string of length $L$ that is approximated by infinitesima... |
It's often stated that the off-diagonal terms in the stress-energy tensor signify shear while the diagonal terms are normal pressure terms (you get a displacement in the direction you apply pressure). I was reading Weinberg and I found this expression of the stress-energy tensor:
$$T(\alpha,\beta)=\sum_n P_n(\alpha) \f... |
why current if flowing if there is no potential difference. if no potential difference then no work is being done on charge so there should be no net displacement of charge but we know that the current flows. current also flows from higher potential to lower potential but across two ends potential is same(potential dif... |
In deriving the master equation, I am coming across the Markov Approximation which says:
Suppose environment $E$ and system $S$ interact and exchange some energy with each other. Then $E$ would recover back to thermal equilibrium faster than $S$ because $E$ is much larger than $S$. Due to this, from the point of view ... |
Question
When a body is immersed in an liquid the liquid exerts buoyant force on it. But does the body also exert a reaction force equal to the buoyant force on liquid as per Newtons 3rd law.
|
I don't have much of a physics background, so my assumptions might be somewhat incorrect. But I've recently seen how sanding tools can be used on materials that are powerful, such as stainless steel. From a Google search, it seems standard sanding tools are made out of materials like aluminum oxide, which (aluminum) I'... |
Charge is quantised then why how do we define $dQ/dt$ as current when graph of $Q$ v/s $x$ will be discontinuous and hence non-differentiable.
Is it an approximation we use?
|
In the integral quantum Hall effect, one has that in regions where $R_{xy}$ (the Hall resistance) is a constant, $R_{xx}$ surprisingly goes to zero. Why does that happen? Do impurities in the material play a role in this?
|
At the very beginning of the unvierse, the Higgs potential had a paraboloid shape.
After the electroweak Symmetry Breaking, it took the mexican hat shape.
Is the analytical dependence of Higgs potential with temperature known ?
|
I was reading six easy pieces by Feynman, and I had reached the section on the Conservation of energy
This chapter was defintly one of the harder ones so far, especially considering that his reversible machines analogy made things somehow more difficult.
Anyway I pushed on, and came across something that confused me. F... |
I was sitting right in front of a big window (with a mesh) with curtains open, suddenly wind swooshes in, curtains sway forth and back. While they sway backward, they stick to the window(mesh) as if they are being sucked due to a vacuum. Somewhat like the image below:
Now my explanation for this phenomenon was using Be... |
Suppose that we have a circular path which has a radius of $r$ and constant velocity $v$ that is tangent to the circle that the object moving around, I know that centripetal acceleration is expressed like this:
$$a_{c}=\frac{v^2}{r}$$
And I know that the direction of $a_c$ is to the center (hence, the name.).
But the ... |
Let's assume I have a conductive rod with mass $m$ and with steady current $I$. I can make the current flow in such a direction and magnitude that the magnetic force will make it move up, thus something is doing work on the rod. But it can't be the magnetic field since it's perpendicular to the direction of motion.
I s... |
I've seen a few cool videos where there is series of gears such that the first gear spins extremely fast while the last gear doesn't appear to spin at all.
I think it would be cool to build a machine like this, but then at the end continue the machine with gear multiplication, such that the first gear spins really fast... |
In short:
For a stress-energy tensor $T^{\mu\nu}$, what are possible additions that will leave the tensor equations of motion $\nabla_\nu T^{\mu\nu} = 0$ unchanged?
Context:
Any modification, $T^{\mu\nu} \rightarrow T^{\mu\nu} + A^{\mu\nu}$ where $\nabla_\nu A^{\mu\nu} = 0$ as an identity, would work.
In various pub... |
I tried to find an answer to this but haven't yet. Going through Jackson's Electrodynamics, the following steps are used to determine the vector potential as the curl of $\mathbf{B}$. The context is magnetostatics, where $\nabla \cdot \mathbf{J} = 0$.
The basic law (5.4) for the magnetic induction can be written down ... |
Milliampere and microampere is quiet common in human-made machines, are there examples of machines that use nanoampere currents?
|
Let's consider a system of three apparatuses. Sequentially these act as
A device that measures momentum of an electron
Parallel plates where electric field between them changes randomly.
Same device as in 1
A electron with $\int{\psi_p dp}$ enters and after we measure with device 1 wave reduction occurs $\int{\psi_p ... |
From the Larmor equation: $P=\frac{q^2a^2}{6\pi\epsilon_0c^3}$ so an accelerated particle radiate. Is this true also for a decelerated particle?
|
I understand the explanation, for example, about a light beam reflecting between two mirrors on the space craft. But what I am looking for is what aspect of traveling at very high velocities must slow down every single process that is time dependent.
Is it anything like the inertia of every particle increases so in som... |
I've edited this question way more times that I like to admit. I'll do my best
Relation between highly symetric charge distributions and $\nabla\times\mathbf{D}$:
In electrostatics, for some charge distributions, we can use Gauss law in their integral from to compute the electric displacement field. This distributions ... |
I am studying the basics of statistical mechanics and Boltzmann distribution.
I tried to use the idea to find natural income distributions, through the method of maximization of probability using Lagrange multipliers, where:
average energy => income per capita
number of particles => number of people
Energy levels => ... |
Others have asked how many quantum fields there are according to the Standard model (How many quantum fields are there?). In a comment on that post, it was claimed that in string theory there is only one "master" quantum field.
Is it true that there is only one master quantum field in string theory?
|
We have two systems of ideal gas with different temperatures. $N$ & $V$ are being kept constant. The number of accessible microstates of each gas is thereby only influenced by a change in $E$.
The number of accessible microstates is:
$$\Omega = \frac{(N-1+U)!}{(N-1)!\,U!}. $$
In regards to $E$ the function is growing ... |
In case of a cell,the positive charges (conventionally)move from Higher potential to lower potential..but how actually it happens when charges reach to lower potential terminal of cell ,whether cell is just supplying extra potential energy to the charge and forcing it to go at higher potential level or it happens that ... |
In Feynman diagrams of QED vertices of interaction are often labelled by the amplitude sqrt(alpha) where alpha is the e.m. fine structure constant. When higher order diagrams are constructed, each time when a virtual photon is created and absorbed the probability of the interaction process gets 1/137 time lower. Is thi... |
Whenever a conductor is connected to a cell,what causes the conventional positivecharges inside it to move towards the lower potential level of cell..
My question is whether the charges experience a force due to electric field or all the positive charges in conductor gain higher potential energy and hence flow towards ... |
I would like to know how the above quantity is derived (Here $\mathbf{M}$ is the rate of change of angular momentum with respect to a non inertial frame).I tried looking at various sources and couldn't find a derivation. I have no idea where $\vec{\omega} \times \mathbf{L}$ came into this equation. In what cases does t... |
Through Rayleigh's Criterion, it is implied that there is a maximum distance beyond which we cannot resolute an object. This limitation is due to the limitation in the size of the aperture of the lense. Rayleigh's Criterion is founded upon diffraction which is exhibited by light after interacting with lenses/ refractor... |
I have a question regarding capacitors and their charge neutrality. When capacitors are used in circuits, the assumption is often made that the plates of the capacitors have equal and opposite charges. I was wondering why this is the case.
I have done some research. One source, The Feynman Lectures on Physics (Vol. 2) ... |
The metric is
\begin{equation}
ds^2 = G^D_{MN}dx^M dx^N
= G_{\mu\nu}dx^\mu dx^\nu + G_{dd}(dx^d + A_\mu dx^\mu)^2.
\end{equation}
Then
\begin{equation}
G^D = \begin{bmatrix}
G_{\mu\nu} + G_{dd}A_\mu A_\nu& G_{dd}A_\mu\\
G_{dd}A_\nu& G_{dd}
\end{bmatrix}.
\end{equation}
In the above $G^D_{MN}$ is $D = d+1$ dimensional... |
I am wondering what's the effect of the number of atoms in the basis onto the heat capacity (phonon part).
I've found this post: How the number of atoms in the basis affects the density of states?
Here the answer says that the density of states is not affected due to the number of phonons in the basis. Can I conclude ... |
Last night I got to thinking about what would happen if Jupiter and Venus suddenly switched places.
Since Venus comes the closest to Earth than any other planet and Jupiter is much larger, does that mean that Jupiter (now following the orbit of Venus) would appear large enough to eclipse the Sun from Earth's perspectiv... |
This answer to What exactly is a “Next Generation Lunar Reflector”? Difference in design and performance? quotes Next Generation Lunar Retroreflectors Should Fly Soon (published in the magazine Forbes) and another section of that article says:
The Apollo retroreflectors are made up of either 100 or 300 individual glas... |
Consider a static equilibrium problem like the following:
The uniform boom shown below weighs 700 N, and the object hanging from its right end weighs 400 N. The boom is supported by a light cable and by a hinge at the wall. Calculate the tension in the cable and the force on the hinge on the boom. Does the force on th... |
Suppose we have some compact Riemann surface $\Sigma$ , and scalar field $\phi$, which takes values in some Kahler manifold (target space) $M$. In other words, we have a map:
$$
\phi : \Sigma \rightarrow M.
$$
The action with topological term, as far I as understand, would have the following form:
$$
\int d^2 x \sqrt{... |
I am currently studying Classical Mechanics, 5th edition, by Kibble and Berkshire. Chapter 1.3 The concepts of Mass and Force says the following:
Clearly, we can compare the inertial masses of two bodies by subjecting them to equal forces and comparing their accelerations, but this does not help unless we have some wa... |
I am studying the Euler Lagrange equations and have some problems understanding its derivation.
Consider a path $y(x)$ where a slight deviation from the path is given by $$Y(x,\epsilon) = y(x) + \epsilon n(x)$$
where $\epsilon$ is a small quantity and $n(x)$ is an arbitrary function.
The integral to minize is the usu... |
I am currently studying the paper by Witten on supersymmetry and Morse theory. In the introduction it is stated that when supersymmetry is not broken, i.e. $Q|0\rangle=0$, the Hilbert space contains bosons and fermions of equal mass. I thought initially that this was the case simply because $[Q,H]=0$ (take f.e. a boson... |
My neighbour and I share a small window at the end of the corridor in the block of flats where we live.
She often wants to close this window leaving notes on the window saying:
"You (me) are letting the hot air in and the cool air out if you keep opening the window."
I thought that it was the OPPOSITE in fact, that ... |
I am reading this paper https://arxiv.org/abs/2002.02577. On page 13, it is written that the $d$-dimensional Einstein equations are
$$G_{\mu\nu}+\frac{(d-1)(d-2)}{6}\Lambda g_{\mu\nu}=8\pi T_{\mu\nu}.\tag{2.6}$$
Of course, for $d=4$ we take what we expect. But I don't see how the the factor $(d-1)(d-2)/6$ shows up if... |
It is folklore that quantum gravity cannot have any exact global symmetry (see Global symmetries in quantum gravity). This follows for example from thought experiments involving black holes (no-hair). Yet electrically charged "hair" is allowed. Gauge symmetries seem to be excepted (due to long range forces). But gauge ... |
I'm trying to prove the relation for angular momentum operator.
$[\hat{L}_i,\hat{r}_j] = i\hbar \sum_{k} \epsilon_{ijk} \hat{r}_k $
$ [\hat{L}_i,\hat{r}_l]$
= $ \sum_{jk} \epsilon_{ijk} [\hat{r}_j\hat{p}_k, \hat{r}_l]$
= $\sum_{jk} \epsilon_{ijk} \{{\hat{r}_j [\hat{p}_k, \hat{r}_l] + [ \hat{r}_j, \hat{r}_l]\hat{p}_k} \... |
Clip; I presume some momentum transfer's at play, but can't put a full picture together. What's going on - why does the laser 'repel' the bubble? ... or is it fake?
|
Over the time i have been doing physics i have noticed a pattern related to energy that gets dissipated in systems which come to equilibrium after a certain time has passed. please hear me out with a few examples
(i) A capacitor connected to a a simple circuit
When we connect a capacitor to a circuit and close the sw... |
In learning about Lagrange's Equations, I had always used generalized coordinates that are independent from each other.
However, in this post it was mentioned that generalized coordinates can be dependent on each other.
My question is, for generalized coordinates that are dependent on each other, does Lagrange's equa... |
I've a foldable quadrotor with rotating arms.
So, the quadrotor can take different morphologies, like the classical one "X", an "H" morphology, "Y", etc.
I've calculated the inertia matrix for each one, but I couldn't interpret why $I_{xx}$ is higher than $I_{yy}$ in some morphologies and the inverse in others.
To simp... |
I know this has been asked before but i could not understand the replies. If someone has a simpler answer please do so.
My simple Geog lesson just said that warm air molecules are further apart leaving bigger gaps for water vapour. Is this correct somewhat is it more than this.
|
Everywhere I look it says that centripetal acceleration changes the velocity direction. That would mean either the velocity direction changes or the centripetal force direction changes at some point in time. The problem with that idea is that centripetal force is said to always be perpendicular to the velocity.
Somet... |
The canonical momentum of a particle in an electromagnetic field is given by $$\textbf{P}=m\textbf{v}+q\textbf{A}$$ Is the term $q \textbf{A}$ equal to the momentum of the electromagnetic field (which would be $\mathbf{P}_\text{field} = \int \epsilon_0 \left(\textbf{E}\times\textbf{B}\right) dV$ ) ?
Otherwise, where i... |
[The same question has been posted in MathStackExchange.]
The projective representation (rep.) of $\mathbb{Z}_N\times\mathbb{Z}_N$ is $\mathbb{Z}_N$-classified.
It can be understood by embedding into a $SU(N)$ representation.
For example, taking $N=2$, the nontrivial projective rep. of $\mathbb{Z}_2\times\mathbb{Z}_2... |
Roger Penrose in this interview says he was trying to find out "... how it is that nerve signals could possibly preserve quantum coherence".
What does he mean by that?
|
Do tangential velocity and tangential acceleration change with radius (change of radius on the same object)?
For example consider a spinning disk. Does the equation $$a_t = \alpha R$$ (where $a_t$ is the tangential acceleration, $\alpha$ is the angular acceleration and $R$ is the radius of the disk) give me the tangen... |
I'd like to learn about (or confirm) certain properties of congruences, concerning some presumably rather simple cases, namely of timelike congruences in the setting of flat spacetimes $\mathcal S$. Therefore I have here three closely related questions:
1.
Are there at least two (or more) distinct timelike congruences,... |
What is the potential energy of a particle in the single bound state $\psi_b(x)=\frac{\sqrt{m\alpha}}{\hbar}e^{-\frac{m\alpha}{\hbar^2}|x|}$ of the Dirac-delta potential well
$$V(x) = -\alpha \delta(x)$$
which has total energy $\langle H\rangle =E=-\frac{m\alpha^2}{2\hbar^2}$? Wouldn't the potential energy become infin... |
I have written in some old notes that the FLRW (also known as FRW) metric can be written as:
$$ds^2=dt^2 + a^2 (t) [dr^2 +r^2(d\theta^2 + sin^2\theta d\varphi ^2)] \tag{1}$$
I believe this is its representation in $4\text{D}$.
But I have seen in other pages, among them, the Wikipedia page and Robertson-Walker metric an... |
Is there any connection between special relativity and general relativity? We know that gravity causes relativistic effects according to general relativity which car similar to special-relativity. so is there any connection between general relativity and special relativity?
Or any thing in the scientific literature whi... |
I have been reading Tong's notes on QHE and Gauge Theories, specifically the part about quantizing the Abelian U(1) Chern-Simons level at finite temperature in the presence of a monopole (These discussions begin on pages 150 and 391 in the documents I refer to, respectively). There, he talks about the proper way of per... |
After I was drinking water in school, I flipped top-to-bottom the bottle.
At that time, I was wondering how it is possible to form the water droplets on top of the bottle; inside the bottle.
I searched for some information about water's force; Capillary action, Surface Tension.
I thought that capillary action is the k... |
I have read that the analogy of gravitational field is similar to electric potential energy..now if I have a ball falling from higher potential level to lower potential level,then the potential energy of ball changes to kinetic energy.
Similarly will the potential energy of a charge gradually decrease and change to kin... |
For example :
$[\hat{x},\hat{p}] = i \hbar \hat{I}$ and $\Delta x \Delta p \ge \hbar/2$ but in case of number states $|n \rangle $
$$[\hat{C},\hat{n}] = i \hat{S}\\
\Delta C \Delta n \ge 0
$$
where $$\hat{C}=\frac{1}{2} [\hat{E}+\hat{E^\dagger}] \\
\hat{S}=\frac{1}{2i} [\hat{E}-\hat{E^\dagger}]\\
\hat{E}=\bigg( \fra... |
In many QFT textbooks, we usually see the calculations of vertex function, vacuum polarization and electron self-energy.
For example, one calculates the vacuum polarization to correct photon propagator $\langle{\Omega}|T\{A_{\mu}A_{\nu}\}|\Omega\rangle$, where $|\Omega\rangle$ is the ground state of an interaction Hami... |
We know that if Hamiltonian commutes with parity operator and energy eigen values are non-degenerate then the corresponding wave function has well defined parity. But my question is what about degenerate eigenvalues(I know then in that case eigen function do not have definite parity), Is there a way to prove it mathema... |
I'm having trouble reconciling these three things I've heard about black holes:
If you fall into a sufficiently large black hole, you won't experience anything in particular when crossing the event horizon. You'll have some time to experience being inside the black hole until tidal forces eventually grow dangerous.
So... |
I'm trying to calculate the amount of work that is needed to dig a hole in the ground (can be very deep) between the surface of the Earth with radius $R_{Earth}$ and some surface with radius $R$. As we know, the gravitational force inside the Earth is proportional to the radius and the second mass: $F_g(r) = \alpha \cd... |
In my book it's written that speed of sound will in increase with increase in density of the medium as molecules with get closer to each other, but after some browsing on internet I found out about Laplace's formula which states that speed of sound in a medium is inversely proportional to density of the medium?Which of... |
Consider the potential
$$V(x)= \frac{x^2}{2} + gx^3.\tag{1}$$
Then the time-independent Schrödinger equation becomes
$$\left(-\frac{1}{2}\frac{d^2}{dx^2} + \frac{x^2}{2} + gx^3 \right)\psi = E(g) \psi.\tag{2}$$
Where $E(g)$ is the energy eigenvalues as a function of parameter $g$.
One obtains the following perturbation... |
Let us consider a classical thermal ensemble
\begin{equation}
\rho_\beta = \frac {1}{Z_\beta} e^{-\beta H}.
\end{equation}
The Hamiltonian generates a mixing dynamics if
\begin{equation}
C_\beta(t) = \langle A B(t) \rangle_\beta \to \langle A\rangle_\beta\langle B \rangle_\beta \hspace{10mm}t\to+\infty
\end{equation}
I... |
I'm trying to plot planets' trajectories as seen from stationary Earth perspective.
I tried to look for some data online, but I wasn't able to find anything but some old manuscripts.
I was thinking about the following approach:
represent the eliptical orbits around the sun as a Fourier series (n.b. harmonic represe... |
Some context: I'm trying to make a molecular dynamics simulation in python and want to initialise the velocities of all particles according to some temperature T.
The Maxwell-Boltzmann distribution (if I understand it correctly) is for the distribution of speeds and not for the component-wise velocities.
What I want to... |
In QCD, the gluon field is described as $A^a_\mu$. In the covariant derivative for the Lagrangian, it is multiplied by the Gell-Mann $SU(3)$ generator matrices $\lambda_a$ ($a=1..8$) as $\lambda_aA^a_\mu$. My question is, what is the mathematical structure of $A_\mu$ (for a given a)? Since $\mu=0..3$, it must have 4 co... |
we know that the simple form of the metric in the special relativity is like this: $ds^2 = dr^2 - (cdt)^2$ that in this metric $dr^2 = dx^2 + dy^2 + dz^2 .$ I want to ask why we minus the time sentence? I know the mathematical reasons but I wanna know what happens in nature and reality by minus of the time sentence.
|
I have just finished my very first quantum theory of matter course and everything we did was strictly non relativistic. No QFTs whatsoever, no creation and annihilation operators, no mention to the Dirac equation. The most relativistic thing we did was the spin orbit interaction, and even then it wasn't fully justified... |
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