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Consider the following graph, which shows the Gibbs free energy per particle for a Van der Waals gas (the x axis is volume per particle, $v$ and the y axis is free Gibbs energy $G$):
Each curve has been drawn for a given and fixed value of $P$ and $T$. I have several questions:
My professor said that the red courbe c... |
I was doing an experiment where I had to measure the current (using an analogue ammeter) from a DC supply. The DC supply actually provided a full-wave rectified current. I was wondering what the current reading on my ammeter would correspond to. For a regular sine curve it would be the RMS but I don't know what it woul... |
Any replies from people who actually understand the topic (better than me, to say the least lol) and are able to clarify the topic (unlike my teacher), are highly appreciated and encouraged.
|
I find this contradictory. In my high school Physics book it says that Bernoulli's theorem applies to incompressible, non-viscious fluid having streamline and irrotational flow.
Then it says that Laminar flow can be viscious or non-viscous.
Later on, in the questions section, it states the Bernoulli's theorem applies i... |
I want to calculate the expectation value of the BCS Hamiltonian
$ H = \sum_k E(k) c_k^\dagger c_k - \frac{V}{2} \sum_{k,q} c_{k+q}^\dagger c_{-k-q}^\dagger c_{-k} c_k $
in the state $| \Psi \rangle = \prod_k a(k) c_k^\dagger c_{-k}^\dagger | G \rangle $.
I know it can be expressed as
$ \langle H \rangle_{\Psi} = 2 \su... |
I'm trying to understand the model described in this paper. I have a question about a claim they make. From page 2:
To describe the fermionic degrees of freedom let, as a preliminary
\begin{align*}
\gamma^i &= (\gamma^i_{\alpha \beta})_{\alpha, \beta = 1, ... ,d},
\end{align*}
be the real representation of smallest... |
I am self-studying Optics by Pedrotti and I'm stuck on the algebra for an example of spherical reflection.
We have a point source at O that reflects off a spherical surface and creates a virtual image at I.
Assume that $\alpha$ and $\phi$ are small so that the small angle approximation holds. Then
$$
\theta = \alpha +... |
That temperature of a black body (or any other body like an ideal gas in a container) is probabilistic in nature.
Temperature represents the most probable energy distribution of particles.
Suppose a black body is at $50^\circ$C. Then there is a chance (no matter how small) that the temperature might get recorded as $0^... |
If I take $U(P,V)$, I can do:
$$ \frac{dU}{dT} = \frac{\partial U }{\partial P } \frac{dP}{dT}+\frac{\partial U }{\partial V} \frac{dV}{dT} \tag1$$
But, I see the following used in books,
$ dU = zPdV + zVdP $
Thinking $$U= zPV \tag 2$$ for ideal gas.
So,
$$\frac{dU}{dT} = zp\frac{dV}{dT}+ zV\frac{dP}{dT} \tag3$$
A... |
I am currently doing a project where I need to find the capacitance of a multi-conductor system. Through my literature review, I read about the concept of a capacitance matrix. After more research, I am unable to find a closed form expression which calculates the total capacitance of the system from the capacitance mat... |
Let's imagine I'm ice skating on a perfectly flat surface.
In the first scenario, I am falling motionless. I expect my forces to looks like this:
In the second scenario, I am falling with some speed, let's say 20 km/h. I anticipate my forces to appear as follows:
Questions:
Will it take the exact same amount of time... |
Let's consider the two Jefimenko Equations:
$$E(r,t) = \frac{1}{4πϵ_0}∭_V[\frac{e_{r-r'}}{|r-r'|^2} ρ(r',t_r' )+ \frac{1}{c} \frac{e_{r-r'}}{|r-r'|} \frac{∂ρ(r',t_r')}{∂t} - \frac{1}{c^2} \frac{1}{|r-r' |} \frac{∂J(r',t_r' )}{∂t}] d^3 r'$$
$$B(r,t) = \frac{μ_0}{4π} ∭_V [\frac{1}{|r-r'|^2} J(r',t_r')+ \frac{1}{c} \fr... |
In physics I always see formulas with variables representing properties of objects like (this is a simplified example):
F = a bodies force.
m = a bodies mass.
a = a bodies acceleration.
But why do I never see variables representing whole objects like
B = a body
and is there actually any way of doing that?
|
Given the following $d+1$ dimensional dilaton-gravity-Maxwell low-energy effective action in the target space of a bosonic string:
$$S=\frac{1}{2\kappa^2}\int d^{d+1}x\sqrt{-\tilde{G}}e^{-2\tilde{\Phi}}\left[\tilde{R}-\frac{1}{12}\tilde{g}^{AB}\tilde{g}^{MG}\tilde{g}^{ND}\tilde{H}_{AMN}\tilde{H}_{BGD}+4\tilde{g}^{MN} \... |
I wonder how to use and manipulate differential forms in thermodynamics.
I see for
$ U= αPV$, it is written $dU = αPdV + αVdP$
But how this works in terms of differentiation? (Proof)
|
I'm just trying to understand this from a purely thermodynamical standpoint. I'm comfortable with the scenario of a blackbody cavity's interior being in thermal equilibrium with the photon gas contained, and they have identical temperature, and then the Planck distribution would apply to photon energy. However, why wou... |
Consider the following picture:
It is given that the liquid in the right tube is denser than the liquid on the left tube.
Call these two liquids $A$ and $B$, so $\rho_A < \rho_B$.
At both points $C$, the pressures are equal, since pressure is given by
$$p = p_0 + \rho gh,$$
and $p_0 = p_C$, $g=g$, and $h=h$ for both s... |
I have some phased array antenna which is installed on aircraft and pointing itself (azimuth, elevation, skew polarization angles) by plane angles (lat, long, roll, pitch, heading) and satellite location.
The antenna is providing its data (azimuth, elevation, skew angles) in plane body and i'd like to verify that it be... |
In Landau/Lifshitz' "Mechanics", $\S43$, 3ed, the authors consider the action of a mechanical system as a function of its final time $t$ and its final position $q$. They consider paths originating at some point $q^{(1)}$ at a time $t_1$, and terminating at the same point $q$ after different times $t$. The total derivat... |
Why do we need two gluons for the decay $$\pi^-+ p\rightarrow\pi^-+n+\pi^+\:\:?$$
If we have always the gluon $$\frac{1}{\sqrt{2}}(r\bar{r}-g\bar{g})$$ it should be possible with only one gluon
instead of 2 gluons
|
I'm confused about the relationship of electromagnetism and gravity, or are they even related?
It has been said the electromagnetic field produces a gravitational field, and so, there is no gravity if there's no electromagnetism.
I'm new to this topic, I don't understand things without imagining them nor how do they ev... |
Let's consider two cases:
Let's say that we have two positive point charges. If we get those charges together very very very close to each other, the repulsive force goes to infinity between those ones. (This fact is so clear to me-according to coulomb's law).
Now lets say that we have a positive point charge and an ... |
I know from special relativity that an costant velocity charged particle generates a magnetic field (from a frame that is still), can I use GR to derive EM generated by an AC current?
|
I'm reading that many articles are using the "axial anomaly equation" (e.g. Fermion number fractionization in quantum field theory pag.142 or eq (2.27) of Spectral asymmetry on an open space), and I know what axial anomaly in QFT is, but I'm not sure to what equation they are referring to. Can someone help me?
The arti... |
As an object approaches the speed of light, its observed mass becomes infinitely large -- Does the Gravity of the object show a corresponding increase and become infinitely large?
|
In my textbook, Introduction to cosmology by Barbara Ryden, the author gives directly the solution for the following integral if $\Omega_0 > 1$:
$$H_ot = \int^a_0 \frac{da}{[\Omega_0/a + (1-\Omega_0)]^{1/2}}$$
With the substitution (she calls it the solution) $$a(\theta) = \frac{\Omega_0(1 - cos \theta)}{2(\Omega_0 -1)... |
A classical pendulum clock is powered by gravitational potential energy by weights. While a hybrid pendulum clock is somehow propelled by electric current. Both have the same pendulum swing as the regulator.
A pendulum's frequency is dependent both on its length as on the value of small g according to Huygens formula. ... |
Wikipedia writes that the Feynman-Kac formula "proves rigorously the real-valued case of Feynman's path integrals. The complex case, which occurs when a particle's spin is included, is still an open question" (https://en.wikipedia.org/wiki/Feynman%E2%80%93Kac_formula). But the citation for this claim is from 1987. Is t... |
We know some supercondutors show multi-gaps feature in superconducting energy gap (for example, two gaps in the MgB2), but other are singe-gap. Why they are different? Under what circumstances will single-gap and multiple-gaps be formed? Are there some references about it? And how can I distinguish them from some theor... |
I am currently taking Physics II and have recently been focused on this problem: Suppose there is a ring of uniform linear charge density $\:\lambda\:$ and radius R and a point P at a height $\: z_{_\mathrm P}=h\:$ vertically upwards the center of the ring. What is the magnitude $\:\mathrm E\:$ of the force $\:\mathbf ... |
I know that a system's energy can be measured with an energy that can be below or above the expectation value, if the system was not in an energy eigenstate, so that energy is only conserved on average over multiple measurements.
Does that mean that energy is not conserved in individual cases and if so, does that mean ... |
This is more of a conceptual question than a mathematical one, but you may answer however you wish.
Suppose we imagine a universe with a single proton in it, then magically create an electron one light year away from it. It is my understanding that the proton will eventually feel the electrostatic force exerted on it b... |
As far as I know, shearing stress is produced when layers shift parallel to each other, which means there is change in shape, and the layers are displaced in the direction of force applied. I imagine shearing strain as, say, the way a deck of cards changes its shape when you apply force on the topmost cards.
But in a s... |
Imagine, 2 persons ('A' & 'B') are 6 light years apart in space, stationary to each other and with no gravitation acting on anybody. Suppose 'B' starts his clock which also shows years, months and days. also lets say he flashes a signal at the same time. When this signal reaches at 'A' he starts his own clock which als... |
What is the relation between stress and strain rate? If I had this as a stress rate:
$$\mathbf \epsilon= \left[ \begin {array}{ccc} 0& \tau_{{xy}}\ &0\\
\tau_{{yx}} & gh &0\\ 0&0&2gh\end {array}
\right]
$$
How would you be able to derive a strain rate tensor from it? Is there an intuitive mathematical and descrip... |
What does it mean the Van der Waals force comes from the fluctuating dipoles of the atoms? Why is the dipole moment fluctuating? Is it because the vacuum EM field is fluctuating then it stimulates the dipoles to fluctuate? Or do they not need to rely on the vacuum field to fluctuate?
|
Consider the following gravitational action in $d+1$ accompanied with a complex scalar field $\chi$ with a mass $m$:
$$S=\int d^{d+1}x\sqrt{-\tilde{g}}\left[\tilde{R}+\tilde{g}^{\mu\nu}\partial_{\mu}\tilde{\chi}\partial_\nu\tilde{\chi}-m^2\chi\chi^* \right]$$
How does the fact that the scalar field is charged under t... |
I got confused while reading about dielectrics, so basically my question is:
(a) what's the difference between a (homogenous and isotropic) dielectric and (linear) dielectric? Does the first imply the second? I know that linear dielectrics obey
$P=\epsilon_0(\chi_e)E$
but does this imply that the dielectric is homogeno... |
Okay I know a perpetuum mobile is impossible, so I think this should be wrong.
I thought about heat pumps with a COP of 3.5, which is like 350% efficiency compared to a simple electrical resistor. Now say you put 100W of electricity into the heat pump, which will pull 350W of heat energy from outside to the inside. Let... |
I want to make sure I correctly understand what this paper is saying. It sounds like it is talking about a two-body Majumdar-Papapetrau outer metric that switches to RN once you enter either of the spherical boundaries. If I understand correctly, it is a case of gluing those parts of the RN metric whose $r$ and $\theta... |
While studying section 7.6 of Carroll's introduction to general relativity, I encountered difficulties deriving equation 7.165 for the gravitational-wave energy-momentum tensor. Unfortunately, I was unable to derive the equation as presented in the book. Here's what I have done so far:
Using $t_{\mu \nu} = -\frac{1}{8\... |
I am reading Wolfgang Nolting's Theoretical
Physics 1, the book reads:
$$
2\langle T\rangle=\left\langle\sum_i \vec r _i \cdot \nabla_i V\right\rangle
$$
The right-hand side is the so-called virial of the forces. The virial theorem (3.33) tells us that under the mentioned assumptions the time average of the kinetic en... |
I am currently an undergraduate taking a course on Newtonian mechanics. The lecturer defines a force to be conservative if there exists a scalar function (we call it potential function), say $V(x,y,z)$, such that the force $$\mathbf{F}=-\Big(\frac{\partial V}{\partial x}\mathbf{\hat i}+\frac{\partial V}{\partial y}\mat... |
In basic continuum mechanics (e.g. fluid dynamics), we label particles of the continuum, i.e., each particle can be identified by a label, e.g., $p$. Then other quantities are defined accordingly, e.g., velocity: $V=\frac{\partial r(p,t)}{\partial t}|_p$ where $r$ is the location vector of $p$ and $t$ is time.
Now, I w... |
how did they reach the conclusion that quantization of the Poisson brackets
$ (A,B) $ was equal to the commutator $ \frac{1}{i\hbar}[A,B] $
in quantum mechanics?
so the quantum equations of motion were $ \frac{dA}{dt}= [A,B]\frac{1}{i\hbar} $
|
imagine I made a measurement of an electron and revealed that it is spin up, however in the room with me are hundreds of cameras and some of which are oriented at different angles. Maybe some are held upside down and some at 15.25°, etc you get the drift. Since I didn't label the directions on my apparatus so that only... |
I am currently trying to go through some literature on symmetry protected topological phases and gauge theories defined on lattices. I am looking for a mathematically precise reference that discusses $\mathbb Z_N$ gauge theory. Or more generally, a resource that discusses discrete gauge theories where the underlying gr... |
If there were 2 sound waves with the same wavelength and amplitude, but different speeds, how would my perception of the waves vary? How would my perception vary if they were light waves instead of sound?
|
The first time I was introduced to the covariant derivative I didn't even realise that was another "kind" of derivative.
Following Hamilton's principle taking an action such that: $$ S=\int g_{\mu\nu} \frac{dx^{\mu}}{d\tau}\frac{dx^{\nu}}{d\tau}d\tau . $$
If you find the extremes of this integral or just apply lagrang... |
While assuming the ideal gas we need to neglect gravity and other forces acting on the molecules but I have seen in many questions that ideal gas equation is used even in presence of gravity
Please tell the actual way in which we can use ideal gas equation in such situations
Consider the following question in which
A ... |
If two bodies are coupled and they are performing oscillations, then do they have only two allowed frequencies (normal modes frequencies) with which they can oscillate or do they have a number of frequencies that depends upon their normal modes frequencies?
|
The time depends on the speed of movement. Protons in the LHC move at near-light speed. Therefore, they perceive a different time than the scientist who is observing them. My question is how much time passes relative to the protons while scientists are watching them accelerate and collide?
|
If a person moves in a rocket with a constant acceleration of 1 G, then sooner or later he will reach about the speed of light. At the same time, time will flow slower for him than for the surrounding universe. But I heard that from the point of view of theory of relativity, the surface of the Earth accelerates relativ... |
In Schwartz' "Quantum Field Theory and the Standard Model", chapter 20, the author calculates the cross section for a process to produce a muon-antimuon pair as well as an extra photon emmitted from the final state. In order to regulate infared divergences, he introduces a ficticuous photon mass, and the variable $\bet... |
Chabay and Sherwood write in Matter and Interactions on page 406 about sticking collisions:
We'll consider an inelastic collision in which a truck and a car collide in an icy intersection and stick together [...]
Part of the energy was radiated away as sound waves in the air,
produced when the vehicles collided with a... |
Can this equation, at least in its non-relativistic limit "if it exist" in 3 dimensional, model holes in the valence band for Zinc blende semiconductor materials for example, since in three dimesions, spinors have two dimensions "Pauli spinors", when coupling with vectors $\ell=1$ $\rightarrow$ $D_{1/2} \otimes \Gamma_... |
The question about measuring the one-way speed of light has been debated in several posts in this forum, and are treated in detail on this wiki page.
In relation to this debate, I wonder how you would calculate the kinetic energy of an object with mass $m$, if the one way speed of light is different from c?
We can reas... |
If I am traveling in a spaceship with uniform motion near the speed of light towards a stationary observer on Earth, assuming I am not aware of the situation, then I would assume that Earth is approaching me at approximately the speed of light. Where is time passing slower now?
According to the theory of relativity, bo... |
An insulated container containing monoatomic gas of mass $m$ is moving with a velocity $v$. If the container is suddenly stopped find the change in the temperature of the gas.
I want to know why change in kinetic energy is $\frac{1}{2} m v^2$.
Can you tell what's wrong in the following ideas?
While considering the velo... |
I have seen many models showing the jet-streams shot out of black holes, and even some images. However, it is always said that a black hole has so strong of a gravity field, that not even light can escape it.
So how can matter accelerated to the speed of light, which is heavier than light escape the black hole in such ... |
I know $W= \int_{x_1}^{x_2}\vec{F}\,.\vec{ds}\ $
I am working with frictional force. Here $x_2>x_1$, $\vec{F}$= - $\mu mgcos\theta \hat{i}$
As $x_2>x_1$, $\vec{ds}= \hat{i}dx $
So the integral turns out negative
But if I think to move the object from $x_2 $ to $ x_1$ and so think $\vec{ds}= -\hat{i}dx$ [ to represen... |
This youtube video shows a simulation of evanescent coupling between a driven optical fiber and another that is not driven. I had never heard of evanescent fields so I looked it up on Wikipedia, where I found the following:
The transmitted wave cannot, however, be a sinusoidal wave, since it would then transport energ... |
Given an infinite plane sheet of time-harmonic ($\text{e}^{j\omega t}$) electric and magnetic surface current densitites, $\textbf{J}_{es}$ & $\textbf{J}_{ms}$, respectively, is located in free space (with wavenumber $k$ and intrinsic impedance $\eta$) in the $xy$-plane of a rectangular $xyz$-coordinate system. For $z>... |
When we create quark-gluon plasma in a lab by colliding lead nuclei, does releasing the nuclear bonds give us energy? Or take it?
An astrophysical jet could be as hot as 10 trillion K:
https://www.space.com/32467-black-hole-jets-hotter-than-expected.html
If any atom got in its way, it would be turned in to QGP, right? ... |
What is this about? I have a question and there are two ways to solve it. One is wrong and other is right and I wanted to know why was the wrong one wrong.
What do I want to know? In the wrong approach why I could not take gravity?
Question - A tube-well pumps out 2400 kg of water per minute. If water is coming out wit... |
In flat spacetime, the point-splitting regularization for (chiral) anomaly is discussed in great details in Peskin and Schroeder's QFT.
Does anyone know any good references for calculating anomaly using the point-splitting regularization in curved spacetime?
|
I know the formula $\nu = \nu_{0}\frac{v + v_{o}}{v - v_{s}}$ for the Doppler Effect and saw that it gives different results in the cases where:
1- The source is stationary and the observer moves towards the source with speed $v$, and
2- The observer is stationary and the source moves towards the observer with speed ... |
In the SI unit system you have stuff like mass and length which are pretty fundamental. But the mole seems to not be as fundamental as the others. I think we can express it in terms of the other constants. And even if we can, are there any other constants in the SI units system that can also be expressed by other units... |
According to Fermat's principle, light travels the fastest path from dot A to dot B. I wondered how light knows which path is the fastest, and found out that light actually goes all path, but non-optimal paths are destructed. However, when the photon is at dot A, how does it know that it will eventually arrive at dot B... |
While fiddling around with certain commutation relations, i noticed the following relation while using spherical coordinates.
What could this relation mean intuitively? Let me know if any information could be provided related to this relation. I've never encountered such a relation in texts dealing with special functio... |
I am interested in diagonalizing the all-to-all quantum spin model
\begin{align}
\hat{H} = \frac{1}{2}\sum_{i,j \neq i} \hat{S}_i \cdot \hat{S}_j
\end{align}
or, if possible, a more general form involving an arbitrary coupling $\tilde{H}$ between the spin states on sites $i$ and $j$:
\begin{align}
\hat{H} = \frac{1}{2}... |
I understand that there are no propagating degrees of freedom (i.e. gravitational waves) in 2+1 dimensions. There are a couple of arguments to show this. One is to count degrees of freedom of general relativity and find that there are $D(D-3)/2$. Another one relates to the fact that the Weyl tensor vanishes identically... |
I'm doing a research on Brownian motion (in 2D) and I want to calculate the MSD values in order to find the diffusion coefficient $D$.
However, online I find different approaches on how to calculate it.
The two that stood out to me were:
From your coordinates calculating the absolute distance $r$ and then calculating ... |
Consider the Minkowski space $\mathbb R^4$ with the Minkowski metric tensor
\begin{align}
\langle,\rangle:\ \mathbb R^4\times\mathbb R^4&\longrightarrow\mathbb R
\\ (u,v)&\longmapsto\langle u,v\rangle=-u_0v_0+u_1v_1+u_2v_2+u_3v_3=[u]^\top\eta\,[v]
\end{align}
where $\eta=$ diag$(-1,I_3)$.
We know that the Lorentz trans... |
How to find out that the value of the synchronous phase for CERN LHC in the case where beams undergo collision, and the RF cavities provide only longitudinal focusing with no net acceleration.
|
I am currently studying General Relativity from M.P. Hobson's "General Relativity: An Introduction for Physicists" and I had difficulty in understanding some concepts in variational field theory. In the textbook it is said on Chapter 19, page 551 that if we have the following action,
$$S=\int \mathcal{L}(\phi(x), \part... |
Let's say I'm taking a picture through a cube of some material where the index of refraction varies in a known way, such as a GRIN lens. I can calculate the optical path difference as a function of position of the image plane. So I know $OPD(x,y)$. What I'm trying to do is calculate what the image would look like when ... |
In conformal gravity theory, the action is given by
$$L=\int \sqrt{-g}C^{abcd} C_{abcd} d^4x=\int \sqrt{-g}(R^{ab}R_{ab}- \frac{1}{3}R^2)d^4 x.$$
However, the variation of the first term $\int \sqrt{-g}R^{ab}R_{ab}d^4 x$ according to the article "Alternatives to dark matter and Dark energy" contains a Ricci scalar term... |
Does anyone have any recommendations on how to get useful information from SAXS of polymers when the system is not dilute?
This is the type of data we're working with:
My understanding is that since there's no plateau at the beginning we can't use the correlation function to get parameters like Lc.
I'd really apprecia... |
My friend asked me about dark matter and started saying that it is likely to be another world made up of things we say dark matter and energy said that quantum fluctuations may be the cause of dark matter although I didn't believe what you says?
|
Electromagnetic waves that are moving can send records such as data that are converted into images.
But could a static electromagnetic field somehow retain information in itself? (Without the need for any form of device)
Thank you
|
In the paper The basic physics of the binary black hole merger GW150914
Equation [A5] states that
$$\dot \omega^3=\left(\frac{96}{5}\right)^3\frac{\omega^{11}}{c^{15}}\left(G\mathscr M\right)^5
\tag{A5}\label{A5}
$$
where $c$, $G$ and $\mathscr M$ are constants, $\omega$ is the orbital frequency (not angular frequency)... |
What are correct abbreviations for torque and energy in US Customary and S.I. systems?
Both include distance and force. Do we write N-m and lbf-ft for both torque and energy? I always heard (years ago) torque expressed in "foot-pounds" of torque, meaning ft-lbf. I'm writing continuing education engineering courses and ... |
I was reading the Hydrogen line explanation on Wikipedia when my attention was caught by the following sentence:
This transition is highly forbidden with an extremely small transition rate of $2.9×10^{−15}$ s$^{−1}$,[4] and a mean lifetime of the excited state of around $11$ million years.
How can we estimate the mea... |
I am studying Berry curvature for a specific material and faced different types of the Berry curvature formula. Some papers use only valence eigenstates (u1) like this $$i*(<(∂U1/∂kx)| (∂U1/∂ky)> − <(∂U1/∂ky)|(∂U1/∂kx)>)$$ and someone uses summation on all the conduction and valence bands like this $$i*(<(∂U1/∂kx)| (∂U... |
Consider a system of $N$ fermions in a periodic box $\Lambda \subset \mathbb{R}^{d}$. The Hamiltonian of the system is:
$$H_{N} = \sum_{k=1}^{N}(-\Delta_{x_{k}}-\mu) + \lambda \sum_{i< j}V(x_{i}-x_{j})$$
where $\mu \in \mathbb{R}$ is the chemical potential and $V$ is a sufficiently well-behaved interaction function. Af... |
Is psi square just an assumption? Or there is a physical reason why they defined like that? My procedure is:
It is intuitive for me to think possibility is proportional to energy distribution. Because lots of energy means lots of electron. Since energy of the wave is square of wave’s amplitude, it is exotic to define ... |
I have been confused by this for days. Consider a ring-shape solenoid with DC current. If we insert a ferromagetic core (cylinder) into the solenoid, how many time it could amplify the field, compared with the case without core?
I understand that the answer would be varied upon materials. However, I have seen dramatica... |
I was working with the following expression related to the Wick's theorem for four fermionic operators.
$$
\langle c^\dagger_i c_j c^\dagger_p c_q \rangle = \langle c^\dagger_i c_q \rangle \langle c_j c^\dagger_p \rangle + \langle c^\dagger_i c_j \rangle \langle c^\dagger_p c_q \rangle.
$$
I tried to show this for the ... |
Disclaimer: I still don't understand the theory of general relativity. I'm completely ignorant.
I was watching the movie Interstellar yesterday and saw their interpretation of time dilation, I also watched the Lightyear movie which is about the same. Those movies got me interested in this supposed phenomenon.
These mo... |
I would like to ask a simple question about quantum mechanics. Consider a 2d Hilbert space $\mathbb{C}^2$ with a orthogonal basis $|x\rangle,|y\rangle$. We can form the $n$-fold tensor product
$$\mathrm{T}^n(\mathbb{C}^2):=\underbrace{\mathbb{C}^2\otimes\cdots\otimes\mathbb{C}^2}_n\cong\mathbb{C}^{2^n}$$
and the $n$-fo... |
Since moving faster makes time move slower. Does that mean that there is an absolute minimum rate at which time passes? If so. Is there also a maximum?
|
Consider a time-dependent Hamiltonian $H=H(t)$, in Schrödinger's picture. Let's say that at time $t_0$ the system is in a state ${\mid\alpha(t_0)\rangle}$ such that
$$
H(t_0){\mid\alpha(t_0)\rangle} = E_0{\mid\alpha(t_0)\rangle}.
$$
If we call ${\mid\alpha(t)\rangle}$ the evolution through time of ${\mid\alpha(t_0)\ran... |
This paper considers a generalised Strum-Liouville equation, that is equations of the form
$$
\left[-\frac{d}{dx}p(x)\frac{d}{dx}-\frac{i}{2}\left(\lambda_1(x)\frac{d}{dx}+\frac{d}{dx}\lambda_2(x)\right)+v(x)\right]\psi(x)=\left(\frac{\omega}{c}\right)^2\psi(x)\tag{1}
$$
and calls $\lambda_i(x)\in\mathbb{C}$ complex ga... |
In the Stern-Garlach experiment the silver atoms are splits into spin up and spin down in a inhomogeneous magnetic field and latter the culprit is identified as the spin states of the 47th electron of the silver atom but there's also 47 protons too so why don't they also affects the experiment?
|
Imagine two platforms side by side. The only difference is one of them is moving while the other is at rest. If a person wants to transition from the moving one to the stationary one he has to jump onto the other platform then run for sometime in the direction of his initial motion. But consider this, if he is initial... |
If i setup to clock to work at the same rate at stationary. The first clock operated on quantum tunneling. Setup electron to tunneling and repel another electron. Which acts as sensor. The second clock using laser to repel electron. Which acts as sensor. Put both clock in the car that travel near speed of light. And t... |
Assume a particle's spin is measured along the vertical axis at time t=0 and position x=2.
An entangled partner particle is measured along the vertical axis at time t=0.5 and position x=0 (also along the vertical direction). In addition a measurement is performed at time t=1 and x=2 in the orthogonal direction. Accordi... |
For a bipartite system:
$\mathcal{H}=\mathcal{H}_{a}\otimes\mathcal{H}_{b}$ described by a density operator $\hat{\rho}_{ab}$, I can promote it to a vector in the Liouville space, $|\hat{\rho}_{ab}\rangle\rangle$. The Schmidt decomposition for such a vector would be:
$$
|\hat{\rho}_{ab}\rangle\rangle=\sum_{n}\gamma_{n}... |
We know some superconductors have a large λ, but a low $T_c$. Some have a small λ but a high $T_c$. Why are they different? From the Eliashberg equations, we know the renormalization function is associated with the λ and $T_c$. Is it because λ contributes to mass renormalization in systems with large λ low $T_c$?
How d... |
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