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I still have some confusions over symmetry breaking in superconductivity.
To begin with it’s clear gauge symmetry can’t be spontaneously broken, since it’s not a symmetry to begin with. I want to understand :
(1) Can global, physical $U(1)$ symmetry be spontaneously broken? This seems to be clearly true, and is what ha... |
The idea is I want to calculate the energy lost by a break (theoretically) while trying to stop a disk.
I have worked put the energy loss due to heat and light however I am not able to pin down on the energy lost by sound.
Assume the environment as ideal for simple calculations if needed. Any and all suggestions are we... |
TL;DR
How to choose an appropriate value for the regularization $\eta$ in correlation functions used in linear response for a discretized Brillouin zone?
For more context, please see below.
Correlation function in linear response
In linear response we try to find a correlation function, which typically looks like
$$
\c... |
I have a blue laser diode that has a focal length of about 2cm. I would like to extend that, so I can engrave things further from the laser, and to lenghten the distance where the beam is focused enough to be suitable for engraving and cutting.
So far I've learned that this could be possible with concave lenses; what s... |
I want to prove that the continuity equation for fluids, $$\dfrac {\partial \rho}{\partial t} + \nabla \cdot (\rho \textbf{u}) = 0$$ is invariant by Galilei transformations. My attempt:
Using index notation, the transformation is:
$$ \begin{cases}
x^{i'} = R_j^{i'} x^j - v^{i'} t - d^{i'} \\
t' = t + \tau,
\end{cases... |
I have two 2d arrays of electric field components:
Ex with (256, 512) and Ez with (256, 512) sizes.
I need to calculate scalar potential. Gradient of scalar potential is the electric field vector. So I need the reverse of the gradient.
I tried using the following loop to calculate the potential Φ (phi):
nx = 256
nz = 5... |
I have a question about the eigenvalue decomposition of an operator, more specifically about the matrix with the eigenvectors as columns.
If i have an operator that i decompose as follows:
$$
\hat{A} = U\Lambda U^\dagger
$$
with $\psi_i$ being the eigenvectors and $a_i$ the according eigenvalues.
I know that if i multi... |
Suppose we have a function of the form $A=A(\vec{x},t)$ that depends on space and time. I want to know why, if $A(\vec{x},t)$ is considered to be a perturbation, then both $\partial A/\partial t$ and $\vec{\nabla}A$ are also perturbations. My reasoning for the time derivative is the following. If we work in Fourier spa... |
I recently read about Hall effect. My understanding of it is that when a current loop is placed in an external magnetic field, its electrons experience a magnetic force. This creates a charge separation in the wire and an electric field is induced inside the wire. This electric field exerts a force on the lattice of th... |
I am confused about a point regarding parallel transport and geodesics. The basic idea of a geodesic is the unaccelerated test particle moves in a straight line, or the tangent vector of a curve $x^b(\lambda)$ will be parallelly transported along the curve. In curved spacetime or in general coordinates, the eqn looks
$... |
I am trying to understand Gauss' law but do not understand this part -- does Gauss' law not consider excess charge (outside the Gaussian surface)?
In a system where we are using a Gaussian surface, and the excess charge is distributed asymmetrically, is Gauss' Law then not a good tool to use to estimate the electric fi... |
I have two systems that are correlated, their energy levels are not independent: $\rho(E_1,E_2) \ne \rho(E_1)\rho(E_2)$.
So I wanted to quantify the amount of dependence they have, I used the mutual information between the two partition functions $ I(Z_1, Z_2)$, also calculated $E_{tot}- E_1 -E_2$, $S_{tot}- S_1 -S_2$ ... |
I have learned that the Matrix Product State (MPS) formulation can only handle systems where the entropy scales up to logarithmically. For gapped systems, as the entanglement entropy is constant, a constant bond dimension independent of the size is enough, while for gapless systems, as the entanglement entropy scales i... |
In the following problem, concerning the stress vectors applied on the surface of the circle, why is there a minus sign in $t(- ê_r) = t(− \cos θ\ ê_1 − \sin θ\ ê_2)$?
In this problem, loads are applied as can be seen:
The solution from my course indicates the following answer:
Stress vector on the boundary of the ci... |
In the Hamiltonian formalism of classical mechanics, a system with configuration space $Q$ is represented by a symplectic manifold $(T^*Q,\omega^\mathrm{can})$ called the phase space. The dynamics are then described by the flow of the Hamitlonian vector field of the Hamiltonian function $H\colon T^*Q \to\mathbb{R}$. If... |
I can't figure out the force acting on a coil in a magnetic field.
Suppose I have a coil with direct current running in it. We know this is an electrical magnet, which means when I put it in a big static magnetic field which points vertically, it will be pulled upward or downward.
However, if we analyze a differential ... |
Is it possible to sustain lightning electricity through lightning rods?
|
According to the Gauss’s law the flux due to external charge always remains zero. Also the total flux is given by the charge enclosed/ epsilon. So consider this surface,what is the fate of the flux which is highlighted and is thick in the diagram. According to me with respect to second surface the charge seems external... |
When I was an undergraduate student, I was comfortable with the concepts of momentum and angular momentum of a particle or of a system of particles. However, the concept of electromagnetic fields carrying momentum and angular momentum occurred to me as somewhat odd to digest. I don't know if everyone feels the same. Wh... |
My question is relatively simple. Assume incompressible, laminar flow.
Will fluid continue to flow through a pipe if I calculate that a 5 psi pressure drop occurs across the pipe using either the Darcy-Weisbach/Hagen-Poiseuille equation but my pressure source only supplies 4 psi? I would assume that it would not contin... |
Electrons in atoms or molecules are of course correlated, in the sense that the many-electron wave function is not a Slater determinant. However, in my personal impression, the Hartree-Fock approximation or the density-functional theory often works reasonably well for atoms and molecules. Therefore, the question is, i... |
Why the Gaussian wavepacket only spreads in the free Schrodinger equation? It doesn't spread in the case where you have a harmonic oscillator. How to prove the situation in a harmonic oscillator?
Your help would be highly appreciated!
|
This question is a continuation of my previous question https://mathematica.stackexchange.com/q/281856/
I have the Gaussian basis set, this basis is non-orthogonal. In the case of non-orthogonal basis set to find min Energy I have to solve the next equation:
$$H\vec{\psi}=EB\vec{\psi}$$ where $H$ is a Hamiltonian matri... |
If there is an $RLC$ circuit where some components are in series with one another and some components are in parallel with one another, how does the total impedance of the circuit is calculated?
I understand that the components that are in series will have their current in phase, while those that are in parallel will ... |
$dS = \delta Q/T$
According to this equation, it seems as though for all adiabatic processes, the entropy change should be 0, since $\delta Q = 0$ always.
I know I'm wrong since for free expansion we use the property that S is a state function hence calculate the change in entropy based on final and initial P,V,T, whic... |
I am trying to calculate the energy it would take to destroy a small celestial object made solely of silica. A lot of literature have defined the energy required to shatter a celestial object as the energy required such that the largest aggregate is half that of the original object.
I have tried going about it from a t... |
I stumbled across an intuition for the Laplace operator that suggests it can be considered "the difference between the value of a function at a point and the average value at "neighboring" points." As a new student, I really benefited from this interpretation - the steady-state heat equation made more sense. I found I... |
Caveat: While I am not a physicist myself, I am extremely interested in physical phenomena. I am well versed in electrical theory, and I am aware of the attraction between the bottoms of clouds and the ground.
However, when I saw the photo of lightning apparently striking a rainbow, I could not come up with a strictly ... |
I was trying to understand how pion decays to muons and not electrons because of helicity suppression. So I was trying to figure out the ratio of the decay widths.
PDG review for kinematics (subsection 49.4.2) (PDF) reports that for a two-body decay we have
$$
d\Gamma = \frac{1}{32 \pi^2} |\mathcal{M}|^2 \frac{|\mat... |
I have a doubt that why does bernoulli's equation doesn't work in some cases, even after considering streamline flow, for example consider the system in image, we can apply A1v=A2v' , where A1 and A2 are cross section area of A and B, and since the motion is streamline, and both areas A1 and A2 are equal, so v=v'.
But... |
In 49:34 of this lecture by Frederic Schuller, it is explained that time is a derived quantity defined through this integral:
$$\tau = \int_{\lambda_o}^{\lambda_1} \sqrt{ g(v_{\gamma}, v_{\gamma}) }$$
Where $g$ is the metric, the integral is done over a world line $\gamma$.
time is associated to world lines, but previ... |
I have a rather involved question regarding the weakly attractive limit of the BCS ground state. We know for exampel from The book of Pitajevski and Stringari (Bose–Einstein Condensation and Superfluidity) or from several previous works, e.g. https://journals.aps.org/pra/pdf/10.1103/PhysRevA.77.023626 or other contribu... |
I've been reading Frankel's Geometry of Physics but I'm struggling to understand a section devoted to "Additional problems on fluid flow" (Sec. 4.3c in my edition).
Consider a fluid flow in $\mathbb R^3$ with density $\rho=\rho(t,x)$ and velocity vector ${\bf v}={\bf v} (t,x)$. Let $vol^3$ be the (standard?) volume for... |
Suppose two particles are non-interacting and under the same potential.
The Hamiltonian doesn't contain spin terms. We suppose the one-particle states are $\psi_n(x)$ with $E_n=n^2K$
For me, it is like the ground state has infinity degenracies because of
Spatial part: $\psi_1(x_1)\psi_1(x_2)$
spin part: $\chi(1,2)$ co... |
There is a well known experiment to determine the specific charge of an electron like in the following picture
Electrons are emitted from a heating spiral and then accelerated by an acceleration voltage $U_{\mathrm{B}}$. Then the electrons describe a circular path in a magnetic field. For an actual setup see for examp... |
Qualitatively, the running of coupling constant is often explained using a charge screening explanation such as that in the images below (1 and 2). It is said that the "bare" charge is not seen as it is shielded by polarized virtual electron-positron pairs, much like a charge in a dielectric medium. Further, it is said... |
I'm just curious how significant is the difference in aging of particles at CERN versus the people observing them. If one second passes for a particle at CERN from it's point of reference going at 99.9999991% of the speed of light, how many seconds, hours, days or years pass for the observer sitting at CERN? Any sugge... |
The problem is:
Given the distribution of the electrons
$$
f_0(\mathbf{p}) = \frac{1}{\pi^2}\frac{mun_e}{(p^2 + m^2u^2)^2}
$$
find longitudinal dielectric function and the dispersion equation for longitudinal waves.
According to the textbook longitudinal dielectric function can be found using the equation
$$
\varepsi... |
I'm working with drawing ray diagrams for different setups with lenses. In this case, I want to try and draw the ray diagram for a converging light onto a diverging lens. Suppose the setup is like this:
We can assume it has focal length of f. Can anyone walk me through the general step by step things to do in order to... |
Since kinetic friction is lower than static friction, and a sled in motion experiences kinetic friction whereas a wheel experiences static friction, which one would go down a hill faster. Let's have a hypothetical scenario where we have a slope which both a sled and a wheel are stationed at the top of, considering all ... |
I am looking for proof that the quantum fidelity $$F(\rho, \sigma) = \left(\text{tr} \sqrt{\sqrt{\rho}\sigma\sqrt\rho}\right)^2$$ is bound from above by 1, i.e., $F(\rho, \sigma) \leq 1$.
I know this is a consequence of Uhlmann's theorem. However, I feel like it is far too complicated for this (seemingly) simple task.... |
I was researching the motivation behind introducing quantum channels and this is essentially what I've gathered.
Suppose we have two subsystems, the system we're interested in where states exist in the Hilbert space $\mathcal{H}_{0}$ and the environment where states exist in the Hilbert space $\mathcal{H}_{e}$ The ove... |
Consider a conformal operator of world sheet spin $n$, for example, $h=a,\bar h=b$ and $s=|a-b|$ then the operator would be labeled by $n$ index, $\mu_1,\mu_2,...,\mu_n$, where each index of dimension $d$.
I thought this might has something to do with the verma module, where at each different level, i.e. $1,2,...,a$ wa... |
Consider pseudoscalar Yukawa theory in 4D:
$$ S =\int d^4x\ \frac{1}{2}(\partial\phi)^2 - \frac{1}{2}m_\phi^2\phi^2 +\bar\psi(i\gamma^\mu\partial_\mu-m_e)\psi - ig\bar\psi\gamma^5\psi\phi -\frac{\lambda}{4!}\phi^4. $$
My question is: Is the 1PI function for 3 bosonic fields $\Gamma_3[\phi(x),\phi(y),\phi(z)]$ zero? How... |
Let $f$ be the Fermi function and $H$ be a function which which vanishes as $\epsilon \to -\infty$ and which diverges at $\infty$ no worse than some power of $\epsilon$. In the Sommerfeld expansion of solid state physics (see e.g. Ashcroft and Mermin Appendix C), one writes an integral of the form
$$\int_{-\infty}^\inf... |
In Euclidean time $\tau$, $\langle \hat O(\tau )\rangle= Z^{-1}\mbox{Tr}(e^{-\beta \hat H} \hat O(\tau ))=Z^{-1}\mbox{Tr}(e^{-\beta \hat H} e^{\hat H\tau}\hat O(0 )e^{-\hat H\tau})=Z^{-1}\mbox{Tr}(e^{-\beta \hat H} e^{\hat H\tau}e^{-\hat H\tau}\hat O(0 ))=Z^{-1}\mbox{Tr}(e^{-\beta \hat H} \hat O(0 ))=\langle \hat O(0)\... |
For normal insulator, as we known, its bulk band is inverted and outside it is the air or vacuum which is normal insulator with band in normal order. So to transit from bulk to outside, the band need to change from inverted order to normal order, which means there must be a gapless state between them. And we know this ... |
How much $\rm D_2O$, by mass and/or percentage, is locked in Earth's polar icepacks? Is the $\rm D_2O$:$\rm H_2O$ ratio the same as elsewhere?
|
In 1927 a piece of pitch was placed in a funnel and since then pitch flowed at rate of about 1 drop per 10 years.
Obviously we can repeat experiment with any amorphous solid. Viscosity of water is about 10^-2 poise, for pitch it's 2 * 10^9 poise, and ~10^20 for glass.
So for a piece of glass we would see about 1 drop e... |
When I write down the Lagrangian for a quantum field, I can derive the equation of motion for the field. Therefore, Lagrangian specifies how field evolves with time completely. Can I derive Schrödinger's equation $$\phi(x, t) = e^{iHt}\phi(x, 0)e^{-iHt}\tag{1}$$ from Euler-Lagrange equation $$\partial_\mu\left(\frac{\p... |
For simplicity, let us suppose quantized scalar field
$$\hat{\phi}=\int{\frac{d^3p}{\left(2\pi\right)^32E_\vec{p}}\left(a_\vec{p}e^{-ipx}+b^\dagger_\vec{p}e^{ipx}\right)}$$
How does one add a particle to the state, that is given by some general distribution, for example normal one?
$$\phi=Ae^{-\frac{x^2}{2\sigma^2}}.$$... |
Looking for a quick clarification on something. I am a layman and I have been trying to find out how much time dilation would exist if there was no gravity anywhere, and ignoring what seem to be debates about whether a universe without matter is even a valid hypothetical, it seems the issue is time dilation is a produc... |
Inspired by this question.
Let's say I'm standing on a frictionless ice rink right next to a $1kg$ block. I push the block with $1N$ force for a distance of $1m$. I do $1J$ of work, obviously. By Newton's 3rd law, the block also exerts a $1N$ force on me for a distance of $1m$, so it does $-1J$ of work on me. This rea... |
Suppose; The strain on my eyes when seeing an object at distance x is a.
The strain on my eyes when seeing an object at distance 2x is b.
Now if I see the image in the mirror (mirror is at distance x) what is the strain in my eye? What I actually see is my VIRTUAL image, so is the strain in my eye a (for seeing the mir... |
First of all consider such a system, in which there's a square loop which is going out of the magnetic field,
thereby an EMF will induce, and B will be at positive potential while A will be at negative potential.
Now as we know by Fleming's right hand rule the current direction will be in anticlockwise direction, but ... |
I could not find accurate data online apart from CSP power generators that could focus sun rays to a single point and heat a liquid to 1000°C.
I imagine many factors can affect the temperature, such as the length and shape of the lens, material of lens. But in applied theory, how hot can the temperature get?
Background... |
place of application.
It is generally given for insulators in questions. But why?
|
If energy depends on frame of reference of observer, then how it can remain conserved?
Same question also for linear and angular momentum.
I think energy is conserved when seen from a specific frame of reference, but I have doubts about it.
If that's the case, then I think that the energy difference between two systems... |
Essentially I want to vary the action
$$
S_M = \int d^3x \sqrt{-g} \left[- \frac{1}{4} F^{\mu \nu} F_{\mu \nu} - \frac{\alpha}{2} \epsilon^{\mu \nu \rho} A_\mu F_{\nu \rho} \right]
$$
with respect to $A_\mu$ in order to find the equation of motion for $A_\mu$. Here, $\epsilon^{\mu \nu \rho}$ is the Levi-Civita tensor. ... |
Imagine, there is an object(objA) which is not a black body. But this object is a kind of object that does not reflect any energy(light). It can only absorb and transmit.
We know that blackbody emits radiation at the perfect efficiency at different wavelengths.
Now imagine light hits the objA which then transmits this ... |
Could anyone correct my explanation for how things move despite the reaction-action force?
(I've just started learning this topic so I might be wrong)
Explanation:
Let's take two scenarios: (I'm going to ignore the - sign mostly)
A book on a table -> the book has a weight of 4 N. According to Newton's third law, the t... |
In relativity, we define proper time for a particle therefore can discuss about casuality-order of events preserved for it.
For statistical mechanics in classical mechanics, macroscopic systems evolving by time follow the same time axis-hence the increase of entropy by time(a.k.a. the second law of thermodynamics) can ... |
This will probably turn out to be a really simple issue, like bad notation in one of my sources confusing me, but here goes.
In Groups, Representations, and Physics (Jones) it's stated that the generators of rotations $X_i$, and boosts $Y_i$ (Jones' notation, I know they're usually written as $J_i$ and $K_i$) can be co... |
My question is to verify if my thought process below is correct.
So in a circuit the charge will flow (the current). When the charge flows there is resistance which is the collisions of the charge with the positive ions, this causes the charge to have to work(energy is transferred to component)to get through components... |
Electromagnetic charges are obviously quantized - I suppose the lowest charge being the $d$ charge of $e/3$. Every other charged particle has a multiple of that charge (actually all stable free particles have charges multiple of just $e$). The same is true for the $U(1)$ hypercharge charges in the unbroken electroweak ... |
We have a three terminal system with one voltage probe as shown in the picture bellow. If I want to calculate voltages at each terminal, how should I proceed? Should I solve this system of equations
$$I_1=G_{11}V_1+G_{12}V_2+G_{13}V_3$$
$$0=G_{21}V_1+G_{22}V_2+G_{23}V_3$$
$$I_3=G_{31}V_1+G_{32}V_2+G_{33}V_3$$
where $G_... |
I've been learning about integrability in the Hamiltonian sense, and trying to wrap my mind around the analytic power afforded by integrability, both in quantum and classical systems. My goal with this post is to develop a better intuition for what can be analytically calculated in integrable systems.
More precisely: t... |
Here are the two equations I'm concerned with:
$$\Psi = \sqrt{\frac2a}\sin\left(n\frac{\pi x}a\right)$$
$$E = n^{2}\frac{\hbar^2π^2}{2ma^2}.$$
If we have a ball with mass 1 kg, confined in a 1 m infinite potential well, and its kinetic energy is 1 J, then the corresponding $n$ will be very high. As a result we get a ve... |
There's a short part in The Feynman Lectures where he explains the why you should never shake a martian's left hand. He introduces a "martian" who we can only communicate with in some limited way, e.g. in binary. It ends with a warning: if you ever meet this martian and they try to shake your left hand, run away, they ... |
When the calculation of the Feynman propagator is introduced in QFT (or QM), the inclusion of the $i\varepsilon$ term is often described as a minor technical detail that is there just to "make the integral converge":
\begin{equation}
G_F(x,y)=\int\frac{d^4p}{(2\pi)^4}\frac{e^{-ip\cdot(x-y)}}{p^2-m^2+i\varepsilon}.
\end... |
I'm doing AP Physics mechanics and I'm learning about the conservation of momentum and the textbook describes the conditions for it's validity as the net force on the system must be 0. I understand how this works for frictionless systems but I was just curious as to how it applies practically since friction is always p... |
We know that all objects emit radiation at different wavelengths.
I am talking about normal objects(not black body).
I would appreciate the explanation how for example a table can emit radiation at different multiple wavelengths at the same time ? I thought it just emitted radiation lets say at x wavelength but turns o... |
Many sources of biological sciences (e.g.https://medium.com/@drvnx/what-is-that-thing-without-which-we-are-dead-f556fb1029ef ) say that the actual weight of brain is almost 1400gwt but as brain floats in a fluid known as cerebrospinal fluid CSF due to which there acts an upward buoyant force on it and hence "WE" do n... |
I have derived the four 4 x 4 block diagonal matrices (e,A,B,C) in accordance with the transformation TST-1 where T is the C-G matrix for the 1/2 ⊗ 1/2 = 1 ⊕ 0 representation. This part is described here. I now want to construct the character table for this. So far I get :
e A B C
Γ1 3 0 0 0 (3 x 3)
Γ2 ... |
For example, I have a stationary object with an applied force that is increasing over time to a maximum of $500\, \rm N$. If this applied force rises to $500\, \rm N$ over $100\, \rm ms$, the object does not move but if this force rises to $500\, \rm N$ over $2\, \rm ms$, the object moves.
How would I calculate the im... |
(I asked a very similar question already, but the core idea is very different in both)
Here are the two equations Im concerned with
$$\psi = \sqrt{2\over a}\sin\Big(n\pi {x\over a}\Big)$$
$$E = {n^2\hbar^2\pi^2\over 2ma^2}.$$
If we have a particle with some energy in the infinite potential well, then we get a probabili... |
In an NEGF calculation describing electron transport through a field effect transistor, we write down the Green function $$G(\epsilon) = \left[\epsilon I- H - \Sigma_L - \Sigma_R\right]^{-1}$$ where $H$ is the device Hamiltonian and $\Sigma_{L(R)}$ is the left (right) lead self-energy.
My question: What is the name of ... |
I'm new so please be nice if I don't know too much about anything.
I was kind of curious about the idea of gravitons in a vacuum. (using string theory, or even superstring theory.) if space is a near-perfect vacuum, how does it have enough gravitons (if any), to keep planets spinning in the orbit of a star? (again plea... |
The question is basically the title, that can two positive or negative electric charges attract each other, there is no constraint on the sizes of the charge.
Can only electrostatic force result in attraction .
|
If, say, the z-spins of two electrons are maximally entangled (so that their composite state can be given by $|\Psi\rangle = \frac{1}{\sqrt{2}}(|u\rangle|d\rangle + |d\rangle|u\rangle)$, how do you compute the total spin of the system (or each component of the system)?
|
When considering the scalar field that solves the Klein-Gordon equation, one can use Green's functions to identify a propagator. This can be constructed from first principles, and can be left as an integral with the boundary conditions to be specified
$$G(x^{\mu};x^{\mu}_0) = \int \frac{d^3k}{(2\pi)^3} e^{i\bf{k} \cdot... |
How can we generalize harmonic oscillator to relativistic case ?
One way (see here, here, and here) is simply to write a relativistic Lagrangian/Hamiltonian with a quadratic potential. Such an oscillator is "harmonic" in the sense that we call a quadratic potential "harmonic". However, it is arguably not Harmonic in te... |
The second-order correction to the energy of an eigenstate due to a perturbation $H'$ is given by:
$$E_n^2=\sum_{m\not=n}^{} \frac{\left \lvert \left \langle \psi_m^0|H'|\psi_n^0 \right \rangle \right \rvert^2}{E_n^0-E_m^0}$$
If $E_n^0 \approx E_m^0$, the expression above blows up. In some undergraduate quantum mechani... |
In this question "vector calculus" refers to the integration and differentiation of vector fields.
Why is vector calculus so much more important in classical electrodynamics than in classical mechanics?
I'm not looking for answers such as "there are these formulas which are prominent in electrodynamics and those formul... |
On page 297 of Peskin and Schroeder, the book obtains the propogator
$$\tag{9.58} \tilde{D}_F^{\mu\nu}(k)=\frac{-i}{k^2+i\epsilon}\bigg(g^{\mu\nu}-(1-\xi)\frac{k^\mu k^\nu}{k^2}\bigg).$$
The book then says"
the Faddeev-Popov procedure guarantees that the value of any correlation function of gauge invariant operators c... |
Context
My problem is related to [1]. I do not dispute the solution in [1], however, it is not helping me to understand the problem that I face. I am working through Example 10.5 in Modern Electrodynamics by Zangwill. This problem pertains to the double-curl equation.
In this example, we integrate $\boldsymbol{\nabla}\... |
This is the solar spectrum by wavelength:
By formula $c=f\lambda$, we can plot the solar spectrum over the frequency domain:
Then we can conduct inverse Fourier transform to transform the plot into the time domain:
Here is my question: What does the solar spectrum over the time domain tell us about the sun light? Why... |
Special Relativity can be used to show that the magnetic force on a charge in parallel motion next to an infinite wire can be understood as an electrostatic force (when viewed from the rest frame of the charge). There are several posts and nice YouTube videos that explains this.
But how does this work in the case of li... |
In quantum mechanics of discrete systems, a state is represented by a linear combination of $n$ basis states:
$$|\Psi\rangle = \sum_{i=1}^n \psi_{i}|\psi_i\rangle$$
In a basis like position, where $n\rightarrow\infty$, the state is represented by an integral:
$$|\Psi\rangle = \int\text{d}x\, \psi(x)|x\rangle$$
I unders... |
Question: If the earth suddenly shrinks to $\frac{1}{64}$th of its original volume keeping mass same, the period of rotation of earth becomes $\frac{24}{x}$ hours, what is $x$?
So basically, why can’t we use the basic Keplers law $T^{2}$ is directly proportional to $R^{3}$
If we use Keplers law, it goes like:
$V = \... |
On page 514 of Peskin and Schroeder, the book derives
$$\tag{16.31} \det\bigg(\frac{1}{g}\partial^\mu D_\mu\bigg)=\int\mathcal{D}c\mathcal{D}\overline{c}\exp\bigg[i\int d^4x\overline{c}(-\partial^\mu D_\mu)c\bigg]$$
From which we get the ghost Lagrangian $$\tag{16.32}\mathcal{L}_{\text{ghost}}=\overline{c}^a(-\partial^... |
The relevant time-dependent Schrodinger equation, for a spinless charged particle in an EM field, reads
$$
i\hslash\frac{\partial \Psi}{\partial t}=\left[\frac{1}{2 m}\left(\vec{p}-\frac{q}{c}\vec{A}\right)^{2}+q\phi\right]\Psi
$$
where $\vec{p}=-i\hslash\nabla$. The wavefunctions, $\Psi$ and $\Psi^\prime$, due to a pa... |
I was reading about superdeterminism and it was a bit counter-intuitive. The idea of having a hidden variable on the measurement device is very rational. For example, if we emit light to a constrained electron like in a hydrogen atom, only photons of certain frequency and polarization can interact with it. Likewise, wh... |
In the lecture notes by Simmons-Duffin on the conformal bootstrap (https://arxiv.org/abs/1602.07982), he outlines in section 10 how operator dimensions are constrained numerically: we look for a linear functional $ \alpha $ acting on the vector space of functions (defined in eq. 191) of the cross ratios $ u $ and $ v $... |
We place a wooden stack upon two supports and place a weight of mass $m$ at one of its ends. Now it is almost obvious intuitively that just at the verge of the mass $m$ falling down, the normal force $P_2$ exerted by the right-most support will be $0$. But is there any way we can prove it mathematically or rigorously?... |
About a year ago I provided a rough outline of what what I thought (based mainly on the book "Relativity Visualized" by L. Epstein) would happen during the twins paradox scenario and sought confirmation that I had it about right:
In the twins paradox of relativity, is this an accurate non-mathematical description of wh... |
The spectral theorem states that for any self adjoint operator $H$ on some Hilbert space $\mathcal{H}$, there exists a projection-valued measure $E_H$ such that
$$H= \int_{\mathbb{R}} \lambda \mathrm{d}E_H(\lambda).$$ We also have that, restricting our attention to $L^2(\mathbb{R})$ and Schrodinger operators, (i.e. $H=... |
I am currently running a numerical simulation for site percolation. Using periodic boundary conditions I am attempting to determine the correlation length following the method set out in this paper https://arxiv.org/pdf/1902.03708.pdf.
The Figure below shows the results of the simulation for different values of the lat... |
Reading different books, I've come upon two apparently different definitions of the $n$-point Green's function.
For simplicity, let's consider a real scalar field $\hat{\phi}(x)$ (in the Heisenberg picture) with an interaction term in the Hamiltonian
$$\hat{H}=\hat{H}_0+\hat{H}_{\text{int}}\tag{1}\label{1}.$$
In ref.1 ... |
I am trying to solve the TOV equation with a given equation of state. So if
$$
\frac{dP}{dr} = TOV
$$
and there we have $P(\rho)$ can we write:
$$
\frac{d\rho}{dr} = TOV/\frac{dP}{d\rho}
$$
these two with the differential mass $dm = 4\pi r^2 \rho\,dr$ should be solved simultaneously to give the right answer, am I right... |
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