instruction stringlengths 31 24.3k |
|---|
I really don't understand the input-output formalism. I've gone through the 1985 paper, and I get completely lost when the following formula is written:
$$b_{out}(t)-b_{in}(t) = \sqrt{\gamma} c(t)$$
To quote the paper:
"We specify the input $b_{in}$ and solve 2.12 [the quantum langevian
equation], for a(t). We then co... |
I understand that energy is transferred electrically from the chemical potential store in the battery to internal store of the resistor.
How do we include the energy transfer in the definitions of electromotive force of the battery and potential difference across the resistor
|
I don't know much CFT, but I'm hoping to learn some of its main results. I'm particularly interested in minimal models in the context of quantum spin chains. I tried reading BPZ, but I'm realizing that I have a fundamental confusion over how to interpret Kac tables and operator product expansions.
Part of my confusion ... |
i nave included some simple information about Fock states for photons in a work.
I wanted to know if:
in the context of a beam splitter when we suppose to have only one photon, always entering from the same port, does the states
$$| 0 \rangle \otimes |1\rangle $$
$$
| 1 \rangle \otimes |0\rangle
$$
form a basis for th... |
I'm working through the problems in Chapter 3 of the 3rd edition of Goldstein's Classical Mechanics and I'm stuck on Derivation 4. This problem asks the reader to rewrite the scattering angle
\begin{equation*}
\Theta(s) = \pi - 2\int_{r_{m}}^{\infty}{\frac{s\mathrm{d}r}{\displaystyle{r\sqrt{r^{2}\left[1-\frac{V(r)}{E}\... |
Suppose we have a a Hamiltonian, $H$. And suppose also we have some operator $Q$ such that $\{Q, Q^{\dagger}\} = H$, and $Q^2 = 0$.
If we find a state $|\psi \rangle$ such that $Q|\psi \rangle = Q^{\dagger}|\psi \rangle = 0$, then it follows that $H|\psi\rangle = 0.$
My question is about the converse. That is, if there... |
Apparently, there is an effect where a moving overdensity/underdensity (or an object, e.g. a galaxy, moving in an overdensity/underdensity) that is going through an evolution of its gravitational potential (due to the linear Integrated Sachs-Wolfe effect, or the non-linear version, the Rees-Sciama effect) will cause a ... |
I'm currently studying thermodynamics and have encountered two expressions relating changes in entropy to temperature, but applied in seemingly different contexts:
$\frac{dS}{dE} = \frac{1}{T}$, often seen in statistical mechanics.
$\frac{dS}{dQ} = \frac{1}{T}$, used specifically for reversible processes (adiabatic, i... |
If I have a solid sample material inside the atmosphere of oxygen-16, after some time diffusion will make the concentration of oxygen-16 uniform inside the sample. If then oxygen-18 (the tracer) is introduced for shorter time compared to oxygen-16, diffusion profile of oxygen-18 will develop and can be measured.
My col... |
Assuming superposition state
$$
\Psi = C_1 \psi_1 + C_2 \psi_2
$$
,one can write the expectation value $\langle A \rangle$ of a physical magnitude A as follows
$$
\langle A\rangle = P_1 \langle A\rangle_1 + P_2 \langle A\rangle_2 + 2 \sqrt{P_1 P_2} A_{12} \cos(\phi_2 - \phi_1)
$$
This last term can be interpreted as in... |
There is an interesting question about the energy we gain from oxygen on StackExchange.
But I want to ask another way around: How much energy would we need to generate enough oxygen out of carbon dioxide for one person per day?
So let's imagine we want to live on the Moon. We enclose it in some kind of glass dome and w... |
I am trying to understand the properties of metals by using them as cores for an inductor in an $RLC$ circuit. Now the resistivity, saturation point, magnetic permeability electric permittivity all should affect the response of the AC circuit. Now I can estimate the magnetic permeabilty by measuring the inductance but ... |
I am trying to find equivalent of Maxwell equations for 2 form gauge theory. My question is
Do we get $\partial_{\mu}F^{\mu \nu\ \rho}$ using Euler-Lagrange equation of motions?
How do we get the remaining two equations? Does it have equivalent of Jacobi identity?
How does it generalize to higher forms?
|
I always understood that gauge invariance of general relativity comes from the fact that the physical observables and states are the same regardless of the coordinates we choose to express them in. I may use Cartesian coordinates, I may use spherical coordinates, I may use whichever coordinate system I choose and the p... |
As a child my father told me about Planck's constant and I wonder whether I may have been confused. I imagined that all metrics are thus quantized, e.g. space has a minimum unit of distance, so for electrical charge, speed, etc.
Reading the Wiki, the extent to which this intuition is correct us unclear: https://en.wiki... |
Consider a maximally mixed state composed of $n$ equal qubits. Its density matrix is then:$$\hat{\rho}^{(n)}=\hat{\rho}^{\otimes n}.$$ The eignevalues of such a matrix, $\lambda$ will all be equal (since it is maximally mixed) and $\lambda=\sigma^{n}$, where $\sigma$ is the eigenvalues of each quibts' density matrix. B... |
I am currently attending a school for electrical science. A small group of students and our instructor are attempting group project to build a liquid fuel rocket. (I know it is a bit out of the scope of our field of study.)
We have encountered a few issues when attempting to calculate the thrust of the rocket. (None of... |
I'm trying to wrap my head around a conceptual problem involving a simple pendulum with a rocket attached to its mass. Imagine the rocket expels gas to provide a tangential thrust force. However, the thrust is calibrated such that it's not sufficient to swing the pendulum upward; instead, it only counteracts the gravit... |
I am learning how to use diagonalization methods applied to Fokker-Planck equations with Gardiner's book and these notes. The idea is to find the probability density, $ P[X_t\in[x,x+dx]]=\rho_t \, dx$, as an expansion on the basis of eigenfunctions of the Fokker-Planck operator,
$$ \rho_t=\sum_\lambda C_\lambda(t) R_\l... |
Our teacher taught us today that instantaneous value of current in Alternating Current is
$$i=I_0 \sin(wt)$$
Where $I_0$ is the amplitude and $wt$ is the angular speed times time. Now, she didn't really explain the mathematics behind this, because we just have to apply it like this. Now I was wondering to know, how com... |
I'm reading Symmetries part from the textbook provided by MIT OCW Physics3 8.03SC course, but have a question about the condition to find normal modes of SHM. In the book they mentioned
$S$ - symmetry matrix
$A^n$ - eigenvector
$b_n$ - eigenvalue
If $SA^n = b_nA^n$, and $b_n != b_m$ for $n != m$, then $A^n$ are normal ... |
i was wondering if it was possible to calculate a mass of object on top a bag filled in with air
as compared to a bag of air filled up with nothing on top of it
assuming the air pressure going into the bag is constant
Would is be possible to calculate the mass of the object with the different in air pressure going in?
|
Now, I am a beginner in Cosmology, so I am not sure if this makes sense.
Since the universe is expanding at an accelerating rate, and thus distant objects are also accelerating away. In that sense, from our (non-comoving) frame of reference, they are gaining kinetic energy. Similarly, for the frame of reference of a fa... |
Is there a way to modify the event horizon to make it generate other particles by affecting quantum fields outside with a giant charge increasing quantum foam disruptions affecting the radiation? Is it possible to get charged particles from this process?
|
I learned some thing called Galilean principle of relativity which says that two inertial frames are equivalent and the laws of physics are the same in both inertial frames.
However here comes the problem with Newton's second law: suppose inertial frame 2 is moving at a constant velocity $\textbf{u}$ with respect to in... |
Consider an ordinary object, e.g. metal or an insulator placed in a simulation mesh to simulate a CFD physics problem, creating a solid-vacuum interface. I cannot model this as a dense ideal gas as it would expand feely. I am simulating the dynamics of another fluid whose behavior is being impacted by this diffusion on... |
Is the process of compactification of hidden dimensions in string theory equivalent to an increasing dilaton field?
Would one expect the compactification process to continue indefinitely?
Could the apparent cosmological expansion of space actually be due to hidden dimensions becoming more compact?
Cosmological distance... |
We know the force on a charged particle in a magnetic field is given by
$$
{\bf{F}} = q({\bf{v}} \times {\bf{B}})
$$
However, my question is that:
Can this equation be derived?
|
In my physical chemistry book, it says:
In the study of molecular speeds, we must consider a range of speeds. If we don’t, the probability would be zero. This probability is proportional to the range $\mathrm du_x$. Maxwell, based on probability theory, deduced that it is also proportional to $\mathrm e^{-\frac\beta3}... |
Does the velocity of the wheel change (and it skids/slides) or does it remain constant? The coefficient of friction will be lower on the ice, but is there any other force that counters that to keep the constant velocity?
|
Hopkinson's law which states that $$\Phi_B \mathcal{R} = \mathcal{F} = NI$$
Where $\Phi_B$ is magnetic flux, $\mathcal{R}$ is reluctance which only depends on the geometry and material of the object in consideration and $\mathcal{F}$ is magnetomotive force or mmf.
This law is said to be analogous to ohm's law specifica... |
I am studying the Lanczos-Lovelock theory of gravity where the Lagrangian density is
$$ \mathcal{L} = \sqrt{-g} \sum_{i=0}^{t} \alpha_{i} \mathcal{R}^i $$
With $ \alpha $ being the coupling constants and
$$ \mathcal{R}^n = \frac{1}{2^n} \delta^{\mu_{1}\nu_{1} ... \mu_{n}\nu_{n}}_{\alpha_1 \beta_1 ... \alpha_n \beta_n} ... |
Yesterday there was a casual discussion of the findings of the scientist Galileo in my German class. It was mentioned that his breakthrough was that, he found a convincing explanation that earth revolves around the sun in an ellipse rather than vice versa.
But is that actually a meaningful thing to say? Wouldn`t we get... |
On the table and near to the computer where I write this question on, is my phone, and in my observation, it is completely still. Now, by Newton´s first law, since it is inertial, there is no net external force.
But, I know for sure that´s not true. The earth moves around the sun, and by extension, my phone does as wel... |
When observing colored fire through a spectrometer after adding substances like copper chloride or magnesium sulfate to change its color, what specific spectra are typically observed? How does the spectral composition of colored fire differ from that of regular fire?
|
Why does the current produced in a metallic conductor follow a circular path specifically during electromagnetic induction?
Is it true that a circle of all geometrical shapes encloses the least perimeter, and hence the current follows a circular path?(as currents flow in the least resistive path)
|
In this video, it is mentioned that the force on charges that are inside the circuit is same throughout the wire when we close the circuit, but after the transient phase, when a steady current is achieved the forces become zero throughout the wire except resistors.
If that is true then there shouldn't be any electric f... |
In the appendix B of Polchinski's book there is a discussion on the compatibility between Majorana and Weyl condition.
My doubts are trough this passages:
He starts constructing the basis in $(2k+2)$ dimension with $k= 0,1,2,....$
using this lower and upper gamma matrix
Then he defins the following gamma matrix
afte... |
I was thinking about electromagnets today and a thought popped up in my mind on what would be a very simple way to create an electromagnet.
Although I have not built and tested it, I am pretty sure that it will function as an electromagnet even though it will be a lot weaker in magnetic strength than a standard electro... |
I am trying to derive the basic properties of positronium. Usually it is stated that we can just set reduced mass of hydrogen atom as $\dfrac{1}{2}m_e$ and obtain:
\begin{equation}
r_n=\dfrac{8\pi\varepsilon_0\hbar^2}{m_ee^2}n^2
\end{equation}
On the other side I am trying to derive that the following way:
\begin{equat... |
The Huygens-Fresnel principle essentially states that in order to propagate an electromagnetic wavefront in free-space, one must superimpose the so-called "secondary wavelets", which are spherical waves emanating from every point of the current wavefront. I have searched for a modified version of this principle when li... |
I am a student majoring in mathematics, my specialization is topology and analysis. I am writing a thesis on the general relativity, and I want to consult about Einstein field equation. I have tried finding and reading some books about general relativity or mathematics of general relativity, but none of them seem satis... |
It is well-established that molecules possess rotational and vibrational quantum states, due to molecular symmetries, in addition to electronic states. In contrast, it is generally accepted that atoms have only electronic states. The absence of vibrational states is understandable. However, the rationale behind the abs... |
I have trouble understanding the derivation of the Lindblad evolution in terms of the time evolution under a Hamiltonian $H$ in a system-environment Hilbert space $H_S\otimes H_E$, where we trace out the environment after some time $\Delta t$.
In particular, I'd like to understand the Lindbladian $\mathcal L$ as the co... |
Do black body radiation of a 40-Earth mass osmium planet with radius of Earth which was just formed and has a temperature of 10000 degrees Celcius emit photons not just near it but even at infinity kind of like a black hole does? The only difference is that Hawking Radiation increases but the osmium planet Radiation wi... |
An electron of kinetic energy $k=100 keV$ (first note, doesn't this mean that its energy is much lower than $0.511 MeV$, and thus that it is a nonrelativistic electron we are dealing with?), collides with a photon of wavelength $\lambda = 0.003 nm$ head-on.
I imagined the electron moving from left to right on the horiz... |
I was curious about the minimum height of a mirror required to see your full body, and I found out that it was half of your height, in other words the minimum height to view the image = your height / 2. Using this, how do you calculate the minimum height of a mirror required to view other objects. For instance, say you... |
I am learning about the lasers and I find one thing confusing about the lasers.
I understand that there is a range of wavelength laser, it is never exactly monochromatic. So, I understand the concept of FWHM to define a linewidth.
What I have difficulty understanding is this: Why is it often stated in terms of frequenc... |
I am wondering what curved 3D grids in GR outreach correspond to in equations. How would I compute such a curved grid if I know the metric tensor $g_{\mu\nu}$ in every point of space? What would be the equation of a line of that grid? What is the physical interpretation of such a grid (what are we really visualizing)?
... |
I'm trying to figure out the step from equation (19) to equation (20) in this document when $\mathcal{F} = 0$ y $\mathcal{A} = 0$. In this case, equation (19) reduces to
$$ - e^{\alpha \phi} \hat{\omega}^{z} {}{b} \wedge e^{b} = \beta e^{\beta} \partial{\mu} \phi (d x^{\mu} \wedge d x^{4} )$$
using $\hat{e}^{z} = e^{\b... |
Actually I was thinking that currently we are able to transmit data via Photons which are excitation in the EM FIELD, but if there exist any other quantum fields, why couldn't we use the excitation in them to transmit data, so that can we transmit data faster than speed of light?
Thank you for your responses btw but I ... |
Using the thickness and refractive index of an optical fiber, is it possible to know the maximum radius of curvature it can be bent before there are losses due to refraction?
In my research, I came across a concept called the critical angle, above which total internal reflection occurs, which is the principle optical f... |
I'm curious about the feasibility, both theoretically and experimentally, of tightly focusing (or spatially trapping) a single photon to guarantee its precise targeting. If it’s possible, isn’t it against the uncertainty principle?
For instance, is it feasible to guide/send a single photon towards precisely hitting a p... |
I am reading about the "Transition Boundary Condition" at this link.
Can someone please explain where the following boundary conditions come from?
$$J_{s1} = \frac{Z_s E_{t1} - Z_T E_{t2}}{Z_S^2 - Z_T^2} \\
J_{s2} = \frac{Z_s E_{t2} - Z_T E_{t1}}{Z_S^2 - Z_T^2} \\
Z_S = \frac{-i\omega \mu}{k} \frac{1}{\tan{(kd)}} \\
Z_... |
I first thought that lateral strain occurs to conserve volume on applying longitudinal stress but later I realised that I was wrong. But now I have a confusion that why lateral strain occurs if volume is not to be conserved? What is the reason behind lateral strain? Is it intramolecular force or something like that?
|
According to literature, the Casimir effect refers to attraction of two parallel neutral metal plates due to the wavelength cutoff of quantum fluctuations between the two plates.
I come from condensed matter / soft condensed matter / classical statistical mechanical background and I am not able to dive into the underly... |
So I'm learning about blackbody radiation and radiation in general. As I understand it, there are 3 ways to transfer energy/heat: convection, conduction and radiation. In chemistry I also learnt about the emission spectrum of hydrogen. I understand that when light is shot at a bunch of Hydrogen atoms some of the electr... |
As a math student, I am doing some quantum computing. In the course notes of Ronald de Wolf, he says that any Boolean function $$f:\{0,1\}^n\to\{0,1\}^m$$ can be made into a unitary operation that sends $|z\rangle|0\rangle \to |z\rangle|f(z)\rangle$. But he doesn't mention how or so?
Does anybody have tips or links to ... |
A question I faced reads
"A ball is thrown horizontally from a height of 25m and hits the ground with a speed that is 4 times its initial speed. What is the initial speed?".
It said the ball was thrown horizontally. But when you look at the solution, it reads "the y component of the initial velocity is 2gd while the ... |
This question will fully refer to the presentation ref. 1, from which I'll take the numbering. Since it involves also diagrams and it appears as a fairly basic question about Wilsonian renormalization, I won't be exhaustive.
After stating their programme, in ref. 1 they proceed to integrate out the "fast" modes in the ... |
If considering the general formula for acceleration, ie.
Δ V/ΔT, we would get zero as the velocity of light is constant and does not change.
However, what about when photons travel through different media? Wouldn't the speed change here?
My understanding is, of course, flawed here. I'm still in high school, so would ap... |
In the lecture notes on Quantum Mechanics I'm reading, the author claims that the position operator $\hat{q}$, the square spin operator $\hat{s}^2$ and the spin operator component $\hat{s}_0$ (in a spherical basis) form a complete set of commuting operators. But how do you prove that the position and spin operators com... |
Apologies if this is a very basic question, but I cannot seem to find anyone else asking or answering it. Is the coefficient of thermal expansion (CTE) the same when cooling and heating a material?
Using the linear CTE as an example, if I start with a length $L_1$ and cool from $T_1$ to $T_2$, my new length $L_2$ shoul... |
Imagine, we have a 2-by-2 Hamiltonian:
$$
H = H_0+H_{imp}.
$$
The impurity Hamiltonian $H_{imp}$ is
$$H_{imp}=u_{imp}I_2\sum_{r_{imp}}\delta(\vec r - \vec r_{imp}).$$
$I_2$ is identity matrix of order 2, $u_{imp}$ is strength of impurities (for example, Eq. 10 of this article). The self-energy for retarded Green's func... |
Let us consider a particle which is rotating in a circle of radius $R$ with a uniform angular velocity of $ω$. We are observing this particle from a frame rotating about the same axis with uniform angular speed $ω'$. Then what'll be the acceleration of particle with respect to us.
If if consider individual angular acce... |
I'm sorry if this is a duplicate but I didn't find my answer. I'm currently studying maxwell's equations and I know that by comparing the wave equation for either the magnetic or the electric field
\begin{equation}
\Delta \vec{B} = \mu_0 \epsilon_0 \frac{\partial^2 \vec{B}}{\partial t^2}.
\end{equation}
By comparing... |
In $k$-space the allowed values for standing waves in a cube of side length $L$
are given by
$$\vec{k} = \left(\frac{\pi}{L}\right) (n_1, n_2, n_3)$$
where the $n_i$ are nonnegative integers. Why are these numbers non-negative only?
|
The CIE198:2011 suggests to simplify the spectral mismatch correction factor (SMCF) using the relation of the color temperatures of the Planckian distributions:
$$
F(T_d,T_A) = \frac{\int P(\lambda,T_d)\cdot V(\lambda)d\lambda}{\int P(\lambda,T_d)\cdot s_{rel}(\lambda)d\lambda}\cdot \frac{\int P(\lambda,T_A)\cdot s_{re... |
I'm reading a book on molecular simulations (Understanding Molecular Simluations, D. Frenkel and B. Smit) and I'm reading derivation of the average perturbation response of an observable $A$ as a function of time, after having applied a perturbation.
This is what is written:
Next, we consider a simple time-dependent p... |
Previous title: How strong of a magnetic field could dissociate water molecules?
(Changed as this is probably not possible)
This is part of an attempt to answer the question 'How much MRI is enough to kill a person?'. I've found the extreme answers (that 16T is enough to levitate a frog and 1 million T would instantly ... |
D. J. Simms in his book "Lie groups and quantum mechanics" (page 9) says that: any representation of $\sigma$ of $\tilde{G}$ (the simplgy connected covering group of the Lie group) in $U(H)$ such that $\sigma (K)\subset U(1)$ (in which $K$ is the kernel of covering map $p:\tilde{G}\to G$) will defines a unique projecti... |
I am self-studying the book “James H. Luscombe, Core Principles of Special and General Relativity”. In “CHAPTER 9 : Energy-momentum of fields” of the book, it starts by introducing Noether’s theorem and then shows that invariance under spacetime translations implies conservation of field energy and momentum:
$$T^{μν}≡g... |
I've often wondered whether dark matter is a by product of the mixing of gravitational fields.
When we look at electromagnetic fields we can observe harmonics and intermodulation effects. This is something of which I have extensive experience in the radio and photonics fields, e.g. beat frequencies, etc.
However, look... |
I am reading a note on Yang-Lee's zeros.
The note first focuses on the grand canonical partition function $\Xi(T, z)$, where $z$ is the complex fugacity conjugate to the number of particles. If the zeros form a curve closing in/reaching onto a special real value $z_0$, it is shown that the curve is a hyperbola when $z_... |
For the time component of momenta with Feynman prescription like $\sqrt{-p10^{2}-i\delta}$ and $\sqrt{p10^{2}+i\delta}$, how to perform it? Here p10 is the time component of four momentum. Any detailed example on such calculation?
|
I'm trying to understand work calculation for a force acting on a rigid body (as opposed to a point particle).
My understanding is that the same basic principle applies: the work done by force F on body B is the line integral of F over the curve C which was travelled by some point P.
My question is, which point is P? D... |
I need pointers about whether there is such thing as a periodic Ising lattice. Those who are familiar with Ising model know that spins form a lattice in $N$ dimensions. Depending on the number of interactions per spin, this lattice can exist in 1D (two connections per spin), 2D (4 connections for square lattice), etc.
... |
Is it possible to derive the graviton propagator in curved spacetime from the graviton propagator in Minkowski spacetime?
|
In the unnumbered equation above (8) the authors of https://arxiv.org/abs/2109.05547 introduce a free parameter $m_x$ (presumably of mass dimension), when switching from the real scalar field $\phi$ (discretized on a spatial lattice) to creation operators:
$$
\phi(x)= \dfrac{1}{\sqrt{2m_x}}(a_x+a^\dagger_x).
$$
They sa... |
So I'm learning about blackbody radiation and radiation in general. As I understand it, there are 3 ways to transfer energy/heat: Convection, Conduction and Radiation. In chemistry I also learnt about the emission spectrum of Hydrogen. I understand that when light is shot at a bunch of Hydrogen atoms some of the elect... |
By using Newtonian gravity, we can equate the kinetic and potential energy of a test mass in order to obtain the escape velocity of an object from a large mass $M$:
$$\frac{1}{2} m v^2 = \frac{GMm}{r}$$
therefore:
$$v_{esc}^2 = \frac{2GM}{r}$$
We can then obtain the Schwarzschild radius $r_s$ by setting $v_{esc}$ to th... |
In my textbook they tried to explain thermal expansion at atomic level with the potential energy curve but it was very complicated.I wish someone could explain it to me:)
A high school level explanation would do.
|
In general relativity, the curvature of spacetime is related to the presence of energy and momentum (the energy-momentum tensor) by Einstein's field equations: $$R_{\mu\upsilon} - \frac12Rg_{\mu\upsilon} = 8\pi GT_{\mu\upsilon}$$ where from left to right, we have the Ricci tensor, the Ricci scalar multiplying the metri... |
I have a pulse signal with frequency f(t)
And i want to generate from it a sine signal with frequency f(t)
(f(t) doesn't vary a lot in time)
Is there a method to do it directly with a function generator ?
If no, How can i acheive this ?
|
If we consider a rod hanging from the ceiling, able to swing freely, and then fire a bullet that hits its end, it will swing like a pendulum. I know the total linear momentum is not conserved since there is a force acting on the top of the rod. But in what direction is that force acting? I suspect its x-component shoul... |
In my high school, the definition of electrical current is "the flow of charges" but I have seen a video about how electricity actually works and it seems to me that electrical current is indeed caused by the electric fields along the conductor and there is nothing to do with the flow of electrons (or charged particles... |
The physical system I'm imagining is pretty simple: suppose there's an atom in free space with three states $|g_0\rangle, |g_1\rangle, |e\rangle$ initialized to some superposition of $|g_0\rangle$ and $|e\rangle$, say $|\psi_0\rangle = (|g_0\rangle + |e\rangle) / \sqrt{2}$. The atom is coupled to a quantized electromag... |
I've read over several other discussions on the topic of "electric field of a sheet of charge vs electric field of a charged plate", on this very site, but I still haven't gotten the answer to my question. And what's made me so curious is a combination of a tutorial exercise from a book called "Tutorials in Introducto... |
I've recently been studying about the General relativity and Einstein field equation. When I reading of the derivation of the field equation, I encounterd a method called Einstein-Hilbert action. This action is given as
\begin{align}
S_{EH}[g_{ij}]\,=\,\intop_M \sqrt{-g}R\,dx_3dx_2dx_1dt
\end{align}
where $S_{EH}[g_{ij... |
To prove it, as Huang does with the microcanonical ensemble, the following equality must be valid. In all sincerity, I can not understand why it must be true. I would appreciate enormously some help with it or some good reference where it explicitly elaborates on the argument.
|
This is a follow up of a recent post I made (Making sense of stationary phase method for the path integral), but here I will work in Euclidean space, i.e. a Wick rotation has been performed.
Let
$$Z[J] = \int D[\phi] e^{\frac1\hbar(S[\phi]-\int J\phi)}$$
denote the generating functional for a source $J(x)$. Letting $W[... |
Within my understanding, (a) for an isolated solenoid in a vacuum (or air) magnetic flux density inside the solenoid is a perfectly linear function of solenoid current; and (b) in significantly permeable materials, flux density B is a highly nonlinear function of field strength.
When a structure of permeable material i... |
When we radially quantize a conformal field theory, is there at least formally a notion of a conjugate momentum $\Pi$ to the primary fields $O$ which would satisfy an equal radius commutation relation $$[O(\Omega), \Pi(\Omega\,')] = i\hbar\hat{\bf 1}\sqrt{g}\delta^{d-1}(\Omega-\Omega\,')$$
where $\Omega$ are the hypers... |
How does measurement in quantum mechanics (QM) impact the system's entropy? The measurement process in QM is considered time-irreversible. Are there principles akin to the second law of thermodynamics governing the entropy of the system during irreversible or spontaneous processes?
|
So here’s my question:
Say there is some ice at -2°C. And water at 0°C. The ice is added to the water. Now this is a completely isolated system. There is no heat exchange whatsoever with the environment. In this case, what will happen?
It’s obvious that heat should flow from the water to the ice, causing it to increase... |
In Sakurai's Modern Quantum Mechanics, its 3.8.39 is
\begin{aligned}\sqrt{(j\mp m)(j\pm m+1)}\langle j_1j_2;m_1m_2|j_1j_2;j,m\pm1 \rangle \\=\sqrt{(j_1\mp m_1+1)(j_1\pm m_1)}\langle j_1j_2;m_1\mp1,m_2|j_1j_2;jm\rangle\\\quad+\sqrt{(j_2\mp m_2+1)(j_2\pm m_2)}\langle j_1j_2;m_1,m_2\mp1|j_1j_2;jm\rangle, ~~~ (3.369) \en... |
While I was reading Mehran Kardar's book 'Statistical Physics of Particles'. The author considers three systems :
a) A wire of length L with tension F
, b) A paramagnet of magnetisation M with applied magnetic field B
, c) A gas of volume V at pressure P
Now when the system are in equilibrium the following constraints ... |
I am reading about the first and second Noether's theorem from https://arxiv.org/abs/2112.05289. In the text, there is this piece, which I am not sure I entirely understand.
Let us reflect briefly on how this proof compares to that of Noether’s 1st theorem. In both proofs, one needs some sort of varying arbitrary func... |
For generators of the Lie group under an arbitrary representation: $[T^a,T^b]=if^{abc}T^c$
$[T_A^c]^{ab}=-if^{cab}$ is the generator of the adjoint representation.
Is $\ \ e^{i\theta^d T^d}T^ae^{-i\theta^e T^e}=[e^{-i\theta^cT_{A}^{c}}]^{ab}T^b\ \ $ correct to all orders? How to prove it?
The formula is obviously true... |
Problem I'm interested in solving: How much radiative heat load is entering the system through optical windows (in SI units - Watts)? (see the images below)
I have tried to break the problem into its most basic components. We have a series of 4 boxes, one inside the other.The boxes themselves are radiation shields and ... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.