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I am seeking a proof of the following:
Suppose we have a theory with $n$ scalar fields $(\phi_1,...,\phi_n)$ such that the Lagrangian $L$ is invariant under the action of some group $G$.
However, $G$ is a spontaneously broken symmetry: The vacuum expectation value (or the minimum of the potential) $\phi^{cl}$ is nonze... |
I am reading a book "General relativity: The theoretical minimum" by Leonard Suskind.
In page 168-169, the author explains the reason why we don't consider the case with two time dimensions in the metric as follow:
It(metric with two (-) signs and two (+) signs) doesn't mean anything in physics.There are never two tim... |
Conventions:
Take the Minkowski metric tensor to have signature $(+, -, -, -)$. Use Hermitian (instead of skew-symmetric) generators of rotations $J_i$ and anti-Hermitian (instead of symmetric) generators of boosts $K_i$.
Background:
The task is to find finite dimensional projective representations of the restricted Lo... |
So, say I describe a perfectly linear field expanding outward from a point (A signed distance field of a sphere, basically) (as described by sqrt(x^2 + y^2 + z^2) or more traditionally length(pos))... How could I, at any point in that field, find a refractive index that would be physically accurate... or atleast a good... |
I was wondering if there are any other means of obtaining exact (or analytical approximations) of the phase space probability density for a system evolving according to Langevin dynamics. The typical approach seems to be to pass to the Fokker-Planck equation corresponding to the underlying Langevin equation and then so... |
In the problem of computing leaning angle ($\theta$) of a turning bike, the traditional approach is to move to the accelerating reference frame and compute the balanced torques with respect to the ground contact point generated by gravity and centrifugal force. I am ok with this solution and able to derive
$$\tan(\thet... |
Freeman J. Dyson in his "Time without end: Physics and biology in an open universe", Lecture 2: Physics, part G: All matter decays to iron, claimed that on a long enough time scale "Elements heavier than iron will decay to iron by various processes such as fission and alpha emission". I'm not able to find why or how wi... |
What is the consensus on whether or not nature actually has functional infinities such as an absolute singularity, or the multiverse itself as a whole, or even some potential for reality always existing in some state (a context from which spacetime or other can emerge).
Given renormalization for instance to deal with i... |
I know that the unitary propagator between two points $x_{i}, x_{f}$ at instants $t_i, t_f$ is given by
$$K(t_i, t_f, x_i, x_f) = \langle x_i, t_i| x_f, t_f\rangle = \langle x_f|e^{i\frac{(t_f-t_i)}{\hbar}H}|x_i\rangle$$
Time slicing into $n$ intervals $\delta t = \frac{(t_f-t_i)}{n}$ gives us
$$\langle x_i, t_i| x_f, ... |
Let's assume that two trains of equal masses are moving along parallel paths. The engine of train 1 exerts a constant force, and the engine of train 2 works at a constant rate. If in time $t$ they have the same velocity $v$ then who has traveled the larger distance?
|
I want look (and plot) how the average number of fermions depends on temperature and the chemical potential.
According to Eq.(13.12) in https://itp.uni-frankfurt.de/~gros/Vorlesungen/TD/13_Ideal_Fermi_gas.pdf, the fermion density $n$ is given by $$n = \frac{2s+1}{\lambda^3}f_{\frac{3}{2}}(z),$$
where $2s+1$ is the spin... |
At a crossing of a knot, if I change the crossing by swapping the two lines, the knot is changed, along with its Jones Polynomial. Witten's path integral
$$
\int {D \mathcal{A}\ e^{i\mathcal{L}}\ W_R(C)},
$$
computes the Jones polynomial and hence should be different when something like this happens. Is there a simple ... |
I understand that the vacuum expectation value (vev) of the Higgs field has changed, resulting in a nonzero energy value throughout space. It takes the shape of a Mexican hat, with its minima less than zero. Therefore, there exists a Yukawa that interacts with fermions.
$$\mathcal{L}_\text{Yukawa} = -g \bar{\psi}\phi\p... |
I've been struggling with question below:
"A metal disc of radius R can rotate about the vertical axis passing through its centre. The top surface of the disc is uniformly covered with dust particles. The axis of the disc is tilted slightly to make an angle θ with the vertical. The disc is rotated with gradually incr... |
Let $(M,g)$ be a 4 dimensional Lorentz spacetime. A smooth curve $\alpha:\ I\to M$ is called lightlike if $\alpha'(s)\in TM_{\alpha(s)}$ is lightlike for all $s\in I$, which means
$$g_{\alpha(s)}\big(\alpha'(s),\alpha'(s) \big)=0,\ \forall s\in I. $$
A geodesic in $M$ is a smooth curve $\alpha:\ I\to M$ such that $\alp... |
I have a question about Kelvin-Helmholtz instability (KHI) for a continuous fluid.
I am new to hydrodynamics and I am currently working on a project about KHI.
For the past few days, I am looking for an intuitive explanation for the occurence of KHI in a continuous fluid. I found multiple intuitive explanations why KHI... |
Reading the book on General Relativity written by R.M. Wald I (tags according to Wald's book) encountered the concept of a twistor
$$ Z = (\omega^A, \pi_{A'}) \tag{14.1.9} $$
which looks very much as a Dirac bispinor (I assume here that the ' notation is the same as the $\dot{}$ notation):
$$ \Psi = \left( \begin{array... |
I'm reading arXiv: 1411.5745 [hep-th]. In Sec. 5, the authors show how the memory effect and Weinberg's soft graviton theorem are two faces of the same coin. I'm interested in understanding a specific statement used in the paper. Let me recollect some statements and establish notation in order to ask my question.
Consi... |
This is a homework problem, however I am not looking for the solution but trying to know why I got the correct solution and why other methods don't work.
Consider the attached diagram. We have two equal spheres of mass m suspended by vertical strings (B and C).A third identical sphere (A) of same mass m simultaneously ... |
I had seen a similar question to this as below. However it considers a charged capacitor disconnected from a voltage source.
Force on dielectric slab
As per my understanding from the comments, the Fringe field and energy stored due to it doesn't change outside the dielectric as its magnitude depends only on the capacit... |
As answered in this question, an antisymmetric tensor on 4D Minkowski space has two Lorentz-invariant degrees of freedom. These are the two scalar combinations of the electromagnetic tensor (as proven for example in Landau & Lifshitz' "Classical Theory of Fields"):
$$
L_1 = \eta_{\mu\rho} \eta_{\nu\sigma} F^{\mu\nu} F^... |
I am doing mathematical modelling in MS Excel Spreadsheet for axial magnetic field (Bz) at different distances away from the centre for a finite model. I see small hump at the fringe (i.e. just outside the length of the solenoid core). What is the real explanation of this effect?
enter link description here
In some pa... |
I am studying Weyl and Dirac spinors. Suppose we have two Weyl fermions $\eta, \chi$ transforming under $(1/2,0)$ representation of the Lorentz group. I learned that to construct Lorentz invariant term in the Lagrangian, we have terms like $i\eta^\dagger\bar\sigma^\mu\partial_\mu\chi$ or $i\eta\sigma^\mu\partial_\mu\ch... |
I am currently doing a project which requires me to figure out the charge density of a strip. Assume that the strip is isolated in a vacuum.
Assume the strip is 1 dimensional, kind of like a rod. What would the function of charge density of the strip be? (The function is f(x) and depends only on 1 variable as it is ass... |
Griffiths Introduction to Electrodynamics problem 3.21
Find the potential outside a charged metal sphere of charge $Q$ and
radius $R$, placed in an otherwise uniform electric field $E_0\hat{z}$.
The Instructor's solution manual says that the electric potential has inverse $xy$-plane symmetry, so it can be solved as t... |
Watching this episode of PBS Space Time, they run an animation of how pi mesons are exchanged by nucleons as the residual strong interaction to overcome proton electromagnetic repulsion.
https://youtu.be/E8hyodMhbRw?si=2v2DbdsVOkDHETqv&t=674
They show one quark being pulled away in its nucleon to a tubule extruding fro... |
I've been wondering why frictional force acts as a centripetal force when a car is turning; my intuition would not lead me to believe it would act perpendicular to velocity, but I think I have at least somewhat of an image as to why it happens.
Is the diagram I've drawn somewhat correct? Is the x component of friction... |
Referring to Plasma Astrophysics, Part 1, Eq 4.32,
The number density of electrons in the beam at a distance $z$ from the injection plane at $z = 0$ is defined as,
$$
n_b(z) = \int_{0}^{\infty} \int_{0}^{\pi} f(z,v, \theta) v^2 dv 2 \pi sin \theta d \theta
$$
where $f(z,v, \theta)$ is the distribution function defined ... |
I'm currently studying the simplest models of potentials in QM, and I've run across an apparent inconsistency in my textbook: when describing a finite potential as a piecewise function, I've noticed the author defines the value of the potential twice in the boundaries, as follows:
$$V(x) = \begin{cases}V_0, \ \ |x|\leq... |
I was reading the book 'The Oxford Solid State Basics', Book by Steven H. Simon. The section explaining Brillouin zones had this paragraph in it
Each Brillouin zone has exactly the same total area (or volume in
three dimensions). This must be the case since there is a one-to-
one mapping of points in each Brillouin zo... |
I know there are antiquarks with anticolor charges. Are there also antiquarks that instead carry color charges?
Basically, which of these lists describes the types of quarks that there are:
List one:
+2/3 with color charge
+1/3 with anticolor charge
-1/3 with color charge
-2/3 with anticolor charge
List two:
+2/3 wi... |
I am currently working on a modified gravity theory which has non-minimal coupling between Ricci scalar and Maxwell term. The precise action is
$$\int d^4x\sqrt{-g} \left(R + \alpha R^2 + (1 + \beta R) F^{\mu \nu} F_{\mu \nu}\right)$$
I want to conformally transform this action to an Einstein frame where I expect there... |
Textbook for bosonization mainly focus on the zero temperature limit. I wonder that at finite temperature, if there exists the boson-fermion dictionary as well.
|
I am reading Planck's work on black-body radiation.
In the paper on the page 19 it is said that the expression
$$R_\nu=\frac{\nu^2}{c^2}U\tag1$$
where $R_\nu$ is the intensity of a linearly polarised light,
is an expression of (electromagnetic) entropy maximum.
In other words, it is a stationary state, i.e.
$$dS = 0, \... |
As far as I know, in free space there can be constellations of $N$ point charges in electrostatic equilibrium (albeit unstable equilibrium) for all $N$ except $N=2$.
Some discussions here already addressed this and also equilibrium situations inside a sphere[ref1, ref2, ref3]. It seems that in a hollow conductive spher... |
Why is cobalt's atomic mass listed on periodic tables as less than 59 amu when its main isotope (virtually 100 %) is cobalt 59 with a trace of cobalt 60? After reading a bit I'm wondering if it has to do with loss of mass through decay. But that seems like it would either change the mass number or only lose an insignif... |
As far as i understand, the full symmetry of relativity is conformal symmetry.
This is represented by the conformal group $ \operatorname{Conf}(1, 3) $
Of Minkowski spacetime which is $ \mathbb{R}^{1, 3} $
This has a very useful amount of information online, however i was wondering about a generalisation of this concep... |
This is a question I've had for several years but never had the knowledge to calculate myself. Please keep in mind I don't have much background in physics (learned some on middle school I guess...), but I'd still love a thorough answer and I'll do the research further needed to understand it.
Years ago, I was told that... |
I'm writing my physics bachelor on the Raman scattering effect in solids. I'm trying to evaluate the scattering intensity response to varying polarization angle. This is the well known linear polarized Raman measurement. The intensity is given by:
\begin{align}
I_s \propto |e_s\mathfrak{R}(X)e_i|^2+|e_s\mathfrak{R}... |
I am currently working on computing the cross section of Compton scattering in QED and in the process need to evaluate an expression of the following form:
$$ \sum_{\lambda}^{} \epsilon^{\mu} (\lambda,k) \, \epsilon^{\nu} (\lambda,k)$$
In my course’s lecture notes, it has been derived that this expression equates to:
... |
My understanding is that all mediums have a complex iindex of refraction where the real component is the "standard" index of refraction, and the imaginary component is the extinction coefficient indicating how well light is absorbed by the medium.
When light is incident on an interface between two mediums with differen... |
I am currently playing around with computing cross sections of several simple interactions in QED like Bhabha and Compton Scattering and I have stumbled upon a question which I havent yet managed to resolve myself.
The situation at hand:
Let us consider the spin averaged sum of the t-channels' squared S-matrix in Comp... |
For example, when light passes through water its velocity decreases and refraction occurs. Why? Why is there a change in direction. If I slow down a car I don’t suddenly turn left.
|
I am trying to obtain the infinitesimal transformation for the Yang-Mills field $A_{\mu}$. I want to show that
$$ A^{\prime a}_\mu=A_\mu^a-\partial_\mu \theta^a-g_s f^{a b c} \theta^b A_\mu^c $$
For them I used the finite transformation:
$$ A^{\prime}_{\mu} = U A_{\mu} U^{\dagger} + \frac{i}{g} U^{\dagger} \partial_{\m... |
Consider the equal time commutation relation of a field given on a $d$ dimensional spacelike hypersurface $\Sigma$ of a $d+1$ dimensional manifold given by
$$[\Pi(t, x), \Phi(t, x')] = i\hbar\delta^{(d)}(x-x')\tag{1}$$
What will this commutation relation look like on the spatial boundary? Will it be $$\big[[\Pi](t, y),... |
Rabi Oscillations are explained as electric interaction between atom and EM field, here. This can be true for any two-level system with specific interactions that can lead to the Hamiltonian given in the link with two important terms, one is detuning frequency and the other is external EM field frequency.
Now, my quest... |
I am trying to find a proof for the formula for entanglement entropy of an evaporating Black Hole. It is introduced and used in many papers such as The entropy of Hawking radiation, by Ahmed Almheiri, Thomas Hartman, Juan Maldacena, Edgar Shaghoulian and Amirhossein Tajdini, REVIEWS OF MODERN PHYSICS, VOLUME 93, JULY–S... |
Our Moon is going away and I read that it is the culprit is our ocean, but then what happens to Newton 3rd law there should be an equal and opposite forces too so where's that? Is it absorbed by the ocean if so in what kind of form?
|
I am self-studying the 3rd edition of Goldstein's Classical Mechanics and I'm having trouble making sense of a certain figure, namely, Figure 3.12 (p. 88), reproduced below.
The figure follows an explanation of the fact that the orbit corresponding to the differential equation for a central force field with potential ... |
The typical definition of a causal net of observables in quantum theory is to consider, for the case of a (globally hyperbolic) spacetime $M$, the category of open sets $O(M)$ ordered by inclusion, in which case the causally local net of observables is a functor
\begin{equation}
\mathfrak{A} : O(M) \to \mathrm{Alg}
\en... |
I am trying to demonstrate this propertie
$$
\not{D}^2= \mathcal{D}^\mu \mathcal{D}_\mu-\frac{i}{4}\left[\gamma^\mu, \gamma^\nu\right] F_{\mu \nu}
$$
where $\not{}~$ is the Feynmann slash, and $D_\mu = \partial_\mu-iA_\mu$. I tried to do the calculation:
$$
\not{D}^2= (\gamma^\mu D_\mu) (\gamma_\nu D^\nu) = (\gamma^\... |
Assume for example that you are given a (2,0) tensor $T^{\mu\nu}$ and you want to create
a vector, i.e., a (1,0) tensor out of it. Is it possible to just fix an index of
$T^{\mu\nu}$ while keeping the other free and thus define a vector?
In other words, could you define a vector with components given by
\begin{equation... |
Let $R\in\text{SO}(3)$ be an arbitrary rotation, and let $U_R$ be the unitary representation of $R$ on some Hilbert space $\mathcal H$. To me, the defining property of $U_R$ is how it conjugates the position operator $\textbf X$:
$$U_R^{-1}\textbf X U_R=R\textbf X$$
And in position space, I would expect that:
$$\langle... |
Can the specific heat capacity be time dependent, but not temperature dependent in a close system that does not have a heat source/sink term?
|
my question is related with Projectile motion, it describes about the high velocity of ball on its trajectory. it asks about the conditions of height, time of flight, range as well.
|
I am reading Nonplanar Relativistic Flow by Peter G. Eltgroth, Phys. Fluids 15, 2140–2144 (1972) doi.
I do not understand how the author arrives at expressions (12), (13) and (14) at page 2. Equation (12) in particular baffles me, since it says:
$$F(\beta) = -\dfrac{r}{ct}$$
As you can see the LHS is a function of $\be... |
I'm trying to use a 3x3 beam transfer matrix from "Generalized Beam Matrices: Gaussian Beam
Propagation in Misaligned Complex Optical Systems" by Anthony A. Tovar and Lee W. Casperson https://pdxscholar.library.pdx.edu/cgi/viewcontent.cgi?article=1068&context=ece_fac to track the modulation of a misligned Gaussian bea... |
I'm currently reading Jules Verne's Mysterious Island and the author, through his engineer character, keeps repeating the statement that if he climbs up to the top of a mountain to a height of 2500 ft (762 m) - the highest peak on the island - he will be able to see about 50 miles (80.5 km) through the horizon.
Is this... |
I am learning the principles of nuclear magnetic resonance, and came across the interaction between two Hydrogen nuclear spins, which affects the relaxation properties of materials like water in NMR. Suppose we have 2 spins, ${\bf S}_1$ at $(x_1, y_1, z_1)$ and ${\bf S}_2$ at $(x_2, y_2, z_2)$. Then the dipolar interac... |
I am currently reading section 10.1 of Classical Electricity and Magnetism by Panofsky and came across their derivation for magnetic energy stored in current systems.
Consider a process in which a battery with a nonelectrostatic field E' is feeding energy both into heat losses and into a magnetic field. If we take the... |
I understand that in order to have a supersymmetric spectrum in string theory, the vacuum has to be a MW (Majorana-Weyl) spinor under $SO(1,9)$. But I don't see where the Majorana condition on the R vacuum comes from. I understand that the GSO projection chooses a chirality, so that the R vacuum is a Weyl spinor, but I... |
I recently found out about the Magic Mirror. Both sides of the mirror look the same, and it appears to be dark, if looked at closely, like sunglasses (but lighter in colour) but looks like a normal mirror from afar.
Why does it appear different from different locations? How exactly is it silvered? It behaves like gla... |
I am trying to demonstrate that the slashed covariant derivative
$$
\gamma^\mu D_\mu = \gamma^\mu(\partial_\mu -iA_\mu)
$$
has real eigenvalues:
$$
\gamma^\mu D_\mu \varphi_m(x)=\lambda_m \varphi_m(x) \Rightarrow \lambda_m \in \mathbb{R}
$$
However I do not know how to prove this.
I am a bit confused and I would reall... |
Consider a porous material in which the pores can be drained or filled with water gradually in time. Thus, the volumetric heat capacity changes with time. Can I write the heat transfer equation ($\dot{q}$ is a heat source due to a chemical reaction) in this form?
$$
\frac{\partial (\rho C T)}{\partial t}=\nabla\cdot(k\... |
Take any gauge invariant theory, for instance QED. The QED Lagrangian is invariant under
$$A_{\mu}(x)\rightarrow A'_{\mu}(x)=A_{\mu}(x)+\partial_{\mu}. \alpha(x)$$
I have chosen a local gauge transformation, but I think it doesn't matter. Usually we try to make a choice of gauge with which we are going to be working. A... |
I am reading Counting the number of propagating degrees of freedom in Lorenz Gauge Electrodynamics. I am thinking that I can apply the same arguments to the case of a two form, whose components are denoted as $B_{\mu\nu}$.
Can I still claim, if the two-form field $B_{\mu\nu}$ in 4D is massless, that I can remove one de... |
I am relatively new to the field of topological materials, and I came across a paper that claims that they found topologically non-trivial states in a material. Basically, the authors found a type-I Dirac cone in the electronic band structure and carried out analysis of non-triviality of these states. The code they use... |
Lami's Theorem states that the magnitude of each force in an equilibrium state consisting of three coplanar, concurrent forces acting at a point is directly proportional to the sine of the angle between the remaining forces in equilibrium.
Let $F_1$, $F_2$ and $F_3$ be the three forces and $\alpha, \beta$ and $\gamma$... |
Because all particles must follow their geodesics, is there any reason we make a differentiation between a geodesic and a "non-geodesic"? And is there any possible way to get a particle to follow a path outside its geodesic without exerting any sort of external force on it (including the 4 fundamental forces)?
|
In the pV diagram an isochoric curve is, of course, a vertical line whereas in the T-s diagram it has the form:
$$T(s)=T_0 \space e^{\frac{s-s_0}{c_V}}\tag1$$
so it is an exponential function (steeper than an isobare). This equation holds for an ideal gas, in a Ts diagram (no phase changes considered).
Since $h=u+pv$ ... |
If let say i have an EMW given by- (Note the difference between $k$ and K)
B(x,y,z)=$B_0sin[(x+y)\frac{K}{√2}+wt]\hat k$
i got confused in 2 different outcomes when i wanted to find out the direction of propogation of the wave.
Case 1
-Since direction of propogation always points towards the wave vector K its should be... |
Related to Distinguish between instantaneous speed and instantaneous velocity
I understand that the average velocity is given by the displacement divided by the change in time, and it is a vector quantity. Similarly, the average speed is given by the distance traveled divided by the change in time, and it is a scalar q... |
Light of two wavelengths, $λ_1$ and $λ_2$, is incident on a metal surface of work function $ϕ$. If there is an equal number of photons of each wavelength incident per second, what is the maximum proportion of the incident energy that could be transformed into the kinetic energy of the photoelectrons? I'm deliberately r... |
The Klein-Gordon equation
$$\left(\frac{\partial ^2}{\partial t^2} - |\nabla|^2 + m^2\right)\phi = 0\tag{1}$$
should describe non interacting particles without spin. So what particles in the standard model are described by it? And what about famous non-elementary particles? For example: is the Higgs boson described by ... |
The Schrodinger equation (SE) admits dark solitons as particular solutions. The SE and the The Korteweg-de Vries (KdV) equations can be used to model them.
Questions:
What are the applications of these equations?
If I work on solving the KdV equations, to what extend the knowledge I obtain is relevant to get insight a... |
We know that work done by conservative forces is path-independent and so is work done by electrostatic force but how can we prove it using Coulomb's law?
I know such a question has already been asked but I want an explanation as a high schooler a I am still not aware of stokes law and surface integrals.
|
A principle of QFT that is frequently invoked, repeated, and potentially subject to rigorous verification is that the theory in question must exhibit Lorentz covariance and be invariant under the Poincaré group. Nevertheless, upon closer inspection of specific facts, it becomes less evident that particular formalisms a... |
While reading on the Plateau Rayleigh instability of fluid jets, the following thought came to my mind: suppose we have a fluid jet with zero cohesion forces (and therefore zero surface tension) falling under the influence of gravity. My understanding is that since fluid parcels with different vertical coordinate move ... |
I read John Hogan’s The End of Science book, and while we are making discoveries and improvements in science all the time; we aren’t discovering things on the fundamental level like fire, gravity, electromagnetism, atoms etc anymore. Why is this so? I don’t believe that the universe is limited in its complexity but all... |
Let's consider a system of free electrons moving in a one dimensional lattice with dispersion $\varepsilon(k) = -2t\cos{ka}$, ($a$ is the lattice spacing and $t$ the hopping amplitude). Let's now superimpose a uniform force $F$ to the system, so that the Hamiltonian reads
$$
H = -\frac{\hbar^2}{2m}\nabla^2 + V(x) - Fx,... |
There have been lots of questions on this site about the use of infinity in different ways in physics.
Infinitely big - Physics near null infinity
Infinitesimals - Using differentials in physics
Renormalization - A simple, easily understandable example of infinities making trouble in physics?
This is all fine. But... |
In quantum mechanics, in the context of studying unidimensional potentials, we studied this case of potential
And to analise the possible looks of the wave function $\phi$, we divided in 3 regions, let's consider only the region $V_0<E<V_+$ with such energy. Now we can take an example of an energy $E_0$ and try to fin... |
So imagine a black hole the size of 100 km, and then there is a giant rod that is 50 km and pretends that the rod doesn't get broken due to tidal forces, and also assumes that the rod has a mini-robot on the other end of it. So once the robot end of the rod enters the event horizon, it can never escape. However, the ro... |
I am curious about physics and astrophysics in particular, although I have no academic basis.
Usually, I find it easy to understand the concepts and explanations, but I have particular difficulty in understanding the premises of why the CMB observation leads to the horizon problem.
In general, the explanations I see st... |
Supergreen is a color with an RGB value of (0, 255, 0), making it fully green, with no other colors. Now, according to my research, it is impossible for the human eye to detect this color. Doing research, I found out that it is impossible for the photoreceptors in the eye to detect only one color; they have to detect m... |
This is somewhat between TeX stackexchange and physics stackexchange. With Latex, it became much more easier to write equations, and with tikz, pictures can be drawn.
However, with the introduction of the generalized symmetry, the equations of the topological defect lines were often equations of diagrams, instead of eq... |
If there's wave packet $\psi(x,t)$ in zero potential and $\psi(x,0)$ is given, what happens when $t<0$? I know that for $t>0$ the wave as a group moves at group velocity $\frac{d\omega}{dk}|_{k_0}$ where we assume that $k$ is strongly peaked around $k_0$. The width of the wave becomes wider when $t$ is large. But what ... |
Consider this question,
Two masses A and B are connected by a massless string. A rest in equilibrium on a rough horizontal table and limiting friction is acting on it. B hang vertically at a distance R below the edge of the table. B is projected horizontally with velocity V, what is initial radius of curvature of B? c... |
In a constant area duct inviscid flow where heat is added, there are some well established results in the literature known as Rayleigh flow (https://en.wikipedia.org/wiki/Rayleigh_flow). In this scenario the initial state (state 1) can be know (ie Mach number, Static Temperature and thus Total Temperature as well) and... |
I read in the book Modern particle physics(page 114-119) from Mark Thomson that for a time-ordered diagram, the energy at each vertex is not conserved, but the momentum is. Furthermore, the energy-momentum relation applies to the intermediate particle X, which is on mass-shell.
On the other hand if we sum over all the ... |
Electrons do not follow fixed orbits around an atom's nucleus but exist within "clouds of probability" (orbitals), where there is a high chance of finding them. As one extends the search for electrons farther from the nucleus, the probability diminishes, though it never reaches zero. Consequently, there is a non-zero p... |
Thought experiment:
Mars — Spaceship — Earth
Spaceship is steadily positioned perfectly between Mars and Earth, same distance. On the spaceship is a photon entangler that laser-projects each entangled pair in opposite directions to Earth and Mars.
On the surface of Earth and Mars is a phosphor screen. A scientist on Ma... |
Am I right to think that black holes are stars that are so dense and heavy that radiation and matter cannot leave from it's surface?
|
As part of a project, I'm calculating deflection of a cantilever beam, something like the image below where the beam bends due to a load.
To do so requires its moment of inertia, and I'm thinking of using the beam's rectangular cross section. However, all the sources I've looked at only describe moment of inertia abou... |
Suppose that two spin-1/2 are in the state:
$$ |\psi \rangle = \frac{1}{\sqrt{2}} |+\rangle|+\rangle + a|+\rangle|x+\rangle + b|-\rangle|-\rangle $$
and we want to find values for a & b such that the state is entangled and separable.
So I started with rewriting state $|x+\rangle$ in z-representation:
$$ |\psi \rangle =... |
When reading about various quantum experiments the apparatus often includes things like "semitransparent mirrors", "regular mirrors", "polarization filters" and others. Usually a photon or an electron is emitted, bounces around in the device, and is measured at the other end.
And in all the experiments, all these in-be... |
From my current current understanding of evaporation and boiling - when we put a beaker filled with water under the sun we observe evaporation. Evaporation is a surface phenomenon. Surface molecules are only held by cohesive forces from one side thus the potential energy binding them from escaping is lesser than that w... |
Why can't the two charges in an electric dipole exist independently in an uniform electric field? What I mean is, why should they behave as if they are connected together by a rod between them? What is the physical significance of electric dipole moment?
|
Why does an individual fermionic electron scatter off lattice defects easily while the Cooper pairs are insusceptible? I know they condensate to a same macroscopic quantum state, but still, why can such a condensate flow effortlessly? What happens when one pair scatter off the lattice? Is there any close analogy?
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What is the relationship between the energy absorbed and emitted by an atom with the model of Lorentz?
In the Lorentz model of an atom, we have that, using the effective cross-sections we might get somewhere since it is the relationship between the power emitted and the Poynting vector: $$\sigma_e=\frac{\langle P_e\ra... |
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