Wigner Definition and 40 Threads

Brilliant paper https://arxiv.org/abs/2202.04203v2 recently published in Nature Communications (open access) https://www.nature.com/articles/s41467-024-47170-2 resolves and demystifies the Frauchiger-Renner paradox associated with the Wigner friend problem. The resolution of the paradox, in...

Consider a simple quantum eraser setup using polarizers: An incident beam polarized at 45º is sent towards a double slit. After slit A there is a horizontal polarizer and after slit B there is a vertical polarizer. At the back screen, if we run this experiment, we will see a particle pattern and...

Hi Pfs, I wrote in another threas that when a source emits maximally entangled pairs of photons with nul global momentum and null global angular momentum, there is no local properies for the photons shared by Alice and Bob. i said that the the source only emits correlations. it has no sense to...

Summary: Suppose that observer ##\mathcal{O}## sees a ##W## boson (spin-1 and ##m > 0##) with momentum ##\boldsymbol{p}## in the ##y##-direction and spin ##z##-component ##\sigma##. A second observer ##\mathcal{O'}## moves relative to the first with velocity ##\boldsymbol{v}## in the...

Suppose i measure the phase and amplitude of some radiation, this might be a coherent state of an entangled state, how would i construct the Wigner function from these measurements?

Motivation: Due to the spectral theorem a complex square matrix ##H\in \mathbb{C}^{n\times n}## is diagonalizable by a unitary matrix iff ##H## is normal (##H^\dagger H=HH^\dagger##). If H is Hermitian (##H^\dagger=H##) it follows that it is also normal and can hence be diagonalized by a...

A human asking Wigner and his friend about the states they assign has certain and complete information about both Wigner's pure state of the lab and his friend's pure state of the device. How do these certainties show up (as certainties) in the pure state of ''lab + Wigner + his friend''...

Hi. I'm trying to prove that [\Omega] = \int dq \int dp \, \rho_{w}(q,p)\,\Omega_{w}(q,p) where \rho_{w}(q,p) = \frac{1}{2\pi\hbar} \int dy \, \langle q-\frac{y}{2}|\rho|q+\frac{y}{2}\rangle\,\exp(i\frac{py}{\hbar}) is the Wigner function, being \rho a density matrix. On the other hand...

I'm trying to calculate a Wigner Function of an entangled state, and I'm not quite sure how to proceed. I have created this state by sending in vacuum and a squeezed state into a 50/50 BS, where the output state has a density operator: $$\rho_{34}=S_{3}S_{4}S_{34}|00\rangle_{34}\langle...

Homework Statement I am trying to calculate the wigner function for the even coherent state or cat state gives by, | \psi \rangle = N_+ \left( |\alpha \rangle + | -\alpha \rangle \right), where ##|\alpha \rangle ## is a coherent state and ## |N_+|^2 = \dfrac{1}{ 2 + 2e^{-2|\alpha|^2}}##. I am...

Homework Statement I've got a given Breit Wigner curve of the number of decays at given energies. I've been told by several sources that the width (FWHM) of the curve gives the rate of the reaction. I can't see however how an energy here actually translates into a rate. Homework Equations I...

Homework Statement The Clebsh Gordon coefficient is < 11;00 |11> = < l_1,m_1;l_2m_2 | kq > Homework Equations My professor determined the CG to be 1 The Attempt at a Solution How do we look up these numbers in the table? What is the direct product basis? 1x1? What is JM and what is m_1 and...

Homework Statement Suppose that observer \cal O sees a W-boson (spin one and mass m \neq 0) with momentum \textbf{p} in the y-direction and spin z-component \sigma. A second observer \cal O' moves relative to the first with velocity \textbf{v} in the z-direction. How does \cal O' describe the...

I understand that Wigner function is a quasi-probability distibution as it can take negative values, but in quantum optics I see that the Q function is mentioned as often. So what is the difference between the Q function and the Wigner Function?

I found two definitions of wigner function on space time. the first uses a Fourier transform of ##\rho (q+ y/2,q-y/2)## the second uses the Weyl transformation and parity operator ## exp (i \pi \theta N)## where N is the occupation number operator. Could you give me a link which shows the...

I have the quantum master equation: $$\frac{\partial\rho}{\partial t}=\frac{1}{i \hbar}[H_0,\rho]+\frac{\gamma}{i \hbar}[q,\{p,\rho\}]-\frac{D}{\hbar^2}[q,[q,\rho]]$$ And have to prove that the coordinates representation is like in the book of the link. I can't undertand how to obtain the...

What is the physical interpretation of the Weisskopf-Wigner approximation, when it is applied in the neutral kaon system? I would say that the approximation means that a decay state has a small probability to suffer a transition (or be "transformed") into another decay state through weak...

I am looking for a way to connect the Condon-Shortley-Wigner to the Edmonds phase convention. Specifically I am writing a program to compute Wigner-d matrix coefficients From tabulated values (e.g. even Wikipedia) d^1/2_{1/2,-1/2}=(-1)^{-1/2-1/2}d^1/2_{-1/2,1/2}=-sin(theta/2) So...

I am writing a program for computing the Wigner d-matrices and ran into an apparent contradiction: Specifically computing d^1/2_{-1/2,1/2} According to Edmonds, p.59, 4.1.27 this is given by (-1)**[1/2-(-1/2)][1!/(1! 0!)]**{1/2} sin(b/2)=-sin(b/2) Now for d^{1/2}_{1/2,-1/2} From...

Hi, Is there any good books which explain/calculate Wigner rotation, tensor operator, two-particle helicity state and related stuff in detail? Thanks.

Hello everyone, I'm reading a bit about the Wigner D matrix, defined by \mathscr{D}\left(\hat{n},\phi \right) = \exp[-\frac{i \phi}{\hbar}\vec{J}\cdot \hat{n}]. Now I'm wondering : is the map \pi : \text{SO(3)} \to \text{GL}\left( \mathscr{H} \right) given by R\left(\hat{n},\phi...

The Wigner function, W(x,p)\equiv\frac{1}{\pi\hbar}\int_{-\infty}^{\infty} \psi^*(x+y)\psi(x-y)e^{2ipy/\hbar}\, dy\; , of the quantum harmonic oscillator eigenstates is given by, W(x,p) = \frac{1}{\pi\hbar}\exp(-2\epsilon)(-1)^nL_n(4\epsilon)\; , where \epsilon =...

For Wigner transforming the function of operators x and p : (xp+px)/2 we need to evaluate something like: g(x,p) = ∫dy <x - y/2 | (xp+px)/2 | x+y/2> e(ipy/h) where h is h/2π. Now I am not sure how to evaluate <x - y/2 | (xp+px)/2 | x+y/2> . I mean what I did was think of |x+y/2> as a...

This is about a specific property of the Wigner distribution in phase space. My professor mentioned the other day that the Wigner distribution treats all functions of momentum and space on the same footing as momentum itself or at least that's what I recall.He mentioned a specific problem where...

Hey guys! Breit Wigner Formula describes the cross section for interactions that proceed dominantly via a intermediate particle (O*) A+B → O* → C + D: σ = \frac{2\Pi}{k^{2}}\frac{Γ_{i}Γ_{f}}{(E-E_{o})^{2} + (Γ/2)^{2}} A short question: Does the formula apply to situations when the...

Hey! I'm hoping someone can help me understand a basic problem I'm having with understanding the BW formula: \sigma(i,j) = \frac{\pi}{k^2} \frac{\Gamma_i \Gamma_j}{(E - E_0)^2 + \Gamma} In this, E_0 is the "characteristic rest mass energy of the resonance." I thought this meant the...

Homework Statement I'm not sure if this is the appropriate board, but quantum mechanics people surely know about spherical harmonics. I need to implement the Wigner D matrix to do spherical harmonic rotations. I am looking at...

Hello, from Weinberg's Quantum Field Theory book I am confused about the equation (2.5.5). I'll describe the problem briefly here, but in any case, here's that page from Weinberg's book (page 64)...

Hi all! Homework Statement I have to show: \sqrt{(j \pm m ) (j \mp m+1} <j_1 j_2 m_1 m_2 | j_1 j_2 j m\mp 1 > = \sqrt{(j_1 \mp m_1 ) (j_1 \pm m_1+1} <j_1 j_2 m_1 \pm1, m_2 | j_1 j_2 j m > +\sqrt{(j_2 \mp m_2 ) (j_2 \pm m_2+1} <j_1 j_2 m_1 , m_2 \pm1 | j_1 j_2 j m > Homework...

Hello guys, I'm reading the attached article, and I found there the Wigner Matrix, the first equation in the second page... is that the Wigner D-Matrix? I really got lost in that. It doesn't look like the Wigner D-Matrix I see everywhere, and it's not the so-called random matrix... anyone...

Hi! Does anyone know how Wigner D-matrices transform under parity? Is it something like D^j_{m m'} (\pi - \theta, \phi + \pi) = (-1)^{j +m-m'} D^j_{m m'}(\theta, \phi)?

How can i develop a sketch of the lattice and reciprocal lattice from vector form a=i+4j b=3i i know how to draw the wigner site cell, but I am having problems developing a sketch from vectors. what is the method for working it out..please help

I originally posted this in the Science Book and discussion forum but received no help. Am posting it here, hoping that I will. I was looking for material that would go over the Wigner Eckart theorem and mathematics of Angular Momentum in more rigor than the traditional texts do (in specific...

i think jordan wigner transform, when applied to open boundary system, can simplify a spin 1/2 system to a free fermion system but there is a difficulty in the case of periodic boundary condition in this case, we have to deal with terms like S_N^+S_1^-=(-)^{\sum_{k=1}^{N-1}n_k}...

Homework Statement I have a question related to representation of rotation operator R in the basis spanned by the eigenvectors of J2 and Jz. I am studying from Quantum Mechanics by Zettili. The development of Wigner D-matrix and its elements Dj (Wigner functions) is clear. But the book goes on...

I have a few questions, first of all I'm trying to figure out how to find the volume of a 3 dimmensional wigner sietz cell. I have the 8th edition intro to solid state physics book by charles kitle and there is no where in the book that shows me how to find the volume of wigner seitz cell...

i have read about wigner rotation but i think i can't understand it well , i want to know the physical meaning of it .

Homework Statement The eletric dipole of the atom D = qR is a vector op, ie transforms according to j = 1 rep of SU(2). Use wigner eckart theorem show <1, 0, 0|D|1, 0, 0> = 0 (<n',l',m'|D|n, l, m> = 0 Homework Equations...

In quantum optics and bose-einstein condensates, this is a well known technique however, i still cannot grasp its essense. in bec, what is its advantage over the gross-pitaevskii equation?

Hi, I'm a bit confused with the Wigner effect concept. This effect is normally associated to damages in moderator material typically graphite. But metallic cladding of the fuel element is also exposed to fast neutron, but Wigner effect is seldom being used as a term to explain the damages in...