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### Anyons as particles?

I'm trying to understand the basics of anyons physics. I understand there is neither a Fock space they live in (because Fock is just the space of (anti-)symmetrized tensor product state, see e.g. ...
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### Is there a Majorana-like representation for singlet states?

I mean the Majorana representation of symmetric states, i.e., states of $n$ qubits invariant under a permutation of the qudits. See, for example, D. Markham, "Entanglement and symmetry in permutation ...
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### Why is (von Neumann) entropy maximized for an ensemble in thermal equilibrium?

Consider a quantum system in thermal equilibrium with a heat bath. In determining the density operator of the system, the usual procedure is to maximize the von Neumann entropy subject to the ...
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### What causes Paulis Exclusion Principle?

Currently I'm taking an astrophysics class and has now come across electron degeneracy. As far as I understand, the reason why white dwarfs and such, does not collapse, is due to this, meaning that ...
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### What is parafermion in condensed matter physics?

Recently, parafermion becomes hot in condensed matter physics (1:Nature Communications, 4, 1348 (2013),[2]:Phys. Rev. X, 2, 041002 (2012), [3]:Phys. Rev. B, 86, 195126 (2012),[4]:Phys. Rev. B,87, ...
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### Irrelevance of parastatistics for space dimension > 2

Consider a system of $n$ undistinguishable particles moving in $d$-dimensional Euclidean space $E^d$. The configuration space is $M=((E^d)^n \setminus \Delta)/S_n$ where $\Delta$ is the diagonal (...
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### Positivity in the Pauli/Bloch/coherence vector representation

Suppose $\rho$ is an $n$-qubit state and $\vec{x}$ is a vector of coefficients in the Pauli representation (also called the Bloch or coherence vector). That is $$x_k = {\rm Tr}(\rho \sigma_k),$$ ...
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### Quantum entropy in term of density matrix

Why in von Neumann expression of quantum entropy we have trace of density matrix expression? Why don't off diagonal term play a role?
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### Bose Einstein condensation and macroscopic occupation

If have been thought, that Bose Einstein condensation occurs of the ground-state is occupied macroscopically, so $n_0\in \mathcal{O}(N)$ when performing the thermodynamic limit. So naively, this ...
I am trying to derive the Fermi-Dirac statistics using density matrix formalism. I know that $$<A>= Tr \rho A.$$ So I started from <n(\epsilon_i)>= Tr \rho n(\epsilon_i)=\frac {1}{Z} ... 2answers 183 views ### How is the degenerate electron gas state “degenerate”? What is "degenerate" in the degenerate electron gas state? Why is it called degenerate? 1answer 86 views ### Mutually unbiased bases This question can be formulated in two ways. Let there be two d-dimensional orthonormal bases B_{1} and B_{2}. I refer to the elements of B_{1} by \lvert\nu_{i}\rangle and to the elements of ... 1answer 55 views ### Quantum versus classical computation of the density of states If I consider for instance N non interacting particles in a box, I can compute the energy spectrum quantum mechanically, and thus the number of (quantum) microstates corresponding to a total energy ... 0answers 39 views ### If 2 fermionic atoms form a molecule, will the molecule always behave as a boson? 2 fermionic atoms give a bosonic molecule. 2 bosonic atoms form a bosonic molecule. Is there a energy scale where these two molecules will behave differently? If yes, will it depend on the ... 2answers 103 views ### Why does number of photons fluctuate? When counting photons (with, e.g., a CCD), there is the so-called ''photon noise'' (important at low photon numbers). What is the explanation in the framework of QED, QFT? Is it the Heisenberg ... 3answers 246 views ### Definition of quantum microcanonical ensemble in Landau & Lifshitz I'm reading the first chapters of Landau&Lifshitz 's [Statistical Physics][1] and I don't understand the definition of the quantum microcanonical ensemble. The microcanonical distribution for a ... 1answer 86 views ### Statistical count I am reading the book"Heat and Thermodynamics" by Mark Waldo Zemansky and Richard Dittman. In the chapter "Statistical Mechanics" it says if I have N_{i} distinguishable particles in any of g_{i} ... 2answers 65 views ### Current Status of the Monte Carlo Sign Problem I've been reading about the Monte Carlo sign problem, and I am a little confused about its current status. Specifically, after reading this post When is the "minus sign problem" in quantum ... 2answers 349 views ### How to prove the Bose enhancement factor (1+f) and the Pauli blocking factor (1-f) in Boltzmann equation? For the collision integral in the Boltzmann equation for particles obeying different statistic, the factor is 1 for classical particles , 1-f for fermions, 1+f for Boson. While why it's exactly this ... 2answers 664 views ### How to deal with mean field method in antiferromagnetism? There are lots of ways to apply the mean field method to deal with the Ising model whose ground state is a ferromagnetic state. Hence, it is easy to find the order parameter named magnetization to ... 1answer 238 views ### Quantum ideal gas - Canonical ensemble - Occupation number summation notation (Huang) (Question at the end, in bold, marked with an b)) For the quantum ideal gas, the hamiltonian (operator) of the system is: \begin{align} \mathcal H=\sum_{i=1}^N H_i=\sum_{i=1}^N \frac{P_i^2}{2m} \... 1answer 106 views ### Statistical sum of physical quantities in a quantum system Let C = A + B (statistical sum, so \mathbb{E}[C] = \mathbb{E}[A] + \mathbb{E}[B]), and let p(A = a) = 1. Are the following true? \mathbb{E}[C^2] = a^2 + 2a\mathbb{E}[B] + \mathbb{E}[B^2] \... 1answer 377 views ### Energy density of a quantum mechanical ensemble How do we determine the energy density of a given system? I have seen that the density operator\rho~=~\frac{\exp(-\beta \hat{H})}{\text{tr}(\exp(-\beta \hat{H}))}.$$What does this mean exactly ... 0answers 44 views ### dependence of braiding matrix element on the fusion product of anyons In the case of Majorana fermions (MFs), one knows that if one braids MF a with MF b, then braiding matrix element R^{c}_{ab} depends on the state c which is the fusion outcome of a and b. ... 0answers 48 views ### Bose-Einstein-statistics out of fermionic many body system ok, let me try this again. How do I get to atoms obeying Bose Einstein statistics from considering the fermionic many body problem of a bunch of electrons, protons and neutrons forming these (bosonic)... 1answer 115 views ### Spin statistics I have a very intrinsic question about quantum field theory and even more general, why in 3+1-dimensional spacetime, we have only two statistics for particles to obey? Therefore why we have only two ... 1answer 492 views ### Partition function for classical particle and quantum particle are the same? Permutation for classical particle$$\Omega=\frac{N!}{\Pi n_i!}$$By using Lagrange method of undetermined multiplier, we get$$n_i=Ae^{\frac{-E}{kT}}$$Probability,$$p=\frac{n_i} {Z}$$where we ... 0answers 41 views ### Link Between the Density Operator and the Partition Function and Boltzmann Distribution in Quantum Statistical Mechanics I have a very limited knowledge of statistical mechanics, but I seem to running into some related concepts for my background readings for the research project this summer. For example, see the ... 0answers 68 views ### Some subtleties in quantizing a fermi field Consider the quantization conditions for a complex Fermi field \Psi=\Phi_1+i\Phi_2:$$\{\Psi(x),\Psi(y)\}=\{\Psi^\dagger(x)\Psi^\dagger(y)\}=0,~~~~ \{\Psi^\dagger(x),\Psi(y)\}=\delta(x-y)$$Compare ... 0answers 28 views ### Thermal wavelength and critical temperature for Bose-Einstein condensate I'm stuck with derivation of critical temperature and thermal wavelength for Bose-Einstein condensate - all sources describe equations very briefly. Suppose we have a system described by Bose-Einstein ... 0answers 27 views ### Magnetisation of a degenerate electron gas in a weak field? So I am looking at Landau's and Lifshitz's "Statistical Physics, Part I" chapter on degenerate fermi gases and specifically at chapter on Pauli's Mangetism or magnetism of degenerate electron gases, §... 0answers 51 views ### What fugacity actually is and how it's plays an important role on Bose gas? We know that the average occupation number cannot be negative for all systems and chemical potential must be negative in Ideal Bose Gas. This fact leads us to arrive a conclusion for fugacity which is ... 0answers 22 views ### What are the instances of usage of four color theorem in the theory of fractional statistics? How important is four-color theorem (Hypothesis) in theory of Fractional Statistics? 0answers 42 views ### The symmetry normalization factor of wave functions in quantum statitics Now I am studying statistical mechanics by R.K.Pathria & Paul D.Beale's Statistical Mechanics(3rd Edition). In page 134, the book claims that the wave function \psi of a system composed of N ... 0answers 74 views ### Exploiting Resonance to Make a Bound State with Gamma Rays (and other Very High Energy Particles) One obvious consequence of any finite potential is that a high enough energy wave-function will not form a bound state, either they are high enough energy they will generally just bypass the barrier ... 0answers 73 views ### grand-canonical ensemble I was wondering if the following reasoning is correct for example for electrons in the classical or qm grand-canonical ensemble? Is it always valid in the grandcanonical ensemble to calculate the ... 0answers 245 views ### Chemical potential related with quantum and classical limit in ideal gas For ideal gas we have chemical potential \mu = \tau \ln \left(\frac{n}{n_Q}\right)  where n = N/V number density and n_Q = \left(\frac{M\tau}{2\pi \hbar^2}\right)^{\frac{3}{2}}  Note we call ... 0answers 93 views ### Diamagnetism of a degenerate electron gas for weak fields In the book "Statistical Physics, Part I (3^{{\rm rd}} edition)" by Landau and Lifshitz, at \S59 when he treats the diamagnetic part of the magnetisation of a degenerate electron gas for weak ... 0answers 125 views ### Is there a systematic way to determine the relevant variables needed to describe a nonequilibrium system? In strong nonequilirium, the statistical operator describing the system depends on an infinite number of variables (BBGKY-hierarchy), contains information about all the previous states starting from ... 1answer 309 views ### Bose–Einstein statistics exercise I've a basic Bose–Einstein statistics exercise. I've tried to solve it in two ways, but each way gives a different result. We have n identical bosons without interactions at temperature T. There ... 3answers 2k views ### Planck's distribution and Bose-Einstein distribution? If the application of the Bose-Einstein distribution is in blackbody radiation, then what is Planck's distribution? Are they same? How did Planck know that he should use a Bose-Einstein distribution ... 1answer 42 views ### Fermi distribution and ideal gas I was wondering about the following: If we have ideal gas particles, then E \ge 0, so one would expect that the state E=0 is occupied with probability one for low temperatures, but this is not ... 1answer 86 views ### What is the density operator for an isothermal–isobaric ensemble (T,p,N)? In the microcanonical ensemble (E,V,N), the density operator is$$\hat{\rho}=\frac{\delta(\hat{H}-E\,\hat{I})}{Tr(\delta(\hat{H}-E\,\hat{I}))} Where $\hat{H}$ is the Hamiltonian of the system and ...
I'm not sure if I'm asking this right. I'm reading ''Introduction to Quantum Mechanics'' by Griffiths and in the chapter 2 exercises he asks to prove that the separation constant, $E$, must be real. ...