Questions tagged [quantum-statistics]

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Confusion about canonical and grand canonical ensembles regarding Fermi-Dirac statistics

All derivations I have seen for the Fermi-Dirac statistics presuppose the grand canonical ensemble. However, all applications of it, e.g. ideal quantum gases, electrons in a metal and semiconductors, ...
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Density of states for non-interacting Bosons

I am tasked with calculating the density of states in terms of the angular frequency given the dispersion relation. But I couldn't help but think: why can't we calculate the density of states by ...
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What's happening in this approximation for the equation of state of an ideal gas of bosons

The way we arrived at the equation of state for an ideal fermion gas was to approximate the right handside of $$\beta PV=\sum_{\vec{p}}\log{(1+fe^{-\beta\frac{p^2}{2m}})}$$ as $$\frac{V}{h^3}\int \log{...
Lourenco Entrudo's user avatar
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Understanding density operator of the bath state for quantisation volume larger than de-broglie wavelength

I have been reading the paper "Collisional decoherence reexamined" by K. Hornberger and J.E. Sipe. In the sub-section II-B titled "Convex decompositions of the bath density operator&...
Lost's user avatar
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Misunderstanding the notion of occupation numbers

In the context of calculating the partition function of a quantum ideal gas of $N$ indistinguishable particles, we introduced the notion of ocupation numbers $n_{p,s_z}$as the number of particles in ...
Lourenco Entrudo's user avatar
6 votes
2 answers
278 views

What is the number of quantum states compatible with isolated ideal gas macrostate $N,V,U$ and molecular mass $m$?

What is the degeneracy of an energy level $U$ of an ideal gas of $N$ particles with molecular mass $m$ in a volume $V$? This sounds like a standard textbook problem about the Boltzmann entropy of ...
Ján Lalinský's user avatar
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Does the relation $U=\sum_k \bar{n_k} \varepsilon_k$ hold in the classical limit?

Let's rewrite entropy in terms of $\bar{n}_k$ (average number of particles in the energy state k) supposing $U=\sum_k \bar{n}_k \varepsilon_k$ (where $\varepsilon_k$ is the energy of the k-th state): $...
Ilya Iakoub's user avatar
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Creating anti-symmetrized boson states under general pair particle permutations

Consider a two-boson system, each with creation and annihilation operators satisfying $[a_{x,s},a^{\dagger}_{y,p}]=\delta_{x,y}\delta_{s,p}$, where $x,y$ are position coordinates of the particle and $...
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Chandrasekhar limit with relativistic electron gas

The problem In David Tong's lecture notes on statistical physics (pages 100-102), there's a chapter on Chandrasekhar limit in relativistic case, where he states that energy degeneracy is $$g(E)=\frac{...
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Questioning a calculation in Kapusta / Infinite entropy of a Fermi gas?

I am going through Kapusta's calculation of the free energy of a Fermi gas, and I find one of his steps dubious (and if I'm right, it would mean the free energy of a Fermi gas is either infinite or ...
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Does quantum decoherence happened in the process towards thermal equilibrium?

In Kardar's "statistical physics of particles" and some other books about statistical physics I've read, when dealing with quantum statistics, they just give the conclusion that the density ...
Dzhou's user avatar
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Why are $U$ and $V$ (and not $N$) the only extensive parameters for blackbody radiation?

In Chapter 3.6 of Callen, he remarks that the particle number $N$ does not appear in the thermodynamic description of blackbody radiation. Why is this? That is, in most simple systems of one component,...
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What is the quantum effect that makes the quantum annealing expectation maximization algorithm robust to local maxima in the likelihood function?

The Expectation Maximization (EM) algorithm is a classic method of maximum likelihood estimation for problems involving missing (latent) variables. This method is particularly useful in estimating ...
Aaron Hendrickson's user avatar
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Why constant voltage applied to pn-junction produces constant current throughout the junction?

Is this assumption just something that turns out to be experimentally valid or there is at least some mathematical model like Kronig-Penney + some statistical mechanics that is able to give a good ...
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Density of states of Fermi gas derivation

I'm going over this book. While deriving the gensity of states for a gas of fermions the author makes the following argument: Remember that we are treating the gas as having a set of states that can ...
Sgg8's user avatar
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Stationary ensemble and intuitive understanding as to how a statistical ensemble is represented via probability density in phase space

In Wikipedia, in the article about the statistical ensemble, it is said that in classical mechanics (thermodynamics and statistical mechanics) the ensemble is represented via the probability density ...
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Eigenvalue of transfer matrix in Shankar (3.3.4), p.34

In the book of Quantum Field Theory and Condensed Matter written by Shankar, (3.3.4), p.34, there defined a transfer matrix $$T=\left( \begin{array}{cc} 1 & e^{-2K} \\ e^{-2K} & 1 \\ \end{...
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Distribution result of flipping coin with same initial conditions repeteadly

Still related with that question Flipping a coin with same initial conditions. While it was asking about flipping coin with same initial conditions and the chosen answer said it's impossible to toss ...
Muhammad Ikhwan Perwira's user avatar
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Absorption spectrum of open quantum systems

I'm trying to understand the properties of continuous absoption spectrum of molecules in a solution using an oversimplified quantum mechanical argument. First, let us model our isolated molecule in ...
stochastic's user avatar
2 votes
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Quantum Harmonic Oscillator density matrix in coherent states base [closed]

I was trying to calculate matrix elements of the density operator for a 1D QHO (with Hamiltonian $\mathcal H = \hbar\omega a^\dagger a $) in the base of coherent states $\{\vert\alpha\rangle\}$ and ...
Hans Gerhard's user avatar
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What is meant exactly by "eigenstate ensemble average"?

I am currently reading about Eigenstate Thermalization Hypothesis (ETH) and Berry's conjecture. In the paper by Srednicki on chaos and quantum thermalization, in Eq.(3.8) he calculates the average of ...
abhijit975's user avatar
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2 answers
228 views

Time reversal symmery and spectrum statistics of generic Hamiltonians

From Random-Matrix Theory, Hamiltonians are classified in three different ensembles depending on the spectrum statistics (Gaussian Orthogonal (GOE) , Gaussian Unitary (GUE), Gaussian Simplectic (GSE))....
Zarathustra's user avatar
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1 answer
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How does thermal wavelength work exactly?

In many sources it is stated that the thermal wavelenth indicates the rough size of the atom. It is then stated that this wavelenght is the de-Broglie wavelength of a particle with a momentum with the ...
Joel Järnefelt's user avatar
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Thermodynamic potential and partition function

I am a bit confused by the relation between thermodynamic potential and partition functions. From my understanding, we can generate all thermodynamical quantities by taking partial derivatives to the ...
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Different Definitions for "Gibbs' Entropy"

This question suggests that for the microcanonical ensemble, additional to the "usual" definition of entropy \begin{align} \omega(E)=Tr \delta(E-H) \\ S_B=\ln \omega(E) \end{align} (Called ...
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Is the total energy of a canonical ensemble system of $N$ particles, with single-particle energy levels given by $\epsilon_i$ fixed?

Is the total energy of a canonical ensemble system of $N$ particles, with single-particle energy levels given by $\epsilon_i$ fixed ? We know the total energy of the system is given by : $$E=\sum_{i} ...
Nakshatra Gangopadhay's user avatar
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Interpretation of probability in Statistical Mechanics

In statistical mechanics, in particular the canonical ensemble, the probability of the system to have a particular state is given by : $$P_i=\frac{e^{-\beta E}}{Z}$$ Here $Z$ is the partition function ...
RayPalmer's user avatar
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Indistinguishability and different pure state decompositions of mixed states in non-simplex convex set of states in Quantum Statistics

In statistical physics (mechanics), the transition from Maxwell-Boltzmann statistics to Bose-Einstein and Fermi-Dirac statistics was motivated by classically inexplicable phenomena such as Bose-...
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If a truncated power law distribution still has no characteristic length scale?

I do know that a power law distribution can extend from 0 to $+\infty$, so due to the shape of the distribution, there is no way to define an average value (this might be a characteristic length scale ...
Tingchang Yin's user avatar
-1 votes
1 answer
281 views

Exact eigenfunctions of two interacting identical particles [closed]

While I was reading about quantum states of $N$ interacting identical particles, I realized that I don't understand some fundamental things. So In order to clear my confusion, I decided to consider a ...
Hans's user avatar
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2 answers
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Particle statistics and interference pattern

Does the particle statistics have some observational effect on interference (for ex. double slit experiment)? My doubt arises because of following reasoning: One particle at a time (Tonomura): ...
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Two point measurement statistics in Quantum systems

I am reading a paper related to fluctuations in Quantum thermodynamics. I am unable to understand the math behind equation no. 10 where the probability density function for work distribution is ...
RISHAV SAGAR's user avatar
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1 answer
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Can two or more bosons concretely exist at the same exact point in space at the same time?

Is it just the probability of finding the 2 particles in the same volume is the same or is it that they can really exist concretely as each other in the same point in time. Also related is, can two ...
tariq nazeem's user avatar
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1 answer
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Nr. of microstates and macrostates for a system

Let's say we have a system S (a quantum gas,either a boson or a fermion-gas), made up by many subsystems, which we will index with $i$. One subsystem is characterized by : $\bar {\epsilon_i}$ it's ...
imbAF's user avatar
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2 votes
1 answer
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Ergodicity in quantum statistical mechanics

Is there an ergodicity assumption in quantum statistical mechanics ? The classical statistical mechanics derives its main results from the assumption that all the states with the same energy (and ...
Roger V.'s user avatar
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Fermi-Dirac vs. Maxwell-Boltzmann distribution in the early universe plasma

From my studies, I remember that the quantum effects relative to the bosonic or fermonic nature of the particles play a role only in the conditions of degenerate gas: when the plasma is very dense and ...
Cristina Benso's user avatar
2 votes
1 answer
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Confusion regarding the average occupation number for a Boson/Fermion

Regarding the average occupation number for a Bose/Fermi gas we have: $$\bar n_\epsilon=\frac 1 {e^{\beta(\epsilon_p - \mu)} \pm 1}$$. Now the problem I am having has to do with the nomenclature of ...
imbAF's user avatar
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3 votes
2 answers
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Braiding anyons in one dimension

In the Rev. Mod. Phys. 80, 1083 (2008) Non-Abelian Anyons and Topological Quantum Computation, they make an aside in Section II.1.a that as an aside, we mention that in 1 + 1D, quantum statistics is ...
Andrew Hardy's user avatar
1 vote
1 answer
108 views

Derivation of $Z = \operatorname{Tr}e^{-\beta H + \mu N}$ [closed]

I've never studied quantum statistical mechanics myself, but I've read that the partition function of a quantum system in the canonical ensemble is given by: $$Z = \operatorname{Tr}e^{-\beta H}$$ ...
MathMath's user avatar
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How does particle-particle interactions affect superfluids?

Ive read that London approach of superfluidity was wrong because he took them as non-interacting bose gas molecules and got incorrect temperature dependence for density, but also one can take ...
SHIN101's user avatar
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Energy changed by displacement of lattice

In the famous textbook Introduction to Many-Body Physics by Piers Coleman,In Chap 8.7, Interacting electrons and phonons, on page 270, the author says Let $\vec{\Phi}(x)$ be dispacement of the ...
xiang sun's user avatar
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A question on probability and expectation concepts

Let A be an observable event. If the expectation of A is zero, does it imply that the probability of A is zero?
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How can two bosons having mass be in the same place at the same time?

I'm fairly new to this topic, so please excuse any amateurism. I'm confused about how a boson (i.e a particle that does not obey Pauli's exclusion principle) can have mass. For example, W and Z bosons ...
Lily Morgan's user avatar
5 votes
2 answers
491 views

Problems met in Matsubara frequency sum

I would like to calculate $\sum\limits_{\omega_{n},\vec{k}}(\ln(-i\omega_{n}+\xi_{\vec{k}})+\ln(-i\omega_{n}-\xi_{\vec{k}}))$, where $\omega_{n}=\frac{(2n+1)\pi}{\beta}$ and $n=0,\pm1,\pm2,\dots$ ...
xiang sun's user avatar
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Effect of Superposition Principle on Statistics

In statistical mechanics, a system is supposedly at some point in phase space, but we don't know which. For this reason, we describe it by some macroscopic variables, and any point in phase space that ...
Tom's user avatar
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Given a thermodynamic ensemble and given a macrostate of this ensemble, is there an associated probability distribution on the microstates?

When I learned statistical physics, and ensembles and such things, the term "macrostate" was introduced as some vague thing that "described the state of the system, and is defined ...
Quantumwhisp's user avatar
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Why does the electronic contribution to the specific heat of a conductor not depend on the heat supplied to it?

The usual explanation given for why electrons do not contribute much to the specific heat of a material (for the purposes of the question consider a conductor) is that the fermi energy of conductors ...
1729's user avatar
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3 answers
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Identicalness and Indistinguishability in quantum mechanics

I've been reading chapter 10.3 'Identical Particles' in Shankar's book on quantum mechanics and also looked through some of other books on this subject and one rather subtle objection started ...
류민석's user avatar
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Does the Fermi distribution also gives the probability of an energy level being full of electrons?

We started to learn about Fermi level and Fermi distribution function and I'm little confused . From what I have understood , the Fermi distribution function gives the probability of a single state in ...
firas's user avatar
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Random phases postulate in quantum statistical mechanics

Quantum statistical mechanics has two postulates, namely i) Assumption of equal a priori equilibrium probabilities ii)Independent random phases The first postulate is in accordance with classical ...
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