Questions tagged [quantum-statistics]
The quantum-statistics tag has no usage guidance.
223
questions
0
votes
1
answer
80
views
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, ...
1
vote
0
answers
47
views
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 ...
1
vote
1
answer
68
views
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 $$\frac{V}{h^3}\int \log{...
0
votes
0
answers
19
views
Understanding density operator of the bath state for quantisation volume larger than de-broglie wavelength
I have been reading the paper "Collisional decoherence reexamined" by K. Hornberger and J.E. Sipe.
In the sub-section II-B titled "Convex decompositions of the bath density operator&...
2
votes
1
answer
79
views
Misunderstanding the notion of occupation numbers
In the context of calculating the partition function of a quantum ideal gas of $N$ indistinguishable particles, we introduced the notion of ocupation numbers $n_{p,s_z}$as the number of particles in ...
6
votes
2
answers
278
views
What is the number of quantum states compatible with isolated ideal gas macrostate $N,V,U$ and molecular mass $m$?
What is the degeneracy of an energy level $U$ of an ideal gas of $N$ particles with molecular mass $m$ in a volume $V$?
This sounds like a standard textbook problem about the Boltzmann entropy of ...
0
votes
0
answers
53
views
Does the relation $U=\sum_k \bar{n_k} \varepsilon_k$ hold in the classical limit?
Let's rewrite entropy in terms of $\bar{n}_k$ (average number of particles in the energy state k) supposing $U=\sum_k \bar{n}_k \varepsilon_k$ (where $\varepsilon_k$ is the energy of the k-th state):
$...
0
votes
0
answers
34
views
Creating anti-symmetrized boson states under general pair particle permutations
Consider a two-boson system, each with creation and annihilation operators satisfying $[a_{x,s},a^{\dagger}_{y,p}]=\delta_{x,y}\delta_{s,p}$, where $x,y$ are position coordinates of the particle and $...
0
votes
0
answers
39
views
Chandrasekhar limit with relativistic electron gas
The problem
In David Tong's lecture notes on statistical physics (pages 100-102), there's a chapter on Chandrasekhar limit in relativistic case, where he states that energy degeneracy is
$$g(E)=\frac{...
5
votes
0
answers
110
views
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 ...
0
votes
0
answers
35
views
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 ...
0
votes
2
answers
68
views
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,...
0
votes
0
answers
16
views
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 ...
1
vote
2
answers
58
views
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 ...
0
votes
1
answer
115
views
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 ...
0
votes
1
answer
190
views
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 ...
0
votes
1
answer
55
views
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{...
0
votes
3
answers
58
views
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 ...
1
vote
0
answers
54
views
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 ...
2
votes
0
answers
347
views
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 ...
1
vote
0
answers
82
views
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 ...
0
votes
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))....
2
votes
1
answer
272
views
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 ...
1
vote
2
answers
1k
views
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 ...
1
vote
0
answers
110
views
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 ...
0
votes
1
answer
417
views
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} ...
2
votes
0
answers
181
views
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 ...
3
votes
1
answer
109
views
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-...
0
votes
1
answer
45
views
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 ...
-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 ...
5
votes
2
answers
320
views
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): ...
1
vote
1
answer
158
views
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 ...
1
vote
1
answer
109
views
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 ...
0
votes
1
answer
301
views
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 ...
2
votes
1
answer
331
views
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 ...
1
vote
0
answers
287
views
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 ...
2
votes
1
answer
2k
views
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 ...
3
votes
2
answers
279
views
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 ...
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:
$$Z = \operatorname{Tr}e^{-\beta H}$$
...
1
vote
1
answer
83
views
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 ...
0
votes
1
answer
31
views
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 ...
0
votes
1
answer
39
views
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?
2
votes
3
answers
578
views
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 ...
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 $n=0,\pm1,\pm2,\dots$
...
1
vote
0
answers
78
views
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 ...
3
votes
1
answer
242
views
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 ...
1
vote
1
answer
510
views
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 ...
1
vote
3
answers
515
views
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 ...
1
vote
1
answer
682
views
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 ...
5
votes
0
answers
744
views
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 ...