Questions tagged [quantum-statistics]
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239 questions
-1 votes
0 answers
65 views
Time-domain algorithm to generate noise with Power Spectral Density (PSD) $S(\omega,T) \propto \coth(\omega/T)$ sequentially
I need to numerically generate colored noise with a Power Spectral Density (PSD) $S(\omega,T) \propto \coth(\omega/T)$ (quantum thermal noise). I cannot use standard Spectral Synthesis (Inverse FFT) ...
- 29
0 votes
0 answers
52 views
Is there a connection between Ehrenfest equation and von Neumann equation? [closed]
I understand how Ehrenfest is sort of giving a correspondence between classical and quantum whereas von Neumann is more like a quantum mechanical equivalent of Liouvilles equation. But do they share ...
- 1
5 votes
2 answers
219 views
How close do two fermions need to be for them to behave like a boson?
A system made of an even number of fermions behaves like a boson in terms of quantum statistics. One example for that would be the hydrogen atom consisting of one proton (spin-1/2) and one electron (...
- 575
0 votes
0 answers
45 views
Difficulty while reading Quantum Statistics [duplicate]
]1 While reading the following topics from Kerson-Huang statistical mechanics, I encountered this . Here $\psi$ is the wavefunction of the system plus surroundings . There is interaction between the ...
- 605
3 votes
2 answers
604 views
Interpretation of a paragraph in quantum statistics
Here we consider the green marked paragraph from Kerson-Huang statistical mechanics book. First of all they say that $\psi$ is a state of the system where $c_n$ is the coefficient of the $n^{th}$ ...
- 605
1 vote
0 answers
65 views
Parastatistics and global gauge group for anyons and plektons
It is known that for spacetime dimension $d \ge 4$, all quantum fields are either parabosons or parafermions, that is they transform under a representation of the permutation group. Regular bosons/...
- 2,617
2 votes
0 answers
135 views
Paraparticles explanation [closed]
Recently, an article was published in nature called: Particle exchange statistics beyond fermions and bosons. https://www.nature.com/articles/s41586-024-08262-7 . Can someone simplify and explain the ...
5 votes
1 answer
371 views
Gibbs paradox: classical vs quantum
I am interested in contrasting the mixing of gases in the quantum and classical systems, and in understanding what Gibbs's paradox has to say about each. Let's begin with the classical case. To ...
- 435
2 votes
0 answers
96 views
What is an efficient way to sample a free fermion pure state from a thermal distribution?
Suppose we have a set of single particle eigenstates of fermions, $\left|\phi_i\right>$ with single particle energies $e_i$, and fixed particle number N. I would like to sample many-body (i.e. N ...
- 113
2 votes
2 answers
598 views
Quantum Phase Transitions in the Standard Model
I have a background in HEP so before asking the question i wish to explain my level of understanding. As far as i know, phase transitions studied in condensed matter describe the difference between ...
- 1,935
1 vote
0 answers
105 views
Finding the quantum canonical density matrix from the microcanonical one by tracing over the reservoir
If we have an isolated quantum system we can use the quantum microcanonical density matrix defined by $$ \rho_{mic}=\sum_n \frac{p_n}{\Omega}|n\rangle\langle n|$$ where $|n\rangle$ are the stationary ...
1 vote
2 answers
197 views
How do we know that the stationary states and corresponding eigenvalues of a quantum system forms a probability distribution?
In both lectures and my textbook (Introduction to Quantum Mechanics 3rd edition by Griffiths), I was told that a general solution to the time-dependent Schrodinger equation is a linear combination of ...
- 43
-1 votes
1 answer
170 views
Occupation number doubt in QFT [closed]
Let say we have the Hamiltonian of a free scalar field in QFT: $$\hat{H} = \mathcal{V}\int{\frac{d^3k}{8\pi^3}\hbar\omega_k\left(\hat{a}^\dagger_k\hat{a}_k+\frac{1}{2}\right)}$$ The question is what ...
- 892
2 votes
1 answer
352 views
Do statistical properties of particles violate conservation of energy?
Electrons can "tunnel" through an energy barrier to appear on the other side. This is because the probability that a particle appears somewhere is never zero, even if very small. However, ...
- 128
1 vote
1 answer
97 views
Single particle state to derive quantum distributions
In An Introduction to thermal physics by Daniel V. Schroeder, while deriving distribution functions for quantum systems, Schroeder states: The idea is to first consider a “system” consisting of one ...
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