# Questions tagged [quantum-statistics]

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### Calculate the number of accessible microscopic states of a system of two localized and independent quantum oscillators [closed]

Calculate the number of accessible microscopic states of a system of two localized and independent quantum oscillators, with fundamental frequencies wo and 3wo, respectively, and total energy E = ...
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### Why can we use Bose-Einstein statistics in this expression for number density

In a system with $N$ particles in some volume $V$ in contact with a reservoir of temperature $T$, we find that $$\bar{n_i}=\frac{g_i}{e^{\frac{{\epsilon}_i -\mu}{kT}} \pm 1}$$ depending on whether the ...
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### Question about Path Integrals and Exchange Statistics in Steve Simon's "Topological Quantum"

In the introduction to the path integral approach leading to exchange statistics for many particles, Steve Simon breaks up the sum of paths into two types: paths where particles do not exchange (type ...
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1 vote
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### A simple derivation of the Heisenberg limit in quantum metrology

I hope to derivate the Heisenberg limit in a simple way. Let $X_1,\cdots,X_n$ be random variables, and let $\bar{X} = \sum_{i=1}^n X_i/n$. Also, let $X_1,\cdots,X_n$ have equal variance and equal ...
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### Calculation of canonical partition function for fermion system with degenerate energy levels

I'm having trouble in visualising the generalized version of the question asked here. We have a system with levels whose energies are $0, \epsilon, 2 \epsilon, ..., n\epsilon$, and the number of ...
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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&...
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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 ...
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### 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 ...
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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 ...
1 vote
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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 ...
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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 ...
1 vote
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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 ...
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### 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))....
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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 ...
1 vote
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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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### 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 ...
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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 ...
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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 ...
673 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 $n=0,\pm1,\pm2,\dots$ ...
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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 ...
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