Related papers: On the validity of classical partition function
In statistical mechanics, for a system with fixed number of particles, e.g., a finite-size system, strictly speaking, the thermodynamic quantity needs to be calculated in the canonical ensemble. Nevertheless, the calculation of the…
The partition function of composite bosons ("cobosons" for short) is calculated in the canonical ensemble, with the Pauli exclusion principle between their fermionic components included in an exact way through the finite temperature…
In classical statistical mechanics, the partition function is defined in phase space. We extend this concept to quantum statistical mechanics using Bohmian trajectories. The quantum partition function in phase space captures the ensemble of…
We study the problem of particle indistinguishability for the three cases known in nature: identical classical particles, identical bosons and identical fermions. By exploiting the fact that different types of particles are associated with…
A new quantum mechanical distribution function $n^I(\varepsilon)$, is derived for the condition $n \ge g$, where in contrast to the exclusion principle $n \le g$ for fermions, each energy state must be populated by at least one particle.…
We find a close correspondence between certain partition functions of ideal quantum gases and certain symmetric polynomials. Due to this correspondence it can be shown that a number of thermodynamic identities which have recently been…
The Euler theorem in partition theory and its generalization are derived from a non-interacting quantum field theory in which each bosonic mode with a given frequency is equivalent to a sum of bosonic mode whose frequency is twice…
Using tools from representation theory, we derive expressions for the coincidence rate of partially-distinguishable particles in an interferometry experiment. Our expressions are valid for either bosons or fermions, and for any number of…
Partition functions for non-interacting particles are known to be symmetric functions. It is shown that powerful group-theoretical techniques can be used not only to derive these relationships, but also to significantly simplify calculation…
We compute the partition function of an anyon-like harmonic oscillator. The well known results for both the bosonic and fermionic oscillators are then reobtained as particular cases as ours. The technique we employ is a non-relativistic…
Quantum mechanical particles in a confining potential interfere with each other while undergoing thermodynamic processes far from thermal equilibrium. By evaluating the corresponding transition probabilities between many-particle…
It is shown that the grand partition function of an ideal Bose system with single particle spectrum $\epsilon_i = (2n+k+3/2)\hbar\omega$ is identical to that of a system of particles with single particle energy $\epsilon_i…
We analyze the so-called classical limit of the quantum-mechanical canonical partition function. In order to do that, we define accurately the density matrix for symmetrized and antisymmetrized wave functions only (Bose-Einstein and…
We consider bosonic random matrix partition functions at nonzero chemical potential and compare the chiral condensate, the baryon number density and the baryon number susceptibility to the result of the corresponding fermionic partition…
In this lecture we compare different QCD-like partition functions with bosonic quarks and fermionic quarks at nonzero chemical potential. Although it is not a surprise that the ground state properties of a fermionic quantum system and a…
Recursion formulae of the N-particle partition function, the occupation numbers and its fluctuations are given using the single-particle partition function. Exact results are presented for fermions and bosons in a common one-dimensional…
We calculate the canonical partition function $Z_N$ for a system of $N$ free particles obeying so-called `quon' statistics where $q$ is real and satisfies $|q|<1$ by using simple counting arguments. We observe that this system is afflicted…
We propose a measure of quantumness based on an addition-then-subtraction operation. We demonstrate how this measure can distinguish between classical and bosonic particles by investigating in detail multi-particle bosonic systems.…
The partition function, $U$, the number of available states in an atom or molecules, is crucial for understanding the physical state of any astrophysical system in thermodynamic equilibrium. There are surprisingly few {\em useful}…
We present a numerical method to evaluate partition functions and associated correlation functions of inhomogeneous 2--D classical spin systems and 1--D quantum spin systems. The method is scalable and has a controlled error. We illustrate…