Related papers: Equivalence of the grand canonical partition funct…
Partition functions, multiplicity distributions, and isospin fluctuations are calculated for canonical ensembles in which additive quantum numbers as well as total isospin are strictly conserved. When properly accounting for Bose-Einstein…
We study mathematically the equilibrium properties of the Bose-Hubbard Hamiltonian in the limit of a vanishing hopping amplitude. This system conserves the energy and the number of particles. We establish the equivalence between the…
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…
A remarkable thermodynamic fermion-boson symmetry is found for the canonical ensemble of ideal quantum gases in harmonic oscillator potentials of odd dimensions. The bosonic partition function is related to the fermionic one extended to…
We question the validity of the grand canonical ensemble for the description of Bose-Einstein condensation of small ideal Bose gas samples in isolated harmonic traps. While the ground state fraction and the specific heat capacity can be…
For a system of a large number of Bose particles, a chain of coupled equations for the averages of field operators is obtained. In the approximation where only the averages of one field operator and the averages of products of two operators…
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…
A new class of identical particles which may exhibit both Bose and Fermi statistics with respective probabilities $p_b$ and $p_f$ is introduced. Such an uncertainity may be either an intrinsic property of a particle or can be viewed as an…
Within the theory of statistical ensemble, the so-called $\mu PT$ ensemble describes equilibrium systems that exchange energy, particles, and volume with the surrounding. General, model-independent features of volume and particle number…
Various phenomenological models of particle multiplicity distributions are discussed using a general form of the grand canonical partition function. These phenomenological models include a wide range of varied processes such as coherent…
A convenient way to calculate $N$-particle quantum partition functions is by confining the particles in a weak harmonic potential instead of using a finite box or periodic boundary conditions. There is, however, a slightly different…
Bounds for the correlation functions of identical bosons are discussed for the general case of a Gaussian density matrix. In particular, for a purely chaotic system the two-particle correlation function must always be greater than one. On…
We show that the particles in the Calogero-Sutherland Model obey fractional exclusion statistics as defined by Haldane. We construct anyon number densities and derive the energy distribution function. We show that the partition function…
We obtain the conditions constituting a thermal equilibrium between two energy levels: (i) the total energy is equal in both levels; (ii) the temperature is equal for all particles. Exploiting these conditions, we derive a differential…
If $ p_k(a,m,n) $ denotes the number of partitions of $n$ into $k$th powers with a number of parts that is congruent to $ a $ modulo $m,$ then $p_2(0,2,n)\sim p_2(1,2,n)$ and the sign of the difference $p_2(0,2,n)- p_k(1,2,n)$ alternates…
The thermodynamic of particles with intermediate statistics interpolating between Bose and Fermi statistics is adressed in the simple case where there is one quantum number per particle. Such systems are essentially one-dimensional. As an…
In some previous articles, we defined several partitions of the total kinetic energy T of a system of N classical particles in the d-dimensional Euclidean space into components corresponding to various modes of motion. In the present paper,…
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…
We study the fluctuation of the number of particles in ideal Bose-Einstein condensates, both within the canonical and the microcanonical ensemble. Employing the Mellin-Barnes transformation, we derive simple expressions that link the…
According to symmetrization postulate for a system of identical particles, wave function has to be completely symmetric or completely anti-symmetric. In this paper we want to mathematically justify this postulate ignoring the spin part of…