Related papers: Equivalence of the grand canonical partition funct…
We present a theory of particles, obeying intermediate statistics ("anyons"), interpolating between Bosons and Fermions, based on the principle of Detailed Balance. It is demonstrated that the scattering probabilities of identical particles…
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…
An interpolation between the canonical partition functions of Bose, Fermi and Maxwell-Boltzmann statistics is proposed. This interpolation makes use of the properties of Jack polynomials and leads to a physically appealing interpolation…
The partition function (quantum transition amplitude) of the gauge system with gauge group $Z_2$ coupled with Majorana fermions is calculated on the regular 3D cubic lattice.
We describe the implications of permutation symmetry for the state space and dynamics of quantum mechanical systems of matrices of general size $N$. We solve the general 11- parameter permutation invariant quantum matrix harmonic oscillator…
The symmetry properties under permutation of tomograms representing the states of a system of identical particles are studied. Starting from the action of the permutation group on the density matrix we define its action on the tomographic…
I discuss ideal and interacting quantum gases obeying general fractional exclusion statistics. For systems with constant density of single-particle states, described in the mean field approximation, the entropy depends neither on the…
We derive the canonical ensemble partition functions for gauged permutation invariant tensor quantum harmonic oscillator thermodynamics, finding surprisingly simple expressions with number-theoretic characteristics. These systems have a…
Correlations among identical bosons, which are familiar from statistical physics, play an increasingly important role in high energy multiple particle production processes. They provide information about the region, where the particles are…
The key problem of statistical physics standing over one hundred years is how to exactly calculate the partition function (or free energy) of many-body interaction systems, which severely hinders application of the theory for realistic…
It is shown that the recently proposed quantum analogue of classical energy equipartition theorem for two paradigmatic, exactly solved models (i.e., a free Brownian particle and a dissipative harmonic oscillator) also holds true for all…
The dark and bright solitons in different systems are already known in Klein-Gordon lattice. Instead of an external driving force, if the intrinsic field is only considered, then the modal dynamics for small oscillations could be…
We open a new discussion of generalized canonical partition function in standard statistical mechanics and apply it for the study of Bose-Einstein condensation. We discuss the possible cases for the generalized canonical partition function…
We consider the possibility that all particles in the world are fundamentally identical, i.e., belong to the same species. Different masses, charges, spins, flavors, or colors then merely correspond to different quantum states of the same…
We derive a stochastic process that describes the kinetics of a one-dimensional Bose gas in a regime where three body collisions are important. In this situation the system becomes non integrable offering the possibility to investigate…
We consider Bose-Einstein condensation of noninteracting homogeneous three-dimensional gas in canonical ensemble when both particle number $N$ and total momentum $\mathbf{P}$ of all particles are fixed. Using the saddle point method, we…
We analyze the collision of three particles with arbitrary mass ratio at zero collision energy, assuming arbitrary short-range potentials, and generalize the three-body scattering hypervolume $D$ first defined for identical bosons in 2008.…
For any quantum state representing a physical system of identical particles, the density operator must satisfy the symmetrisation principle (SP) and for massive particles also conform to super-selection rules (SSR) that prohibit coherences…
In the framework of the Gibbs statistical theory, the question of the size of the particles forming the statistical system is investigated. This task is relevant for a wide variety of applications. The distribution for particle sizes and…
Grand canonical and canonical ensembles become equivalent in the thermodynamic limit, but when the system size is finite the results obtained in the two ensembles deviate from each other. In many important cases, the canonical ensemble…