Related papers: Equivalence of the grand canonical partition funct…
The grand canonical partition functions for primitive droplet nucleation models with an excess energy epsilon_n = - mu n + sigma n^{1-eta}, eta = 1/d, for droplets of n constituents in d dimensions are calculated exacly in closed form in…
Usual separability criteria applicable to distinguishable particles are not applicable to identical particles. Here we show that Partial transposition and symmetrization (or anti symmetrization) of density matrix of bipartite boson systems…
The statistical mechanical partition function can be used to construct different forms of phase space distributions not restricted to the Gibbs-Boltzmann factor. With a generalised Lorentzian both the Kappa-Bose and Kappa-Fermi partition…
We derive an expression for the reduced density matrices of ideal Bose and Fermi gases in the canonical ensemble, which corresponds to the Bloch--De Dominicis (or Wick's) theorem in the grand canonical ensemble for normal-ordered products…
The partition function is an essential quantity in statistical mechanics, and its accurate computation is a key component of any statistical analysis of quantum system and phenomenon. However, for interacting many-body quantum systems, its…
A simple explicit construction is provided of a partition-valued fragmentation process whose distribution on partitions of $[n]=\{1,...,n\}$ at time $\theta \ge 0$ is governed by the Ewens sampling formula with parameter $\theta$. These…
In an isolated ideal Bose system with a fixed energy, the number of microstates depends solely on the configurations of bosons in excited states, implying zero entropy for particles in the ground state. When two such systems merge, the…
According to the well-known analysis by Nozi\'{e}res, the fragmentation of the condensate increases the energy of a uniform interacting Bose system. Therefore, at $T= 0$ the condensate should be nonfragmented. We perform a more detailed…
This paper presents a new way to construct single-valued many-body wavefunctions of identical particles with intermediate exchange phases between Fermi and Bose statistics. It is demonstrated that the exchange phase is not a representation…
The thermodynamic properties of an ideal bosonic system composed of particles and antiparticles at finite temperatures are examined within the framework of a scalar field model. It is assumed that particle-antiparticle pair creation occurs;…
We study a system consisting of a heavy quantum particle, called tracer particle, coupled to an ideal gas of light Bose particles, the ratio of masses of the tracer particle and a gas particle being proportional to the gas density. All…
We formulate and study the microscopic statistical mechanics of systems of particles with exclusion statistics in a discrete one-body spectrum. The statistical mechanics of these systems can be expressed in terms of effective single-level…
We introduce the boson and the fermion point processes from the elementary quantum mechanical point of view. That is, we consider quantum statistical mechanics of canonical ensemble for a fixed number of particles which obey Bose-Einstein,…
In this note I revisit the calculation of partition function of simple one dimensional systems solvable by Bethe Ansatz. Particularly I show that by the precise definition and treatment of the partition function the nontrivial normalization…
This article presents a study of the grand canonical Bose-Einstein (BE) statistics for a finite number of particles in an arbitrary quantum system. The thermodynamical quantities that identify BE condensation -- namely, the fraction of…
We consider the emission or absorption of $n$ identical bosons from an energetic or a massive particle, in which the bosons and the source particle are allowed to be offshell. The Bose-Einstein symmetrized amplitude can be decomposed into…
In the paper, the quantum-statistical approach is used to estimate the number of restricted plane partitions of an integer $n$ with the number of parts not exceeding some finite $N$. The analogy between this number-theoretical problem and…
We study peculiarities of Bose-Einstein condensation of photons that are in thermodynamic equilibrium with atoms of noninteracting gases. General equations of the thermodynamic equilibrium of the system under study are obtained. We examine…
We study the statistical mechanics of the self-gravitating gas at thermal equilibrium with two kinds of particles. We start from the partition function in the canonical ensemble which we express as a functional integral over the densities…
We consider a random model of diffusion and coagulation. A large number of small particles are randomly scattered at an initial time. Each particle has some integer mass and moves in a Brownian motion whose diffusion rate is determined by…