相关论文: Factorising numbers with a Bose-Einstein condensat…

The number partitioning problem can be interpreted physically in terms of a thermally isolated non-interacting Bose gas trapped in a one-dimensional harmonic oscillator potential. We exploit this analogy to characterize, by means of a…

By constructing the super-particle representation of the free boson gas, we propose a new statistics in which the particles are non-exclusive. This statistics can be considered as a generalization of Bose-Einstein's. The possible…

The analytical probability distribution of finite systems obeying Bose-Einstein statistics in one, two, and three dimensions are investigated by using a canonical ensemble approach. Starting from the canonical partition function of the…

Asymptotic behavior of a class of nonlinear Schr\"odinger equations are studied. Particular cases of 1D weakly focusing and Bose-Einstein condensates are considered. A statistical approach is presented to describe the stationary probability…

We develop an analytical technique to derive explicit forms of thermodynamical quantities within the asymptotic approach to non-extensive quantum distribution functions. Using it, we find an expression for the number of particles in a boson…

We discuss the phenomenon of Bose-Einstein condensation of an ideal non-relativistic Bose gas in an arbitrarily shaped cavity. The influence of the finite extension of the cavity on all thermodynamical quantities, especially on the critical…

We obtain an asymptotic expansion for $p(n)$, the number of partitions of a natural number $n$, starting from a formula that relates its generating function $f(t), t\in (0,1)$ with the characteristic functions of a family of sums of…

It is pointed out that the quantum statistical phenomenon of Bosonic stimulation, inherent to Bose statistics and the associated Bose-Einstein correlation, can be effectively mapped on to the statistical problem of the Polya urn scheme.…

We show that the visibility in interference experiments with Bose-Einstein condensates is directly related to the condensate fraction. The probability distribution of the contrast over many runs of an interference experiment thus gives the…

Factorization of numbers with the help of Gauss sums relies on an intimate relationship between the maxima of these functions and the factors. Indeed, when we restrict ourselves to integer arguments of the Gauss sum we profit from a…

Motivated by the Asynchronous Finite Differences Method utilized for the calculation of the most probable distributions of finite particle number systems, this study employs numerical variation and central difference techniques to provide…

Each natural number can be associated with some tree graph. Namely, a natural number $n$ can be factorized as $$ n = p_1^{\alpha_1}\ldots p_k^{\alpha_k},$$ where $p_i$ are distinct prime numbers. Since $\alpha_i$ are naturals, they can be…

We derive an exact recursion formula for the calculation of thermodynamic functions of finite systems obeying Bose-Einstein statistics. The formula is applicable for canonical systems where the particles can be treated as noninteracting in…

The factorization problem of $q$-exponential distribution within nonextensive statistical mechanics is discussed on the basis of Abe's general pseudoadditivity for equilibrium systems. it is argued that the factorization of compound…

We calculate certain features of Bose-Einstein condensation in the ideal gas by using recurrence relations for the partition function. The grand canonical ensemble gives inaccurate results for certain properties of the condensate that are…

Bose-Einstein-condensed gases in external spatially random potentials are considered in the frame of a stochastic self-consistent mean-field approach. This method permits the treatment of the system properties for the whole range of the…

A continuous approximation for the results of [1] is obtained. In this approximation the energy distribution is represented in the form of the product of the Gibbs factor and superstatistics factor. The mutual weights of the factors are…

We develop the dilute Bose gas model with random potential in order to understand the Bose system in random media such as 4He in porous glass. Using the random potential taking account of the pore size dependence, we can compare…

Bayesian inference is a widely used statistical method. The free energy and generalization loss, which are used to estimate the accuracy of Bayesian inference, are known to be small in singular models that do not have a unique optimal…

For a non-self-interacting Bose gas with a fixed, large number of particles confined to a trap, as the ground state occupation becomes macroscopic, the condensate number fluctuations remain micrscopic. However, this is the only significant…