相关论文: Fermi-Dirac statistics and the number theory

In the present article a new method of deriving integral representations of combinations and partitions in terms of harmonic products has been established. This method may be relevant to statistical mechanics and to number theory.

We compute the full order statistics of a one-dimensional gas of fermions in a harmonic trap at zero temperature, including its large deviation tails. The problem amounts to computing the probability distribution of the $k$th smallest…

From sand piles to electrons in metals, one of the greatest challenges in modern physics is to understand the behavior of an ensemble of strongly interacting particles. A class of quantum many-body systems such as neutron matter and cold…

Number partitioning is a classical problem from combinatorial optimisation. In physical terms it corresponds to a long range anti-ferromagnetic Ising spin glass. It has been rigorously proven that the low lying energies of number…

We use a semiclassical approximation to derive the partition function for an arbitrary potential in one-dimensional Quantum Statistical Mechanics, which we view as an example of finite temperature scalar Field Theory at a point. We rely on…

We develop the basis of the two dimensional generalized quantum statistical systems by using results on $r$-generalized Fibonacci sequences. According to the spin value $s$ of the 2d-quasiparticles, we distinguish four classes of quantum…

Consistent statistical physical description is given for systems where the elementary excitations are composite objects. Explicit calculational scheme is constructed for the energy density and the total number of thermodynamical degrees of…

We show that a dilute 2-species gas of Fermi-Dirac alkali-metal atoms in a periodic optical lattice may exhibit fractionization of particle number when the two components are coupled via a coherent electromagnetic field with a topologically…

In many fields of statistical physics, for instance in the study of the liquid-gas phase transition in finite nuclear matter, the Virial coefficients of the Fermi gas play a major role. In this note, we provide relations, sum rules,…

We present a full treatment of the microcanonical ensemble of the ideal hadron-resonance gas in a quantum-mechanical framework which is appropriate for the statistical model of hadronization. By using a suitable transition operator for…

We investigate dynamical properties of a one-component Fermi gas with dipole-dipole interaction between particles. Using a variational function based on the Thomas-Fermi density distribution in phase space representation, the total energy…

In the first part we associate a periodic sequence to a partition and study the connection the distribution of elements of uniform limit of the sequences. Then some facts of statistical independence of these limits are proved

We compute the spatial population statistics for one-dimensional fermi-gases and for bose-gases with hard core repulsions in periodic potentials. We show how the statistics depend on the atomic density in the ground state of the system, and…

I show that if the total energy of a system of interacting particles may be written as a sum of quasiparticle energies, then the system of quasiparticles can be viewed in general as an ideal gas with fractional exclusion statistics (FES).…

A novel approach to parton distributions parameterization in terms of quantum statistical functions is here outlined. The description, already proposed in previous publications, is here improved by adding to the statistical distributions an…

We present a theory that accurately describes the counting of excited states of a noninteracting fermionic gas. At high excitation energies the results reproduce Bethe's theory. At low energies oscillatory corrections to the many--body…

We study the thermodynamical properties of a mesoscopic Fermi gas in view of recent possibilities to trap ultracold atoms in a harmonic potential. We focus on the effects of shell closure for finite small atom numbers. The dependence of the…

Numerical modelling of quantum effects caused by bosonic or fermionic character of secondaries produced in high energy collisions of different sorts is at the moment still far from being established. In what follows we propose novel…

Assuming that the maximal allowed number of identical particles in state is an integer parameter, q, we derive the statistical weight and analyze the associated equation which defines the statistical distribution. The derived distribution…

The methods of statistical mechanics are applied to two-dimensional foams under macroscopic agitation. A new variable -- the total cell curvature -- is introduced, which plays the role of energy in conventional statistical thermodynamics.…