Related papers: Reciprocal Symmetric Boltzmann Function and Unifie…
Boltzmann's differential equation is replaced by the corresponding reciprocal symmetric finite difference equation. Finite difference translates discreteness of energy. Boltzmann's function, then, splits into two reciprocally related…
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…
Difference Boltzmann Equation is derived in a plane wavelets representation with account of two-particle correlations. It is shown that the set of plane wavelet orthonormal functions is complete. The set of ket vectors is used as the second…
The Boltzmann equation with the Bhatnagar-Gross-Krook collision operator is considered for the Bose-Einstein and Fermi-Dirac equilibrium distribution functions. We show that the expansion of the microscopic velocity in terms of Hermite…
It is well known that bosons and fermions exhibit opposite behaviors when experiencing interference, in the sense that bosons have a tendency to bunch whereas fermions have a tendency to antibunch. Recently, this complementarity was…
Bosonic and fermionic statistics are well known to give rise to antinomic behaviors, most notably boson bunching vs fermion antibunching. Here, we establish a fundamental relation that combines bosonic and fermionic multiparticle…
The notion of distance between a global Maxwellian function and an arbitrary solution $f$ (with the same total density $\rho$ at the fixed moment $t$) of Boltzmann equation is introduced. In this way we essentially generalize the important…
Identical quantum particles exhibit only two types of statistics: bosonic and fermionic. Theoretically, this restriction is commonly established through the symmetrization postulate or (anti)commutation constraints imposed on the algebra of…
In this paper we study algebraic and combinatorial properties of Grothendieck polynomials and their dual polynomials by means of the Boson-Fermion correspondence. We show that these symmetric functions can be expressed as a vacuum…
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…
The time evolution of a finite fermion system towards statistical equilibrium is investigated using analytical solutions of a nonlinear partial differential equation that had been derived earlier from the Boltzmann collision term. The…
A framework for relativistic thermodynamics and statistical physics is built by first exploiting the symmetries between energy and momentum in the derivation of the Boltzmann distribution, then using Einstein's energy-momentum relationship…
Some new representations of the supersymmetric transformations are derived, and the supermultiplets are introduced. Based on these representations, various formulations (equations, commutation relations, propagators, Jacobi identities,…
The iterative Boltzmann inversion is an iterative scheme to determine an effective pair potential for an ensemble of identical particles in thermal equilibrium from the corresponding radial distribution function. Although the method is…
Boson-fermion pairing is considered in a discrete environment of bosons and fully spin-polarized fermions, coupled via an attractive Bose-Fermi Hubbard Hamiltonian in one dimension. The results of the T-matrix approximation for particles of…
A method for the calculation of translationally invariant wave functions for systems of identical fermions with arbitrary potential of pair interaction is developed. It is based on the well-known result that the essential dynamic part of…
We show that a dynamical supersymmetry can appear in a purely fermionic system. This ``supersymmetry without bosons" is constructed by application of a recently introduced boson-fermion Dyson mapping from a fermion space to a space…
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…
Boson, fermion, and super oscillators and (statistical) mechanism of cosmological constant; finite approximation of the zeta-function and fermion factorization of the bosonic statistical sum considered.
In multiparticle quantum interference, bosons show rather generally the tendency to bunch together, while fermions can not. This behavior, which is rooted in the different statistics of the particles, results in a higher coincidence rate…