Related papers: Exact Maxwell-Boltzmann, Bose-Einstein and Fermi-D…
The Boltzmann entropy $S^{(B)}$ is true in the case of equal probability of all microstates of a system. In the opposite case it should be averaged over all microstates that gives rise to the Boltzmann--Shannon entropy (BSE). Maximum…
Using the quantum statistical method, the difficulty of solving the wave equation on the background of the black hole is avoided.We directly solve the partition functions of Bose and Fermi field on the background of an axisymmetric…
In this paper we derive accurate numerical methods for the quantum Boltzmann equation for a gas of interacting bosons. The schemes preserve the main physical features of the continuous problem, namely conservation of mass and energy, the…
The tomographic reconstruction of the state of a quantum-mechanical system is an essential component in the development of quantum technologies. We present an overview of different tomographic methods for determining the quantum-mechanical…
When using the finite element method (FEM) in inverse problems, its discretization error can produce parameter estimates that are inaccurate and overconfident. The Bayesian finite element method (BFEM) provides a probabilistic model for the…
A derivation of the Boltzmann equation from the Liouville equation by the use of the Grad limiting procedure in a finite volume is proposed. We introduce two scales of space-time: macro- and microscale and use the BBGKY hierarchy and the…
The empirical rule that systems of identical particles always obey either Bose or Fermi statistics is customarily imposed on the theory by adding it to the axioms of nonrelativistic quantum mechanics, with the result that other statistical…
Based on the q-exponential distribution which has been observed in more and more physical systems, the varentropy method is used to derive the uncertainty measure of such an abnormal distribution function. The uncertainty measure obtained…
The random matrix ensembles (RME) of quantum statistical Hamiltonian operators, {\em e.g.} Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied to following quantum statistical systems:…
The quantum corrections related to the ideal gas model that are often considered are those which are related to the particles nature: bosons or fermions. These corrections lead respectively to the Bose-Einstein and Fermi-Dirac statistics.…
The Boltzmann equation is the traditional framework in which one extends the time-dependent mean field classical description of a many-body system to include the effect of particle-particle collisions in an approximate manner. A…
The connection between the Maximum Entropy (MaxEnt) formalism and Restricted Boltzmann Machines (RBMs) is natural, as both give rise to a Boltzmann-like distribution with constraints enforced by Lagrange multipliers, which corresponds to…
We compare two proposals for the dynamical entropy of quantum deterministic systems (CNT and AFL) by studying their extensions to classical stochastic systems. We show that the natural measurement procedure leads to a simple explicit…
Macroscopic mechanical properties of polymers are determined by their microscopic molecular chain distribution. Due to randomness of these molecular chains, probability theory has been used to find their micro-states and energy…
The exact nonequilibrium steady state solution of the nonlinear Boltzmann equation for a driven inelastic Maxwell model was obtained by Ben-Naim and Krapivsky [Phys. Rev. E 61, R5 (2000)] in the form of an infinite product for the Fourier…
Identical systems, or entities, are indistinguishable in quantum mechanics (QM), and the symmetrization postulate rules the possible statistical distributions of a large number of identical quantum entities. However, a thorough analysis on…
The relative entropy for two different degenerate diffusion processes is estimated by using the Wasserstein distance of initial distributions and the difference between coefficients. As applications, the entropy cost inequality and…
Entanglement plays a prominent role in the study of condensed matter many-body systems: Entanglement measures not only quantify the possible use of these systems in quantum information protocols, but also shed light on their physics.…
When independent Bose-Einstein condensates (BEC), described quantum mechanically by Fock (number) states, are sent into interferometers, the measurement of the output port at which the particles are detected provides a binary measurement,…
Quantum effects in a system of coupled atomic and molecular Bose-Einstein condensates in the framework of a two-mode model are studied numerically and analytically, using the discrete WKB approach. In contrast to the mean-field…