Related papers: The Phase Space Elementary Cell in Classical and G…
We calculate the power spectrum of density fluctuations in the statistical non-equilibrium field theory for classical, microscopic degrees of freedom to first order in the interaction potential. We specialise our result to cosmology by…
Non-equilibrium phase transitions of a scalar field in an expanding spacetime are discussed. These transitions are shown to lead, for appropriate potential energy functions, to a biased choice of vacuum structure which can be analytically…
A novel theory of hybrid quantum-classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum-classical phase space. Both, the quantum and the classical descriptions of the respective…
We investigate the time evolution of the Boltzmann entropy of a dilute gas of N particles, N>>1, as it undergoes a free expansion doubling its volume. The microstate of the system, a point in the 4N dimensional phase space, changes in time…
Equilibrium statistics of Hamiltonian systems is correctly described by the microcanonical ensemble. Classically this is the manifold of all points in the $N-$body phase space with the given total energy. Due to Boltzmann's principle,…
In Schroedinger picture we study the possible effects of trans-Planckian physics on the quantum evolution of massive non-minimally coupled scalar field in de Sitter space. For the nonlinear Corley-Jacobson type dispersion relations with…
The present study investigates the interaction of an equidistant three-level atom and a single-mode cavity field that has been initially prepared in a generalized coherent state. The atom-field interaction is considered to be, in general,…
Unidirectionally coupled systems which exhibit phase transitions into an absorbing state are investigated at the multicritical point. We find that for initial conditions with isolated particles, each hierarchy level exhibits an…
Representative Elementary Volume (REV) at which the material properties do not vary with change in volume is an important quantity for making measurements or simulations which represent the whole. We discuss the geometrical method to…
As in an earlier paper we start from the hypothesis that physics on the Planck scale should be described by means of concepts taken from ``discrete mathematics''. This goal is realized by developing a scheme being based on the dynamical…
The algebra of polynomials in operators that represent generalized coordinate and momentum and depend on the Planck constant is defined. The Planck constant is treated as the parameter taking values between zero and some nonvanishing $h_0$.…
We present our study on the emergent states of two interacting nonlinear systems with differing dynamical time scales. We find that the inability of the interacting systems to fall in step leads to difference in phase as well as change in…
We introduce a model of long-range interacting particles evolving under a stochastic Monte Carlo dynamics, in which possible increase or decrease in the values of the dynamical variables is accepted with preassigned probabilities. For…
At the minisuperspace level of homogeneous models, the bare probability for a classical universe has a huge peak at small universes for the Hartle-Hawking `no-boundary' wavefunction, in contrast to the suppression at small universes for the…
We study theoretically two consequences of the mixed classical phase space for three repulsively-interacting bosonic particles in a circular trap. First, we show that the energy levels of the corresponding quantum system are well described…
Increasing the number $N$ of elements of a system typically makes the entropy to increase. The question arises on {\it what particular entropic form} we have in mind and {\it how it increases} with $N$. Thermodynamically speaking it makes…
We present a statistical mechanics description to study the ground state of quantum systems. In this approach, averages for the complete system are calculated over the non-interacting energy levels. Taking different interaction parameter,…
In this paper we study the structure of the phase space in noncommutative geometry in the presence of a nontrivial frame. Our basic assumptions are that the underlying space is a symplectic and parallelizable manifold. Furthermore, we…
Any variation of the fundamental physical constants, and more particularly of the fine structure constant, $\alpha$, or of the mass of the electron, $m_e$, would affect the recombination history of the Universe and cause an imprint on the…
The nature of statistics, statistical mechanics and consequently the thermodynamics of stochastic systems is largely determined by how the number of states $W(N)$ depends on the size $N$ of the system. Here we propose a scaling expansion of…