Related papers: State equation for the three-dimentional system of…
The Van der Waal's equation of state for a (slightly) non-ideal classical gas is usually derived in the context of classical statistical mechanics by using the canonical ensemble. We use the hard sphere potential with no short range…
We consider classical N-particle system with arbitrary central pair potential. Mechanical equilibrium condition in spherically-symmetric case leads to a nonlinear integro-differential equation for concentration n(r). For special state…
We derive a quantum version of the classical-optics Wiener-Khintchine theorem within the framework of detection of phase-space displacements with a suitably designed quantum ruler. A phase-pace based quantum mutual coherence function is…
We study the general properties of fluid spheres satisfying the heuristic assumption that their areas and proper radius are equal (the Euclidean condition). Dissipative and non-dissipative models are considered. In the latter case, all…
For hyperbolic first-order systems of linear partial differential equations (master equations), appearing in description of kinetic processes in physics, biology and chemistry we propose a new procedure to obtain their complete closed-form…
We study a spontaneous collapse model for a two-level (spin) system, in which the Hamiltonian and the stochastic terms do not commute. The numerical solution of the equations of motions allows to give precise estimates on the regime at…
We solve the Percus-Yevick equation in even dimensions by reducing it to a set of simple integro-differential equations. This work generalizes an approach we developed previously for hard discs. We numerically obtain both the pair…
A new discrete model for energy relaxation of a quantum particle is described via a projection operator, causing the wave function collapse. Power laws for the evolution of the particle coordinate and momentum dispersions are derived. A new…
In this note, we prove blow-up results for semilinear wave models with damping and mass in the scale-invariant case and with nonlinear terms of derivative type. We consider the single equation and the weakly coupled system. In the first…
The act of measurement on a quantum state is supposed to "collapse" the state into one of several eigenstates of the operator corresponding to the observable being measured. This measurement process is sometimes described as outside…
One of the unsolved issues in the quantum gravity comes from the Wheeler-DeWitt equation, which is second order functional derivative equation. In this paper, we introduce a new method to solve the Wheeler-DeWitt equation. Usually one…
We calculate the non-retarded dispersion force exerted on an electrically polarizable quantum particle by a perfectly conducting toroid, which is one of the most common objects exhibiting a non-trivial topology. We employ a convenient…
We propose a deterministic particle method for a one-dimensional nonlocal equation with interactions through the repulsive Morse potential. We show that the particle method converges as the number of particles goes to infinity towards weak…
This work derives exact solutions to the problem of interacting particle density evolution in relativistic and quasi-relativistic approximations for electromagnetic and gravitational interactions. Two types of radial symmetry for the…
We construct a coupled quantum vortex superposition state (CVSS), since in actual physical systems, linear Schrodinger equations will not be available because of a nonlinear effect. By studying the dynamic evolution of CVSS both…
Few equilibrium --even less so nonequilibrium-- statistical-mechanical models with continuous degrees of freedom can be solved exactly. Classical hard-spheres in infinitely many space dimensions are a notable exception. We show that even…
We consider degenerate porous medium equations with a divergence type of drift terms. We establish the existence of $L^{q}$-weak solutions (satisfying energy estimates or even further with moment and speed estimates in Wasserstein spaces),…
We compute the first order correction of the effective viscosity for a suspension containing solid particles with arbitrary shapes. We rewrite the computation as an homogenization problem for the Stokes equations in a perforated domain.…
We study the three-dimensional compressible Navier-Stokes equations coupled with the $Q$-tensor equation perturbed by a multiplicative stochastic force, which describes the motion of nematic liquid crystal flows. The local existence and…
The coherent states for a particle on a sphere are introduced. These states are labelled by points of the classical phase space, that is the position on the sphere and the angular momentum of a particle. As with the coherent states for a…