Related papers: Diffusion equations in inhomogeneous solid having …

This paper is devoted to the study of some qualitative and quantitative aspects of nonlinear propagation phenomena in diffusive media. More precisely, we consider the case a reaction-diffusion equation in a periodic medium with…

In a recent arXiv preprint we proposed a statistical approach to the quantal effects in nucleation rate, addressed particularly to solid state physics. We now turn to transient nucleation rates incorporating either classical or quantal…

We consider the evolution of a quantum particle hopping on a cubic lattice in any dimension and subject to a potential consisting of a periodic part and a random part that fluctuates stochastically in time. If the random potential evolves…

We propose an alternative method for one-dimensional continuum diffusion models with spatially variable (heterogeneous) diffusivity. Our method, which extends recent work on stochastic diffusion, assumes the constant-coefficient homogenized…

Analytic solutions to the nonlinear radiation diffusion equation with an instantaneous point source for a non-homogeneous medium with a power law spatial density profile, are presented. The solutions are a generalization of the well known…

A new microcanonical equilibrium state is introduced for quantum systems with finite-dimensional state spaces. Equilibrium is characterised by a uniform distribution on a level surface of the expectation value of the Hamiltonian. The…

We present basic equations of nonequilibrium thermo field dynamics of dense quantum systems. A formulation of nonequilibrium thermo field dynamics has been performed using the nonequilibrium statistical operator method by D.N.Zubarev.…

The non-equilibrium statistical mechanics and kinetic theory for a model of a confined quasi-two-dimensional gas of inelastic hard spheres is presented. The dynamics of the particles includes an effective mechanism to transfer the energy…

We present a first-principles formalism for studying dynamical heterogeneities in glass forming liquids. Based on the Non-Equilibrium Self-Consistent Generalized Langevin Equation theory, we were able to describe the time-dependent local…

We present a microscopic approach to quantum dissipation and sketch the derivation of the kinetic equation describing the evolution of a simple quantum system in interaction with a complex quantum system. A typical quantum complex system is…

Many approaches to quantum gravity have resorted to diffusion processes to characterize the spectral properties of the resulting quantum spacetimes. We critically discuss these quantum-improved diffusion equations and point out that a…

A new nonlinear Schroedinger equation is obtained explicitly from the fractal Brownian motion of a massive particle with a complex-valued diffusion constant. Real-valued energy (momentum) plane wave and soliton solutions are found in the…

The equation which describes a particle diffusing in a logarithmic potential arises in diverse physical problems such as momentum diffusion of atoms in optical traps, condensation processes, and denaturation of DNA molecules. A detailed…

The effect of nonlinear friction forces in quantum mechanics is studied via dissipative Madelung hydrodynamics. A new thermo-quantum diffusion equation is derived, which is solved for the particular case of quantum Brownian motion with a…

We propose to use spin hydrodynamics, a two-fluid model of spin propagation, as a generalization of the diffusion equation. We show that in the dense limit spin hydrodynamics reduces to Fick's law and the diffusion equation. In the opposite…

We present a quantum algorithm for computational fluid dynamics based on the Lattice-Boltzmann method. Our approach involves a novel encoding strategy and a modified collision operator, assuming full relaxation to the local equilibrium…

For ergodic adiabatic quantum systems, we study the evolution of energy distribution as the system evolves in time. Starting from the von Neumann equation for the density operator, we obtain the quantum analogue of the Smoluchowski equation…

We derive the hydrodynamic limit of a kinetic equation where the interactions in velocity are modelled by a linear operator (Fokker-Planck or Linear Boltzmann) and the force in the Vlasov term is a stochastic process with high amplitude and…

The dynamics of a kicked quantum system undergoing repeated measurements of momentum is investigated. A diffusive behavior is obtained even when the dynamics of the classical counterpart is not chaotic. The diffusion coefficient is…

In view of the usefulness and importance of the kinetic equation in certain physical problems, the authors derive the explicit solution of a fractional kinetic equation of general character, that unifies and extends earlier results.…