Related papers: The Escape Problem in a Classical Field Theory Wit…
The ground state of a classical two-dimensional (2D) system with finite number of charged particles, trapped by two positive impurities charges localized at a distance (zo) from the 2D plane and separated from each other by a distance xp…
A setup for studying the influence of external electric fields on dynamic surface processes is described. Spatially-extended homogeneous electric fields are realized by applying a DC voltage in between a planar electrode and a metallic…
The zero-noise limit of differential equations with singular coefficients is investigated for the first time in the case when the noise is an $\alpha $-stable process. It is proved that extremal solutions are selected and the respective…
We investigate fluid transport in random velocity fields with unsteady drift. First, we propose to quantify fluid transport between flow regimes of different characteristic motion, by escape probability and mean residence time. We then…
A long-standing challenge in mixed quantum-classical trajectory simulations is the treatment of entanglement between the classical and quantal degrees of freedom. We present a novel approach which describes the emergence of entangled states…
We introduce the mathematical theory of the particle systems that interact via permutations, where the transition rates are assigned not to the jumps from a site to a site, but to the permutations themselves. This permutation processes can…
We study the noisy dynamics of two coupled bistable modes of a nanomechanical beam. When de-coupled, each driven mode obeys the Duffing equation of motion, with a well-defined bistable region in the frequency domain. When both modes are…
Thermally activated escape over a potential barrier in the presence of periodic driving is considered. By means of novel time-dependent path-integral methods we derive asymptotically exact weak-noise expressions for both the instantaneous…
The two ways of constrained systems quantization are considered from the point of view of their self-consistency at the quantum level. With a transparent example of a particle in the external electromagnetic field we demonstrate that the…
We introduce a model for a two configurations system, and we study the transition from quantum to classical behaviour. We first consider the effect of the interaction with the environment as an external noise and we show that it produces…
We consider a model dissipative quantum-mechanical system realized by coupling a quantum oscillator to a semi-infinite classical string which serves as a means of energy transfer from the oscillator to the infinity and thus plays the role…
The problem of the passage of the neutral massless particle with anomalous magnetic moment through the external electromagnetic field is considered both in pseudoclassical and quantum mechanics. The quantum description uses the hamiltonian…
This work addresses the problem of relaxation of open systems to quasi-equilibrium states. Time-dependent density matrix of two arbitrary coupled quantum oscillators of arbitrary properties interacting with separate reservoirs is derived…
In this paper we propose local and global existence results for the solution of systems characterized by the coupling of ODEs and PDEs. The coexistence of distinct mathematical formalisms represents the main feature of hybrid approaches, in…
In this manuscript, we propose a structural condition on non-separable Hamiltonians, which we term displacement monotonicity condition, to study second order mean field games master equations. A rate of dissipation of a bilinear form is…
Quantum escapes of two particles with Coulomb interactions from a confined one-dimensional region to a semi-infinite lead are discussed by the probability of particles remaining in the confined region, i.e. the survival probability, in…
We present an analytical framework to study the escape rate from a metastable state under the influence of two external multiplicative cross-correlated noise processes. Starting from a phenomenological stationary Langevin description with…
We consider the problem of two interacting particles on a sphere. The potential of the interaction depends on the distance between the particles. The case of Newtonian-type potentials is studied in most detail. We reduce this system to a…
Poisson-Nernst-Planck equations are widely used to describe the electrodiffusion of ions in a solvated biomolecular system. Two kinds of two-grid finite element algorithms are proposed to decouple the steady-state Poisson-Nernst-Planck…
We describe kinetic simulations of transient problems in partially ionized weakly-collisional plasma around spherical bodies absorbing or emitting charged particles. Numerical solutions of kinetic equations for electrons and ions in 1D2V…