Related papers: A Liouville equation for systems which exchange pa…
We study a driven system in which interaction between particles causes their directional, coupled movement. In that model system, two particles move alternatingly in time on two coupled chains. Without interaction, both particles diffuse…
In periodic, two-dimensional potentials a classical particle might be expected to escape from any finite region if it has enough energy to escape from a single cell. However, for a class of sinusoidal potentials in which the barriers…
A new approximate solution to the quantum-classical Liouville equation is derived starting from the formal solution of this equation in forward-backward form. The time evolution of a mixed quantum-classical system described by this equation…
The center-of-mass motion of a single optically levitated nanoparticle resembles three uncoupled harmonic oscillators. We show how a suitable modulation of the optical trapping potential can give rise to a coupling between two of these…
In a recently proposed computational model of open molecular systems out of equilibrium [Ebrahimi Viand et al. J.Chem.Phys. 153, 101102 (2020)], the action of different reservoirs enters as a linear sum into the Liouville-type evolution…
We present a formalism to study many-particle quantum transport across a lattice locally connected to two finite, non-stationary (bosonic or fermionic) reservoirs, both of which are in a thermal state. We show that, for conserved total…
We develop a dynamical theory of heat transfer between two nano systems. In particular, we consider the resonant heat transfer between two nanoparticles due to the coupling of localized surface modes having a finite spectral width. We model…
Schr\"odinger equation with given, {\it a priori} known current is formulated. A non-zero current density is maintained in the quantum system via a subsidiary condition imposed by vector, local Lagrange multiplier. Constrained minimization…
We investigate the nonstationary electronic transport in noninteracting nanostructures driven by a finite bias and time-dependent signals applied at their contacts to the leads. The systems are modelled by a tight-binding Hamiltonian and…
The motion of charged particles can be interfaced with electric circuitry via the current induced in nearby pick-up electrodes. Here we show how the rotational and translational dynamics of levitated objects with arbitrary charge…
Theoretical and experimental values to date for the resistances of single molecules commonly disagree by orders of magnitude. By reformulating the transport problem using boundary conditions suitable for correlated many-electron systems, we…
We consider charge transport in nanopores where the dielectric constant inside the nanopore is much greater than in the surrounding material, so that the flux of the electric fields due to the charges is almost entirely confined to the…
One-dimensional non-equilibrium models of particles subjected to a coagulation-diffusion process are important in understanding non-equilibrium dynamics, and fluctuation-dissipation relation. We consider in this paper transport properties…
A large class of classical dynamical systems with an external rapidly oscillating driving action is considered and the effective Hamiltonian-like equations for the mean motion are obtained. The respective Liouville equation for the…
A general transport equation for the center of mass motion is constructed to study transports of electronic system under uniform magnetic field and microwave radiation. The equation is applied to study 2D electron system in the limit of…
Mixed quantum-classical methods provide powerful algorithms for the simulation of quantum processes in large and complex systems. The forward-backward trajectory solution of the mixed quantum-classical Liouville equation in the mapping…
We study Liouville-type results for the stationary Navier--Stokes equations in $\mathbb{R}^3$. We prove that any $\dot{H}^1(\mathbb{R}^3)$ solution is trivial under an integrability condition imposed only on the radial component of the…
A single-sort continuum Curie-Weiss system of interacting particles is studied. The particles are placed in the space $\mathbb{R}^d$ divided into congruent cubic cells. For a region $V\subset \mathbb{R}^d$ consisting of $N\in \mathbb{N}$…
An equation describing subdiffusion with possible immobilization of particles is derived by means of the continuous time random walk model. The equation contains a fractional time derivative of Riemann--Liouville type which is a…
We study the Radiative Transfer equations coupled with the time dependent temperature equation of a fluid: existence, uniqueness, a maximum principle are established. A short numerical section illustrates the pros and cons of the method.