Related papers: Integrability in the mesoscopic dynamics
A binary mixture of particles interacting with spherically-symmetric potentials leading to microsegregation is studied by theory and molecular dynamics (MD) simulations. We consider spherical particles with equal diameters and volume…
I formulate a general finite element method (FEM) for self-gravitating stellar systems. I split the configuration space to finite elements, and express the potential and density functions over each element in terms of their nodal values and…
This paper is a computational bifurcation analysis of a non-linear partial differential equation (PDE) characterizing equilibrium configurations in Micro electromechanical Systems (MEMS). MEMS are engineering systems that utilize…
We study noninvasive measurement of stationary currents in mesoscopic systems. It is shown that the measurement process is fully described by the Schr\"odinger equation without any additional reduction postulate and without the introduction…
We present, for the first time, exact solutions for the Schr\"{o}dinger equation in Moon and Spencer's toroidal coordinates, and in the electromagnetic toroidal--poloidal coordinate systems. Curiously, both systems present a fractional…
Complex physical dynamics can often be modeled as a Markov jump process between mesoscopic configurations. When jumps between mesoscopic states are mediated by thermodynamic reservoirs, the time-irreversibility of the jump process is a…
We study the analytical solution of the Monte Carlo dynamics in the spherical Sherrington-Kirkpatrick model using the technique of the generating function. Explicit solutions for one-time observables (like the energy) and two-time…
This paper provides a rigorous analysis of boundary element methods for the magnetic field integral equation on Lipschitz polyhedra. The magnetic field integral equation is widely used in practical applications to model electromagnetic…
In this paper, we propose a linearized finite element method (FEM) for solving the cubic nonlinear Schr\"{o}dinger equation with wave operator. In this method, a modified leap-frog scheme is applied for time discretization and a Galerkin…
A unified theory for the current through a nanoscale region of interacting electrons connected to two leads which can be either ferromagnet or superconductor is presented, yielding Meir-Wingreen-type formulas when applied to specific…
We study the nonequilibrium dynamics of a mesoscopic metallic ring threaded by a time-dependent magnetic field and coupled to an electronic reservoir. We analyze the relation between the (non-stationary) real-time Keldysh and retarded Green…
We present a theory for Coulomb drag between two mesoscopic systems which expresses the drag in terms of scattering matrices and wave functions. The formalism can be applied to both ballistic and disordered systems and the consequences can…
Coulomb screening, together with degeneracy, is characteristic of the metallic electron gas. While there is little trace of its effects in transport and noise in the bulk, at mesoscopic scales the electronic fluctuations start to show…
In the article, we discuss the conservation laws for the nonlinear Schr\"{o}dinger equation with wave operator under multisymplectic integrator (MI). First, the conservation laws of the continuous equation are presented and one of them is…
We propose a simple theory for the dynamics of model glass-forming fluids, which should be solvable using a mean-field-like approach. The theory is based on transparent physical assumptions, which can be tested in computer simulations. The…
Integration of the Dirac equation with an external electromagnetic field is explored in the framework of the method of separation of variables and of the method of noncommutative integration. We have found a new type of solutions that are…
In this paper we will study some interesting properties of modifications of the Euler-Poincar\'e equations when we add a special type of dissipative force, so that the equations of motion can be described using the metriplectic formalism.…
A novel approach to the dynamics of dilute solutions of polymer molecules under flow conditions is proposed by applying the rules of mesoscopic nonequilibrium thermodynamics (MNET). The probability density describing the state of the system…
Mesoscopic physics concerns itself with systems which are intermediate between a single atom and a bulk solid. Besides the many intrinsically interesting properties of mesoscopic systems, they can also provide physical insight into the…
We consider a two dimensional semiconductor with carriers subject to spin-orbit interactions and scattered by randomly distributed magnetic impurities. We solve the time-dependent Schroedinger equation to investigate the relationship…