Related papers: A Master Equation for Multi-Dimensional Non-Linear…
The supersymmetry of the electron in both the nonstationary magnetic and electric fields in a two-dimensional case is studied. The supercharges which are the integrals of motion and their algebra are established. Using the obtained algebra…
The aim of this article is to study a nonlinear system modeling a Non-Newtonian fluid of polymer aqueous solutions. We are interested here in the existence of weak solutions for the stationary problem in a bounded plane domain or in…
In this work we present a structure preserving discretization for turbidity currents based on a mass-, energy-, enstrophy-, and vorticity-conserving formulation for 2D incompressible flows. This discretization exploits a dual-field…
In this paper we introduce a new property of two-dimensional integrable systems -- existence of infinitely many local three-dimensional conservation laws for pairs of integrable two-dimensional commuting flows. Infinitely many…
A number of characteristics of integrable nonlinear partial differential equations (PDE's) for classical fields are reviewed, such as Backlund transformations, Lax pairs, and infinite sequences of conservation laws. An algebraic approach to…
Symmetries and conservation laws are studied for two classes of physically and analytically interesting radial wave equations with power nonlinearities in multi-dimensions. The results consist of two main classifications: all symmetries of…
We introduce a method to construct conservation laws for a large class of linear partial differential equations. In contrast to the classical result of Noether, the conserved currents are generated by any symmetry of the operator, including…
In the field of atom optics, the basis of many experiments is a two level atom coupled to a light field. The evolution of this system is governed by a master equation. The irreversible components of this master equation describe the…
A short review is given of the simplified differential equations approach to Master Integrals, which was recently proposed by one of the authors. We show its applicability by calculating some non-trivial two-loop planar Master Integrals,…
A mean field argument is used to derive a master equation for systems simultaneously interacting with external fields and coupled environmental degrees of freedom. We prove that this master equation preserves positivity of the reduced…
Despite recent advances in quantum sciences, a quantum master equation that accurately and simply characterizes open quantum dynamics across extremely long timescales and in dispersive environments is still needed. In this study, we…
We present new approaches for solving constrained multicomponent nonlinear Schr\"odinger equations in arbitrary dimensions. The idea is to introduce an artificial time and solve an extended damped second order dynamic system whose…
All low-order conservation laws are found for a general class of nonlinear wave equations in one dimension with linear damping which is allowed to be time-dependent. Such equations arise in numerous physical applications and have attracted…
Master equations are increasingly popular for the simulation of time-dependent electronic transport in nanoscale devices. Several recent Markovian approaches use "extended reservoirs" - explicit degrees of freedom associated with the…
We introduce a versatile method to compute electronic steady state properties of strongly correlated extended quantum systems out of equilibrium. The approach is based on dynamical mean-field theory (DMFT), in which the original system is…
A detailed quantum kinetic master equation is developed which couples the kinetics of a trapped condensate to the vapor of non-condensed particles. This generalizes previous work which treated the vapor as being undepleted.
It has been recently shown that collisional models can be used to derive a general form for the master equations which describe the reduced time evolution of a composite multipartite quantum system, whose components "propagate" in an…
In some higher dimensional nonlinear field theories integrable subsectors with infinitely many conservation laws have been identified by imposing additional integrability conditions. Originally, the complex eikonal equation was chosen as…
The general concept of nonlinear self-adjointness of differential equations is introduced. It includes the linear self-adjointness as a particular case. Moreover, it embraces the strict self-adjointness and quasi self-adjointness introduced…
This note is based on the summary of our book entitled "Non-perturbative field theoryfrom two dimensional conformal field theory to QCD in four dimensions", published recently by Cambridge University Press. It includes 436 pages. The book…