We develop a numerical procedure to efficiently model the nonequilibrium steady state of one-dimensional arrays of open quantum systems based on a matrix-product operator ansatz for the density matrix. The procedure searches for the null eigenvalue of the Liouvillian superoperator by sweeping along the system while carrying out a partial diagonalization of the single-site stationary problem. It...

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Following the revival of interest in the behavior of classical, nonlinear systems, a variety of new theoretical tools was developed to allow for a description of the essential properties of those systems. One of the most powerful mathematical methods developed recently is the Lie-Poisson bracket technique [1], the use of which has led to considerable progress in our understanding of conservativ...

We analyze temporal approximation schemes based on overlapping domain decompositions. As such schemes enable computations on parallel and distributed hardware, they are commonly used when integrating large-scale parabolic systems. Our analysis is conducted by first casting the domain decomposition procedure into a variational framework based on weighted Sobolev spaces. The time integration of a...

in this paper we study properties of symbols such that these belong to class of symbols sitting insidesm ρ,φ that we shall introduce as the following. so for because hypoelliptic pseudodifferential operatorsplays a key role in quantum mechanics we will investigate some properties of m−hypoelliptic pseudodifferential operators for which define base on this class of symbols. also we consider maxi...

This paper considers a nonlinear dynamical system on a complex, finite dimensional Banach space which has an asymptotically stable, hyperbolic fixed point. We investigate the connection between the so-called principle eigenfunctions of the Koopman operator and the existence of a topological conjugacy between the nonlinear dynamics and its linearization in the neighborhood of the fixed point. Th...

We present a discussion of the charge response and the charge fluctuations of mesoscopic chaotic cavities in terms of a generalized Wigner-Smith matrix. The Wigner-Smith matrix is well known in investigations of time-delay of quantum scattering. It is expressed in terms of the scattering matrix and its derivatives with energy. We consider a similar matrix but instead of an energy derivative we ...

We investigate the dynamics associated to nearly–integrable dissipative systems, with particular reference to some models of Celestial Mechanics which can be described in a weakly dissipative framework. We start by studying some paradigmatic models provided by the dissipative standard maps in 2 and 4 dimensions. The dynamical investigation is performed applying frequency analysis and computing ...

In this paper we discuss the dissipative property of near-equilibrium classical solutions to the Cauchy problem of the Vlasov-Maxwell-Boltzmann System in the whole space R3 when the positive charged ion flow provides a spatially uniform background. The most key point of studying this coupled degenerately dissipative system here is to establish the dissipation of the electromagnetic field which ...