Related papers: Current density operator in systems with non-parab…
We derive a closed equation of motion for the current density of an inhomogeneous quantum many-body system under the assumption that the time-dependent wave function can be described as a geometric deformation of the ground-state wave…
This paper aims to develop numerical approximations of the Keller--Segel equations that mimic at the discrete level the lower bounds and the energy law of the continuous problem. We solve these equations for two unknowns: the organism (or…
The problem of determining a current density confined to a volume from measurements of the magnetic field it produces exterior to that volume is known to have non-unique solutions. To uniquely determine the current density, or the…
We provide very mild sufficient conditions for space-time domains (non-necessarily cylindrical) which ensure that the continuous Dirichlet problem and the H\"older Dirichlet problem are well-posed, for any parabolic operator in divergence…
We propose a highly-scalable method to compute the statistics of charge transfer in driven conductors. The framework can be applied in situations of non-zero temperature, strong coupling to terminals and in the presence of non-periodic…
We analyze non-equilibrium current transport in molecular electronic devices, using as an example devices formed by two terphenyl dithiol molecules attached to gold electrodes. Using a first-principles based self-consistent matrix Green's…
We show that the time-dependent particle density $n(\vec r,t)$ and the current density ${\vec j}(\vec r,t)$ of a many-particle system that evolves under the action of external scalar and vector potentials $V(\vec r,t)$ and $\vec A(\vec…
We formulate macroscopic quantum electrodynamics for the most general linear, absorbing media. In particular, Onsager reciprocity is not assumed to hold. For media with a non-local response, the field quantisation is based on the…
The theoretical description of strongly correlated quantum systems out of equilibrium presents several challenges and a number of open questions persist. In this paper we focus on nonlinear electronic transport through a quantum dot…
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…
The master equation for the reduced density matrix of a charged particle interacting with a translation invariant weakly coupled environment is considered. The electric current is renormalized by the system-environment interaction, leading…
We have developed new methods to calculate dispersion curves (analytically in the simpler cases) from which we are able to derive the spatial distribution of electron and current densities. We investigate the case where the magnetic field…
In this article we review a less known unperturbative and powerful many-body method in the framework of classical statistical mechanics and then we show how it works by means of explicit calculations for a nontrivial classical model. The…
We study the higher-order correlation functions of covariant families of observables associated with random Schr\"odinger operators on the lattice in the strong disorder regime. We prove that if the distribution of the random variables has…
We review the literature on the Pauli equation and its current density, discussing the progression from the original phenomenological version of Pauli to its derivation by $\text{L\'{e}vy-Leblond}$ from a linearization of the…
We have studied the effects of interactions on persistent currents in half-filled and quarter-filled Hubbard models with weak and intermediate strength disorder. Calculations are performed using a variational Gutzwiller ansatz that…
We present a general multi-component density functional theory in which electrons and nuclei are treated completely quantum mechanically, without the use of a Born-Oppenheimer approximation. The two fundamental quantities in terms of which…
The presence of bound states in a nanoscale electronic system attached to two biased, macroscopic electrodes is shown to give rise to persistent, non-decaying, localized current oscillations which can be much larger than the steady part of…
We study the transport of energy in a finite linear harmonic chain by solving the Heisenberg equation of motion, as well as by using nonequilibrium Green's functions to verify our results. The initial state of the system consists of two…
This paper is devoted to constructing approximate solutions for the classical Keller--Segel model governing \emph{chemotaxis}. It consists of a system of nonlinear parabolic equations, where the unknowns are the average density of cells (or…