Related papers: Generalized Ohm's law
We introduce and study a generalized energy conservation relation for scattering of time-modulated waves, where conventional energy conservation does not hold. Based on this relation, we derive an optical theorem and compute the active…
A new statistical model for the combined effects of decoherence, energy redistribution and dissipation on electron transport in large quantum systems is introduced. The essential idea is to consider the electron phase information to be lost…
We review some known facts in the transport theory of mesoscopic systems, including counting statistics, and discuss its relation with the mathematical treatment of open systems.
Quantum mechanical scattering theory is studied for time-dependent Schroedinger operators, in particular for particles in a rotating potential. Under various assumptions about the decay rate at infinity we show uniform boundedness in time…
Quantum walks in general graphs, or more specifically scattering on graphs, encompass enough complexity to perform universal quantum computation. Any given quantum circuit can be broken down into single- and two-qubit gates, which can then…
We present a study of sound wave propagation in a time dependent random medium and an application to imaging. The medium is modeled by small temporal and spatial random fluctuations in the wave speed and density, and it moves due to an…
The first two lectures are devoted to describing the basic concepts of scattering theory in a very compressed way. A detailed presentation of the abstract part can be found in \cite{I} and numerous applications in \cite{RS} and \cite{Y2}.…
Electrons move along potential or thermal gradients. In the presence of a global gradient, applied e.g. to the two terminals of a conductor, this induces electric charge and heat currents. They can also flow between two equilibrated…
Binary mixtures of electrons with protons and of electrons with photons subjected to external electromagnetic fields are analyzed by using the Anderson and Witting model equation. The relativistic laws of Ohm and Fourier are determined as…
A rigorous theory of electromagnetic (EM) wave scattering by small perfectly conducting particles is developed. The limiting case when the number of particles tends to infinity is discussed.
Optimal Transport (OT) is a resource allocation problem with applications in biology, data science, economics and statistics, among others. In some of the applications, practitioners have access to samples which approximate the continuous…
We present a one-dimensional scattering theory which enables us to describe a wealth of effects arising from the coupling of the motional degree of freedom of scatterers to the electromagnetic field. Multiple scattering to all orders is…
Fully relativistic and causal equations for the flow of charge in curved spacetime are derived. It is believed that this is the first set of equations to be published that correctly describes the flow of charge, and evolution of the…
We consider a charged particle following the boundary of a two-dimensional domain because a homogeneous magnetic field is applied. We develop the basic scattering theory for the corresponding quantum mechanical edge states. The scattering…
We study electron propagation through a random array of rare, opaque and large (compared the de Broglie wavelength of electrons) scatterers. It is shown that for any convex scatterer the ratio of the transport to quantum lifetimes…
Many important transport phenomena are described by simple mathematical models rooted in the diffusion equation. Geometrical constraints present in such phenomena often have influence of a universal sort and manifest themselves in scaling…
A theoretical framework is developed for scattering of scalar radiation from stationary, three-dimensional media with correlation functions of scattering potentials obeying $\mathcal{PT}$-symmetry. It is illustrated that unlike in…
The basic quantum mechanical relation between fluctuations of transported charge and current correlators is discussed. It is found that, as a rule, the correlators are to be time-ordered in an unusual way. Instances where the difference…
The theory of transport of charged particles in cosmic magnetic fields is at the very center of the investigation of non-thermal phenomena in the universe, ranging from our local neighborhood to supernovae, clusters of galaxies or distant…
We present an atomistic theory of electronic transport through single organic molecules that reproduces the important features of the current-voltage characteristics observed in recent experiments. We trace these features to their origin in…