Related papers: Generalized Ohm's law
We consider the scattering theory for the Schr\"odinger operator $-\Dc_x^2+V(x)$ on graphs made of one-dimensional wires connected to external leads. We derive two expressions for the scattering matrix on arbitrary graphs. One involves…
We give a method of describing thermodynamical transport phenomena, based on a quantum scattering theoretical approach. We consider a quantum system of particles connected to thermodynamical reservoirs by leads. The effects of the…
The purpose of this paper is to provide an introduction to the physics of scattering theory, to define the dosimetric concept of linear energy transfer in terms of scattering theory, and to provide an introduction to the concepts underlying…
The chaotic scattering theory is here extended to obtain escape-rate expressions for the transport coefficients appropriate for a simple classical fluid, or for a chemically reacting system. This theory allows various transport coefficients…
A generalized continuity equation extending the ordinary continuity equation has been found using quanternions. It is shown to be compatible with Dirac, Schrodinger, Klein-Gordon and diffusion equations. This generalized equation is Lorentz…
In my thesis I study mesoscopic corrections on diffuse transport. I first describe the diffuse transport of light, using the scalar approximation and the radiative transfer approach. Next, I focus on the correlations in transmission, I…
Disordered nanostructures are commonly encountered in many nanophotonic systems, from colloid dispersions for sensing, to heterostructured photocatalysts. Randomness, however, imposes severe challenges for nanophotonics modeling, often…
The statistics of charge transport across a tunnel junction with energy-dependent scattering is investigated. A model with quadratic dispersion relation is discussed in general and, independently, in the two limiting cases of a large…
Scattering theory is a standard tool for the description of transport phenomena in mesoscopic systems. Here, we provide a detailed derivation of this method for nano-scale conductors that are driven by oscillating electric or magnetic…
We report a theory for analyzing nonlinear DC transport properties of mesoscopic or nanoscopic normal-superconducting (N-S) systems. Special attention was paid such that our theory satisfies gauge invariance. At the linear transport regime…
The derivation of Lorentz-covariant generalizations of Ohm's law has been a long-term issue in theoretical physics with deep implications for the study of relativistic effects in optical and atomic physics. In this article, we propose an…
A general proof of the optical theorem (also known as the optical cross-section theorem) is presented that reveals the intimate connection between the forward scattering amplitude and the absorption-plus-scattering of the incident wave…
We continue our study of scattering theory and dispersive properties for one-dimensional charge transfer models, namely linear Schr\"odinger equations with multiple moving potentials. By the discovery of a refined structure of the…
We provide an informal overview on the theory of transport equations with non smooth velocity fields, and on some applications of this theory to the well-posedness of hyperbolic systems of conservation laws.
A general theoretical framework is developed for interpreting spectropolarimetric observations of optically thin emission line scattering from small dust particles. Spatially integrated and spatially resolved line profiles of both scattered…
If the information is encoded into the state of the subsystem $S$ of a quantum system initially (at $t=0$), then it becomes distributed over the whole quantum system at $t>0$ due to the quantum interactions. Consequently, this information,…
Optimal Transport is a foundational mathematical theory that connects optimization, partial differential equations, and probability. It offers a powerful framework for comparing probability distributions and has recently become an important…
Many practical applications require the analysis of electromagnetic scattering properties of local structures using different sources of illumination. The Optical Theorem (OT) is a useful result in scattering theory, relating the extinction…
We investigate electron transport through a mono-atomic wire which is tunnel coupled to two electrodes and also to the underlying substrate. The setup is modeled by a tight-binding Hamiltonian and can be realized with a scanning tunnel…
The circuit theory of mesoscopic transport provides a unified framework to describe spin-dependent or superconductivity-related phenomena. We extend this theory to hybrid systems of normal metals, ferromagnets and superconductors. Our main…