Related papers: Diffusion models for atomic scale electron current…
A novel principle is presented which allows for the proof of bounded weak solutions to a class of physically relevant, strongly coupled parabolic systems exhibiting a formal gradient-flow structure. The main feature of these systems is that…
An improved real-time quantum Monte Carlo procedure is presented and applied to describe the electronic transfer dynamics along molecular chains. The model consists of discrete electronic sites coupled to a thermal environment which is…
Long ago, life discovered how to efficiently push electrons thermodynamically uphill to lower potential by harnessing energy released by an equal number of electrons moving downhill. Known as electron bifurcation, this form of energy…
We describe mathematically the apparently paradoxical phenomenon that an electronic current in a semiconductor can flow because of collisions, and not despite them. A transport model of charge transport in a one-dimensional semiconductor…
The mathematical modeling and numerical simulation of semiconductor-electrolyte systems play important roles in the design of high-performance semiconductor-liquid junction solar cells. In this work, we propose a macroscopic mathematical…
Maximization of the entropy rate is an important issue to design diffusion processes aiming at a well-mixed state. We demonstrate that it is possible to construct maximal-entropy random walks with only local information on the graph…
We investigate a recombination-drift-diffusion model coupled to Poisson's equation modelling the transport of charge within certain types of semiconductors. In more detail, we study a two-level system for electrons and holes endowed with an…
The methods of non-equilibrium thermodynamics of systems with an interface have been applied to the study of transport processes in semiconductor junctions. A complete phenomenological model for drift-diffusion processes in a junction has…
We consider a random walk on the support of an ergodic simple point process on R^d, d>1, furnished with independent energy marks. The jump rates of the random walk decay exponentially in the jump length and depend on the energy marks via a…
Near-critical quantum circuits are ideal physical systems for asymptotically large-scale quantum computers, because their low energy collective excitations evolve reversibly, effectively isolated from the environment. The design of…
Molecular conduction operating in dielectric solvent environments are often described using kinetic rates based on Marcus theory of electron transfer at a molecule-metal electrode interface. However, the successive nature of charge transfer…
Semiconductor model is a system of parabolic partial differential equations with cross-diffusion phenomenon. Previous results showed that a weak solution exists and is not bounded in general. So semiconductor model was categorized as a…
Based on a semi-empirical generalized Anderson-Newns model we construct a pseudo-particle description for electron emission due to de-excitation of metastable molecules at surfaces. The pseudo-particle approach allows us to treat resonant…
A new variational method for studying the equilibrium states of an interacting particles system has been proposed. The statistical description of the system is realized by means of a density matrix. This method is used for description of…
The Abelian Sandpile Model is a discrete diffusion process defined on graphs (Dhar \cite{DD90}, Dhar et al. \cite{DD95}) which serves as the standard model of \textit{self-organized criticality}. The transience class of a sandpile is…
Strongly interacting electron systems can provide insight into quantum many-body phenomena, such as Mott insulating behavior and spin liquidity, facilitating semiconductor optimization. The Fermi-Hubbard model is the prototypical model used…
Spatial spread of minority carriers produced by optical excitation in semiconductors is usually well described by a diffusion equation. The classical diffusion process can be viewed as a result of a random walk of particles in which every…
Random walks are fundamental tools for analyzing complex networked systems, including social networks, biological systems, and communication infrastructures. While classical random walks focus on pairwise interactions, many real-world…
One-dimensional non-equilibrium models of particles subjected to a coagulation-diffusion process are important in understanding non-equilibrium dynamics, and fluctuation-dissipation relation. We consider in this paper transport properties…
In this paper we present analytical and random walk based solutions to diffusion in semi-permeable layered media with varying diffusivity. We propose a new random walk transit model (hybrid model) based on treating the membrane permeability…