Related papers: Diffusion models for atomic scale electron current…
Electron transfer processes at molecule-semiconductor interfaces involve a complex mixture of thermionic, tunneling and hopping events. Traditionally these processes have been modeled in a piece-meal fashion, relying on phenomenological…
A theory for non-equilibrium systems is derived from a maximum entropy approach similar in spirit to the equilibrium theory given by Gibbs. Requiring Hamilton's principle of stationary action to be satisfied on average during a trajectory,…
Quantum-confined semiconductor structures are the cornerstone of modern-day electronics. Spatial confinement in these structures leads to formation of discrete low-dimensional subbands. At room temperature, carriers transfer among different…
A contour dynamics model for electrical discharges is obtained and analyzed. The model is deduced as the asymptotic limit of the minimal streamer model for the propagation of electric discharges, in the limit of small electron diffusion.…
Motivated by contact resistance on the front side of a crystalline silicon solar cell, we formulate and analyse a two-dimensional mathematical model for electron flow across a poorly conducting (glass) layer situated between silver…
Unusually large spontaneous and piezoelectric fields in the III-V nitrides have led to the making of an entirely new class of two-dimensional electron gas. Fluctuation from a perfectly periodic binary structure in highly polar semiconductor…
The semi-classical Bloch-Boltzmann theory is at the heart of our understanding of conduction in solids, ranging from metals to semi-conductors. Physical systems that are beyond the range of applicability of this theory are thus of…
We present a method to analyze the results of first-principles based calculations of electronic currents including inelastic electron-phonon effects. This method allows us to determine the electronic and vibrational symmeties in play, and…
Traditional equivalent circuit models (ECMs) have difficulties in estimating battery internal states due to the lack of relevant physics, such as the lithium diffusion in active particles. Here we configure a circuit network to describe the…
Mathematically modelling diffusive and advective transport of particles in heterogeneous layered media is important to many applications in computational, biological and medical physics. While deterministic continuum models of such…
Diffusion in an evolving environment is studied by continuos-time Monte Carlo simulations. Diffusion is modelled by continuos-time random walkers on a lattice, in a dynamic environment provided by bubbles between two one-dimensional…
For an arbitrary initial configuration of discrete loads over vertices of a distributed graph, we consider the problem of minimizing the {\em discrepancy} between the maximum and minimum loads among all vertices. For this problem, this…
For electron-phonon Hamiltonians with the couplings linear in the phonon operators we construct a class of unitary transformations that separate the normal modes into two groups. The modes in the first group interact with the electronic…
Path-dependent stochastic processes are often non-ergodic and observables can no longer be computed within the ensemble picture. The resulting mathematical difficulties pose severe limits to the analytical understanding of path-dependent…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
Atomic and single-molecule junctions represent the ultimate limit to the miniaturization of electrical circuits. They are also ideal platforms to test quantum transport theories that are required to describe charge and energy transfer in…
Mesoscopic integrated circuits achieving high-fidelity control of elementary quantum systems require new methodology for benchmarking. We offer circuit-level statistical description of rare-error accumulation in terms of a universal…
We have studied the extended Hubbard model with pair hopping in the atomic limit for arbitrary electron density and chemical potential. The Hamiltonian considered consists of (i) the effective on-site interaction U and (ii) the intersite…
This work describes a new 1D hybrid approach for modeling atmospheric pressure discharges featuring complex chemistry. In this approach electrons are described fully kinetically using Particle-In-Cell/Monte-Carlo (PIC/MCC) scheme, whereas…
Two-dimensional networks of ordered quantum dots beyond the percolation threshold are studied, as typical example of conducting nanostructures with quenched random disorder. Theory predicts anomalous diffusion with stretched-exponential…