Related papers: Generalized DMPK equation for strongly localized r…
We propose a multiscale spectral generalized finite element method (MS-GFEM) for discontinuous Galerkin (DG) discretizations. The method builds local approximations on overlapping subdomains as the sum of a local source solution and a…
We present a field-theoretic framework to characterize the distribution of transmission eigenvalues for coherent wave propagation through disordered media. The central outcome is a transport equation for a matrix-valued radiance, analogous…
We study transport equations for quantum many-particle systems in terms of correlations by applying the general formalism developed in an earlier paper to exactly soluble electron-phonon models. The one-dimensional models considered are the…
We introduce fast algorithms for generalized unnormalized optimal transport. To handle densities with different total mass, we consider a dynamic model, which mixes the $L^p$ optimal transport with $L^p$ distance. For $p=1$, we derive the…
We demonstrate that with a stepwise introduction of complexity to a model of an electron system embedded in a photonic cavity and a carefully controlled stepwise truncation of the ensuing many-body space it is possible to describe the…
We have previously shown an analysis of our dimer model in the over-damped regime to show directed transport in equilibrium. Here we analyze the full model with inertial terms present to establish the same result. First we derive the…
We study the conductance of disordered wires with unitary symmetry focusing on the case in which $m$ perfectly conducting channels are present due to the channel-number imbalance between two-propagating directions. Using the exact solution…
The exact solution of the Dorokhov-Mello-Pereyra-Kumar-equation for quasi one-dimensional disordered conductors in the unitary symmetry class is employed to calculate all $m$-point correlation functions by a generalization of the method of…
We present a theoretical approach to solve Markovian master equation for quantum transport with stochastic telegraph noise. Considering probabilities as functionals of a random telegraph process we use the Novikov's functional method to…
We present and analyze a discontinuous Galerkin method for the numerical modelling of the non-linear fully-coupled thermo-poroelastic problem. For the spatial discretization, we design a high-order discontinuous Galerkin method on polygonal…
We consider the forward Kolmogorov equation corresponding to measure-valued processes stemming from a class of interacting particle systems in population dynamics, including variations of the Bolker-Pacala-Dieckmann-Law model. Under the…
We present a simplified model consisting on two linear elliptic boundary-value problems that represent a single step and single fixed-point iteration in an electrochemical battery model. The main variables are the concentration and the…
Distributed-order PDEs are tractable mathematical models for complex multiscaling anomalous transport, where derivative orders are distributed over a range of values. We develop a fast and stable Petrov-Galerkin spectral method for such…
We consider quantum trajectories arising from disordered, repeated generalized measurements, which have the structure of Markov chains in random environments (MCRE) with dynamically-defined transition probabilities; we call these disordered…
The Discretizable Molecular Distance Geometry Problem (DMDGP) aims to determine the three-dimensional protein structure using distance information from nuclear magnetic resonance experiments. The DMDGP has a finite number of candidate…
The purpose of this paper is (i) to present a generic and fully functional implementation of the density-matrix renormalization group (DMRG) algorithm, and (ii) to describe how to write additional strongly-correlated electron models and…
We recall theoretical studies on transient transport through interacting mesoscopic systems. It is shown that a generalized master equation (GME) written and solved in terms of many-body states provides the suitable formal framework to…
Recent developments are reviewed in the scaling theory of phase-coherent conduction through a disordered wire. The Dorokhov-Mello-Pereyra-Kumar equation for the distribution of transmission eigenvalues has been solved exactly, in the…
Through multiscale analysis of the adjoint Fokker-Planck equation, strict bounds are derived for the center of mass diffusivity of an overdamped harmonic chain in a periodic potential, often known as the discrete Frenkel-Kontorova model.…
For disordered quantum wires which belong to all ten universality classes, the universal quantities of transport properties are obtained through DMPK approach. Calculated are the universal parts of one- and two-point correlation functions…