Related papers: A reduced-order modeling approach for electron tra…
A classical reduced order model for dynamical problems involves spatial reduction of the problem size. However, temporal reduction accompanied by the spatial reduction can further reduce the problem size without losing accuracy much, which…
Quantum transport and other phenomena are typically modeled by coupling the system of interest to an environment, or bath, held at thermal equilibrium. Realistic bath models are at least as challenging to construct as models for the quantum…
In this paper we consider a geothermal energy storage in which the spatio-temporal temperature distribution is modeled by a heat equation with a convection term. Such storages often are embedded in residential heating systems and control…
We develop a numerical procedure to efficiently model the nonequilibrium steady state of one-dimensional arrays of open quantum systems, based on a matrix-product operator ansatz for the density matrix. The procedure searches for the null…
Using a stochastic quantum approach, we study thermoelectric transport phenomena at low temperatures in disordered electrical systems connected to external baths. We discuss three different models of one-dimensional disordered electrons,…
Using an autoencoder for dimensionality reduction, this paper presents a novel projection-based reduced-order model for eigenvalue problems. Reduced-order modelling relies on finding suitable basis functions which define a low-dimensional…
We propose and analyze a mechanism for rectification of spin transport through a small junction between two spin baths or leads. For interacting baths we show that transport is conditioned on the spacial asymmetry of the quantum junction…
We consider a Markov process in continuous time with a finite number of discrete states. The time-dependent probabilities of being in any state of the Markov chain are governed by a set of ordinary differential equations, whose dimension…
High-resolution simulations of particle-based kinetic plasma models typically require a high number of particles and thus often become computationally intractable. This is exacerbated in multi-query simulations, where the problem depends on…
We simulate the nonequilibrium dynamics of two generic many-body quantum impurity models by employing the recently developed iterative influence-functional path integral method [Phys. Rev. B {\bf 82}, 205323 (2010)]. This general approach…
We describe a numerical algorithm for approximating the equilibrium-reduced density matrix and the effective (mean force) Hamiltonian for a set of system spins coupled strongly to a set of bath spins when the total system (system+bath) is…
The infinite-U Anderson model is applied to transport through a quantum dot. The current and density of states are obtained via the non-crossing approximation for two spin-degenerate levels weakly coupled to two leads. At low temperatures,…
We extend the second-order von Neumann approach within the generalized master equation formalism for quantum electronic transport to include the counting field. The resulting non-Markovian evolution equation for the reduced density matrix…
The Driven Liouville von Neumann approach [J. Chem. Theory Comput. 10, 2927-2941 (2014)] is a computationally efficient simulation method for modeling electron dynamics in molecular electronics junctions. Previous numerical simulations have…
Reduced-order models were derived for plane Couette flow using Galerkin projection, with orthonormal basis functions taken as the leading controllability modes of the linearised Navier-Stokes system for a few low wavenumbers. Resulting…
In this review article, we present a non-equilibrium quantum transport theory for transient electron dynamics in nanodevices based on exact master equation derived with the path integral method in the fermion coherent-state representation.…
In various physical implementations of quantum information processing, qubits are realized in a Lambda type system configuration as two stable lower energy levels coupled indirectly via an unstable higher energy level, that is, in…
We consider linear dynamical systems consisting of ordinary differential equations with high dimensionality. The aim of model order reduction is to construct an approximating system of a much lower dimension. Therein, the reduced system may…
Recent experiments in hybrid-quantum systems facilitate the potential realization of one of the most fundamental interacting Hamiltonian-Reservoir system, namely, the single-site Bose-Hubbard model coupled to two reservoirs at different…
Linear kinetic transport equations play a critical role in optical tomography, radiative transfer and neutron transport. The fundamental difficulty hampering their efficient and accurate numerical resolution lies in the high dimensionality…