Effective single-particle order-N scheme for the dynamics of open non-interacting many-body systems

Abstract

Quantum master equations are common tools to describe the dynamics of many-body systems open to an environment. Due to the interaction with the latter, even for the case of non-interacting electrons, the computational cost to solve these equations increases exponentially with the particle number. We propose a simple scheme, that allows to study the dynamics of $N$ non-interacting electrons taking into account both dissipation effects and Fermi statistics, with a computational cost that scales linearly with $N$. Our method is based on a mapping of the many-body system to a specific set of effective single-particle systems. We provide detailed numerical results showing excellent agreement between the effective single-particle scheme and the exact many-body one, as obtained from studying the dynamics of two different systems. In the first, we study optically-induced currents in quantum rings at zero temperature, and in the second we study a linear chain coupled at its ends to two thermal baths with different (finite) temperatures. In addition, we give an analytical justification for our method, based on an exact averaging over the many-body states of the original master equations.

9 pages, 8 figures. Expanded version, additional examples added

References in corpus (7)

• Thermopower of atomic-size metallic contacts
• Approach to steady state transport in nanoscale conductors
• Stochastic Time-Dependent Current-Density-Functional Theory
• Laser-controlled local magnetic field with semiconductor quantum rings
• Absence of Wigner Crystallization in Graphene
• Kinetic theory of quantum transport at the nanoscale
• Persistent and radiation-induced currents in distorted quantum rings

Cited by in corpus (17)

• A phenomenological position and energy resolving Lindblad approach to quantum kinetics
• Fourier's Law: insight from a simple derivation
• Stochastic time-dependent current-density functional theory: a functional theory of open quantum systems
• Reconstructing Fourier's law from disorder in quantum wires
• Stochastic Quantum Molecular Dynamics
• Relaxation times in an open interacting two-qubit system
• Origin of thermoelectric response fluctuations in single-molecule junctions
• Stochastic quantum molecular dynamics for finite and extended systems
• Functional theories of thermoelectric phenomena
• Ultrafast spin dynamics in inhomogeneous systems: a density-matrix approach applied to Co/Cu interfaces
• Foundations of stochastic time-dependent current-density functional theory for open quantum systems: Potential pitfalls and rigorous results
• Markovian kinetic equation approach to electron transport through quantum dot coupled to superconducting leads
• Application of a time-convolutionless stochastic Schrödinger equation to energy transport and thermal relaxation
• Ultrafast spin dynamics: complementing theoretical analyses by quantum-information measures
• Unraveling open-system quantum dynamics of non-interacting Fermions
• The decay of excited He from Stochastic Density-Functional Theory: a quantum measurement theory interpretation
• Preserving fermionic statistics for single-particle approximations in microscopic quantum master equations