Time-dependent transport in open systems based on quantum master equations

Abstract

Electrons in the active region of a nanostructure constitute an open many-body quantum system, interacting with contacts, phonons, and photons. We review the basic premises of the open system theory, focusing on the common approximations that lead to Markovian and non-Markovian master equations for the reduced statistical operator. We highlight recent progress on the use of master equations in quantum transport, and discuss the limitations and potential new directions of this approach.

Review paper in Journal of Computational Electronics, part of the special issue "Quantum Transport Beyond DC"

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• Master Equations for Electron Transport: The Limits of the Markovian Limit
• Passive and hybrid mode locking in multi-section terahertz quantum cascade lasers
• Dissipative transport in superlattices within the Wigner function formalism
• Self-excited current oscillations in a resonant tunneling diode described by a model based on the Caldeira-Leggett Hamiltonian
• Dielectric function and plasmons in graphene: A self-consistent-field calculation within a Markovian master equation formalism
• Performance of Reservoir Discretizations in Quantum Transport Simulations
• Time-dependent Andreev bound states of a quantum dot coupled to two superconducting leads
• Analytic expressions for the steady-state current with finite extended reservoirs
• Construction of propagators for divisible dynamical maps
• Density-matrix model for photon-driven transport in quantum cascade lasers
• Decoherence of an entangled state of a strongly-correlated double quantum dot structure through tunneling processes
• Transport in a periodically driven tilted lattice via the extended reservoir approach: Stability criterion for recovering the continuum limit
• Dual current anomalies and quantum transport within extended reservoir simulations