Derivation of nonlinear single-particle equations via many-body Lindblad superoperators: A density-matrix approach

Abstract

A recently proposed Markov approach provides Lindblad-type scattering superoperators, which ensure the physical (positive-definite) character of the many-body density matrix. We apply the mean-field approximation to such many-body equation, in the presence of one- and two-body scattering mechanisms, and we derive a closed equation of motion for the electronic single-particle density matrix, which turns out to be non-linear as well as non-Lindblad. We prove that, in spite of its nonlinear and non-Lindblad structure, the mean-field approximation does preserve the positive-definite character of the single-particle density matrix, an essential prerequisite of any reliable kinetic treatment of semiconductor quantum devices. This result is in striking contrast with conventional (non-Lindblad) Markov approaches, where the single-particle mean-field equations can lead to positivity violations and to unphysical results. Furthermore, the proposed single-particle formulation is extended to the case of quantum systems with spatial open boundaries, providing a formal derivation of a recently proposed density-matrix treatment based on a Lindblad-like system-reservoir scattering superoperator.

arXiv comment10 pages, 1 figure (submitted to Phys. Rev. B)

References in corpus (7)

• Current noise in a vibrating quantum dot array
• Current in open quantum systems
• Quantum-transport theory for semiconductor nanostructures: A density-matrix formulation
• Decoherence due to contacts in ballistic nanostructures
• Interplay between energy dissipation and reservoir-induced thermalization in nonequilibrium quantum nanodevices
• Scattering nonlocality in quantum charge transport: Application to semiconductor nanostructures
• Quantum diffusion due to scattering non-locality in nanoscale semiconductors

Cited by in corpus (18)

• A phenomenological position and energy resolving Lindblad approach to quantum kinetics
• Optoelectronic device simulations based on macroscopic Maxwell-Bloch equations
• Spin-phonon relaxation from a universal \emph{ab initio} density-matrix approach
• Master Equations for Electron Transport: The Limits of the Markovian Limit
• Tracing the nonequilibrium topological state of Chern insulators
• Ab initio Ultrafast Spin Dynamics in Solids
• Wigner-function formalism applied to semiconductor quantum devices: Need for nonlocal scattering models
• Electron-phonon coupling in metallic carbon nanotubes: Dispersionless electron propagation despite dissipation
• Lindblad approach to spatio-temporal quantum dynamics of phonon-induced carrier capture processes
• Dispersionless propagation of electron wavepackets in single-walled carbon nanotubes
• Analytic expressions for the steady-state current with finite extended reservoirs
• Spatial control of carrier capture in two-dimensional materials: Beyond energy selection rules
• Electronic Transport and Thermopower in 2D and 3D Heterostructures--A Theory Perspective
• Electronic phase coherence versus dissipation in solid-state quantum devices: Two approximations are better than one
• Energetic cost for speedy synchronization in non-Hermitian quantum dynamics
• Advancing Simulations of Coupled Electron and Phonon Nonequilibrium Dynamics Using Adaptive and Multirate Time Integration
• Transport in Conductors and Rectifiers: Mean-Field Redfield Equations and Non-Equilibrium Green's Functions
• Preserving fermionic statistics for single-particle approximations in microscopic quantum master equations