Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Workshop on Computational Electronics

Microscopic modeling of quantum devices at high carrier densities via Lindblad-type scattering superoperators

Roberto Rosati, Rita Claudia Iotti, Fausto Rossi

Published Jun 1, 2014• 1 citation
Publisher

Abstract

We derive a local equation of motion for the electronic single-particle density matrix in the presence of one- as well as two-body scattering processes. This is done by applying the mean-field approximation to the many-electron dynamics obtained via a recently proposed Markov limit, able to furnish many-body Lindblad-type scattering superoperators. The resulting time evolution at finite/high carrier densities turns out to be non-linear (and therefore non-Lindblad), and to recover a Lindblad form in the low-density limit.

DOI
10.1109/iwce.2014.6865848

Related papers

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

Roberto Rosati, Rita Claudia Iotti, Fabrizio Dolcini +1 more

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 a 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 nonlinear 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 thus 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:1408.1898•Physical Review B•Sep 23, 2014•52 citations

Microscopic treatment of energy dissipation and decoherence via many-body Lindblad superoperators

Roberto Rosati, Rita Claudia Iotti, Fabrizio Dolcini +1 more

Starting from a recent reformulation of the Markov limit, we apply the mean- field approximation to the resulting Lindblad-type many-electron dynamics, and derive a closed equation of motion for the electronic single-particle density matrix in the presence of one- and two-body scattering mechanisms. The proposed formulation preserves the positive- definite character of the single-particle density matrix. This result is in striking contrast with conventional Markov approaches, where the single-particle mean-field equations can lead to positivity violations and therefore to unphysical results.

Journal of Physics Conference Series•Oct 13, 2015•2 citations

Lindblad approach to spatiotemporal quantum dynamics of phonon-induced carrier capture processes

Roberto Rosati, Doris E. Reiter, T. Kühn

In view of the ultrashort spatial and temporal scales involved, carrier capture processes in nanostructures are genuine quantum phenomena. To describe such processes, methods with different levels of approximations have been developed. By properly tailoring the Lindblad-based nonlinear single-particle density matrix equation provided by an alternative Markov approach, in this work we present a Lindblad superoperator to describe how the phonon-induced carrier capture affects the spatiotemporal quantum dynamics of a flying wave packet impinging on a quantum dot. We compare the results with non-Markovian quantum kinetics calculations and discuss the advantages and drawbacks of the two approaches.

arXiv:1703.02772•Physical review. B./Physical review. B•Apr 6, 2017•16 citations

Microscopic Modeling of Energy Dissipation and Decoherence in Open Quantum Systems: Application to Semiconductor Nanodevices

David Taj, Rita Claudia Iotti, Fausto Rossi

A general density-matrix description of energy-dissipation and decoherence phenomena in open quantum systems is presented. More specifically, contrary to the conventional single-particle correlation expansion, we shall investigate the effect of the adiabatic or Markov limit, before considering/performing any reduction procedure. Our fully operatorial approach allows us to better identify the general properties of the scattering superoperators entering our effective quantum-transport theory at various description levels. In particular, we shall show that—contrary to the semiclassical case—the conventional Markov limit does not preserve the positive-definite character of the corresponding density matrix, thus leading to highly non-physical results. To overcome this serious limitation, originally pointed out and partially solved by Davies and co-workers almost three decades ago, we shall propose an alternative and more general adiabatic procedure, which (i) in the semiclassical limit reduces to the standard Fermi's golden rule, and (ii) describes a genuine Lindblad evolution, thus providing a reliable/robust treatment of energy-dissipation and dephasing processes in semiconductor quantum devices

Journal of Computational and Theoretical Nanoscience•Aug 1, 2009•0 citations

A STOCHASTIC GOLDEN RULE AND QUANTUM LANGEVIN EQUATION FOR THE LOW DENSITY LIMIT

Luigi Accardi, Alexander Nikolaevich Pechen, Igor Vasil'evich Volovich

A rigorous derivation of quantum Langevin equation from microscopic dynamics in the low density limit is given. We consider a quantum model of a microscopic system (test particle) coupled with a reservoir (gas of light Bose particles) via interaction of scattering type. We formulate a mathematical procedure (the so-called stochastic golden rule) which allows us to determine the quantum Langevin equation in the limit of large time and small density of particles of the reservoir. The quantum Langevin equation describes not only dynamics of the system but also the reservoir. We show that the generator of the corresponding master equation has the Lindblad form of most general generators of completely positive semigroups.

arXiv:math-ph/0206032•Infinite Dimensional Analysis Quantum Probability and Related Topics•Sep 1, 2003•18 citations

Dissipation and decoherence in nanodevices: a generalized Fermi's golden rule

David Taj, Rita Claudia Iotti, Fausto Rossi

We shall revisit the conventional adiabatic or Markov approximation, which --contrary to the semiclassical case-- does not preserve the positive-definite character of the corresponding density matrix, thus leading to highly non-physical results. To overcome this serious limitation, originally pointed out and partially solved by Davies and co-workers almost three decades ago, we shall propose an alternative more general adiabatic procedure, which (i) is physically justified under the same validity restrictions of the conventional Markov approach, (ii) in the semiclassical limit reduces to the standard Fermi's golden rule, and (iii) describes a genuine Lindblad evolution, thus providing a reliable/robust treatment of energy-dissipation and dephasing processes in electronic quantum devices. Unlike standard master-equation formulations, the dependence of our approximation on the specific choice of the subsystem (that include the common partial trace reduction) does not threaten positivity, and quantum scattering rates are well defined even in case the subsystem is infinitely extended/has continuous spectrum.

arXiv:0905.1026•Semiconductor Science and Technology•May 5, 2009•4 citations
We derive a local equation of motion for the electronic single-particle density matrix in the presence of one- as well as two-body scattering processes. This is done by applying the mean-field approximation to the many-electron dynamics obtained via a recently proposed Markov limit, able to furnish many-body Lindblad-type scattering superoperators. The resulting time evolution at finite/high carrier densities turns out to be non-linear (and therefore non-Lindblad), and to recover a Lindblad form in the low-density limit.
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 a 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 nonlinear 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 thus 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.
Starting from a recent reformulation of the Markov limit, we apply the mean- field approximation to the resulting Lindblad-type many-electron dynamics, and derive a closed equation of motion for the electronic single-particle density matrix in the presence of one- and two-body scattering mechanisms. The proposed formulation preserves the positive- definite character of the single-particle density matrix. This result is in striking contrast with conventional Markov approaches, where the single-particle mean-field equations can lead to positivity violations and therefore to unphysical results.
In view of the ultrashort spatial and temporal scales involved, carrier capture processes in nanostructures are genuine quantum phenomena. To describe such processes, methods with different levels of approximations have been developed. By properly tailoring the Lindblad-based nonlinear single-particle density matrix equation provided by an alternative Markov approach, in this work we present a Lindblad superoperator to describe how the phonon-induced carrier capture affects the spatiotemporal quantum dynamics of a flying wave packet impinging on a quantum dot. We compare the results with non-Markovian quantum kinetics calculations and discuss the advantages and drawbacks of the two approaches.
A general density-matrix description of energy-dissipation and decoherence phenomena in open quantum systems is presented. More specifically, contrary to the conventional single-particle correlation expansion, we shall investigate the effect of the adiabatic or Markov limit, before considering/performing any reduction procedure. Our fully operatorial approach allows us to better identify the general properties of the scattering superoperators entering our effective quantum-transport theory at various description levels. In particular, we shall show that—contrary to the semiclassical case—the conventional Markov limit does not preserve the positive-definite character of the corresponding density matrix, thus leading to highly non-physical results. To overcome this serious limitation, originally pointed out and partially solved by Davies and co-workers almost three decades ago, we shall propose an alternative and more general adiabatic procedure, which (i) in the semiclassical limit reduces to the standard Fermi's golden rule, and (ii) describes a genuine Lindblad evolution, thus providing a reliable/robust treatment of energy-dissipation and dephasing processes in semiconductor quantum devices
A rigorous derivation of quantum Langevin equation from microscopic dynamics in the low density limit is given. We consider a quantum model of a microscopic system (test particle) coupled with a reservoir (gas of light Bose particles) via interaction of scattering type. We formulate a mathematical procedure (the so-called stochastic golden rule) which allows us to determine the quantum Langevin equation in the limit of large time and small density of particles of the reservoir. The quantum Langevin equation describes not only dynamics of the system but also the reservoir. We show that the generator of the corresponding master equation has the Lindblad form of most general generators of completely positive semigroups.
We shall revisit the conventional adiabatic or Markov approximation, which --contrary to the semiclassical case-- does not preserve the positive-definite character of the corresponding density matrix, thus leading to highly non-physical results. To overcome this serious limitation, originally pointed out and partially solved by Davies and co-workers almost three decades ago, we shall propose an alternative more general adiabatic procedure, which (i) is physically justified under the same validity restrictions of the conventional Markov approach, (ii) in the semiclassical limit reduces to the standard Fermi's golden rule, and (iii) describes a genuine Lindblad evolution, thus providing a reliable/robust treatment of energy-dissipation and dephasing processes in electronic quantum devices. Unlike standard master-equation formulations, the dependence of our approximation on the specific choice of the subsystem (that include the common partial trace reduction) does not threaten positivity, and quantum scattering rates are well defined even in case the subsystem is infinitely extended/has continuous spectrum.