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 Journal of Modern Physics E

MICROSCOPIC COEFFICIENTS FOR THE QUANTUM MASTER EQUATION OF A FERMI SYSTEM

Eliade N. Stefanescu, Aurel Sǎndulescu

Published Apr 1, 2002• 6 citations
Publisher

Abstract

In a previous paper, we derived a master equation for fermions, of Lindblad's form, with coefficients depending on microscopic quantities. In this paper, we study the properties of the dissipative coefficients taking into account the explicit expressions of: (a) the matrix elements of the dissipative potential, evaluated from the condition that, essentially, this potential induces transitions among the system eigenstates without significantly modifying these states, (b) the densities of the environment states according to the Thomas–Fermi model, and (c) the occupation probabilities of these states taken as a Fermi–Dirac distribution. The matrix of these coefficients correctly describes the system dynamics: (a) for a normal, Fermi–Dirac distribution of the environment population, the decays dominate the excitation processes; (b) for an inverted (exotic) distribution of this population, specific to a clustering state, the excitation processes are dominant.

DOI
10.1142/s0218301302000739

Related papers

The Lindblad dynamics of a Fermi system in a particle dissipative environment

Eliade N. Stefanescu, Paul E. Sterian, Andreea-Rodica P. Sterian

An essential problem of the quantum information systems is the controllability and observability of the quantum states, generally described by Lindblad's master equation with phenomenological coefficients. However, in its general form, this equation describes a decay of the mean-values, but not necessarily the expected decaying transitions. We propose a quantum master equation with microscopic coefficients where these transitions are correctly described, and investigate the properties of the dissipative coefficients. Being of Lindblad's form, this equation preserves the quantum-mechanical properties of the density matrix during the whole evolution of the system and is in accordance with the entropy principle. On this basis, generalized Bloch-Feynman equations with microscopic coefficients for N-level systems are obtained.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Nov 14, 2003•5 citations

THE COLLISIONAL DECAY OF A FERMI SYSTEM INTERACTING WITH A MANY-MODE ELECTROMAGNETIC FIELD

Eliade N. Stefanescu, A. Sãndulescu, W. Scheid

We consider a system of Z fermions coupled to a dissipative environment through a two-body potential. We represent the system in a basis of single-particle, two-particle, … Z-particle excitated states. Using a procedure for averaging the rapid oscillations of the reduced density matrix in the interaction picture, the master equation of the system takes the form of a series expansion of powers of the dissipative potential matrix elements. The term of the second-order describes single-particle transitions, while the higher-order terms correspond to correlated transitions of the system particles. For the second- and the third-order terms, we derive microscopic expressions of the dissipative coefficients. For dissipative systems, when the state collectivity is broken into pieces through quantum diffusion, we use the quantum master equation of the second-order approximation. This equation satisfies basic physical conditions: particle conservation, Fermi–Dirac or Bose–Einstein distributions as asymptotic solutions of the populations, and entropy increase. On this basis, the decay of a Fermi system interacting with a many-mode electromagnetic field is described in terms of microscopic quantities: the matrix elements of the dissipative potential, the densities of the environment states, and the occupation probabilities of these states. A near-dipode–dipode interaction of the system with other neighbouring systems is taken into account. In addition to the coupling of the polarization with the population, included in the usual equations for two-level systems as a non-linear detuning, in equations for N-level systems two new couplings of the polarizations appear: a coupling due to the proximity potential, and a coupling due to the local field corrections, as a renormalization of the Rabi frequencies.

International Journal of Modern Physics E•Feb 1, 2000•8 citations

Dynamics of a Fermi system in a complex dissipative environment

Eliade N. Stefanescu, Paul E. Sterian

We derive a quantum master equation for a system of femions coupled to the blackbody radiation field and to many other excitations of the surrounding particles. In comparison with other master equations for many-level systems, the new master equation depends on microscopic coefficients (as functions of physical constants, matrix elements, densitie of the environment states, and occupation probabilities of these states), and includes two additional terms: (1) a term depending on the selfconsistent field of the collective motion of the system or of other surrounding particles, and (2) a non-Markovian term.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Aug 9, 2002•1 citation

DYNAMICS OF A FERMI SYSTEM IN A BLACKBODY RADIATION FIELD

Eliade N. Stefanescu, Aurel Sǎndulescu

We derive a quantum master equation for a system of fermions coupled to the blackbody radiation field through the electric-dipole interaction. This equation is of Lindblad's form, with a hamiltonian part of the shell-model, and a dissipative art with microscopic coefficients, depending on physical constants, matrix elements, and parametrically only on temperature.

International Journal of Modern Physics E•Oct 1, 2002•5 citations

Study on the fermion systems coupled by electric dipol interaction with the free electromagnetic field

Eliade N. Stefanescu, Andreea Rodica Sterian, Paul E. Sterian

We established a master equation for a system of fermions coupled by electric dipol interaction with the free electromagnetic field. This equation has a Lindblad equation form, with a hamiltonian part corresponding to the shell model and a dissipative part with microscopic coefficients depending on physical constants, matrix elements, and temperature. The dependence on the transition energy of the dissipative coefficients satisfies asymptothycal conditions for the energy transfer in full agreement with the principle of the detailed balance.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jun 7, 2005•11 citations

Mathematical Models of Dissipative Systems in Quantum Engineering

Andreea Rodica Sterian, Paul E. Sterian

The paper shows the results of theoretical research concerning the modeling and characterization of the dissipative structures generally, the dissipation being an essential property of the system with self‐organization which include the laser‐type systems also. The most important results presented are new formulae which relate the coupling parametersainfrom Lindblad equation with environment operators Γi; microscopic quantitative expressions for the dissipative coefficients of the master equations; explicit expressions which describe the changes of the environment density operator during the system evolution for fermion systems coupled with free electromagnetic field; the generalized Bloch‐Feynman equations forN‐level systems with microscopic coefficients in agreement with generally accepted physical interpretations. Based on Maxwell‐Bloch equations with consideration of the interactions between nearing atomic dipoles, for the dense optical media we have shown that in the presence of the short optical pulses, the population inversion oscillates between two extreme values, depending on the strength of the interaction and the optical pulse energy.

Mathematical Problems in Engineering•Jan 1, 2012•11 citations
In a previous paper, we derived a master equation for fermions, of Lindblad's form, with coefficients depending on microscopic quantities. In this paper, we study the properties of the dissipative coefficients taking into account the explicit expressions of: (a) the matrix elements of the dissipative potential, evaluated from the condition that, essentially, this potential induces transitions among the system eigenstates without significantly modifying these states, (b) the densities of the environment states according to the Thomas–Fermi model, and (c) the occupation probabilities of these states taken as a Fermi–Dirac distribution. The matrix of these coefficients correctly describes the system dynamics: (a) for a normal, Fermi–Dirac distribution of the environment population, the decays dominate the excitation processes; (b) for an inverted (exotic) distribution of this population, specific to a clustering state, the excitation processes are dominant.
An essential problem of the quantum information systems is the controllability and observability of the quantum states, generally described by Lindblad's master equation with phenomenological coefficients. However, in its general form, this equation describes a decay of the mean-values, but not necessarily the expected decaying transitions. We propose a quantum master equation with microscopic coefficients where these transitions are correctly described, and investigate the properties of the dissipative coefficients. Being of Lindblad's form, this equation preserves the quantum-mechanical properties of the density matrix during the whole evolution of the system and is in accordance with the entropy principle. On this basis, generalized Bloch-Feynman equations with microscopic coefficients for N-level systems are obtained.
We consider a system of Z fermions coupled to a dissipative environment through a two-body potential. We represent the system in a basis of single-particle, two-particle, … Z-particle excitated states. Using a procedure for averaging the rapid oscillations of the reduced density matrix in the interaction picture, the master equation of the system takes the form of a series expansion of powers of the dissipative potential matrix elements. The term of the second-order describes single-particle transitions, while the higher-order terms correspond to correlated transitions of the system particles. For the second- and the third-order terms, we derive microscopic expressions of the dissipative coefficients. For dissipative systems, when the state collectivity is broken into pieces through quantum diffusion, we use the quantum master equation of the second-order approximation. This equation satisfies basic physical conditions: particle conservation, Fermi–Dirac or Bose–Einstein distributions as asymptotic solutions of the populations, and entropy increase. On this basis, the decay of a Fermi system interacting with a many-mode electromagnetic field is described in terms of microscopic quantities: the matrix elements of the dissipative potential, the densities of the environment states, and the occupation probabilities of these states. A near-dipode–dipode interaction of the system with other neighbouring systems is taken into account. In addition to the coupling of the polarization with the population, included in the usual equations for two-level systems as a non-linear detuning, in equations for N-level systems two new couplings of the polarizations appear: a coupling due to the proximity potential, and a coupling due to the local field corrections, as a renormalization of the Rabi frequencies.
We derive a quantum master equation for a system of femions coupled to the blackbody radiation field and to many other excitations of the surrounding particles. In comparison with other master equations for many-level systems, the new master equation depends on microscopic coefficients (as functions of physical constants, matrix elements, densitie of the environment states, and occupation probabilities of these states), and includes two additional terms: (1) a term depending on the selfconsistent field of the collective motion of the system or of other surrounding particles, and (2) a non-Markovian term.
We established a master equation for a system of fermions coupled by electric dipol interaction with the free electromagnetic field. This equation has a Lindblad equation form, with a hamiltonian part corresponding to the shell model and a dissipative part with microscopic coefficients depending on physical constants, matrix elements, and temperature. The dependence on the transition energy of the dissipative coefficients satisfies asymptothycal conditions for the energy transfer in full agreement with the principle of the detailed balance.
The paper shows the results of theoretical research concerning the modeling and characterization of the dissipative structures generally, the dissipation being an essential property of the system with self‐organization which include the laser‐type systems also. The most important results presented are new formulae which relate the coupling parametersainfrom Lindblad equation with environment operators Γi; microscopic quantitative expressions for the dissipative coefficients of the master equations; explicit expressions which describe the changes of the environment density operator during the system evolution for fermion systems coupled with free electromagnetic field; the generalized Bloch‐Feynman equations forN‐level systems with microscopic coefficients in agreement with generally accepted physical interpretations. Based on Maxwell‐Bloch equations with consideration of the interactions between nearing atomic dipoles, for the dense optical media we have shown that in the presence of the short optical pulses, the population inversion oscillates between two extreme values, depending on the strength of the interaction and the optical pulse energy.