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

Optics and Spectroscopy

Kinetic equations for the density matrix of two-level particles in a strong field

Е. А. Титов

Published Oct 1, 2004• 2 citations
Publisher

Abstract

On the basis of the Green’s function method for nonequilibrium systems, the kinetic equation for two-level particles in a strong field is derived. In the binary approximation, all diagrams are expressed in terms of the reducible vertex part, whose calculation is reduced to the problem of two-channel scattering and finding the corresponding scattering amplitudes.

DOI
10.1134/1.1813703

Related papers

Derivation of the Kinetic Equation for the Density Matrix of Two-Level Particles by the Green’S Function Method

Е. А. Титов

On the basis of the Green’s function method for nonequilibrium systems, the kinetic equation for the density matrix of two-level particles used in laser spectroscopy is derived. The assumptions made in deriving the kinetic equation impose certain restrictions on this equation. In the binary approximation, all diagrams are expressed via the reducible vertex part, which can be expressed in terms of the amplitude of scattering of a two-level atom by a buffer gas.

Optics and Spectroscopy•Jun 29, 2004•6 citations

The shape of the statistical wing of an absorption line: Derivation by the Green’s function method

Е. А. Титов

A formula is derived for the absorption coefficient in the statistical wing of an absorption line in the case in which both levels of a two-level system are involved in collisions. For this purpose, the kinetic equations for two-level particles in a strong field at an arbitrary detuning of the field frequency from the transition frequency are used, which were derived previously with the Green’s function method for nonequilibrium systems.

Optics and Spectroscopy•Mar 1, 2006•0 citations

Nonequilibrium Green function approach to the pair distribution function of quantum many-body systems out of equilibrium

M. Bönitz, S Hermanns, K Kobusch +1 more

The pair distribution function (PDF) is a key quantity for the analysis of correlation effects of a quantum system both in equilibrium and far from equilibrium. We derive an expression for the PDF in terms of the single-particle Green functions—the solutions of the Keldysh/Kadanoff-Baym equations in the two-time plane—for a one- or two-component system. The result includes initial correlations and generalizes previous density matrix expressions from single-time quantum kinetic theory. Explicit expressions for the PDF are obtained in second Born approximation.

arXiv:1211.0209•Journal of Physics Conference Series•Mar 27, 2013•8 citations

Derivation of kinetic equation, up to order λ6, for the interaction between radiation and a two-level system. Part I

Françoise Hénin, Michel De Haan

In the bare particle representation, the kinetic operator Ψ(z) and its first derivatives play a very important role in the asymptotic equation for the evolution of the diagonal elements of the density matrix. Explicit expressions for these operators are derived, up to order λ6, for the interaction between radiation and a two level system. The transformation to the dressed particle distribution function will be given in a next paper.

Bulletin de la Classe des sciences•Jan 1, 1968•0 citations

Nonequilibrium Green’s Functions in the Atomic Representation and the Problem of Quantum Transport of Electrons Through Systems With Internal Degrees of Freedom

Valerii Vladimirovich Val'kov, S. V. Aksenov

We develop the theory of quantum transport of electrons through systems with strong correlations between fermionic and internal spin degrees of freedom. The atomic representation for the Hamiltonian of a device and nonequilibrium Green’s functions constructed using the Hubbard operators allow overcoming difficulties in the perturbation theory encountered in the traditional approach because of a larger number of bare scattering amplitudes. Representing the matrix elements of effective interactions as a superposition of terms each of which is split in matrix indices, we obtain a simple method for solving systems of very many equations for nonequilibrium Green’s functions in the atomic representation. As a result, we obtain an expression describing the electron currents in a device one of whose sites is in tunnel coupling with the left contact and the other, with the right contact. We derive closed kinetic equations for the occupation numbers under conditions where the electron flow leads to significant renormalization of them.

Theoretical and Mathematical Physics•Feb 1, 2018•1 citation

Equations for the correlation functions using a generalized Keldysh technique

Sh. M. Kogan

Equations for correlation functions in nonequilibrium systems are derived using a generalization of the diagrammatic Keldysh method. The four field operators of the correlation function are ordered on a time contour that consists of four axes extending from -\ensuremath{\infty} to +\ensuremath{\infty} and from +\ensuremath{\infty} to -\ensuremath{\infty} (doubled Keldysh contour). For those correlation functions that may be considered as correlation functions of one-particle Green-functions' fluctuations, a closed system of equations is obtained in the case of weak interaction of the particles with the scattering system. Its structure may be related to the Langevin approach: on the left-hand side a linear operator acts on each of two pairs of the correlation-function arguments, each of these two operators being just the operator of the linearized quantum kinetic equation. The expression for the right-hand side of this equation is derived. It has the meaning of the correlation function of extraneous Langevin sources, and the equation may be called the quantum Boltzmann-Langevin equation. In the quasi-classical limit it reduces to the usual Boltzmann-Langevin equation for the particles' distribution-function fluctuations. Possible applications of the method are discussed.

Physical Review A•Dec 1, 1991•13 citations
On the basis of the Green’s function method for nonequilibrium systems, the kinetic equation for two-level particles in a strong field is derived. In the binary approximation, all diagrams are expressed in terms of the reducible vertex part, whose calculation is reduced to the problem of two-channel scattering and finding the corresponding scattering amplitudes.
The pair distribution function (PDF) is a key quantity for the analysis of correlation effects of a quantum system both in equilibrium and far from equilibrium. We derive an expression for the PDF in terms of the single-particle Green functions—the solutions of the Keldysh/Kadanoff-Baym equations in the two-time plane—for a one- or two-component system. The result includes initial correlations and generalizes previous density matrix expressions from single-time quantum kinetic theory. Explicit expressions for the PDF are obtained in second Born approximation.
We develop the theory of quantum transport of electrons through systems with strong correlations between fermionic and internal spin degrees of freedom. The atomic representation for the Hamiltonian of a device and nonequilibrium Green’s functions constructed using the Hubbard operators allow overcoming difficulties in the perturbation theory encountered in the traditional approach because of a larger number of bare scattering amplitudes. Representing the matrix elements of effective interactions as a superposition of terms each of which is split in matrix indices, we obtain a simple method for solving systems of very many equations for nonequilibrium Green’s functions in the atomic representation. As a result, we obtain an expression describing the electron currents in a device one of whose sites is in tunnel coupling with the left contact and the other, with the right contact. We derive closed kinetic equations for the occupation numbers under conditions where the electron flow leads to significant renormalization of them.
Equations for correlation functions in nonequilibrium systems are derived using a generalization of the diagrammatic Keldysh method. The four field operators of the correlation function are ordered on a time contour that consists of four axes extending from -\ensuremath{\infty} to +\ensuremath{\infty} and from +\ensuremath{\infty} to -\ensuremath{\infty} (doubled Keldysh contour). For those correlation functions that may be considered as correlation functions of one-particle Green-functions' fluctuations, a closed system of equations is obtained in the case of weak interaction of the particles with the scattering system. Its structure may be related to the Langevin approach: on the left-hand side a linear operator acts on each of two pairs of the correlation-function arguments, each of these two operators being just the operator of the linearized quantum kinetic equation. The expression for the right-hand side of this equation is derived. It has the meaning of the correlation function of extraneous Langevin sources, and the equation may be called the quantum Boltzmann-Langevin equation. In the quasi-classical limit it reduces to the usual Boltzmann-Langevin equation for the particles' distribution-function fluctuations. Possible applications of the method are discussed.