Green's function approach to the dynamics-controlled truncation formalism: Derivation of the χ(3) equations of motion

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Abstract

The dynamics-controlled truncation (DCT) formalism is a successful microscopic approach that describes coherent correlations in optically excited semiconductors. For practical reasons (including numerical evaluations), its application is limited to lowest-order nonlinearities, such as the χ(3) regime. Therefore, it is not convenient to use this formalism to examine the role played by incoherent many-body effects, such as carrier-carrier scattering and screening. Traditionally, the most powerful approach to study incoherent effects and correlations in highly excited semiconductors is that of nonequilibrium Green's functions (NGF). A combination of the insights and technical advantages provided by the two (NGF and DCT) approaches will lead to a comprehensive microscopic theory for nonlinear optical phenomena in semiconductors. In this paper, we take a first step in this direction by presenting detailed one-to-one relations between the two formalisms within the χ(3) approximation. Starting from the standard perturbation theory of nonequilibrium Green's functions, we derive the essential minimal order factorization theorems, to arbitrary order, of DCT and the equations of motions for the interband polarization and the "biexcitonic" correlation function. This lays the foundation for future diagrammatic high-intensity generalizations of the DCT formalism.

Original languageEnglish (US)
Pages (from-to)8341-8358
Number of pages18
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume61
Issue number12
StatePublished - 2000

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Green's function
Equations of motion
equations of motion
Green's functions
derivation
formalism
Semiconductor materials
approximation
Factorization
Screening
factorization
Scattering
Polarization
screening
theorems
perturbation theory
nonlinearity
evaluation
polarization
scattering

ASJC Scopus subject areas

  • Condensed Matter Physics

Cite this

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title = "Green's function approach to the dynamics-controlled truncation formalism: Derivation of the χ(3) equations of motion",
abstract = "The dynamics-controlled truncation (DCT) formalism is a successful microscopic approach that describes coherent correlations in optically excited semiconductors. For practical reasons (including numerical evaluations), its application is limited to lowest-order nonlinearities, such as the χ(3) regime. Therefore, it is not convenient to use this formalism to examine the role played by incoherent many-body effects, such as carrier-carrier scattering and screening. Traditionally, the most powerful approach to study incoherent effects and correlations in highly excited semiconductors is that of nonequilibrium Green's functions (NGF). A combination of the insights and technical advantages provided by the two (NGF and DCT) approaches will lead to a comprehensive microscopic theory for nonlinear optical phenomena in semiconductors. In this paper, we take a first step in this direction by presenting detailed one-to-one relations between the two formalisms within the χ(3) approximation. Starting from the standard perturbation theory of nonequilibrium Green's functions, we derive the essential minimal order factorization theorems, to arbitrary order, of DCT and the equations of motions for the interband polarization and the {"}biexcitonic{"} correlation function. This lays the foundation for future diagrammatic high-intensity generalizations of the DCT formalism.",
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T2 - Derivation of the χ(3) equations of motion

AU - Kwong, Nai-Hang

AU - Binder, Rudolf

PY - 2000

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N2 - The dynamics-controlled truncation (DCT) formalism is a successful microscopic approach that describes coherent correlations in optically excited semiconductors. For practical reasons (including numerical evaluations), its application is limited to lowest-order nonlinearities, such as the χ(3) regime. Therefore, it is not convenient to use this formalism to examine the role played by incoherent many-body effects, such as carrier-carrier scattering and screening. Traditionally, the most powerful approach to study incoherent effects and correlations in highly excited semiconductors is that of nonequilibrium Green's functions (NGF). A combination of the insights and technical advantages provided by the two (NGF and DCT) approaches will lead to a comprehensive microscopic theory for nonlinear optical phenomena in semiconductors. In this paper, we take a first step in this direction by presenting detailed one-to-one relations between the two formalisms within the χ(3) approximation. Starting from the standard perturbation theory of nonequilibrium Green's functions, we derive the essential minimal order factorization theorems, to arbitrary order, of DCT and the equations of motions for the interband polarization and the "biexcitonic" correlation function. This lays the foundation for future diagrammatic high-intensity generalizations of the DCT formalism.

AB - The dynamics-controlled truncation (DCT) formalism is a successful microscopic approach that describes coherent correlations in optically excited semiconductors. For practical reasons (including numerical evaluations), its application is limited to lowest-order nonlinearities, such as the χ(3) regime. Therefore, it is not convenient to use this formalism to examine the role played by incoherent many-body effects, such as carrier-carrier scattering and screening. Traditionally, the most powerful approach to study incoherent effects and correlations in highly excited semiconductors is that of nonequilibrium Green's functions (NGF). A combination of the insights and technical advantages provided by the two (NGF and DCT) approaches will lead to a comprehensive microscopic theory for nonlinear optical phenomena in semiconductors. In this paper, we take a first step in this direction by presenting detailed one-to-one relations between the two formalisms within the χ(3) approximation. Starting from the standard perturbation theory of nonequilibrium Green's functions, we derive the essential minimal order factorization theorems, to arbitrary order, of DCT and the equations of motions for the interband polarization and the "biexcitonic" correlation function. This lays the foundation for future diagrammatic high-intensity generalizations of the DCT formalism.

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