Self-energy operator and self-energy fields in many-body systems: Liouvillian approach

An explicit definition for the self-energy field operator and the self-energy fields obtained from an average of the associated operator within the algebraic formalism of superoperators is presented. It stems from the formal expansion of the many-body propagator equations of motion hierachy in quant...

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Detalles Bibliográficos
Autores principales:	Bochicchio, Roberto Carlos, Grinberg, Horacio
Publicado:	2002
Materias:	Dyson equation Liouvillian approach Propagators Reduced density matrices Self-energy fields Electron energy levels Equations of motion Green's function Mathematical operators Matrix algebra Reduced density matrices (RDM) Quantum theory
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00207608_v90_n1_p148_Bochicchio http://hdl.handle.net/20.500.12110/paper_00207608_v90_n1_p148_Bochicchio
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_00207608_v90_n1_p148_Bochicchio
record_format	dspace
spelling	paper:paper_00207608_v90_n1_p148_Bochicchio2023-06-08T14:41:45Z Self-energy operator and self-energy fields in many-body systems: Liouvillian approach Bochicchio, Roberto Carlos Grinberg, Horacio Dyson equation Liouvillian approach Propagators Reduced density matrices Self-energy fields Electron energy levels Equations of motion Green's function Mathematical operators Matrix algebra Reduced density matrices (RDM) Quantum theory An explicit definition for the self-energy field operator and the self-energy fields obtained from an average of the associated operator within the algebraic formalism of superoperators is presented. It stems from the formal expansion of the many-body propagator equations of motion hierachy in quantum many-body systems within the scenario of the Liouvillian decoupling scheme developed in previous works. An essential theoretical property of such fields for the complete expansion of the propagator to any order in the interaction potential is shown. This states that the interaction potential to a given order only depends on one q-reduced density matrix. The contraction order q of the density matrix depends on both the nature of the operators defining the propagator and the actual order of the expansion. This result is rigorous regarding infinite summation of the irreducible terms of the self-energy fields and provides a direct way to estimate the extent to which many-body effects are involved in successive approximations, i.e., truncation of the excitation level given by the reference state throughout the reduced density matrix and the expansion of the propagator. © 2002 Wiley Periodicals, Inc. Int. J. Quantum Chem. Fil:Bochicchio, R.C. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Grinberg, H. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2002 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00207608_v90_n1_p148_Bochicchio http://hdl.handle.net/20.500.12110/paper_00207608_v90_n1_p148_Bochicchio
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Dyson equation Liouvillian approach Propagators Reduced density matrices Self-energy fields Electron energy levels Equations of motion Green's function Mathematical operators Matrix algebra Reduced density matrices (RDM) Quantum theory
spellingShingle	Dyson equation Liouvillian approach Propagators Reduced density matrices Self-energy fields Electron energy levels Equations of motion Green's function Mathematical operators Matrix algebra Reduced density matrices (RDM) Quantum theory Bochicchio, Roberto Carlos Grinberg, Horacio Self-energy operator and self-energy fields in many-body systems: Liouvillian approach
topic_facet	Dyson equation Liouvillian approach Propagators Reduced density matrices Self-energy fields Electron energy levels Equations of motion Green's function Mathematical operators Matrix algebra Reduced density matrices (RDM) Quantum theory
description	An explicit definition for the self-energy field operator and the self-energy fields obtained from an average of the associated operator within the algebraic formalism of superoperators is presented. It stems from the formal expansion of the many-body propagator equations of motion hierachy in quantum many-body systems within the scenario of the Liouvillian decoupling scheme developed in previous works. An essential theoretical property of such fields for the complete expansion of the propagator to any order in the interaction potential is shown. This states that the interaction potential to a given order only depends on one q-reduced density matrix. The contraction order q of the density matrix depends on both the nature of the operators defining the propagator and the actual order of the expansion. This result is rigorous regarding infinite summation of the irreducible terms of the self-energy fields and provides a direct way to estimate the extent to which many-body effects are involved in successive approximations, i.e., truncation of the excitation level given by the reference state throughout the reduced density matrix and the expansion of the propagator. © 2002 Wiley Periodicals, Inc. Int. J. Quantum Chem.
author	Bochicchio, Roberto Carlos Grinberg, Horacio
author_facet	Bochicchio, Roberto Carlos Grinberg, Horacio
author_sort	Bochicchio, Roberto Carlos
title	Self-energy operator and self-energy fields in many-body systems: Liouvillian approach
title_short	Self-energy operator and self-energy fields in many-body systems: Liouvillian approach
title_full	Self-energy operator and self-energy fields in many-body systems: Liouvillian approach
title_fullStr	Self-energy operator and self-energy fields in many-body systems: Liouvillian approach
title_full_unstemmed	Self-energy operator and self-energy fields in many-body systems: Liouvillian approach
title_sort	self-energy operator and self-energy fields in many-body systems: liouvillian approach
publishDate	2002
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00207608_v90_n1_p148_Bochicchio http://hdl.handle.net/20.500.12110/paper_00207608_v90_n1_p148_Bochicchio
work_keys_str_mv	AT bochicchiorobertocarlos selfenergyoperatorandselfenergyfieldsinmanybodysystemsliouvillianapproach AT grinberghoracio selfenergyoperatorandselfenergyfieldsinmanybodysystemsliouvillianapproach
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Self-energy operator and self-energy fields in many-body systems: Liouvillian approach

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