Mean–Field Evolution of Fermionic Systems
Abstract The mean field limit for systems of many fermions is naturally coupled with a semiclassical limit. This makes the analysis of the mean field regime much more involved, compared with bosonic systems. In this paper, we study the dynamics of initial data close to a Slater determinant, whose re...
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| Autor*in: |
Benedikter, Niels [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2014 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer-Verlag Berlin Heidelberg 2014 |
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| Übergeordnetes Werk: |
Enthalten in: Communications in mathematical physics - Springer Berlin Heidelberg, 1965, 331(2014), 3 vom: 23. Apr., Seite 1087-1131 |
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| Übergeordnetes Werk: |
volume:331 ; year:2014 ; number:3 ; day:23 ; month:04 ; pages:1087-1131 |
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| DOI / URN: |
10.1007/s00220-014-2031-z |
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OLC2038907951 |
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| 520 | |a Abstract The mean field limit for systems of many fermions is naturally coupled with a semiclassical limit. This makes the analysis of the mean field regime much more involved, compared with bosonic systems. In this paper, we study the dynamics of initial data close to a Slater determinant, whose reduced one-particle density is an orthogonal projection ωN with the appropriate semiclassical structure. Assuming some regularity of the interaction potential, we show that the evolution of such an initial data remains close to a Slater determinant, with reduced one-particle density given by the solution of the Hartree–Fock equation with initial data ωN. Our result holds for all (semiclassical) times, and gives effective bounds on the rate of the convergence towards the Hartree–Fock dynamics. | ||
| 650 | 4 | |a Fermionic System | |
| 650 | 4 | |a Slater Determinant | |
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| 650 | 4 | |a Bogoliubov Transformation | |
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| 700 | 1 | |a Porta, Marcello |4 aut | |
| 700 | 1 | |a Schlein, Benjamin |4 aut | |
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10.1007/s00220-014-2031-z doi (DE-627)OLC2038907951 (DE-He213)s00220-014-2031-z-p DE-627 ger DE-627 rakwb eng 530 510 VZ Benedikter, Niels verfasserin aut Mean–Field Evolution of Fermionic Systems 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2014 Abstract The mean field limit for systems of many fermions is naturally coupled with a semiclassical limit. This makes the analysis of the mean field regime much more involved, compared with bosonic systems. In this paper, we study the dynamics of initial data close to a Slater determinant, whose reduced one-particle density is an orthogonal projection ωN with the appropriate semiclassical structure. Assuming some regularity of the interaction potential, we show that the evolution of such an initial data remains close to a Slater determinant, with reduced one-particle density given by the solution of the Hartree–Fock equation with initial data ωN. Our result holds for all (semiclassical) times, and gives effective bounds on the rate of the convergence towards the Hartree–Fock dynamics. Fermionic System Slater Determinant Hartree Equation Bogoliubov Transformation Canonical Anticommutation Relation Porta, Marcello aut Schlein, Benjamin aut Enthalten in Communications in mathematical physics Springer Berlin Heidelberg, 1965 331(2014), 3 vom: 23. Apr., Seite 1087-1131 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:331 year:2014 number:3 day:23 month:04 pages:1087-1131 https://doi.org/10.1007/s00220-014-2031-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4318 AR 331 2014 3 23 04 1087-1131 |
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10.1007/s00220-014-2031-z doi (DE-627)OLC2038907951 (DE-He213)s00220-014-2031-z-p DE-627 ger DE-627 rakwb eng 530 510 VZ Benedikter, Niels verfasserin aut Mean–Field Evolution of Fermionic Systems 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2014 Abstract The mean field limit for systems of many fermions is naturally coupled with a semiclassical limit. This makes the analysis of the mean field regime much more involved, compared with bosonic systems. In this paper, we study the dynamics of initial data close to a Slater determinant, whose reduced one-particle density is an orthogonal projection ωN with the appropriate semiclassical structure. Assuming some regularity of the interaction potential, we show that the evolution of such an initial data remains close to a Slater determinant, with reduced one-particle density given by the solution of the Hartree–Fock equation with initial data ωN. Our result holds for all (semiclassical) times, and gives effective bounds on the rate of the convergence towards the Hartree–Fock dynamics. Fermionic System Slater Determinant Hartree Equation Bogoliubov Transformation Canonical Anticommutation Relation Porta, Marcello aut Schlein, Benjamin aut Enthalten in Communications in mathematical physics Springer Berlin Heidelberg, 1965 331(2014), 3 vom: 23. Apr., Seite 1087-1131 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:331 year:2014 number:3 day:23 month:04 pages:1087-1131 https://doi.org/10.1007/s00220-014-2031-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4318 AR 331 2014 3 23 04 1087-1131 |
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10.1007/s00220-014-2031-z doi (DE-627)OLC2038907951 (DE-He213)s00220-014-2031-z-p DE-627 ger DE-627 rakwb eng 530 510 VZ Benedikter, Niels verfasserin aut Mean–Field Evolution of Fermionic Systems 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2014 Abstract The mean field limit for systems of many fermions is naturally coupled with a semiclassical limit. This makes the analysis of the mean field regime much more involved, compared with bosonic systems. In this paper, we study the dynamics of initial data close to a Slater determinant, whose reduced one-particle density is an orthogonal projection ωN with the appropriate semiclassical structure. Assuming some regularity of the interaction potential, we show that the evolution of such an initial data remains close to a Slater determinant, with reduced one-particle density given by the solution of the Hartree–Fock equation with initial data ωN. Our result holds for all (semiclassical) times, and gives effective bounds on the rate of the convergence towards the Hartree–Fock dynamics. Fermionic System Slater Determinant Hartree Equation Bogoliubov Transformation Canonical Anticommutation Relation Porta, Marcello aut Schlein, Benjamin aut Enthalten in Communications in mathematical physics Springer Berlin Heidelberg, 1965 331(2014), 3 vom: 23. Apr., Seite 1087-1131 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:331 year:2014 number:3 day:23 month:04 pages:1087-1131 https://doi.org/10.1007/s00220-014-2031-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4318 AR 331 2014 3 23 04 1087-1131 |
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10.1007/s00220-014-2031-z doi (DE-627)OLC2038907951 (DE-He213)s00220-014-2031-z-p DE-627 ger DE-627 rakwb eng 530 510 VZ Benedikter, Niels verfasserin aut Mean–Field Evolution of Fermionic Systems 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2014 Abstract The mean field limit for systems of many fermions is naturally coupled with a semiclassical limit. This makes the analysis of the mean field regime much more involved, compared with bosonic systems. In this paper, we study the dynamics of initial data close to a Slater determinant, whose reduced one-particle density is an orthogonal projection ωN with the appropriate semiclassical structure. Assuming some regularity of the interaction potential, we show that the evolution of such an initial data remains close to a Slater determinant, with reduced one-particle density given by the solution of the Hartree–Fock equation with initial data ωN. Our result holds for all (semiclassical) times, and gives effective bounds on the rate of the convergence towards the Hartree–Fock dynamics. Fermionic System Slater Determinant Hartree Equation Bogoliubov Transformation Canonical Anticommutation Relation Porta, Marcello aut Schlein, Benjamin aut Enthalten in Communications in mathematical physics Springer Berlin Heidelberg, 1965 331(2014), 3 vom: 23. Apr., Seite 1087-1131 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:331 year:2014 number:3 day:23 month:04 pages:1087-1131 https://doi.org/10.1007/s00220-014-2031-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4318 AR 331 2014 3 23 04 1087-1131 |
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10.1007/s00220-014-2031-z doi (DE-627)OLC2038907951 (DE-He213)s00220-014-2031-z-p DE-627 ger DE-627 rakwb eng 530 510 VZ Benedikter, Niels verfasserin aut Mean–Field Evolution of Fermionic Systems 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer-Verlag Berlin Heidelberg 2014 Abstract The mean field limit for systems of many fermions is naturally coupled with a semiclassical limit. This makes the analysis of the mean field regime much more involved, compared with bosonic systems. In this paper, we study the dynamics of initial data close to a Slater determinant, whose reduced one-particle density is an orthogonal projection ωN with the appropriate semiclassical structure. Assuming some regularity of the interaction potential, we show that the evolution of such an initial data remains close to a Slater determinant, with reduced one-particle density given by the solution of the Hartree–Fock equation with initial data ωN. Our result holds for all (semiclassical) times, and gives effective bounds on the rate of the convergence towards the Hartree–Fock dynamics. Fermionic System Slater Determinant Hartree Equation Bogoliubov Transformation Canonical Anticommutation Relation Porta, Marcello aut Schlein, Benjamin aut Enthalten in Communications in mathematical physics Springer Berlin Heidelberg, 1965 331(2014), 3 vom: 23. Apr., Seite 1087-1131 (DE-627)129555002 (DE-600)220443-5 (DE-576)015011755 0010-3616 nnns volume:331 year:2014 number:3 day:23 month:04 pages:1087-1131 https://doi.org/10.1007/s00220-014-2031-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_70 GBV_ILN_2002 GBV_ILN_2018 GBV_ILN_2088 GBV_ILN_2279 GBV_ILN_2409 GBV_ILN_4266 GBV_ILN_4277 GBV_ILN_4305 GBV_ILN_4318 AR 331 2014 3 23 04 1087-1131 |
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Abstract The mean field limit for systems of many fermions is naturally coupled with a semiclassical limit. This makes the analysis of the mean field regime much more involved, compared with bosonic systems. In this paper, we study the dynamics of initial data close to a Slater determinant, whose reduced one-particle density is an orthogonal projection ωN with the appropriate semiclassical structure. Assuming some regularity of the interaction potential, we show that the evolution of such an initial data remains close to a Slater determinant, with reduced one-particle density given by the solution of the Hartree–Fock equation with initial data ωN. Our result holds for all (semiclassical) times, and gives effective bounds on the rate of the convergence towards the Hartree–Fock dynamics. © Springer-Verlag Berlin Heidelberg 2014 |
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Abstract The mean field limit for systems of many fermions is naturally coupled with a semiclassical limit. This makes the analysis of the mean field regime much more involved, compared with bosonic systems. In this paper, we study the dynamics of initial data close to a Slater determinant, whose reduced one-particle density is an orthogonal projection ωN with the appropriate semiclassical structure. Assuming some regularity of the interaction potential, we show that the evolution of such an initial data remains close to a Slater determinant, with reduced one-particle density given by the solution of the Hartree–Fock equation with initial data ωN. Our result holds for all (semiclassical) times, and gives effective bounds on the rate of the convergence towards the Hartree–Fock dynamics. © Springer-Verlag Berlin Heidelberg 2014 |
| abstract_unstemmed |
Abstract The mean field limit for systems of many fermions is naturally coupled with a semiclassical limit. This makes the analysis of the mean field regime much more involved, compared with bosonic systems. In this paper, we study the dynamics of initial data close to a Slater determinant, whose reduced one-particle density is an orthogonal projection ωN with the appropriate semiclassical structure. Assuming some regularity of the interaction potential, we show that the evolution of such an initial data remains close to a Slater determinant, with reduced one-particle density given by the solution of the Hartree–Fock equation with initial data ωN. Our result holds for all (semiclassical) times, and gives effective bounds on the rate of the convergence towards the Hartree–Fock dynamics. © Springer-Verlag Berlin Heidelberg 2014 |
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Mean–Field Evolution of Fermionic Systems |
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Porta, Marcello Schlein, Benjamin |
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