On the singular limit of the quantum classical molecular dynamics model:
Abstract: "In molecular dynamics applications there is a growing interest in so-called mixed quantum-classical models. These models describe most atoms of the molecular system by the means of classical mechanics but an important, small portion of the system by the means of quantum mechanics. A...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Konrad-Zuse-Zentrum für Informationstechnik
1997
|
| Schriftenreihe: | Preprint SC / Konrad-Zuse-Zentrum für Informationstechnik Berlin
1997,7 |
| Schlagworte: | |
| Zusammenfassung: | Abstract: "In molecular dynamics applications there is a growing interest in so-called mixed quantum-classical models. These models describe most atoms of the molecular system by the means of classical mechanics but an important, small portion of the system by the means of quantum mechanics. A particularly extensively used model, the QCMD model, consists of a singularly perturbed Schrödinger equation nonlinearly coupled to a classical Newtonian equation of motion. This paper studies the singular limit of the QCMD model for finite dimensional Hilbert spaces. The main result states that this limit is given by the time-dependent Born-Oppenheimer model of quantum theory -- provided the Hamiltonian under consideration has a smooth spectral decomposition. This result is strongly related to the quantum adiabatic theorem. The proof uses the method of weak convergence by directly discussing the density matrix instead of the wave functions. This technique avoids the discussion of highly oscillatory phases. On the other hand, the limit of the QCMD model is of a different nature if the spectral decomposition of the Hamiltonian happens not to be smooth. We will present a generic example for which the limit set is not a unique trajectory of a limit dynamical system but rather a funnel consisting of infinitely many trajectories." |
| Beschreibung: | 19 S. |
Internformat
MARC
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| 100 | 1 | |a Bornemann, Folkmar |d 1967- |e Verfasser |0 (DE-588)120096269 |4 aut | |
| 245 | 1 | 0 | |a On the singular limit of the quantum classical molecular dynamics model |c Folkmar A. Bornemann ; Christof Schütte |
| 264 | 1 | |a Berlin |b Konrad-Zuse-Zentrum für Informationstechnik |c 1997 | |
| 300 | |a 19 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Preprint SC / Konrad-Zuse-Zentrum für Informationstechnik Berlin |v 1997,7 | |
| 520 | 3 | |a Abstract: "In molecular dynamics applications there is a growing interest in so-called mixed quantum-classical models. These models describe most atoms of the molecular system by the means of classical mechanics but an important, small portion of the system by the means of quantum mechanics. A particularly extensively used model, the QCMD model, consists of a singularly perturbed Schrödinger equation nonlinearly coupled to a classical Newtonian equation of motion. This paper studies the singular limit of the QCMD model for finite dimensional Hilbert spaces. The main result states that this limit is given by the time-dependent Born-Oppenheimer model of quantum theory -- provided the Hamiltonian under consideration has a smooth spectral decomposition. This result is strongly related to the quantum adiabatic theorem. The proof uses the method of weak convergence by directly discussing the density matrix instead of the wave functions. This technique avoids the discussion of highly oscillatory phases. On the other hand, the limit of the QCMD model is of a different nature if the spectral decomposition of the Hamiltonian happens not to be smooth. We will present a generic example for which the limit set is not a unique trajectory of a limit dynamical system but rather a funnel consisting of infinitely many trajectories." | |
| 650 | 4 | |a Quantentheorie | |
| 650 | 4 | |a Adiabatic invariants | |
| 650 | 4 | |a Molecular dynamics | |
| 650 | 4 | |a Quantum theory | |
| 700 | 1 | |a Schütte, Christof |d 1966- |e Verfasser |0 (DE-588)1049564030 |4 aut | |
| 810 | 2 | |a Konrad-Zuse-Zentrum für Informationstechnik Berlin |t Preprint SC |v 1997,7 |w (DE-604)BV004801715 |9 1997,7 | |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-010359963 | |
Datensatz im Suchindex
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| author | Bornemann, Folkmar 1967- Schütte, Christof 1966- |
| author_GND | (DE-588)120096269 (DE-588)1049564030 |
| author_facet | Bornemann, Folkmar 1967- Schütte, Christof 1966- |
| author_role | aut aut |
| author_sort | Bornemann, Folkmar 1967- |
| author_variant | f b fb c s cs |
| building | Verbundindex |
| bvnumber | BV017188964 |
| classification_rvk | SS 4777 |
| ctrlnum | (OCoLC)37991489 (DE-599)BVBBV017188964 |
| discipline | Informatik |
| format | Book |
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| id | DE-604.BV017188964 |
| illustrated | Not Illustrated |
| indexdate | 2025-01-10T17:07:56Z |
| institution | BVB |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010359963 |
| oclc_num | 37991489 |
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| owner | DE-703 |
| owner_facet | DE-703 |
| physical | 19 S. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Konrad-Zuse-Zentrum für Informationstechnik |
| record_format | marc |
| series2 | Preprint SC / Konrad-Zuse-Zentrum für Informationstechnik Berlin |
| spelling | Bornemann, Folkmar 1967- Verfasser (DE-588)120096269 aut On the singular limit of the quantum classical molecular dynamics model Folkmar A. Bornemann ; Christof Schütte Berlin Konrad-Zuse-Zentrum für Informationstechnik 1997 19 S. txt rdacontent n rdamedia nc rdacarrier Preprint SC / Konrad-Zuse-Zentrum für Informationstechnik Berlin 1997,7 Abstract: "In molecular dynamics applications there is a growing interest in so-called mixed quantum-classical models. These models describe most atoms of the molecular system by the means of classical mechanics but an important, small portion of the system by the means of quantum mechanics. A particularly extensively used model, the QCMD model, consists of a singularly perturbed Schrödinger equation nonlinearly coupled to a classical Newtonian equation of motion. This paper studies the singular limit of the QCMD model for finite dimensional Hilbert spaces. The main result states that this limit is given by the time-dependent Born-Oppenheimer model of quantum theory -- provided the Hamiltonian under consideration has a smooth spectral decomposition. This result is strongly related to the quantum adiabatic theorem. The proof uses the method of weak convergence by directly discussing the density matrix instead of the wave functions. This technique avoids the discussion of highly oscillatory phases. On the other hand, the limit of the QCMD model is of a different nature if the spectral decomposition of the Hamiltonian happens not to be smooth. We will present a generic example for which the limit set is not a unique trajectory of a limit dynamical system but rather a funnel consisting of infinitely many trajectories." Quantentheorie Adiabatic invariants Molecular dynamics Quantum theory Schütte, Christof 1966- Verfasser (DE-588)1049564030 aut Konrad-Zuse-Zentrum für Informationstechnik Berlin Preprint SC 1997,7 (DE-604)BV004801715 1997,7 |
| spellingShingle | Bornemann, Folkmar 1967- Schütte, Christof 1966- On the singular limit of the quantum classical molecular dynamics model Quantentheorie Adiabatic invariants Molecular dynamics Quantum theory |
| title | On the singular limit of the quantum classical molecular dynamics model |
| title_auth | On the singular limit of the quantum classical molecular dynamics model |
| title_exact_search | On the singular limit of the quantum classical molecular dynamics model |
| title_full | On the singular limit of the quantum classical molecular dynamics model Folkmar A. Bornemann ; Christof Schütte |
| title_fullStr | On the singular limit of the quantum classical molecular dynamics model Folkmar A. Bornemann ; Christof Schütte |
| title_full_unstemmed | On the singular limit of the quantum classical molecular dynamics model Folkmar A. Bornemann ; Christof Schütte |
| title_short | On the singular limit of the quantum classical molecular dynamics model |
| title_sort | on the singular limit of the quantum classical molecular dynamics model |
| topic | Quantentheorie Adiabatic invariants Molecular dynamics Quantum theory |
| topic_facet | Quantentheorie Adiabatic invariants Molecular dynamics Quantum theory |
| volume_link | (DE-604)BV004801715 |
| work_keys_str_mv | AT bornemannfolkmar onthesingularlimitofthequantumclassicalmoleculardynamicsmodel AT schuttechristof onthesingularlimitofthequantumclassicalmoleculardynamicsmodel |