Energy absorption and dissipation in quantum systems
Stemming from the time-dependent Schrödinger equation, it is noted that any Hermitian form representing work done on a system yields a bounded expectation of energy. This expectation can be periodic, quasiperiodic or even chaotic. Such boundedness is unrealistic because energy may be added to or rem...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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2004
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| _version_ | 1797069999158853632 |
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| author | Liboff, R Porter, M |
| author_facet | Liboff, R Porter, M |
| author_sort | Liboff, R |
| collection | OXFORD |
| description | Stemming from the time-dependent Schrödinger equation, it is noted that any Hermitian form representing work done on a system yields a bounded expectation of energy. This expectation can be periodic, quasiperiodic or even chaotic. Such boundedness is unrealistic because energy may be added to or removed from the system. Thus, a complex non-Hermitian form is introduced into the Hamiltonian of a system which, when positive represents work being done on the system and gives an increasing energy expectation, and when negative represents a dissipation of energy from the system and gives a decreasing energy expectation. Two cases are studied. In the first, the perturbative term is purely time-dependent. In the second, it is also space-dependent. This latter case is applied to the kicked quantum rotor. A number of other applications of this formalism to systems of experimental and theoretical interest are noted. © 2004 Elsevier B.V. All rights reserved. |
| first_indexed | 2024-03-06T22:32:42Z |
| format | Journal article |
| id | oxford-uuid:58ccd6ce-d5c9-4f1a-8860-d4be8d65b63c |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T22:32:42Z |
| publishDate | 2004 |
| record_format | dspace |
| spelling | oxford-uuid:58ccd6ce-d5c9-4f1a-8860-d4be8d65b63c2022-03-26T17:05:49ZEnergy absorption and dissipation in quantum systemsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:58ccd6ce-d5c9-4f1a-8860-d4be8d65b63cEnglishSymplectic Elements at Oxford2004Liboff, RPorter, MStemming from the time-dependent Schrödinger equation, it is noted that any Hermitian form representing work done on a system yields a bounded expectation of energy. This expectation can be periodic, quasiperiodic or even chaotic. Such boundedness is unrealistic because energy may be added to or removed from the system. Thus, a complex non-Hermitian form is introduced into the Hamiltonian of a system which, when positive represents work being done on the system and gives an increasing energy expectation, and when negative represents a dissipation of energy from the system and gives a decreasing energy expectation. Two cases are studied. In the first, the perturbative term is purely time-dependent. In the second, it is also space-dependent. This latter case is applied to the kicked quantum rotor. A number of other applications of this formalism to systems of experimental and theoretical interest are noted. © 2004 Elsevier B.V. All rights reserved. |
| spellingShingle | Liboff, R Porter, M Energy absorption and dissipation in quantum systems |
| title | Energy absorption and dissipation in quantum systems |
| title_full | Energy absorption and dissipation in quantum systems |
| title_fullStr | Energy absorption and dissipation in quantum systems |
| title_full_unstemmed | Energy absorption and dissipation in quantum systems |
| title_short | Energy absorption and dissipation in quantum systems |
| title_sort | energy absorption and dissipation in quantum systems |
| work_keys_str_mv | AT liboffr energyabsorptionanddissipationinquantumsystems AT porterm energyabsorptionanddissipationinquantumsystems |