A simple derivation of the Lindblad equation
We present a derivation of the Lindblad equation -an important tool for the treatment of nonunitary evolutions -that is accessible to undergraduate students in physics or mathematics with a basic background on quantum mechanics. We consider a specific case, corresponding to a very simple situation,...
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| Format: | Article |
| Language: | Portuguese |
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Sociedade Brasileira de Física
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| Series: | Revista Brasileira de Ensino de Física |
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| Online Access: | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172013000100003&lng=en&tlng=en |
| _version_ | 1819226619360837632 |
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| author | Carlos Alexandre Brasil Felipe Fernandes Fanchini Reginaldo de Jesus Napolitano |
| author_facet | Carlos Alexandre Brasil Felipe Fernandes Fanchini Reginaldo de Jesus Napolitano |
| author_sort | Carlos Alexandre Brasil |
| collection | DOAJ |
| description | We present a derivation of the Lindblad equation -an important tool for the treatment of nonunitary evolutions -that is accessible to undergraduate students in physics or mathematics with a basic background on quantum mechanics. We consider a specific case, corresponding to a very simple situation, where a primary system interacts with a bath of harmonic oscillators at zero temperature, with an interaction Hamiltonian that resembles the Jaynes-Cummings formato We start with the Born-Markov equation and, tracing out the bath degrees of freedom, we obtain an equation in the Lindblad formo The specific situation is very instructive, for it makes it easy to realize that the Lindblads represent the effect on the main system caused by the interaction with the bath, and that the Markov approximation is a fundamental condition for the emergence of the Lindbladian operator. The formal derivation of the Lindblad equation for a more general case requires the use of quantum dynamical semi-groups and broader considerations regarding the environment and temperature than we have considered in the particular case treated here. |
| first_indexed | 2024-12-23T10:28:22Z |
| format | Article |
| id | doaj.art-94a379bd066c429fbf203eeb53872e5a |
| institution | Directory Open Access Journal |
| issn | 1806-1117 1806-9126 |
| language | Portuguese |
| last_indexed | 2024-12-23T10:28:22Z |
| publisher | Sociedade Brasileira de Física |
| record_format | Article |
| series | Revista Brasileira de Ensino de Física |
| spelling | doaj.art-94a379bd066c429fbf203eeb53872e5a2022-12-21T17:50:30ZporSociedade Brasileira de FísicaRevista Brasileira de Ensino de Física1806-11171806-912635110.1590/S1806-11172013000100003S1806-11172013000100003A simple derivation of the Lindblad equationCarlos Alexandre Brasil0Felipe Fernandes Fanchini1Reginaldo de Jesus Napolitano2Universidade Estadual de CampinasUniversidade Estadual de CampinasUniversidade Estadual de CampinasWe present a derivation of the Lindblad equation -an important tool for the treatment of nonunitary evolutions -that is accessible to undergraduate students in physics or mathematics with a basic background on quantum mechanics. We consider a specific case, corresponding to a very simple situation, where a primary system interacts with a bath of harmonic oscillators at zero temperature, with an interaction Hamiltonian that resembles the Jaynes-Cummings formato We start with the Born-Markov equation and, tracing out the bath degrees of freedom, we obtain an equation in the Lindblad formo The specific situation is very instructive, for it makes it easy to realize that the Lindblads represent the effect on the main system caused by the interaction with the bath, and that the Markov approximation is a fundamental condition for the emergence of the Lindbladian operator. The formal derivation of the Lindblad equation for a more general case requires the use of quantum dynamical semi-groups and broader considerations regarding the environment and temperature than we have considered in the particular case treated here.http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172013000100003&lng=en&tlng=enlindblad equationopen quantum systems |
| spellingShingle | Carlos Alexandre Brasil Felipe Fernandes Fanchini Reginaldo de Jesus Napolitano A simple derivation of the Lindblad equation Revista Brasileira de Ensino de Física lindblad equation open quantum systems |
| title | A simple derivation of the Lindblad equation |
| title_full | A simple derivation of the Lindblad equation |
| title_fullStr | A simple derivation of the Lindblad equation |
| title_full_unstemmed | A simple derivation of the Lindblad equation |
| title_short | A simple derivation of the Lindblad equation |
| title_sort | simple derivation of the lindblad equation |
| topic | lindblad equation open quantum systems |
| url | http://www.scielo.br/scielo.php?script=sci_arttext&pid=S1806-11172013000100003&lng=en&tlng=en |
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