Quantum Maps with Memory from Generalized Lindblad Equation
In this paper, we proposed the exactly solvable model of non-Markovian dynamics of open quantum systems. This model describes open quantum systems with memory and periodic sequence of kicks by environment. To describe these systems, the Lindblad equation for quantum observable is generalized by taki...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-04-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/23/5/544 |
| _version_ | 1797535994796310528 |
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| author | Vasily E. Tarasov |
| author_facet | Vasily E. Tarasov |
| author_sort | Vasily E. Tarasov |
| collection | DOAJ |
| description | In this paper, we proposed the exactly solvable model of non-Markovian dynamics of open quantum systems. This model describes open quantum systems with memory and periodic sequence of kicks by environment. To describe these systems, the Lindblad equation for quantum observable is generalized by taking into account power-law fading memory. Dynamics of open quantum systems with power-law memory are considered. The proposed generalized Lindblad equations describe non-Markovian quantum dynamics. The quantum dynamics with power-law memory are described by using integrations and differentiation of non-integer orders, as well as fractional calculus. An example of a quantum oscillator with linear friction and power-law memory is considered. In this paper, discrete-time quantum maps with memory, which are derived from generalized Lindblad equations without any approximations, are suggested. These maps exactly correspond to the generalized Lindblad equations, which are fractional differential equations with the Caputo derivatives of non-integer orders and periodic sequence of kicks that are represented by the Dirac delta-functions. The solution of these equations for coordinates and momenta are derived. The solutions of the generalized Lindblad equations for coordinate and momentum operators are obtained for open quantum systems with memory and kicks. Using these solutions, linear and nonlinear quantum discrete-time maps are derived. |
| first_indexed | 2024-03-10T11:53:18Z |
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| id | doaj.art-ab3a44d7e19d472daf233ea347e43755 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T11:53:18Z |
| publishDate | 2021-04-01 |
| publisher | MDPI AG |
| record_format | Article |
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| spelling | doaj.art-ab3a44d7e19d472daf233ea347e437552023-11-21T17:33:33ZengMDPI AGEntropy1099-43002021-04-0123554410.3390/e23050544Quantum Maps with Memory from Generalized Lindblad EquationVasily E. Tarasov0Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, 119991 Moscow, RussiaIn this paper, we proposed the exactly solvable model of non-Markovian dynamics of open quantum systems. This model describes open quantum systems with memory and periodic sequence of kicks by environment. To describe these systems, the Lindblad equation for quantum observable is generalized by taking into account power-law fading memory. Dynamics of open quantum systems with power-law memory are considered. The proposed generalized Lindblad equations describe non-Markovian quantum dynamics. The quantum dynamics with power-law memory are described by using integrations and differentiation of non-integer orders, as well as fractional calculus. An example of a quantum oscillator with linear friction and power-law memory is considered. In this paper, discrete-time quantum maps with memory, which are derived from generalized Lindblad equations without any approximations, are suggested. These maps exactly correspond to the generalized Lindblad equations, which are fractional differential equations with the Caputo derivatives of non-integer orders and periodic sequence of kicks that are represented by the Dirac delta-functions. The solution of these equations for coordinates and momenta are derived. The solutions of the generalized Lindblad equations for coordinate and momentum operators are obtained for open quantum systems with memory and kicks. Using these solutions, linear and nonlinear quantum discrete-time maps are derived.https://www.mdpi.com/1099-4300/23/5/544non-Markovian quantum dynamicsopen quantum systempower-law memoryLindblad equationdiscrete map with memoryfractional dynamics |
| spellingShingle | Vasily E. Tarasov Quantum Maps with Memory from Generalized Lindblad Equation Entropy non-Markovian quantum dynamics open quantum system power-law memory Lindblad equation discrete map with memory fractional dynamics |
| title | Quantum Maps with Memory from Generalized Lindblad Equation |
| title_full | Quantum Maps with Memory from Generalized Lindblad Equation |
| title_fullStr | Quantum Maps with Memory from Generalized Lindblad Equation |
| title_full_unstemmed | Quantum Maps with Memory from Generalized Lindblad Equation |
| title_short | Quantum Maps with Memory from Generalized Lindblad Equation |
| title_sort | quantum maps with memory from generalized lindblad equation |
| topic | non-Markovian quantum dynamics open quantum system power-law memory Lindblad equation discrete map with memory fractional dynamics |
| url | https://www.mdpi.com/1099-4300/23/5/544 |
| work_keys_str_mv | AT vasilyetarasov quantummapswithmemoryfromgeneralizedlindbladequation |