Derivation of some translation-invariant lindblad equations for a quantum Brownian particle
We study the dynamics of a Brownian quantum particle hopping on an infinite lattice with a spin degree of freedom. This particle is coupled to free boson gases via a translation-invariant Hamiltonian which is linear in the creation and annihilation operators of the bosons. We derive the time evolutio...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
January 2013
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| In: |
Journal of statistical physics
Year: 2013, Volume: 150, Issue: 2, Pages: 320-352 |
| ISSN: | 1572-9613 |
| DOI: | 10.1007/s10955-012-0649-9 |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1007/s10955-012-0649-9 Verlag, Volltext: http://link.springer.com/10.1007/s10955-012-0649-9 
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| Author Notes: | Wojciech De Roeck, Dominique Spehner |
| Summary: | We study the dynamics of a Brownian quantum particle hopping on an infinite lattice with a spin degree of freedom. This particle is coupled to free boson gases via a translation-invariant Hamiltonian which is linear in the creation and annihilation operators of the bosons. We derive the time evolution of the reduced density matrix of the particle in the van Hove limit in which we also rescale the hopping rate. This corresponds to a situation in which both the system-bath interactions and the hopping between neighboring sites are small and they are effective on the same time scale. The reduced evolution is given by a translation-invariant Lindblad master equation which is derived explicitly. |
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| Item Description: | Published online: 14 December 2012 Gesehen am 29.11.2018 |
| Physical Description: | Online Resource |
| ISSN: | 1572-9613 |
| DOI: | 10.1007/s10955-012-0649-9 |