Effective time-dependent temperature for fermionic master equations beyond the Markov and the secular approximations
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866915133683400704 |
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| author | Litzba, Lukas Kleinherbers, Eric König, Jürgen Schützhold, Ralf Szpak, Nikodem |
| author_facet | Litzba, Lukas Kleinherbers, Eric König, Jürgen Schützhold, Ralf Szpak, Nikodem |
| contents | We consider a fermionic quantum system exchanging particles with an environment at a fixed temperature and study its reduced evolution by means of a Redfield-I equation with time-dependent (non-Markovian) coefficients. We find that the description can be efficiently reduced to a standard-form Redfield-II equation, however, with a time-dependent effective bath temperature obeying a universal law. At early times, after the system and environment start in a product state, the effective temperature appears to be very high, yet eventually it settles down towards the true environment value. In this way, we obtain a time-local master equation, offering high accuracy at all times and preserving the crucial properties of the density matrix. It includes non-Markovian relaxation processes beyond the secular approximation and time-averaging methods and can be further applied to various types of Gorini-Kossakowski-Sudarshan-Lindblad equations. We derive the theory from first principles and discuss its application using a simple example of a single quantum dot. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_10591 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Effective time-dependent temperature for fermionic master equations beyond the Markov and the secular approximations Litzba, Lukas Kleinherbers, Eric König, Jürgen Schützhold, Ralf Szpak, Nikodem Mesoscale and Nanoscale Physics Strongly Correlated Electrons Quantum Physics We consider a fermionic quantum system exchanging particles with an environment at a fixed temperature and study its reduced evolution by means of a Redfield-I equation with time-dependent (non-Markovian) coefficients. We find that the description can be efficiently reduced to a standard-form Redfield-II equation, however, with a time-dependent effective bath temperature obeying a universal law. At early times, after the system and environment start in a product state, the effective temperature appears to be very high, yet eventually it settles down towards the true environment value. In this way, we obtain a time-local master equation, offering high accuracy at all times and preserving the crucial properties of the density matrix. It includes non-Markovian relaxation processes beyond the secular approximation and time-averaging methods and can be further applied to various types of Gorini-Kossakowski-Sudarshan-Lindblad equations. We derive the theory from first principles and discuss its application using a simple example of a single quantum dot. |
| title | Effective time-dependent temperature for fermionic master equations beyond the Markov and the secular approximations |
| topic | Mesoscale and Nanoscale Physics Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2403.10591 |