Limit cycles in periodically driven open quantum systems
We investigate the long-time behavior of quantum N-level systems that are coupled to a Markovian environment and subject to periodic driving. As our main result, we obtain a general algebraic condition ensuring that all solutions of a periodic quantum master equation with Lindblad form approach a un...
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| Published in | Journal of physics. A, Mathematical and theoretical Vol. 52; no. 43; pp. 43 - 51 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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25.10.2019
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| Abstract | We investigate the long-time behavior of quantum N-level systems that are coupled to a Markovian environment and subject to periodic driving. As our main result, we obtain a general algebraic condition ensuring that all solutions of a periodic quantum master equation with Lindblad form approach a unique limit cycle. Quite intuitively, this criterion requires that the dissipative terms of the master equation connect all subspaces of the system Hilbert space during an arbitrarily small fraction of the cycle time. Our results provide a natural extension of Spohn's algebraic condition for the approach to equilibrium to systems with external driving. Moreover, our theory leads to a rigorous condition for the emergence of dissipative discrete time crystals and covers also classical, periodically modulated Markov jump processes. |
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| AbstractList | We investigate the long-time behavior of quantum N-level systems that are coupled to a Markovian environment and subject to periodic driving. As our main result, we obtain a general algebraic condition ensuring that all solutions of a periodic quantum master equation with Lindblad form approach a unique limit cycle. Quite intuitively, this criterion requires that the dissipative terms of the master equation connect all subspaces of the system Hilbert space during an arbitrarily small fraction of the cycle time. Our results provide a natural extension of Spohn's algebraic condition for the approach to equilibrium to systems with external driving. Moreover, our theory leads to a rigorous condition for the emergence of dissipative discrete time crystals and covers also classical, periodically modulated Markov jump processes. |
| Author | Brandner, Kay Menczel, Paul |
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| Cites_doi | 10.1016/0034-4877(78)90050-2 10.1103/PhysRevX.6.041031 10.1103/PhysRevA.81.062306 10.1088/0953-4075/45/15/154002 10.1063/1.523789 10.1103/PhysRevLett.120.040404 10.1007/BF01608499 10.1103/RevModPhys.88.021002 10.1088/1751-8113/49/14/143001 10.1007/978-3-642-23354-8 10.1017/CBO9780511813993 10.1103/PhysRevA.97.062121 10.1007/BF00420668 10.1103/PhysRevLett.122.015701 10.1103/PhysRevE.93.062134 10.1038/nphys3169 10.1007/BF01212314 10.1016/j.physrep.2017.05.008 10.1080/00107514.2016.1201896 10.1063/1.522979 10.3390/e15062100 10.3390/e19040136 10.1103/PhysRevE.70.046110 |
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| Snippet | We investigate the long-time behavior of quantum N-level systems that are coupled to a Markovian environment and subject to periodic driving. As our main... |
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| SubjectTerms | asymptotics cyclic machines functional analysis and operator theory mathematical physics nonequilibrium systems open quantum systems |
| Title | Limit cycles in periodically driven open quantum systems |
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