TY - JOUR
T1 - Effective Floquet-Gibbs states for dissipative quantum systems
AU - Shirai, Tatsuhiko
AU - Thingna, Juzar
AU - Mori, Takashi
AU - Denisov, Sergey
AU - Hänggi, Peter
AU - Miyashita, Seiji
N1 - Funding Information:
TS acknowledges JSPS for financial support (Grant No. 258794). TS is supported by advanced leading graduate course for photon science (ALPS). JT acknowledges financial support from SMART. TM is supported by JSPS KAKENHI Grant No. 15K17718. PH and SD acknowledge support of the Russian science foundation (project No. 15-12-20029). SM was supported by grants-in-aid for scientific research C (25400391) from MEXT of Japan. The numerical calculations were supported by the supercomputer center of ISSP of Tokyo University. TS, TM, and SM also acknowledge the JSPS core-to-core program: non-equilibrium dynamics of soft matter and information.
PY - 2016/5/1
Y1 - 2016/5/1
N2 - A periodically driven quantum system, when coupled to a heat bath, relaxes to a non-equilibrium asymptotic state. In the general situation, the retrieval of this asymptotic state presents a rather non-trivial task. It was recently shown that in the limit of an infinitesimal coupling, using the so-called rotating wave approximation (RWA), and under strict conditions imposed on the time-dependent system Hamiltonian, the asymptotic state can attain the Gibbs form. A Floquet-Gibbs state is characterized by a density matrix which is diagonal in the Floquet basis of the system Hamiltonian with the diagonal elements obeying a Gibbs distribution, being parametrized by the corresponding Floquet quasi-energies. Addressing the non-adiabatic driving regime, upon using the Magnus expansion, we employ the concept of a corresponding effective Floquet Hamiltonian. In doing so we go beyond the conventionally used RWA and demonstrate that the idea of Floquet-Gibbs states can be extended to the realistic case of a weak, although finite system-bath coupling, herein termed effective Floquet-Gibbs states.
AB - A periodically driven quantum system, when coupled to a heat bath, relaxes to a non-equilibrium asymptotic state. In the general situation, the retrieval of this asymptotic state presents a rather non-trivial task. It was recently shown that in the limit of an infinitesimal coupling, using the so-called rotating wave approximation (RWA), and under strict conditions imposed on the time-dependent system Hamiltonian, the asymptotic state can attain the Gibbs form. A Floquet-Gibbs state is characterized by a density matrix which is diagonal in the Floquet basis of the system Hamiltonian with the diagonal elements obeying a Gibbs distribution, being parametrized by the corresponding Floquet quasi-energies. Addressing the non-adiabatic driving regime, upon using the Magnus expansion, we employ the concept of a corresponding effective Floquet Hamiltonian. In doing so we go beyond the conventionally used RWA and demonstrate that the idea of Floquet-Gibbs states can be extended to the realistic case of a weak, although finite system-bath coupling, herein termed effective Floquet-Gibbs states.
KW - Non-equilibrium asymptotic states
KW - Open quantum system
KW - Time-periodic driving field
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U2 - 10.1088/1367-2630/18/5/053008
DO - 10.1088/1367-2630/18/5/053008
M3 - Article
AN - SCOPUS:84973926470
VL - 18
JO - New Journal of Physics
JF - New Journal of Physics
SN - 1367-2630
IS - 5
M1 - 053008
ER -