We present a non-Markovian master equation for a qubit interacting with a general reservoir, which is derived according to the Nakajima-Zwanzig and the time convolutionless projection operator technique. The non-Marko...We present a non-Markovian master equation for a qubit interacting with a general reservoir, which is derived according to the Nakajima-Zwanzig and the time convolutionless projection operator technique. The non-Markovian solutions and Markovian solution of dynamical decay of a qubit are compared. The results indicate the validity of non-Markovian approach in different coupling regimes and also show that the Markovian master equation may not precisely describe the dynamics of an open quantum system in some situation. The non-Markovian solutions may be effective for many qubits independently interacting with the heated reservoirs.展开更多
The generalized quantum master equation(GQME)provides a general and exact approach for simulating the reduced dynamics in open quantum systems where a quantum system is embedded in a quantum environment.Dynamics of op...The generalized quantum master equation(GQME)provides a general and exact approach for simulating the reduced dynamics in open quantum systems where a quantum system is embedded in a quantum environment.Dynamics of open quantum systems is important in excitation energy,charge,and quantum coherence transfer as well as reactive photochemistry.The system is usually chosen to be the interested degrees of freedom such as the electronicstates in light-harvesting molecules or tagged vibrational modes in a condensed-phase system.The environment is also called the bath,whose influence on the system has to be considered,and for instance can be described by the GQME formalisms using the projection operator technique.In this review,we provide a heuristic description of the development of two canonical forms of GQME,namely the time-convoluted Nakajima-Zwanzig form(NZ-GQME)and the time-convolutionless form(TCL-GQME).In the more popular NZ-GQME form,the memory kernel serves as the essential part that reflects the non-Markovian and non-perturbative effects,which gives formally exact dynamics of the reduced density matrix.We summarize several schemes to express the projection-based memory kernel of NZ-GQME in terms of projection-free time correlation function inputs that contain molecular information.In particular,the recently proposed modified GQME approach based on NZ-GQME partitions the Hamiltonian into a more general diagonal and off-diagonal parts.The projection-free inputs in the above-mentioned schemes expressed in terms of different system-dependent time correlation functions can be calculated via numerically exact or approximate dynamical methods.We hope this contribution would help lower the barrier of understanding the theoretical pillars for GQME-based quantum dynamics methods and also envisage that their combination with the quantum computing techniques will pave the way for solving complex problems related to quantum dynamics and quantum information that are currently intractable even with today’s state-of-the-art展开更多
基金Project supported by the Natural Science Foundation of Hunan Province of China (Grant No. 09JJ6011)the Natural Science Foundation of the Education Department of Hunan Province of China (Grant Nos. 06C652 and 07C528)
文摘We present a non-Markovian master equation for a qubit interacting with a general reservoir, which is derived according to the Nakajima-Zwanzig and the time convolutionless projection operator technique. The non-Markovian solutions and Markovian solution of dynamical decay of a qubit are compared. The results indicate the validity of non-Markovian approach in different coupling regimes and also show that the Markovian master equation may not precisely describe the dynamics of an open quantum system in some situation. The non-Markovian solutions may be effective for many qubits independently interacting with the heated reservoirs.
基金support from NYU Shanghai,the National Natural Science Foundation of China(No.21903054)the Hefei National Laboratory for Physical Sciences at the Microscale(No.KF2020008)+1 种基金the Shanghai Sailing Program(No.19YF1435600)the Program for Eastern Young Scholar at Shanghai Institutions of Higher Learning。
文摘The generalized quantum master equation(GQME)provides a general and exact approach for simulating the reduced dynamics in open quantum systems where a quantum system is embedded in a quantum environment.Dynamics of open quantum systems is important in excitation energy,charge,and quantum coherence transfer as well as reactive photochemistry.The system is usually chosen to be the interested degrees of freedom such as the electronicstates in light-harvesting molecules or tagged vibrational modes in a condensed-phase system.The environment is also called the bath,whose influence on the system has to be considered,and for instance can be described by the GQME formalisms using the projection operator technique.In this review,we provide a heuristic description of the development of two canonical forms of GQME,namely the time-convoluted Nakajima-Zwanzig form(NZ-GQME)and the time-convolutionless form(TCL-GQME).In the more popular NZ-GQME form,the memory kernel serves as the essential part that reflects the non-Markovian and non-perturbative effects,which gives formally exact dynamics of the reduced density matrix.We summarize several schemes to express the projection-based memory kernel of NZ-GQME in terms of projection-free time correlation function inputs that contain molecular information.In particular,the recently proposed modified GQME approach based on NZ-GQME partitions the Hamiltonian into a more general diagonal and off-diagonal parts.The projection-free inputs in the above-mentioned schemes expressed in terms of different system-dependent time correlation functions can be calculated via numerically exact or approximate dynamical methods.We hope this contribution would help lower the barrier of understanding the theoretical pillars for GQME-based quantum dynamics methods and also envisage that their combination with the quantum computing techniques will pave the way for solving complex problems related to quantum dynamics and quantum information that are currently intractable even with today’s state-of-the-art