2017 Fiscal Year Annual Research Report
Quantum langevin equation method in non-Markovian dynamics
| Project/Area Number |
17F17821
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| Research Institution | Institute of Physical and Chemical Research |
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Principal Investigator |
NORI FRANCO 国立研究開発法人理化学研究所, 創発物性科学研究センター, グループディレクター (50415262)
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| Co-Investigator(Kenkyū-buntansha) |
ZHOU ZHENG-YANG 国立研究開発法人理化学研究所, 創発物性科学研究センター, 外国人特別研究員
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| Project Period (FY) |
2017-11-10 – 2020-03-31
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| Keywords | open quantum systems / nonlinear coupling / two-level system / wave approximation |
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| Outline of Annual Research Achievements |
This fiscal year, my research mainly focuses on the development of the methods for the open quantum systems. At the same time, a subject related to quantum thermal dynamics is studied.
I extended the quantum state diffusion method to the system with nonlinear coupling to a zero-temperature bath. Two ways are given to deal with such models. One is defining an O operator to get a time local equation which is suitable to get analytical expressions. The other is the hierarchy equation method which is convenient to calculate the dynamics of the system numerically. This method can be used to study the effects of non-linear coupling on the thermal dynamics behaviors of quantum systems.
I have also studied the steady state of a two-level system (TLS) at zero temperature beyond the rotating wave approximation (RWA). The steady state is shown to be different from the ordinary result under the RWA even with a weak coupling, if the electro-magnetic field coupled to the system is a broad-band one. Then the case of atom cluster is considered. According to our calculation, the electro-magnetic field induced coupling among different TLSs can make the steady state similar to the result under the RWA. This work provides some insights into the steady states of the open quantum systems.
These two manuscripts are still under preparing.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
The research plan for the first year is to develop methods for the non-Markovian dynamics of the open quantum systems so that the thermodynamics properties of quantum systems can be studied with them in the second year. The study of quantum state diffusion method with non-linear coupling has been finished. However, the manuscript is still under progress. The Langevin approach for the quantum dynamics is partially completed. In my plan, this method should have two functions. The first one is to deal with nonlinear coupling between bath and systems. This part is finished because it is similar to the case of quantum state diffusion method with non-linear coupling. The second function is to study the correlation between the system and bath. I plan to achieve this target by applying stochastic method. The derivation of the formalisms is completed, but the computer program is still under adjustment. I have also moved a part of the plan for the second year forward. The time left for me to finish the plan for the first year is about half a year, and the progress of the plan is also about a half. Thus, the studies are going on according to my plan.
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| Strategy for Future Research Activity |
In next fiscal year, I will complete all the ongoing works first. Then I plan to study the open dynamics of many-body systems, because many-body effects have significant influence on the thermodynamics properties of closed systems according to the present works. A quantum Langevin approach for few-body or many-body systems will be developed. After achieving these targets, my research focus will be changed to quantum thermodynamics.
I plan to begin the study of quantum thermodynamics with some comparatively simple models. The thermodynamics properties of these systems are mainly decided by the environment. I will focus on the effect of non-Markovian bath and non-equilibrium bath. At the same time, the effects of correlation between the system and bath will also be considered. Then systems with many- body effects will be considered. I plan to study the thermodynamics properties of systems in which bath effects and many-body effects are equally important.
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