Non-Markovian Dynamics And Its Influence On Quantum Heat Engine

The interaction between a quantum system and its environment is unavoidable in prac-tice. The theory to describe such a system is the so-call open system theory, which is usually based on weak coupling and Markovian approximation, leading to a Markovian dynamics. However, in many situations these two approximations or one of them are not held, espe-cially in the case when the coupling is strong and the correlation between the system and the environment can not be ignored. In this situation, we need a theory to take the cor-relation between the quantum system and the environment into account. This results in a non-Markovian dynamics, which and the influence of it on the quantum heat engine are the topics of this thesis.This thesis consist of three part:the chapter 2 is the first part. In this part we mainly introduce how to derive the non-Markovian master equation by Nakajima-Zwanzing projec-tion operator technique, time-convolutionless projection operator technique and path inte-gral method. We apply the Nakajima-Zwanzing and time-convolutionless projection operator technique to the two-level quantum system which interacts with non-Markovian environment. By comparing with the exact solution, we find that these two projection operator techniques meet with the exact solution very well for short time evolution; however for long time evo-lution these two projection operator techniques are incompatible with the exact solution. For the rest of this chapter, we derive the master equation of optical cavity which interacts with non-Markovian environment. From the simulation results, we find that optical cavity can absorb more heat from non-Markovian environment than Markovian environment. It is from this point we conjecture that non-Markovian reservoir can enhance the performance of quantum heat engine. Details see chapter 4.In chapter 3, we introduce four different measures of non-Markovianity, which include RHP measure, BLP measure, LFS measure and BCM measure. We also discuss the relative merits of these four measures from four different perspectives i.e. computability, physical meanings, their Markovian to non-Markovian crossover and their additivity properties with respect to the number of qubits. Different definitions and corresponding measures of non-Markovianity do not coincide. So we should not insist on the concept of "the best" definition of non-Markovianity but rather look different measures as descriptions of different proper- ties of the open quantum system. We also compare these four measures quantitatively by using the dynamics of single qubits interacting with pure-dephasing and amplitude-damping environment, respectively. In the last section of this chapter, we use the model of two-level system which is coupled to two non-Markovian reservoirs to demonstrate that the interference between these two reservoirs can enhance the non-Markovianity of the system.In chapter 4, we introduce classical thermodynamic process and classical heat engine first. Then we present their quantum counterparts as well. At the end of this chapter, we discuss the influence of non-markovian environment to the performance of quantum Otto heat engine. From the results we find that non-Markovian environment can enhance the performance of quantum Otto heat engine. At certain conditions, the efficiency of quantum Otto heat engine can surpass the standard classical Carnot efficiency. We also demonstrate that quantum Otto heat engine can transfer heat from cool non-Markovian reservoir to hot Markovian reservoir and output work.Finally, the conclusions and discussions are presented in chapter 5.