Performance Investigation Of The Thermodynamic Cycle With Interacting Quantum System

In recent years, with rapid developments of quantum information science and the experimental technology, some fundamental issues in quantum mechanics and statistical mechanics have attracted great interest. Under many researchers'effort, the thermodynamic theory, which is based on the quantum mechanics and called quantum thermodynamics, has been discussed in a series of papers. In reviewing the history of thermodynamics, one can find that the study of the heat engine played an important role in the development of classical thermodynamics. Similarly, the quantum heat engines serve as a platform for studying fundamental topics of the quantum thermodynamics. Quantum heat engine produce work using quantum system as the working substance, which includes the spin system, harmonic oscillator system, the particles in the infinite potential trap and the qubit system. There are many differences between the quantum heat engine and the classical counterparts because of the nature of the quantum matter. Therefore, the quantum heat engine become the research field of great interest in recent years, aiming to find some novel phenomenon and interesting results.In this dissertation, the main task is to analyze and optimize the performance of the quantum cycle. Through studying various quantum thermodynamic cycles, we inverstigate the fundamental issue about the quantum thermodynamics.In the chapter â…¡, a new cycle model of an irreversible quantum harmonic heat engine is established, which is composed of two isothermal processes, an adiabatic process and a constant frequency process. Based on the quantum master equation and semi-group approach, the general optimal performance characteristics of the cycle are investigated. Expressions for several important performance parameters such as the efficiency, the power output and the ecological function are derived in high temperature limit. By using numerical calculation, a set of performance characteristic curves is plotted, such as the optimal curves between the power output and efficiency, the ecological function and efficiency, and so on. The optimal regions of the efficiency, power output and temperature ratio of the working substance at the condition of the maximum ecological function are determined. Moreover, a comparison of the corresponding efficiencies at the maximum ecological function and power output is also presented.In the chapter III, we discussed the performance characteristics of the irreverable quantum Otto refrigeration cycle with intrinsic quantum friction. An irreversible quantum Otto refrigeration cycle working with harmonic systems is established. Base on Heisenberg quantum master equation, the equations of motion for the set of harmonic systems the thermodynamic observables are derived. The simulated diagrams of the quantum Otto refrigeration cycle are plotted. The relationship between average power of friction, cooling rate, power input, and the time of adiabatic process is analyzed by using numerical calculation. Moreover, the influence of the heat conductance and the time of iso-frequency process on the performance of the cycle is discussed.In chapter â…£, We study the performance characteristics of the four level entangled quantum heat engine, whose work substance is composed of the two-qubit Heisenberg XY model. Based on the theory of the quantum thermodynamics, we inverstigate the several thermodynamic quantities such as the heat transferred, the work, the efficiency and the condition of the positive work. Moreover, relationship between the thermodynamic quantities and the concurrence of the quantum entanglement is analyzed by using graph. We found that the requirements of an entangled quantum heat engine are looser than that of a non-entangled quantum heat engine.In chapter â…¤, we continued to study the effect of the quantum entanglement in the quantum thermodynamics. Based on a two-qubit Heisenberg XX model, a four-level entangled quantum refrigeration cycle is constructed. We analysed the relationship between several thermodynamic quantities and the concurrence of the quantum entanglement. We also found some novelty performance characteristics which is different with the entangled quantum heat engine, and it is very useful for people to understand the entangle quantum thermodynamic cycle.In chapter â…¥, we set up a four-level heat engine model which consist of two atoms resonantly interact with a quantized electromagnetic field inside a cavity, and the dipole-dipole interaction of the atoms cannot be neglected. Here, we investigated the influence of the interactiong working medium on the heat engine performance, and analysed the positive work conditions in different cases. An upper bound for the efficiency is derived, which is smaller than the carnot efficieny. Additionally, the local description of each atom are discussed, this study further shows that the interaction between two atoms have important effects on the heat flow of the heat engine.The research topics about quantum thermodynamic theory, which deserve a deeper study for the thermodynamic of the interaction quantum system, are listed in the chapter VII.The results in this dissertation allow to understand well the quantum thermodynamics, and thus provide the theoretical guidelines for the future experiments including the quantum heat engines and quantum entanglement.