Quantum Coherence-based Researches On Thermal Phenomena Of Macroscopic System

Quantum interference is in the heart of quantum mechanics. It describes the situation when several different states of a quantum system coherently superpose a new pure state. When the quantum system is in coherent superposition of several possible states, it would be impossible to know which state on earth is the system in, as long as the superposed state was not destructed. Quantum entangled state is a special coherently superposed state, i.e., it is a coherently superposed state in a compound system. Nowadays quantum information technology is one of the most popular interdisciplinary, whose essence is the utilization and exploitation of non-classical properties, such as quantum coherence and quantum entanglement, in order to accomplish the storage, transmission and processing of information.Thermology is a subject that studies thermal phenomena and laws related to heat. In retrospect of the development course of thermology, it is the combination of thermodynamics and atomic-molecular theory that leads to the foundation of statistical mechanics. Also quantum statistics is established with the emergence of quantum mechanics. Every introduction of new theories can deepen the understanding of macroscopic system.With further and extensive researches on quantum coherence and quantum entanglement in recent years, researchers can not only realize macroscopic quantum coherence and quantum entanglement, but also experimentally observe the influence of microscopic quantum entanglement on macroscopic properties. Therefore, it is so necessary to include quantum coherent properties to the theoretical system of thermology, that can continue thorough understanding of macroscopic system. We believe that the study of thermal phenomena and heat related laws based on quantum coherence can further improve the development of thermology, as well as deepen the understanding of quantum coherence and solve certain fundamental problem in quantum mechanics. It is also possible to play a fundamental role in the practical quantum information technology.The main contents of this dissertation include(1) Researches on quantum heat engine. Firstly, we introduce and deeply analyze a two-level quantum heat engine, whose work substance is two-level systems. Some ambiguous statements in certain references, such as "The probabilistic nature of quantum mechanics leads to a violation of Kelvin's expression of the second law of thermodynamics", "The second law holds on average", are clarified. We prove the second law of thermodynamics would always be valid, as long as the quantum heat engine could export some useful work. Secondly, entanglement is introduced in the study on quantum heat engine for the first time . We construct a four-level quantum heat engine, whose work substance are four-level systems composed of two entangled two-level systems. The relations between heat, work, efficiency and entanglement are investigated. The second law of thermodynamics is proved valid in an indeed entangled systems. We also explore the condition under which the quantum heat engine can produce useful work. It is found that the requirements of an entangle quantum heat engine are looser than that of a non-entangled quantum heat engine.(2) Researches on the properties of thermal entanglement. Thermal entanglement is the entanglement of a system when it is at thermal equilibrium. Firstly, we investigate the characteristics of thermal entanglement in a particular Heisenberg spin chain. We plot the variation of thermal entanglement with the change of temperature and magnetic field. By the analysis of eigenstates, we explain the characteristics accurately. Secondly, based on the features of eigenstates of Heisenberg spin chain, we summarize three universal characteristics of thermal entanglement, which hold for any n-party entanglement in arbitrary-length Heisenberg spin chain.(3) Researches on inequivalent entanglement witness. For the first time, an inequivalent entanglement witness is clearly defined. We also clarify two key points of an inequivalent entanglement witness. It is shown that the absolute value of magnetization can serve as an inequivalent entanglement witness for the eigenstates of a Heisenberg spin chain.(4) Researches on the connection between quantum phase transition and quantum entanglement. For the first time, we explore the relation between quantum phase transition and the classification of inequivalently entangled ground states. We think that when quantum phase transition occur, the type of ground-state entanglement should change simultaneously. The conjecture is verified in the Heisenberg spin chain and one dimensional XY spin model.