A Special Entanglement Quantum Heat Engine Based On The Two-qubit Heisenberg XX Model

With the development of the theory and experiences, the study on physics has graduallybeen transferred to the microscopic world. Ever since the concept of a quantum heat enginewas first introduced by Scovil and Schultz-Dubois, it immediately attracted much attention.The main feature of the quantum thermodynamical cycles is that the working substances arequantum mechanical systems. Because of the quantum nature of the working substances, thequantum heat engine exhibit the different properties from the classical thermodynamicalcounterpart. For example, under some special conditions, the efficiency of the quantum heatengine approaches the Carnot efficiency, or even surpass it. Some interesting phenomena canbe found in quantum systems, which are attributable to the existence of entanglement. It hasbeen an interesting topic about the potential applications of entanglement in quantumcommunication and information processing, and we are interested in the study about theperformance of the entanglement on quantum heat engine.In chapter I, the history of the quantum mechanical and the developments of the quantumthermodynamical cycle are presented.In chapter II, some basic knowledge including the quantum entangled states, theentanglement, the measure of the adiabatic theorem, and reversible cycle are introduced.In chapter III, a quantum heat engine is established. Based on the two-qubit HeisenbergXX model, the performance of the quantum heat engine under the two different conditions arestudied, one is that change the coupling constant but fix the external magnetic field, the otherthat is change the external magnetic field but fix the coupling constant. The results show thatthe second law of thermodynamics holds in the whole cycle. Heat transferred changemonotonically withc1andc2in both cases. For the previous case the coupling constantcan affect the value of the efficiency, when the coupling constant is large enough, theefficiency can approach the Carnot efficiency. In the latter case, the maximum efficiency ofthe quantum engine cannot achieve the Carnot efficiency. When the strength of the magneticfield is increased, the working region of the quantum engine expand fromc1c2toc1c2andc1c2.In chapter IV, we construct a special four-level entangled quantum Otto heat enginebased on the two-qubit Heisenberg XX model, in which we assume that all the energy gaps arechanged in the same ratio in two quantum adiabatic processes. Hence during the whole cycle, the relative coupling constant k=J/Bis fixed, where J and B are the coupling constantand the external magnetic field, respectively. The dependence of the basic thermodynamicalquantities on the two entanglements at the end of two quantum isochoric processes withdifferent relative coupling constant k is studied. Our results show that in the weak couplingregion, i.e. k＜1, the heat engine can be operated in both areas wherec1c2andc1c2,whereas when k≥1, it can only be operated under the conditionc1c2. Herec1andc2are entanglements of the working substance when the heat engine comes into contact with hotand cold baths, respectively. Moreover, we find that the maximal work output for increases with the relative coupling constant.