Quantum Otto Heat Engine Based On Three-qubit Heisenberg XXZ Model With DM Interaction

With the progress of nanotechnology and the development of quantum information processing,the study of the interface between quantum physics and thermodynamics have attracted more and more attentions.Studies of quantum thermodynamics not only promise important potential applications in nanotechnology and quantum information processing,but also bring new insights to some fundamental problems of thermodynamics.Quantum heat engine is an important problem in quantum thermodynamics.Various quantum mechanical systems and experimental schemes have been used to explore and implement quantum thermal engines and the performances of quantum thermal engines are optimized.In this paper,based on the basic theory of quantum thermodynamics and the research background of quantum heat engine,a quantum Otto heat engine is established with a three-qubit Heisenberg XXZ model with Dzyaloshinskii–Moriya(DM)interaction under a homogeneous magnetic field as the working substance.The work output and efficiency are calculated.In the three different adiabatic branches,the effects of DM interaction parameters,anisotropic parameters and entanglement on the performance of the thermal machine are studied.In addition,in the third case,the possible adiabatic compression ratio of the heat engine and the ratio of the work output between the three qubit systems and the single qubit system are analyzed.In the first chapter,the background and recent progress of quantum mechanics,thermodynamics and quantum heat engine are introduced.In the second chapter,the basic theory of quantum thermodynamics related to the content of this article are described.In the third chapter,a quantum Otto heat engine is established with a three-qubit Heisenberg XXZ model with DM interaction under a homogeneous magnetic field as the working substance.The model contains the results of the XX model(?=0)and the XXX model(?=1),so the differences between them can be compared.The output work and efficiency of the cycle are calculated at first,and then in the adiabatic processes,only where the external magnetic field changes between two selected values(B_h?B_c?B_h),but the coupling constant is fixed(J_h=J_c=J)and only the coupling constant changes between the two selected values(J_h?J_c?J_h),but the external magnetic field is fixed(B_h=B_c=B),the effects of DM interaction parameters Dand anisotropic parameters?on the performance of the quantum heat engine are discussed.In the fourth chapter,another special case,where the magnetic field and the coupling constant are changed in the same proportion in the two adiabatic processes B_cB_h=J_cJ_h=rare considered.Here r is the adiabatic compression ratio.Under this constraint,the the influence of anisotropic parameters?and DM interaction parameters D on the cycle are analyzed.Moreover,the positive work conditions,possible adiabatic compression ratios,and the ratios of work output between three-qubit system and a single qubit system under the same conditions are discussed.The results show that due to the complexity of the energy spectrum,the results are quite different from the two-qubit case.Finally,the effects of pairwise entanglements on the heat engine efficiency are discussed.Finally,the main conclusions of this article are summarized and prospected.