Quantum Dissipation Theory:Applications To Strongly Correlated Quantum Impurity Systems

The thesis focuses on the application of quantum dissipation theory to strongly correlated quantum impurity systems.The local properties of the system is signifi-cantly influenced by the dissipative couplings between the system and its surrounding environment,as well as the strong electron-electron interactions among the impurity states.Accurate characterization of quantum impurity systems is the key to the under-standing of the mechanisms of strong electron correlations.It may also help design novel functional materials and nanoscale electronic devices,and provide new insights into understanding some fundamental problems in physics and chemistry.This thesis is organized as follows:In Chapter 1,I briefly review the theoretical efforts that have been devoted to ad-dress the strong correlation effects in quantum impurity systems.Particularly,the de-velopment history of the hierarchical equations of motion(HEOM)approach based on the quantum dissipation theory is introduced.A representative quantum impurity sys-tem-the quantum dot,and two important physical phenomena-the Coulomb blockade and Kondo effect,are then discussed in detail.Chapter 2 introduces the methodological construction of HEOM approach.The theoretical construction starts with the Feynman-Vernon path-integral formalism,in which the electron creation and annihilation operators are Grassmann variables.The HEOM formalism is formally rigorous,as long as the reservoir environment satisfies Gaussian statistics,which is true for noninteracting electron reservoirs.It captures the combined effects of impurity-environment dissipative coupling,strong e-e interaction,and non-Markovian memory in a nonperturbative manner.The accuracy and efficiency of HEOM are then performed for addressing equilibrium and nonequilibrium,static and dynamic properties of quantum impurity systems.The numerical algorithms and pro-gramming techniques of the simulation program,the Hierarchical Equations of Motion for QUantum Impurity with a Correlated Kernel(HEOM-QUICK),are described in de-tail.In particular,the numerous efforts devoted to reducing the computational cost are highlighted.In chapter 3,I present a comprehensive picture which elucidates the underlying relations between the thermopower and the spectral density function of two-level quan-tum dots.The effects of various electronic states,including the Kondo states originating from both spin and orbital degrees of freedom,are clearly unraveled.Such a physical picture is affirmed by accurate numerical data obtained with the HEOM approach.Our findings and understandings provide an effective and viable way to control the thermo-electric properties of strongly correlated quantum dot systems.In Chapter 4,some fundamental problems in nonequilibrium thermodynamics are studied.An operational definition of local temperature for nonequilibrium open quan-tum systems is proposed by using a "minimal-perturbation condition".The opera-tional definition applies equally well to systems ranging from noninteracting to Kondo-correlated regimes.Since this definition does not require measurements of heat currents,its experimental realization is straightforward.By performing analytical and numerical analysis of bias-driven quantum dot systems,we show that,the local temperature deter-mined by the minimal-perturbation protocol establishes a quantitative correspondence between the nonequilibrium system of interest and a reference equilibrium system,pro-vided the probed system observable and the related electronic excitations are fully local.The quantitative correspondence thus allows the well-established thermodynamic con-cept to be extended to nonequilibrium situations.In concluding this thesis,I discuss the direction of future development and appli-cation of quantum dissipation theory for quantum impurity systems.