Quantum Dynamics and Transport in Closed and Open Models of Interacting Spins

Abstract

Based on the references [P1–P6], we investigate in this cumulative PhD thesis the dynamics and transport in closed and open interacting spin chain models. We focus on (i) the connection between the open and the closed system dynamics [P1, P2], (ii) the influence of various system parameters on the transport behavior in closed and open systems [P3, P5], and in addtion (iii) the dynamics and transport in closed models [P4, P6]. As for (i), we explore the connection of the dynamics in open systems, modeled by the Lindblad equation, and the correlation functions in the closed system [P1]. Building on this connection for magnetization transport, we study whether the time evolution of the open quantum system can be described in terms of classical correlation functions generated by the Hamiltonian equations of motion for real vectors [P2]. Second, we study in (ii) the influence of different parameters on the diffusion constants in closed and open systems [P3, P5]. In Ref. [P3], we study the impact of integrability-breaking perturbations in both closed and open spin chain systems. While we find a continuous change of the diffusion constant with perturbation strength in the closed system, in the open system, in the weak-perturbation limit, we indicate the possibility of a diverging diffusion constant. Also, we investigate the influence of the system-bath coupling on the transport behavior in boundary-driven open systems [P5]. We observe that the diffusion constants depend on the system-bath coupling and that in the nonequilibrium steady state, they inevitably retain finite-size effects, limiting the computation of long-time transport coefficients. Additional for (iii), in Ref. [P4], we first examine the impact of perturbations on the dynamics in closed spin chain models. We employ projector-operator techniques to understand, on perturbative grounds, the nontrivial damping of the standard correlation function. Second, we also discuss a dynamical quantum typicality approach for studying the energy transport in bipartite systems at low temperatures [P6]