Normal Transport Behavior in Finite One-Dimensional Chaotic Quantum Systems

– We investigate the transport of energy, magnetization, etc. in several finite one-dimensional (1D) quantum systems only by solving the corresponding time-dependent Schrödinger equation. We explicitly renounce on any other transport-analysis technique. Varying model parameters we find a sharp transition from non-normal to normal transport and a transition from integrability to chaos, i.e., from Poissonian to Wigner-like level statistics. These transitions always appear in conjunction with each other. We investigate some rather abstract “design models” and a (locally perturbed) Heisenberg spin chain. The transport behavior of one-dimensional (1D) systems has intensively been investigated for several decades, as well in the context of classical mechanics as in the context of quantum mechanics [1–16]. Nevertheless, the precise conditions under which normal transport occurs, i.e., under which there is neither ballistic transport nor localization but normal spatial diffusion, are still not known [17]. In the classical domain it seems to be largely accepted that normal transport (in any dimension) requires the chaotic dynamics of a non-integrable system whereas non-normal transport is typical for the regular dynamics of (completely) integrable systems, see [3]. However, there have also been successful attempts to observe normal transport in the absence of exponential instability, the latter being a basic feature of (deterministic) chaos [4]. In the quantum domain there are only very few examples which can be reliably shown to exhibit normal, diffusive transport at all [5–7]. But, also in this field, it has been argued that non-normal transport is related to the macroscopic number of conserved quantities which characterize integrable systems [10–13]. Moreover, recent numerical computations for spin chains have led to the assumption that normal transport might strictly depend on quantum chaos [1, 2]. Although this assumption is plausible, it has not been proved yet [15]. Moreover, almost all computations are either based on special models of reservoirs which might effect the transport (∗) Email: [email protected]