arXiv subjects

Daniel Schmidtke

Publications and source records attributed to Daniel Schmidtke.

5 recordsLinked to original sources

arXiv2017

Stiffness of Probability Distributions of Work and Jarzynski Relation for Non-Gibbsian Initial States

We consider closed quantum systems (into which baths may be integrated) that are driven, i.e., subject to time-dependent Hamiltonians. Our point of departure is the assumption that, if systems start in microcanonical states at some initial energies, the resulting probability distributions of work may be largely independent of the specific initial energies. It is demonstrated that this assumption has some far-reaching consequences, e.g., it implies the validity of the Jarzynski relation for a large class of non-Gibbsian initial states. By performing numerical analysis on integrable and non-integrable spin systems, we find the above assumption fulfilled for all considered examples. Through an analysis based on Fermi's Golden Rule, we partially relate these findings to the applicability of the eigenstate thermalization ansatz to the respective driving operators.

quant-ph↗

arXiv2017

Interaction-Induced Weakening of Localization in Few-Particle Disordered Heisenberg Chains

We investigate real-space localization in the few-particle regime of the XXZ spin-$1/2$ chain with a random magnetic field. Our investigation focuses on the time evolution of the spatial variance of non-equilibrium densities, as resulting for a specific class of initial states, namely, pure product states of densely packed particles. Varying the strength of both particle-particle interactions and disorder, we numerically calculate the long-time evolution of the spatial variance $σ(t)$. For the two-particle case, the saturation of this variance yields an increased but finite localization length, with a parameter scaling different to known results for bosons. We find that this interaction-induced increase is the stronger the more particles are taken into account in the initial condition. We further find that our non-equilibrium dynamics are clearly inconsistent with normal diffusion and instead point to subdiffusive dynamics with $σ(t) \propto t^{1/4}$.

cond-mat.str-el↗

arXiv2016

Initial State Independent Equilibration at the Breakdown of the Eigenstate Thermalization Hypothesis

This work aims at understanding the interplay between the Eigenstate Thermalization Hypothesis (ETH), initial state independent equilibration and quantum chaos in systems that do not have a direct classical counterpart. It is based on numerical investigations of asymmetric Heisenberg spin ladders with varied interaction strengths between the legs, i.e., along the rungs. The relaxation of the energy difference between the legs is investigated. Two different parameters, both intended to quantify the degree of accordance with the ETH, are computed. Both indicate violation of the ETH at large interaction strengths but at different thresholds. Indeed the energy difference is found not to relax independently of its initial value above some critical interaction strength which coincides with one of the thresholds. At the same point the level statistics shift from Poisson-type to Wigner-type. Hence the system may be considered to become integrable again in the strong interaction limit.

quant-ph↗

arXiv2016

Numerical Evidence for Approximate Consistency and Markovianity of some Quantum Histories in a Class of Finite Closed Spin Systems

Closed quantum systems obey the Schroedinger equation whereas nonequilibrium behavior of many of systems is routinely described in terms of classical, Markovian stochastic processes. Evidently, there are fundamental differences between those two types of behavior. We discuss the conditions under which the unitary dynamics may be mapped onto pertinent classical stochastic processes. This is first principally addressed based on the notions of "consistency" and "Markovianity." Numerical data are presented that show that the above conditions are to good approximation fulfilled for Heisenberg-type spin models comprising 12-20 spins. The accuracy to which these conditions are met increases with system size.

quant-ph↗

arXiv2014

Transport in tight-binding bond percolation models

Most of the investigations to date on tight-binding, quantum percolation models focused on the quantum percolation threshold, i.e., the analogue to the Anderson transition. It appears to occur if roughly 30% of the hopping terms are actually present. Thus, models in the delocalized regime may still be substantially disordered, hence analyzing their transport properties is a nontrivial task which we pursue in the paper at hand. Using a method based on quantum typicality to numerically perform linear response theory we find that conductivity and mean free paths are in good accord with results from very simple heuristic considerations. Furthermore we find that depending on the percentage of actually present hopping terms, the transport properties may or may not be described by a Drude model. An investigation of the Einstein relation is also presented.

cond-mat.dis-nn↗