Reservoir-induced stabilization of a periodically driven many-body system.

Exploiting the rich phenomenology of periodically driven many-body systems is notoriously hindered by persistent heating in both the classical and the quantum realm. Here, we investigate to what extent coupling to a large thermal reservoir makes stabilization of a nontrivial steady state possible. To this end, we model both the system and the reservoir as classical spin chains where driving is applied through a rotating magnetic field, and we simulate the Hamiltonian dynamics of this setup. We find that the intuitive limits of infinite frequency and vanishing frequency, where the system dynamics is governed by the average and the instantaneous Hamiltonian, respectively, can be smoothly extended into entire regimes separated only by a small crossover region. At high frequencies, the driven system stroboscopically attains a Floquet-type Gibbs state at the reservoir temperature. At low frequencies, a global synchronized Gibbs state emerges, whose temperature may depart significantly from the initial temperature of the reservoir. Although our analysis in some parts relies on the specific properties of our setup, we argue that much of its phenomenology could be generic.

Reservoir-induced stabilization of a periodically driven classical spin chain: Local versus global relaxation.

Floquet theory is an indispensable tool for analyzing periodically driven quantum many-body systems. Although it does not universally extend to classical systems, some of its methodologies can be adopted in the presence of well-separated timescales. Here we use these tools to investigate the stroboscopic behaviors of a classical spin chain that is driven by a periodic magnetic field and coupled to a thermal reservoir. We detail and expand our previous work: we investigate the significance of higher-order corrections to the classical Floquet-Magnus expansion in both the high- and low-frequency regimes; explicitly probe the evolution dynamics of the reservoir; and further explore how the driven system and the reservoir synchronize with the applied field at low frequencies. In line with our earlier results, we find that the high-frequency regime is characterized by a local Floquet-Gibbs ensemble with the reservoir acting as a nearly-reversible heat sink. At low frequencies, the driven system rapidly enters a synchronized state, which can only be fully described in a global picture accounting for the concurrent relaxation of the reservoir in a fictitious magnetic field arising from the drive. We highlight how the evolving nature of the reservoir may still be incorporated in a local picture by introducing an effective temperature. Finally, we show that generic local-dissipation models that account for the influence of the reservoir on the driven system phenomenologically through Markovian dissipative equations of motion can generally not reproduce the rich behavior that our microscopic simulations reveal. In particular, such models prove insufficient to account for the suppression of overall energy absorption that is induced by the here observed synchronization between driven system and reservoir.

Landauer Formula for a Superconducting Quantum Point Contact.

We generalize the Landauer formula to describe the dissipative electron transport through a superconducting point contact. The finite-temperature, linear-in-bias, dissipative dc conductance is expressed in terms of the phase- and energy-dependent scattering matrix of the Bogoliubov quasiparticles in the quantum point contact. The derived formula is also applicable to hybrid superconducting-normal structures and normal contacts, where it agrees with the known limits of Andreev reflection and normal-state conductance, respectively.

Atypical energy eigenstates in the Hubbard chain and quantum disentangled liquids.

We investigate the implications of integrability for the existence of quantum disentangled liquid (QDL) states in the half-filled one-dimensional Hubbard model. We argue that there exist finite energy-density eigenstates that exhibit QDL behaviour in the sense of Grover & Fisher (2014 J. Stat. Mech.2014, P10010. (doi:10.1088/1742-5468/2014/10/P10010)). These states are atypical in the sense that their entropy density is smaller than that of thermal states at the same energy density. Furthermore, we show that thermal states in a particular temperature window exhibit a weaker form of the QDL property, in agreement with recent results obtained by strong-coupling expansion methods in Veness et al. (2016 (http://arxiv.org/abs/1611.02075)).This article is part of the themed issue 'Breakdown of ergodicity in quantum systems: from solids to synthetic matter'.