Abstract
Does a closed quantum many-body system that is continually driven with a time-dependent Hamiltonian finally reach a steady state? This question has only recently been answered for driving protocols that are periodic in time, where the long time behavior of the local properties synchronize with the drive and can be described by an appropriate periodic ensemble. Here, we explore the consequences of breaking the time-periodic structure of the drive with additional aperiodic noise in a class of integrable systems. We show that the resulting unitary dynamics leads to new emergent steady states in at least two cases. While any typical realization of random noise causes eventual heating to an infinite temperature ensemble for all local properties in spite of the system being integrable, noise which is self-similar in time leads to an entirely different steady state, which we dub as "geometric generalized Gibbs ensemble", that emerges only after an astronomically large time scale. To understand the approach to steady state, we study the temporal behavior of certain coarse-grained quantities in momentum space that fully determine the reduced density matrix for a subsystem with size much smaller than the total system. Such quantities provide a concise description for any drive protocol in integrable systems that are reducible to a free fermion representation.
Highlights
AND MOTIVATIONStatistical mechanics can be derived from Jaynes’ principle of maximum entropy [1,2], given the constants of motion for any generic many-body system
We again look at the behavior of the coarse-grained quantities to understand the nature of the resulting nonequilibrium steady state
100 000 200 000 300 000 400 000 500 000 n nonequilibrium steady state is locally described by an infinite-temperature ensemble as n → ∞, unlike the case with dT 1⁄4 0
Summary
AND MOTIVATIONStatistical mechanics can be derived from Jaynes’ principle of maximum entropy [1,2], given the constants of motion for any generic many-body system. Jaynes’ principle may again be applied here by considering the extensive number of conservation laws due to integrability that leads to a generalized Gibbs ensemble (GGE) [9,10,11] instead of the standard Gibbs ensemble. These statistical descriptions are expected to hold only for local properties (i.e., properties that are determined by the degrees of freedom in a subsystem that is much smaller than the rest of the system, as shown schematically in Fig. 1) and not for the wave function of the entire system, which is, after all, in a pure state [12]
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