Reversible to Irreversible Transitions in Periodic Driven Many Body Systems and Future Directions for Classical and Quantum Systems

Luca D’Alessio, Anatoli Polkovnikov

Luca D’Alessio, Anatoli Polkovnikov

Craig Callender

In a classical mechanical world, the fundamental laws of nature are reversible. The laws of nature treat the past and future as mirror images of each other. Temporally asymmetric phenomena are ultimately said to arise from initial conditions. But are the laws of nature also reversible in a quantum world? This paper argues that they are not, that time in a quantum world prefers a particular ‘hand’ or ordering. I argue, first, that the probabilistic algorithm used in the theory picks out a preferred direction of time for almost all interpretations of the theory, and second, that contrary to the received wisdom the Schrödinger evolution is also irreversible. The status of Wigner reversal invariance is then discussed. I conclude that the quantum world is fundamentally irreversible, but manages to appear (thanks to Wigner reversal invariance) reversible at the classical level.

Giulio Casati

Owen Howell, Phillip Weinberg, Dries Sels +2 more

We reveal a continuous dynamical heating transition between a prethermal and an infinite-temperature stage in a clean, chaotic periodically driven classical spin chain. The transition time is a steep exponential function of the drive frequency, showing that the exponentially long-lived prethermal plateau, originally observed in quantum Floquet systems, survives the classical limit. Even though there is no straightforward generalization of Floquet's theorem to nonlinear systems, we present strong evidence that the prethermal physics is well described by the inverse-frequency expansion. We relate the stability and robustness of the prethermal plateau to drive-induced synchronization not captured by the expansion. Our results set the pathway to transfer the ideas of Floquet engineering to classical many-body systems, and are directly relevant for photonic crystals and cold atom experiments in the superfluid regime.

Raisa I. Karasik