Dynamical Stability of a Many-body Kapitza Pendulum

TL;DR

This paper investigates the stability of a many-body sine-Gordon model under periodic driving, revealing conditions under which the system remains stable against heating, contrary to common expectations for driven interacting systems.

Contribution

It introduces a stability analysis of a many-body driven sine-Gordon model, showing stability conditions and phase transitions using multiple analytical and numerical methods.

Findings

The system remains stable under finite-frequency, finite-amplitude drives.

Stability is linked to the sign change of the kinetic term in the Floquet Hamiltonian.

A phase diagram of stability is developed using high-frequency expansion, variational, and semiclassical methods.

Abstract

We consider a many-body generalization of the Kapitza pendulum: the periodically-driven sine-Gordon model. We show that this interacting system is dynamically stable to periodic drives with finite frequency and amplitude. This finding is in contrast to the common belief that periodically-driven unbounded interacting systems should always tend to an absorbing infinite-temperature state. The transition to an unstable absorbing state is described by a change in the sign of the kinetic term in the effective Floquet Hamiltonian and controlled by the short-wavelength degrees of freedom. We investigate the stability phase diagram through an analytic high-frequency expansion, a self-consistent variational approach, and a numeric semiclassical calculations. Classical and quantum experiments are proposed to verify the validity of our results.