Dynamics and transport in the boundary-driven dissipative Klein-Gordon chain

TL;DR

This paper studies the classical Klein-Gordon chain with boundary driving and dissipation, revealing various transport regimes and a novel nonlinear wave state, with implications for understanding dissipative phase transitions and chaos in open systems.

Contribution

It introduces a detailed analysis of boundary-driven Klein-Gordon chains, identifying new dynamical regimes and proposing a measurable chaos diagnostic for open many-body systems.

Findings

Identification of superdiffusive and ballistic energy transport regimes

Discovery of a resonant nonlinear wave regime with coherent oscillations

Proposal of a non-local Lyapunov exponent as a chaos diagnostic

Abstract

Motivated by experiments on chains of superconducting qubits, we consider the dynamics of a classical Klein-Gordon chain coupled to coherent driving and subject to dissipation solely at its boundaries. As the strength of the boundary driving is increased, this minimal classical model recovers the main features of the "dissipative phase transition" seen experimentally. Between the transmitting and non-transmitting regimes on either side of this transition (which support ballistic and diffusive energy transport respectively), we observe additional dynamical regimes of interest. These include a regime of superdiffusive energy transport at weaker driving strengths, together with a "resonant nonlinear wave" regime at stronger driving strengths, which is characterized by emergent translation symmetry, ballistic energy transport, and coherent oscillations of a nonlinear normal mode. We propose a non-local Lyapunov exponent as an experimentally measurable diagnostic of many-body chaos in this system, and more generally in open systems that are only coupled to an environment at their boundaries.