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

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.

23 pages, 16 figures; v2: typos fixed and references added; v3: improved ansatz for the resonant nonlinear wave solution, close to published version

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Cited by in corpus (5)

• Chaotic and quantum dynamics in driven-dissipative bosonic chains
• Hidden time-reversal in driven XXZ spin chains: exact solutions and new dissipative phase transitions
• Heat flow in a periodically forced, thermostatted chain II
• Ballistic conductance with and without disorder in a boundary-driven XXZ spin chain
• Chaos and quantum regimes in $n$-photon driven, dissipative bosonic chains