Heat Flow in a Periodically Forced, Thermostatted Chain II

Article Physics, Mathematical

Heat Flow in a Periodically Forced, Thermostatted Chain

Tomasz Komorowski et al.

Summary: We study a harmonic chain in contact with a thermal bath, subjected to a periodic force at one end while undergoing random velocity reversals. This leads to a limited heat conductivity and the system approaches a time periodic state. We compute the heat current, which represents the time averaged work done on the system, and find that it approaches a finite positive value as the chain's length increases. By rescaling space and adjusting the strength and/or period of the force, we observe a macroscopic temperature profile consistent with the stationary solution of a continuum heat equation with Dirichlet-Neumann boundary conditions.

COMMUNICATIONS IN MATHEMATICAL PHYSICS (2023)

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Article Materials Science, Multidisciplinary

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

Abhinav Prem et al.

Summary: Motivated by experiments on chains of superconducting qubits, we study the dynamics of a classical Klein-Gordon chain coupled to coherent driving and dissipation at its boundaries. The minimal classical model exhibits the main features of the dissipative phase transition observed experimentally when the strength of the boundary driving increases. In addition to the transmitting and nontransmitting regimes, which support ballistic and diffusive energy transport, respectively, we observe other interesting dynamical regimes such as superdiffusive energy transport at weaker driving strengths and a resonant nonlinear wave regime at stronger driving strengths.

PHYSICAL REVIEW B (2023)

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Article Statistics & Probability

Hydrodynamic limit for a chain with thermal and mechanical boundary forces

Tomasz Komorowski et al.

Summary: In this study, the hydrodynamic limit of a one-dimensional harmonic chain with a random flip of the momentum sign is proven. The system is affected by two thermostats at the boundaries and an external tension at one endpoint. Through diffusive scaling of space-time, it is shown that the empirical profiles of two locally conserved quantities converge to the solution of a non-linear diffusive system of conservative partial differential equations.

ELECTRONIC JOURNAL OF PROBABILITY (2021)

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Article Physics, Mathematical