Abstract
We consider 1D integrable systems supporting ballistic propagation of excitations, perturbed by a localised defect that breaks most conservation laws and induces chaotic dynamics. Focusing on classical systems, we study an out-of-equilibrium protocol engineered activating the defect in an initially homogeneous and far from the equilibrium state. We find that large enough defects induce full thermalisation at their center, but nonetheless the outgoing flow of carriers emerging from the defect is non-thermal due to a generalization of the celebrated Boundary Thermal Resistance effect, occurring at the edges of the chaotic region. Our results are obtained combining ab-initio numerical simulations for relatively small-sized defects, with the solution of the Boltzmann equation, which becomes exact in the scaling limit of large, but weak defects.
Highlights
An ideal laboratory to investigate transport phenomena is offered by the one dimensional world: here, efficient numerical algorithms [11] and powerful analytical methods have unveiled a plethora of exciting phenomena, as the suppression of transport in disordered [12] and confined [13–15] systems, ballistic transport in exactly solvable models [16, 17] with the possibility of diffusion [18, 19] and superdiffusion [20–22]
The phase-space distribution of the carriers flowing out of the defect is of central interest: these excitations are scrambled when passing in the defect region and it might seem natural to assume a thermal distribution. While this has been contradicted for small impurities [35], the scenario is less clear at the mesoscopic scale, lying between impurity physics and thermodynamics: a strongly-interacting extended defect is itself a macroscopic system obeying the laws of thermodynamics
We show how carriers flowing out from the defect are in general not thermally distributed even in the extreme case of extended defects which thermalise in the center. This is due to a generalization of the Boundary Thermal Resistance, taking place at the interface between the defect and the bulk of the system
Summary
The problem of thermalisation is a paramount question for many facets of physics at the center of hectic research. The phase-space distribution of the carriers flowing out of the defect is of central interest: these excitations are scrambled when passing in the defect region and it might seem natural to assume a thermal distribution While this has been contradicted for small impurities [35], the scenario is less clear at the mesoscopic scale, lying between impurity physics and thermodynamics: a strongly-interacting extended defect is itself a macroscopic system obeying the laws of thermodynamics. We present a systematic study showing on general grounds that the emitted distribution of carriers is not thermal This remains true even in the extreme situation where the defect is mascroscopically large and regions deep within the defect are well described by thermal ensembles. Our claim is based on extensive numerical simulations, physical arguments and on Boltzmann-kinetic equations for weakly interacting, but extended defects
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