Thermalization of interacting quasi-one-dimensional systems

Abstract

Many experimentally relevant systems are quasi-one-dimensional, consisting of nearly decoupled chains. In these systems, there is a natural separation of scales between the strong intra-chain interactions and the weak interchain coupling. When the intra-chain interactions are integrable, weak interchain couplings play a crucial part in thermalizing the system. Here, we develop a Boltzmann-equation formalism involving a collision integral that is asymptotically exact for any interacting integrable system, and apply it to develop a quantitative theory of relaxation in coupled Bose gases in the experimentally relevant Newton's cradle setup. We find that relaxation involves a broad spectrum of timescales. We provide evidence that the Markov process governing relaxation at late times is gapless; thus, the approach to equilibrium is generally non-exponential, even for spatially uniform perturbations.

v2: improved presentation, 6 pages + 15 pages of supplemental materials

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• Finite-temperature lineshapes in gapped quantum spin chains
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• Density form factors of the 1D Bose gas for finite entropy states
• Spinon Confinement and a Sharp Longitudinal Mode in Yb${}_2$Pt${}_2$Pb in Magnetic Fields
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• The Theory of Generalised Hydrodynamics for the One-dimensional Bose Gas
• Macroproperties vs. Microstates in the Classical Simulation of Critical Phenomena in Quench Dynamics of 1D Ising Models
• Quantum fluctuating theory for one-dimensional shock waves
• Chapman-Enskog theory and crossover between diffusion and superdiffusion for nearly integrable quantum gases
• Extending the Thermodynamic Form Factor Bootstrap Program: Multiple particle-hole excitations, crossing symmetry, and reparameterization invariance
• Dynamic structure factor of quantum hard rods from exact form-factors
• Exotic critical states as fractional Fermi seas in the one-dimensional Bose gas