We develop a general kinetic theory framework to describe the hydrodynamics of strongly interacting, nonequilibrium quantum systems in which integrability is weakly broken, leaving a few residual conserved quantities. This framework is based on a generalized relaxation-time approximation; it gives a simple, but surprisingly accurate, prescription for computing nonequilibrium transport even in strongly interacting systems. We validate the predictions of this approximation against matrix product operator calculations on chaotic quantum spin chains, finding surprisingly good agreement. We show that despite its simplicity, our framework can capture phenomena distinctive to strongly interacting systems, such as widely separated charge and energy diffusion constants.

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• Diffusion
• Kinetic theory
• Nonequilibrium statistical mechanics
• Transport phenomena
• 1-dimensional spin chains
• Bose gases
• Approximation methods for many-body systems
• Hydrodynamics
• Integrable systems
• Tensor network methods