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Abstract |
Finding a theoretical framework to explain how phenomenological transport laws
on macroscopic scales emerge from microscopic deterministic dynamics poses one
of the most significant challenges of condensed matter and statistical physics.
Recently there has been an influx of new numerical and analytical results for
the transport theory of quantum and classical many-body 1D Hamiltonian systems,
both integrable and not. I will provide a general framework to understand the
main classes of transport observed: diffusion, super-diffusion and logarithmic
corrections to diffusion. I will review how diffusive spreading is generically
present in integrable chains and how KPZ dynamics emerges in both integrable
and non-integrable rotationally invariant magnets. |
