Abstract
We introduce non-trivial contributions to diffusion constants in generic many-body systems with Hamiltonian dynamics arising from quadratic fluctuations of ballistically propagating, i.e. convective, modes. Our result is obtained by expanding the current operator in terms of powers of local and quasi-local conserved quantities. We show that only the second-order terms in this expansion carry a finite contribution to diffusive spreading. Our formalism implies that whenever there are at least two coupled modes with degenerate group velocities the system behaves super-diffusively, in accordance with non-linear fluctuating hydrodynamics. Finally, we show that our expression saturates the exact diffusion constants in quantum and classical interacting integrable systems, providing a general framework to derive these expressions.
Highlights
We introduce non-trivial contributions to diffusion constants in generic many-body systems with Hamiltonian dynamics arising from quadratic fluctuations of ballistically propagating, i.e. convective, modes
In order to determine the contribution to diffusion constant from expansion (6), we have to deduce the dynamics of the second order term in the leading order in, i.e. Euler scale
We have introduced an operatorial expansion of the currents in a many-body system in terms of hydrodynamical densities of conservation laws in generic stationary states
Summary
From its inception statistical physics has strived to derive the laws of hydrodynamics and thermodynamics. Proving the emergence of diffusive transport and in particular computing diffusion constants in generic interacting many-body systems directly from their Hamiltonian reversible dynamics is still largely an open question [4] This is a very non-trivial task even with the powerful numerical methods available for one-dimensional systems [5,6,7]. The main accomplishment of NLFHD was to show that the presence of a quadratic coupling of the modes in the second-order expansion gives rise to Kardar-Parisi-Zhang [36] or Lévy super-diffusive universal transport. Generalization of this result manifests itself within the framework of our theory as a divergence of the diffusion constant in the presence of degenerate group velocities
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