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arXiv · 2304.13028

Unifying Emergent Hydrodynamics and Lindbladian Low Energy Spectra across Symmetries, Constraints, and Long-Range Interactions

Olumakinde Ogunnaike·Johannes Feldmeier·Jong Yeon Lee
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Abstract

We identify emergent hydrodynamics governing charge transport in Brownian random circuits with various symmetries, constraints, and ranges of interactions. This is accomplished via a mapping between the averaged dynamics and the low energy spectrum of a Lindblad operator, which acts as an effective Hamiltonian in a doubled Hilbert space. By explicitly constructing dispersive excited states of this effective Hamiltonian using a single mode approximation, we provide a comprehensive understanding of diffusive, subdiffusive, and superdiffusive relaxation in many-body systems with conserved multipole moments and variable interaction ranges. Our approach further allows us to identify exotic Krylov-space-resolved hydrodynamics exhibiting diffusive relaxation despite the presence of dipole conservation, which we verify numerically. Our approach provides a general and versatile framework to qualitatively understand the dynamics of conserved operators under random unitary time evolution.

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Olumakinde Ogunnaike, Johannes Feldmeier, Jong Yeon Lee. 2023-04-25. Unifying Emergent Hydrodynamics and Lindbladian Low Energy Spectra across Symmetries, Constraints, and Long-Range Interactions. https://doi.org/10.1103/physrevlett.131.220403

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