Related Experiment Video
Updated: Jul 8, 2025

An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
Unifying Emergent Hydrodynamics and Lindbladian Low-Energy Spectra across Symmetries, Constraints, and Long-Range
Olumakinde Ogunnaike1, Johannes Feldmeier2, Jong Yeon Lee3,4
1Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Abstract:
We identify emergent hydrodynamics governing charge transport in Brownian random time evolution 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 diffusive relaxation despite the presence of dipole conservation, which we verify numerically. Therefore, we provide a general and versatile framework to qualitatively understand the dynamics of conserved operators under random unitary time evolution.
Related Concept Videos
Symmetry in Maxwell's Equations
The Wave Nature of Light
Emission Spectra
Dimensionless Groups in Fluid Mechanics
First Law: Particles in One-dimensional Equilibrium
The Quantum-Mechanical Model of an Atom

