From a microscopic inertial active matter model to the Schrödinger equation

Abstract

Field theories for the one-body density of an active fluid, such as the paradigmatic active model B+, are simple yet very powerful tools for describing phenomena such as motility-induced phase separation. No comparable theory has been derived yet for the underdamped case. In this work, we introduce active model I+, an extension of active model B+ to particles with inertia. The governing equations of active model I+ are systematically derived from the microscopic Langevin equations. We show that, for underdamped active particles, thermodynamic and mechanical definitions of the velocity field no longer coincide and that the density-dependent swimming speed plays the role of an effective viscosity. Moreover, active model I+ contains the Schrödinger equation in Madelung form as a limiting case, allowing to find analoga of the quantum-mechanical tunnel effect and of fuzzy dark matter in the active fluid. We investigate the active tunnel effect analytically and via numerical continuation.

arXiv comment16 pages, 1 figure

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• When does an active bath behave as an equilibrium one?
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• Statistics of carrier-cargo complexes
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• Inertia-chirality interplay in active Brownian motion: exact dynamics and phase maps
• Schrödinger-Navier-Stokes equation for capillary fluids
• Thermodynamics of an Empty Box