From a microscopic inertial active matter model to the Schrödinger equation

Michael Vrugt, Tobias Frohoff-Hülsmann, Eyal Heifetz, Uwe Thiele () and Raphael Wittkowski ()
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Michael Vrugt: Westfälische Wilhelms-Universität Münster
Tobias Frohoff-Hülsmann: Westfälische Wilhelms-Universität Münster
Eyal Heifetz: Tel Aviv University
Uwe Thiele: Westfälische Wilhelms-Universität Münster
Raphael Wittkowski: Westfälische Wilhelms-Universität Münster

Nature Communications, 2023, vol. 14, issue 1, 1-18

Abstract: Abstract Active field theories, such as the paradigmatic model known as ‘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 an analog of the Schrödinger equation in Madelung form as a limiting case, allowing one to find analoga of the quantum-mechanical tunnel effect and of fuzzy dark matter in active fluids. We investigate the active tunnel effect analytically and via numerical continuation.

Date: 2023
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DOI: 10.1038/s41467-022-35635-1

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