TY - JOUR
T1 - From a microscopic inertial active matter model to the Schrödinger equation
AU - te Vrugt, Michael
AU - Frohoff-Hülsmann, Tobias
AU - Heifetz, Eyal
AU - Thiele, Uwe
AU - Wittkowski, Raphael
N1 - Publisher Copyright:
© 2023, The Author(s).
PY - 2023/12
Y1 - 2023/12
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85148722591&partnerID=8YFLogxK
U2 - 10.1038/s41467-022-35635-1
DO - 10.1038/s41467-022-35635-1
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C2 - 36894573
AN - SCOPUS:85148722591
SN - 2041-1723
VL - 14
JO - Nature Communications
JF - Nature Communications
IS - 1
M1 - 1302
ER -