From a microscopic inertial active matter model to the Schrödinger equation

Area of Science:

• Statistical Mechanics
• Soft Matter Physics
• Theoretical Physics

Background:

• Active field theories, like active model B+, model motility-induced phase separation.
• Existing theories lack a description for underdamped active particles with inertia.

Purpose of the Study:

• Introduce active model I+, extending active model B+ to include inertia.
• Systematically derive governing equations from microscopic Langevin equations.
• Explore novel phenomena in underdamped active systems.

Main Methods:

• Derivation of active model I+ from Langevin equations.
• Analysis of thermodynamic vs. mechanical velocity fields.
• Investigation of the active tunnel effect using analytical and numerical methods.

Main Results:

• Active model I+ describes underdamped active particles with inertia.
• Thermodynamic and mechanical velocity fields diverge for underdamped active particles.
• Density-dependent swimming speed acts as an effective viscosity.
• Active model I+ exhibits analogs of quantum-mechanical tunnel effect and fuzzy dark matter.

Conclusions:

• Active model I+ provides a theoretical framework for inertial active matter.
• The model uncovers unique behaviors in underdamped active systems, including quantum analogs.
• This work opens new avenues for studying complex phenomena in active fluids.