Effective Gauge Fields and Topological Band Structures in Pilot-Wave Hydrodynamics

• URL: http://arxiv.org/abs/2512.21477v1
• Date: Thu, 25 Dec 2025 02:41:36 GMT
• Title: Effective Gauge Fields and Topological Band Structures in Pilot-Wave Hydrodynamics
• Authors: Ethan Andersson, Valeri Frumkin,
• Abstract summary: We show that pilot-wave hydrodynamics provides a macroscopic platform for realizing band-structure physics.<n>A submerged square lattice produces frequency-dependent transmission governed by Bloch bands.<n>A honeycomb lattice confines the droplet to a domain wall, revealing a hydrodynamic analog of a valley-Hall edge state.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We demonstrate that pilot-wave hydrodynamics provides a macroscopic platform for realizing band-structure physics, topological edge states, and gauge-field-induced phase shifts. We show that a submerged square lattice produces frequency-dependent transmission governed by Bloch bands. An inversion-asymmetric honeycomb lattice confines the droplet to a domain wall, revealing a hydrodynamic analog of a valley-Hall edge state. And a chiral annular structure generates an effective gauge field that produces an Aharonov-Bohm-like phase difference between clockwise and counter-clockwise orbits. Unlike conventional wave analogs, pilot-wave hydrodynamics couples a localized particle to its self-generated wave field, providing direct access to topological wave-particle behavior normally associated with quantum systems.

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