Imaginary Gauge Field and Non-Hermitian Topological Transition Emerging Through Attenuation-Gauge Duality in Conservative Systems

TL;DR

This paper introduces a passive, conservative system approach to non-Hermitian topology via an attenuation-gauge duality, enabling topological transitions and skin effects without active gain or loss.

Contribution

It presents a novel attenuation-gauge duality framework that induces non-Hermitian topological phenomena in passive systems through structured reservoirs.

Findings

Demonstrates boundary skin modes in mechanical metamaterials

Reverses skin effect direction by tuning passive coupling

Identifies a topological phase transition via spectral winding number

Abstract

Non-Hermitian physics traditionally relies on active gain--loss modulation or non-reciprocal couplings, which often introduce significant complexity, compromise stability, and offer very limited scalability in conservative systems. Here we propose an attenuation-gauge duality paradigm in which non-Hermitian topology emerges within fully passive, conservative systems through coupling to a structured reservoir. We derive that a spatially varying reservoir can establish an attenuation-gauge duality, where the spatial variation manifests as an emergent imaginary gauge field in the effective dynamics. It drives the boundary accumulation of skin modes while preserving energy conservation, analogous to Feshbach projection in quantum open systems. We validate this universal wave paradigm via macroscopic mechanical metamaterials, demonstrating that the direction of the skin effect can be reversed by tuning a single passive coupling parameter$t_\perp$, driven by a topological phase transition characterized by the spectral winding number. This framework also allows for a nonlinear extension, where amplitude-dependent coupling can induce intrinsic topological transitions.