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

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.

Figures (3)

• Figure 1: Emergence of non-Hermitian dynamics in a passive conservative system via structured reservoir engineering. (a) Theoretical paradigm: Partitioning the total Hermitian system $W$ into a subsystem $S$ and a structured reservoir $R$. A spatial varying interaction $v(x)$ induces a quadratic decay profile $\Gamma(x) \propto |v(x)|^2$, establishing the Attenuation-Gauge duality. (b,c) Numerical validation on a single chain ($N=30$, $\bar{\lambda} \approx 0.3$). The projection-induced decay generates a complex spectrum of subsystem $S$, resulting in the exponential skin mode envelope in (b) and the corresponding spectral winding loop in (c). (d) A coupled double-chain model representing the subsystem $S$, characterized by intra-chain coupling $t$ and inter-chain coupling $t_\perp$. The structured reservoir induces spatial varying outflow $\Gamma_\alpha(x)$ and $\Gamma_\beta(x)$ on the respective chains, where their opposite gradients compete. The imaginary part of $W$ and $S$'s energy spectra are exhibited at the bottom panels. Clearly $W$ is conserved with 0 imaginary part, while $S$ does have non-zero imaginary part. (e) Verification of the topological phase transition. The low-energy spectral trajectory of the determinant crosses at the critical coupling $t_\perp = t_c$ (navy line), confirming the point-gap closing mechanism ($\det H_{\text{ref}}=0$) that separates the $w=1$ (grey dashed) and $w=-1$ (red solid) topological phases. (f) Winding number jumps from 1 to -1 at the critical coupling $t_\perp=t_c$.
• Figure 2: Topological phase transition and skin mode reversal driven by passive coupling. (a)--(c) Evolution of the skin mode localization as the inter-chain coupling $t_\perp$ increases across the critical point $t_c$. The mode switches from the right boundary ($t_\perp < t_c$) to the left boundary ($t_\perp > t_c$), governed by the point-gap closing and the resulting inversion of the spectral winding between the two coupled chains with opposing gradient in grounded springs. (d)--(f) A 2D view of the complex energy spectrum $E(k)$ shows that the spectral winding direction of the lower energy band (indicated in blue) reverses as $t_\perp$ crosses $t_c$, resulting in a change in the winding number from $w=1$ to $w=-1$. (g)--(i) Corresponding vibration amplitude profiles of the mechanical chains, confirming the spatial reversal of the skin modes, where $t=1,\nabla v_\alpha=0.2,\nabla v_\beta=-0.05, t_c\simeq2.1$ and $v_{\alpha}=2, v_{\beta}=1,$ at left end point. (j, k) Collective skin effect in a 2D stacked configuration. Despite the opposing gradients in the top and bottom halves, the bulk modes collectively localize to a single boundary, dictated by the dominant gradient direction.
• Figure 3: Experimental validation of the passive skin mode reversal. (a) Photograph of the mechanical double-chain prototype (top) and detailed structure (bottom). The inter-chain coupling $t_\perp$ is continuously tunable via movable clamps on the connecting springs, while the onsite potential gradients are engineered by the grounded springs. (b) Experimental measurements and (c) numerical simulations of the steady-state vibrational modes at 26.57Hz. As $t_\perp$ is tuned from 21.07N/m ($<t_c$) to 29.86N/m ($>t_c$), the localization of vibrational energy sharply switches from the right to the left boundary. This observation quantitatively confirms the theoretically predicted topological phase transition induced by passive structured coupling.