Defect-driven incoherent skin localization

Abstract

The process of dephasing during wave evolution has traditionally been viewed as an obstacle to localization, leading to diffusion even in strongly disordered Hermitian lattices. In contrast, here we demonstrate how the interplay of dephasing with non-Hermitian defects can be harnessed to engineer wave localization. Specifically, we identify a novel dynamical localization phenomenon characterized by wavefunction accumulation at the lattice's boundary due solely to dephasing, despite globally reciprocal couplings. Furthermore, we study the incoherent skin effect arising from coupling asymmetry, and investigate the interplay between these antagonistic localization mechanisms. By reframing dephasing from a hindrance into a tool, this study overturns established paradigms of wave localization and paves the way for novel approaches to controlling localization phenomena in non-Hermitian physics.

Figures (4)

• Figure 1: Schematic representation of the waveguide lattice models examined in this work. (a) Lattice with symmetric couplings between neighboring sites, including a few on-site lossy defects. (b) Hatano–Nelson lattice with asymmetric couplings between neighboring sites. In both configurations, blue lines along the propagation direction $z$ indicate the periodic action of dephasing.
• Figure 2: For a lattice of $N = 30$ sites with dephasing period $l = 0.01$. (a)–(b): Single defect $\epsilon_n = 0.5\,i\,\delta_{n,14}$; (c)–(d): Two defects $\epsilon_n = 0.5\,i\,\delta_{n,5} + 0.5\,i\,\delta_{n,21}$. (a)/(c): Amplitudes $|v_{1,n}|$; (b)/(d): Evolution of the averaged probability density $P(z)$, normalized at each $z$, for initial conditions $\psi_{n}(0) = \delta_{n,15}$ and $\psi_{n}(0) = \delta_{n,20}$, respectively. Defect sites are indicated by blue dashed lines in (b)/(d).
• Figure 3: Dynamical skin effects under incoherent dynamics in a lattice of $N=30$ sites with dephasing period $l=0.01$, top row: symmetric couplings, defects with $V=0.5$ applied at sites $q_j=\{3,10,18,26\}$, bottom row: asymmetric couplings with $h=0.2$, no defects; (a)/(c) Amplitude $\lvert v_{1,n}\rvert$/$\lvert g_{1,n}^{R}\rvert$; (b)/(d) Evolution of the averaged probability density $P(z)$, for initial condition $\psi_{n}(0)=\delta_{n,1}$ for (b) and $\psi_{n}(0)=\delta_{n,30}$ for (d), normalized at each $z$. In (b) the lattice sites corresponding to defects are marked with blue dashed lines.
• Figure 4: Interplay between non-Hermitian skin effects in a lattice of $N=30$ sites with defects of strength $V=0.5$ placed at sites $q_j=\{3,10,18,26\}$ under dephasing $l=0.01$; (a) amplitude $\lvert g_{1,n}^{R}\rvert$ for $h=0$ (blue), $h=0.3$ (green) and $h=0.8$ (red); (b) asymptotic mean position $\langle n\rangle_f$; (c) position uncertainty $\Delta n_f$ as functions of $h$ and $V$.