⚛️ quantum physics

Quasi-Non-Hermitian Edge Bursts Induced by Nonuniform Loss

This paper demonstrates that spatially nonuniform loss in non-Hermitian quantum walks can induce a "quasi-non-Hermitian edge burst," a boundary-localized loss anomaly that persists even without the non-Hermitian skin effect and follows a distinct bulk-edge scaling relation.

Original authors: Ze Yang, Wei Li, Fuxiang Li

Published 2026-07-22

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Ze Yang, Wei Li, Fuxiang Li

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine a world where the usual rules of physics take a slight, fascinating detour. In our everyday life, if you drop a ball, it bounces and eventually stops, but the energy doesn't just vanish; it turns into heat or sound. But in a special branch of physics called "non-Hermitian quantum mechanics," scientists study systems that are open to their environment, constantly losing energy or gaining it, much like a leaky bucket or a radio station that gets louder or quieter depending on the signal. A key player in this field is something called the "Non-Hermitian Skin Effect" (NHSE). Think of this like a crowd of people in a hallway who, for some strange reason, all decide to huddle tightly against one specific wall, leaving the rest of the hallway empty. This happens because of how the "walls" of the system interact with the particles inside. Another famous phenomenon is the "Edge Burst," where the loss of energy (like people leaving the room) suddenly spikes dramatically at the very edge of the system, creating a massive pile-up of activity right at the boundary. Scientists have long believed that this dramatic edge pile-up only happens if the "skin effect" is present, forcing everyone to the wall first.

But what if the edge burst could happen even without the crowd huddling against the wall? That is the big question tackled in this new research. The scientists, working with a model of a quantum walk (which is like a particle taking random steps on a grid), wanted to see if they could create this dramatic edge burst using something else entirely: a gradient of loss. Imagine a hallway where the floor gets progressively stickier or more "leaky" as you move toward one end. The researchers asked: If we make the loss uneven across the system, can we still get a massive burst of activity at the edge, even if the "skin effect" isn't pushing everyone there? They used computer simulations to test this, mixing magnetic fields (which act like invisible winds pushing the particles) with this uneven loss.

The paper reveals a surprising new phenomenon called the "Quasi-Non-Hermitian Edge Burst" (quasi-NHEB). The researchers found that even when the "skin effect" is completely turned off—meaning the particles aren't being forced to huddle against the wall by magnetic forces—a strong burst of loss still appears at the boundary. This happens simply because the loss gets stronger as you get closer to the edge, acting like a funnel that guides the particles toward the exit. It's as if, even without a crowd control officer (the skin effect) shoving people to the door, the fact that the floor is stickier near the exit is enough to cause a traffic jam right at the doorway.

Crucially, the study shows that this "quasi" burst is different from the traditional one. In the old version, the burst was sharp and intense, confined to a tiny spot because of the skin effect. In this new version, the burst is a bit more spread out, covering a few steps near the edge, but it is still very real and significant. The researchers also discovered that the direction of the magnetic field matters a lot. Sometimes, the uneven loss works with the magnetic field to make the burst even stronger; other times, it works against it, actually suppressing the burst and making the particles behave more normally.

One of the most interesting findings is how this new burst behaves when you start the particle in different places. If you use the traditional skin effect, where the particle starts matters a lot; the further you start from the edge, the weaker the burst gets. But with this new "quasi" burst caused by uneven loss, it doesn't matter much where you start the particle in the middle of the system. The burst at the edge remains strong and consistent, driven purely by the "stickiness" of the floor near the exit. The authors suggest that this means we can create these boundary anomalies without needing the complex skin effect, opening up new ways to control how energy or information leaks out of quantum systems. They also noted that while the energy levels of the system looked normal on paper, the actual behavior of the particles was quite different, hinting that looking at the energy map alone isn't enough to predict what will happen in these leaky, uneven systems.

Technical Summary: Quasi-Non-Hermitian Edge Bursts Induced by Nonuniform Loss

Problem Statement
Non-Hermitian quantum walks on lossy lattices with open boundaries are known to exhibit the Non-Hermitian Edge Burst (NHEB), characterized by an anomalous peak in loss probability at the system boundary. Conventional understanding attributes this phenomenon to the interplay between the Non-Hermitian Skin Effect (NHSE)—where eigenstates accumulate at boundaries due to non-reciprocity—and a gapless imaginary energy spectrum. While recent studies have explored spatially nonuniform dissipation, the specific role of nonuniform loss in shaping boundary phenomena, particularly in the absence of the NHSE, remains insufficiently understood. Specifically, it is unclear how spatially varying loss gradients influence the NHSE and whether they can induce boundary-localized loss anomalies independently of the skin effect.

Methodology
The authors investigate a one-dimensional non-Hermitian tight-binding model consisting of two coupled sublattices (A and B). The model incorporates:

Spatially Nonuniform Loss: An imaginary on-site potential $-i\gamma_x$ applied exclusively to the B-sublattice, where the loss rate $\gamma_x$ varies linearly with position ( $\gamma_x = \gamma x$ ).
Magnetic Flux Control: A finite magnetic flux is introduced via the Peierls substitution, modifying hopping amplitudes ( $t_1, t_3$ ) with position-dependent phase factors. This allows for the continuous tuning of the NHSE strength and direction.
Quantum Walk Dynamics: The system is initialized with a quantum walker at a specific site $x_0$ on the A-sublattice. The dynamics are solved numerically under open boundary conditions (OBC).
Quantitative Metrics:
- Mean Inverse Participation Ratio (MIPR): Used as a global indicator of skin localization.
- Loss Probability ( $P_x$ ): Calculated as the integral of the probability density at dissipative sites over infinite time, quantifying where the walker escapes.
- Spectral Analysis: Examination of complex energy spectra under both periodic (PBC) and open boundary conditions to identify spectral winding and gap closing.

Key Contributions and Results

Discovery of the Quasi-NHEB:
The study identifies a new phenomenon termed the Quasi-Non-Hermitian Edge Burst (quasi-NHEB). This occurs in the absence of magnetic flux ( $\phi = 0$ ), where the NHSE is absent (MIPR $\approx 0.018$ ). Despite the lack of skin localization, an anomalous accumulation of loss probability persists at the boundary.
- Mechanism: The quasi-NHEB is driven solely by the loss gradient ( $\gamma$ ). The linearly increasing imaginary potential acts as an effective barrier that suppresses intercell hopping, preferentially directing particles toward regions of lower loss (near the boundary) before they escape.
- Characteristics: Unlike the conventional NHEB, the quasi-NHEB exhibits relatively weak spatial localization and an extended profile, yet the loss probability at the boundary increases with the loss gradient $\gamma$ .
Flux-Dependent Interplay and Hybrid NHEB:
When magnetic flux is introduced, the interplay between nonuniform loss and the NHSE leads to a Hybrid NHEB.
- Asymmetric Suppression: The effect of nonuniform loss is highly sensitive to the direction of the magnetic flux. For $\phi \in (-\pi, 0)$ , the NHSE persists but is weakened by the loss gradient. For $\phi \in (0, \pi)$ , the nonuniform loss completely suppresses the NHSE, even when the spectral structure (under PBC) suggests the presence of skin modes (enclosing OBC spectrum).
- Spectral vs. Localization Decoupling: The authors demonstrate that spatially nonuniform loss can significantly alter eigenstate localization without producing substantial changes in the energy spectrum. This indicates that spectral criteria (such as spectral winding numbers or PBC/OBC spectral enclosure) may not fully predict boundary phenomena in systems with inhomogeneous dissipation.
Bulk-Edge Scaling and Initial-State Dependence:
The paper distinguishes the three identified regimes (Conventional NHEB, Hybrid NHEB, and Quasi-NHEB) through their dependence on the walker's initial position ( $x_0$ ):
- Conventional NHEB: The boundary loss probability $P_{edge}$ decays as a power law as $x_0$ moves away from the boundary.
- Quasi-NHEB: $P_{edge}$ is essentially independent of $x_0$ (insensitive to initial position) and scales positively with the loss gradient $\gamma$ .
- Hybrid NHEB: Exhibits a nontrivial scaling where $P_{edge}$ increases with the distance from the boundary, reflecting the complex interplay between flux-induced skin effects and nonuniform dissipation.

Significance and Claims
The paper claims that spatially nonuniform loss alone is sufficient to generate boundary-localized loss anomalies, providing a mechanism for the NHEB that is distinct from the NHSE. The primary significance of these findings includes:

New Mechanism: Establishing that boundary anomalies can arise from dissipation gradients (quasi-NHEB) even when the topological skin effect is absent.
Control Parameter: Demonstrating that spatially structured dissipation offers an additional degree of control over non-Hermitian boundary effects, extending beyond the conventional framework of asymmetric hopping.
Limitations of Spectral Criteria: Highlighting that in systems with inhomogeneous dissipation, spectral properties alone may not accurately predict the emergence or strength of boundary phenomena, as localization properties can be decoupled from the energy spectrum.
Platform for Exploration: Providing a broader platform for exploring non-Hermitian boundary phenomena, with potential relevance to engineered dissipation in synthetic quantum and photonic systems.

The authors conclude that their results offer a complementary perspective on the origin of boundary-localized phenomena, suggesting that future investigations should account for the specific spatial distribution of dissipation, not just the presence of non-reciprocity.

Technical Summary: Quasi-Non-Hermitian Edge Bursts Induced by Nonuniform Loss

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