Hidden Signals Reveal New States Within Materials Lacking Traditional Bounds

Ao Yang and colleagues at Chinese Academy of Sciences in collaboration with University of Chinese Academy of Sciences and Chinese Academy of Sciences demonstrate how signals decay when electrons scatter off imperfections in materials that do not follow standard quantum rules. The late-time behaviour of these scattering events is governed by ‘dynamical poles’, complex frequencies revealed through analysing the material’s response over time. The findings establish a key link between the real-time dynamics of electrons and the underlying structure of non-Hermitian systems, showing that static properties alone are insufficient to describe scattering behaviour and that new, transient states can emerge. Dynamical poles dictate late-time exponential decay in non-Hermitian systems Late-time exponential signals in non-Hermitian systems have, for the first time, been observed appearing without a corresponding static bound state, overturning a previously held assumption that each discrete exponential corresponded to a trapped particle. Previously, identification of late-time behaviour relied solely on static eigenvalue problems, a method focused on determining the stationary states of the system. Now, the real-time analytic structure of the Green’s function, specifically ‘dynamical poles’, dictates signal decay in these systems. Hermitian systems, which adhere to the conventional rules of quantum mechanics where energy is conserved, exhibit a direct correspondence between these late-time exponentials and the existence of bound states, localised states where a particle is confined. However, non-Hermitian systems, characterised by a lack of energy conservation due to the inclusion of gain or loss terms, break this established link. This discovery establishes that static properties are insufficient to describe impurity scattering and opens new avenues for understanding complex material behaviour where energy is not conserved. ‘Dynamical poles’ within the Green’s function, complex frequencies dictating signal decay, are distinct from traditional static bound states. These poles emerge from the analytic continuation of the Green’s function, revealing a more complex relationship between static properties and dynamic behaviour. Static bound states can be ‘dynamically dark’, present in the eigenvalue spectrum but undetectable in time-domain signals, highlighting a fundamental mismatch between spectroscopic and time-resolved measurements. A clear late-time exponential signal appeared using a one-dimensional Hatano-Nelson chain model with a single impurity, despite the absence of a static impurity pole within a specific frequency gap. The Hatano-Nelson model is a paradigmatic example of a non-Hermitian system exhibiting a non-reciprocal band structure, meaning that propagation is different in opposite directions, and is often used to model systems with asymmetric hopping or gain/loss potentials.

Mapping Dynamical Poles via Green’s Function Analytic Continuation Analytic continuation of the Green’s function proved central to uncovering these findings; this mathematical tool describes how a wave propagates through a medium, much like a weather map predicts the spread of a storm, but extended to complex frequencies. The Green’s function, in its original form, is defined for real frequencies, representing the system’s response to perturbations at specific energies. However, analytic continuation allows us to extend this function into the complex frequency plane, revealing information about the system’s behaviour at frequencies that are not directly accessible through standard measurements. This is achieved by finding an analytic function that matches the Green’s function on a small region of the real frequency axis and then extending it to a larger region of the complex plane. The technique was employed to map the system’s response beyond what is immediately observable on the real energy scale, effectively looking ‘around corners’ at hidden frequencies. Identifying ‘dynamical poles’ via analytical continuation of the Green’s function allowed researchers to pinpoint complex frequencies that dictate the late-time signal, even if those frequencies don’t correspond to stable, long-lived states within the material. These dynamical poles manifest as singularities in the complex frequency plane, representing the frequencies at which the system’s response diverges. By locating these poles, researchers can determine the characteristic timescales of the late-time decay. This approach enabled the team to disentangle the complex interaction between energy loss and signal decay, revealing a richer dynamic than previously understood. They focused on a single impurity within a non-Hermitian lattice to understand how signals propagate over time, a contrast to previous work examining static bound states. The mathematical technique extends wave propagation analysis to complex frequencies, identifying complex frequencies which dictate late-time signals because static eigenvalues alone fail to fully describe the observed dynamics in these systems. The use of a single impurity simplifies the analysis, allowing for a clear identification of the dynamical poles associated with the scattering event. Dynamical poles dominate electron scattering decay in non-Hermitian materials Understanding how electrons scatter within materials is important for designing better electronic devices and exploring novel quantum phenomena.

This research clarifies the behaviour of electrons in non-Hermitian systems, materials where energy isn’t necessarily conserved, a departure from standard physics. Non-Hermitian systems are increasingly relevant in areas such as metamaterials, topological photonics, and open quantum systems, where gain and loss mechanisms play a crucial role. Pinpointing the factors that dominate the late-time signal, the decay of the scattering, remains a challenge. The incoherent background arises from the complex interplay of multiple scattering events and energy dissipation processes, making it difficult to isolate the contribution of the dynamical poles. This is because mechanisms play a crucial role. Pinpointing the factors that dominate the late-time signal, the decay of the scattering, remains a challenge, particularly disentangling the influence of these ‘dynamical poles’ from a broader, less-defined ‘incoherent background’. By pinpointing the role of these complex frequencies, scientists can better predict electron behaviour and refine designs for future electronics. Electrons scatter within non-Hermitian systems, materials defying standard energy conservation rules, and identifying ‘dynamical poles’, complex frequencies governing electron behaviour, allows for more accurate predictions of material properties. Separating these poles from background noise remains a persistent challenge in this field. Analysing the complex frequency structure of a material’s response, via the analytic continuation of the Green’s function, is key to understanding how signals decay following impurity scattering. Unlike traditional models relying on static, trapped states, this research demonstrates that ‘dynamical poles’ govern late-time signal behaviour, and these poles can exist independently of stable states or a stable state may remain undetectable in time-domain measurements, fundamentally altering established scattering theory. The implications extend to the development of novel devices where non-Hermitian physics can be harnessed to achieve unique functionalities, such as unidirectional transmission or enhanced sensing capabilities. Scientists discovered that in non-Hermitian systems, the decay of scattered electrons is governed by complex frequencies called ‘dynamical poles’, rather than simply by static, trapped states. This finding challenges previous understandings of impurity scattering, where late-time signals were directly linked to bound states. The research demonstrates that these dynamical poles can appear without a corresponding stable state, or a stable state may be undetectable, and are distinguished from a complex incoherent background. By analysing the complex frequency structure of materials, researchers can more accurately predict electron behaviour in systems where energy is not conserved. 👉 More information 🗞 Dynamical Poles in Non-Hermitian Impurity Scattering 🧠 ArXiv: https://arxiv.org/abs/2604.12939 Tags: