Saturday 01 February 2025
The peculiar properties of non-Hermitian systems have long fascinated physicists, and recent studies have revealed new insights into their behavior. A team of researchers has made a significant discovery in this field, shedding light on the dynamics of wave spreading in non-Hermitian disordered systems.
In traditional Hermitian systems, waves tend to spread diffusively over time, but in non-Hermitian systems, this is not always the case. The researchers found that for certain types of disorder, waves can exhibit subdiffusive or even localized behavior, meaning they do not spread as quickly or at all.
The team used a model known as the Aubry-Andr´e model to study this phenomenon. This model is particularly useful because it exhibits both localized and delocalized phases, allowing researchers to explore the transition between these two regimes. By analyzing the Lyapunov exponent (LE) of the system, which measures its sensitivity to initial conditions, the team was able to determine the spreading exponent δ, which characterizes the rate at which waves spread.
The results show that in the localized phase, δ is approximately 1/3, indicating subdiffusive behavior. In contrast, in the delocalized phase, δ is closer to 1/2, corresponding to diffusive behavior. The team also found that the spreading exponent is determined by the properties of the imaginary part of the energy spectra at the band tail.
The researchers used a variety of methods to study this phenomenon, including numerical simulations and analytical calculations. They found that the Van Hove singularity in the imaginary part of the energy spectra, which occurs at the band tail, plays a crucial role in determining the spreading exponent.
In addition to the localized and delocalized phases, the team also explored the behavior of waves near the mobility edge, where the system transitions from localized to delocalized. They found that the fractal dimension (FD) of eigenstates can be used to characterize this transition, with localized states having an FD close to 0 or 1.
The study provides new insights into the complex dynamics of non-Hermitian systems and has implications for our understanding of wave spreading in disordered media. The results could also have practical applications in fields such as optics, acoustics, and quantum computing, where non-Hermitian effects play a crucial role.
Cite this article: “Unveiling the Mysteries of Non-Hermitian Systems: Insights into Wave Spreading Dynamics”, The Science Archive, 2025.
Non-Hermitian Systems, Wave Spreading, Disorder, Localization, Delocalization, Aubry-Andr´E Model, Lyapunov Exponent, Spreading Exponent, Imaginary Part Energy Spectra, Fractal Dimension.
