Non-Hermitian random matrices and the calogero-sutherland model

Area of Science:

• Statistical mechanics
• Quantum physics
• Complex systems analysis

Background:

• Non-Hermitian operators are crucial for modeling open quantum systems and dissipative dynamics.
• Understanding eigenvalue statistics provides insights into system behavior and stability.

Purpose of the Study:

• To analyze the statistical properties of eigenvalues for non-Hermitian operators in dissipative complex systems.
• To uncover hierarchical relations within eigenvalue correlators.
• To explore the underlying connections and universality in spectral behavior.

Main Methods:

• Utilizing Gaussian ensembles of non-Hermitian operators.
• Deriving hierarchical relations between eigenvalue correlators.
• Modeling eigenvalue dynamics as interacting particles on a complex plane.

Main Results:

• A hierarchical relation between correlators of eigenvalues was established.
• Eigenvalues exhibit behavior analogous to particles under two-body and three-body interactions.
• Evidence for a deep connection and universality in spectral properties across different complex systems was found.

Conclusions:

• The study reveals a fundamental structure in the spectral statistics of dissipative complex systems.
• The particle analogy offers a new perspective for understanding complex system dynamics.
• Universality in spectral behavior suggests broader applicability of these findings.