Level statistics of real eigenvalues in non-Hermitian systems

Understand

Symmetries associated with complex conjugation and Hermitian conjugation, such as time-reversal symmetry and pseudo-Hermiticity, have great impact on eigenvalue spectra of non-Hermitian random matrices.

• Here, we show that time-reversal symmetry and pseudo-Hermiticity lead to universal level statistics of non-Hermitian random matrices on and around the real axis.
• From the extensive numerical calculations of large random matrices, we obtain the five universal level-spacing and level-spacing-ratio distributions of real eigenvalues, each of which is unique to the symmetry class.
• Furthermore, we analyse spacings of real eigenvalues in physical models, such as bosonic many-body systems and free fermionic systems with disorder and dissipation.