We investigate spacing statistics for ensembles of various real random matrices where the matrixelements have various Probability Distribution Function (PDF: f(x)) including Gaussian. For two modifications of 2 × 2 matrices with various PDFs, we derived that spacing distribution p(s) of adjacent energy eigenvalues are distinct. Nevertheless, they show the linear level repulsion near s = 0 as αs...

Abstract The present paper deals with the eigenvalues of complex nonlocal Sturm-Liouville boundary value problems. bounds real and imaginary parts for differential equation involving potential terms associated conditions are obtained in integrable coefficients part eigenvalues.

The effect of non-Hermiticity in band topology has sparked many discussions on non-Hermitian topological physics. It long been known that Hamiltonians can exhibit real energy spectra under the condition parity-time ($PT$) symmetry---commonly implemented with balanced loss and gain---but only when is relatively weak. Sufficiently strong non-Hermiticity, other hand, will destroy reality spectra, ...