4 papers
A pseudo-unitary ensemble of random matrices, PT-symmetry and the Riemann Hypothesis
Zafar Ahmed, Sudhir R. Jain
An ensemble of 2 x 2 pseudo-Hermitian random matrices is constructed that possesses real eigenvalues with level-spacing distribution exactly as for the Gaussian Unitary Ensemble fo…
Quantum Expression of Classical Chaos
Sudhir R. Jain, Benoit Gremaud, Avinash Khare
Even as we understand for long that the world is quantal and buried in it is classical dynamics which is chaotic, finding eigenfunctions analytically from the the Schroedinger equa…
Spacing distributions for rhombus billiards
B. Gremaud, S. R. Jain
We show that the spacing distributions of rational rhombus billiards fall in a family of universality classes distinctly different from the Wigner-Dyson family of random matrix the…
Brownian motion model of random matrices revisited
Sudhir R. Jain, Zafar Ahmed
We present a modified Brownian motion model for random matrices where the eigenvalues (or levels) of a random matrix evolve in "time" in such a way that they never cross each other…