Shashi C. L. Srivastava

Random cyclic matrices

We present a Gaussian ensemble of random cyclic matrices on the real field and study their spectral fluctuations. These cyclic matrices are shown to be pseudosymmetric with respect to generalized parity. We calculate the joint probability distribution function of eigenvalues and the spacing distributions analytically and numerically. For small spacings, the level spacing distribution exhibits either a Gaussian or a linear form. Furthermore, for the general case of two arbitrary complex eigenvalues, leaving out the spacings among real eigenvalues, and, among complex conjugate pairs, we find that the spacing distribution agrees completely with the Wigner distribution for a Poisson process on a plane. The cyclic matrices occur in a wide variety of physical situations, including disordered linear atomic chains and the Ising model in two dimensions. These exact results are also relevant to two-dimensional statistical mechanics and nu -parametrized quantum chromodynamics.

Pseudo-Hermitian random matrix theory

Complex extension of quantum mechanics and the discovery of pseudo-unitarily invariant random matrix theory has set the stage for a number of applications of these concepts in physics. We briefly review the basic ideas and present applications to problems in statist ical mechanics where new results have become possible. We have found it important to mention the precise directions where advances could be made if further results become available. Copyright line will be provided by the publisher

Entanglement dynamics following a sudden quench: An exact solution

We present an exact and fully analytical treatment of the entanglement dynamics for an isolated system of

Record statistics in random vectors and quantum chaos

N

Biased random walks on a disordered one-dimensional lattice

coupled oscillators following a sudden quench of the system parameters. The system is analyzed using the solutions of the time dependent Schrodingers equation, which are obtained by solving the corresponding nonlinear Ermakov equations. The entanglement entropies exhibit a multi-oscillatory behaviour, where the number of dynamically generated time scales increases with

Ordered level spacing probability densities

N

Eigenstate entanglement between quantum chaotic subsystems: Universal transitions and power laws in the entanglement spectrum

. The harmonic chains exhibit entanglement revival and for larger values of

Random Reverse Cyclic matrices and screened harmonic oscillator

N (> 10)

Kolmogorov stochasticity parameter as a measure of quantum chaos

, we find near-critical logarithmic scaling for the entanglement entropy, which is modulated by a time dependent factor. The

Quasiparticle spectra via Kolmogorov stochasticity parameter

N=2