Kicked rotor is a paradigmatic model for classical and quantum chaos in time-dependent
Hamiltonian systems. More than fifty years since the introduction of this model, there is an …

We review the development of random-matrix theory (RMT) during the last fifteen years. We
emphasize both the theoretical aspects, and the application of the theory to a number of …

Inspired by the Kolmogorov-Arnold representation theorem, we propose Kolmogorov-Arnold
Networks (KANs) as promising alternatives to Multi-Layer Perceptrons (MLPs). While MLPs …

The discovery of topological phases in non-Hermitian open classical and quantum systems
challenges our current understanding of topological order. Non-Hermitian systems exhibit …

By analyzing the Lyapunov exponent (LE), we develop a rigorous, fundamental scheme for
the study of general non-Hermitian quasicrystals with both a complex phase factor and …

A bstract Quantum complexity, suitably defined, has been suggested as an important probe
of late-time dynamics of black holes, particularly in the context of AdS/CFT. A notion of …

We demonstrate the existence of generalized Aubry-André self-duality in a class of non-
Hermitian quasiperiodic lattices with complex potentials. From the self-duality relations, the …

The distinction between level clustering and level repulsion is one of the quantum
analogues of the classical distinction between globally regular and predominantly chaotic …

CHAPTER I THE DETERMINISTIC SCHRODINGER OPERATOR 187 1. The difference
equation. Hyperbolic structures 187 2. Self adjointness of H. Spectral properties. 190 3 …

The venerable phenomena of Anderson localization, along with the much more recent many-
body localization, both depend crucially on the presence of disorder. The latter enters either …