Energy level statistics following the Gaussian Symplectic Ensemble (GSE) of Random Matrix
Theory have been predicted theoretically and observed numerically in numerous quantum …

Understanding the far-from-equilibrium dynamics of dissipative quantum systems, where
dissipation and decoherence coexist with unitary dynamics, is an enormous challenge with …

We bring together the semiclassical approximation, matrix integrals, and the theory of
symmetric polynomials in order to solve a long-standing problem in the field of quantum …

We compute the spectral form factor of two integrable quantum-critical many-body systems
in one spatial dimension. The spectral form factor of the quantum Ising chain is periodic in …

In their seminal 1984 paper Bohigas, Giannoni and Schmit (1984-a)(see also Bohigas,
Giannoni and Schmit 1984-b), stated a conjecture describing the statistical properties of …

We use semiclassical methods to evaluate the spectral two-point correlation function of
quantum chaotic systems with discrete geometrical symmetries. The energy spectra of these …

Open chaotic systems are expected to possess universal transport statistics and recently
there have been many advances in understanding and obtaining expressions for their …

We show that chaotic classical dynamics associated with the volume of discrete grains of
space leads to quantal spectra that are gapped between zero and nonzero volume. This …

We review the construction of the supersymmetric sigma model for unitary maps, using the
color-flavor transformation. We then illustrate applications by three case studies in quantum …

This review is a contribution to a book dedicated to the memory of Michael E. Fisher. The first
example of a quantum many body system not expected to have any quasiparticle excitations …