A review is given on the foundations and applications of non-Hermitian classical and
quantum physics. First, key theorems and central concepts in non-Hermitian linear algebra …

This review focuses on the field of quantum entanglement applied to condensed matter
physics systems with strong correlations, a domain which has rapidly grown over the last …

A new class of boundary conditions is described for quantum systems integrable by means
of the quantum inverse scattering (R-matrix) method. The method proposed allows the …

This review is devoted to the problem of thermalization in a small isolated conglomerate of
interacting constituents. A variety of physically important systems of intensive current interest …

Spectral statistics of disordered systems encode Thouless and Heisenberg timescales,
whose ratio determines whether the system is chaotic or localized. We show that the scaling …

We discuss in this paper algebraic structures that are common to finite integrable lattice
systems and conformal field theories. The concept of quantum group plays a major role in …

Many complex systems of interacting particles that one encounters in nature behave on a
phenomenological level in some random fashion. Therefore the theoretical treatment of …

T-and Y-systems are ubiquitous structures in classical and quantum integrable systems.
They are difference equations having a variety of aspects related to commuting transfer …

7.1 Mathematical preliminaries 228 7.1. l'The center of Uq (s£(2))\228 7.1. 2 Finite-
dimensional irreps 229 7.1. 3 The co-adjoint action 231 7.1. 4 Intertwiners" 234 7.2 A family …

We show that a local non-Hermitian perturbation in a Hermitian lattice system generically
induces scale-free localization for the continuous-spectrum eigenstates. When the …