We consider the time evolution following a quantum quench in spin-1/2 chains. It is well
known that local conservation laws constrain the dynamics and, eventually, the stationary …

This book on integrable systems and symmetries presents new results on applications of
symmetries and integrability techniques to the case of equations defined on the lattice. This …

A higher rank generalization of the (rank one) Racah algebra is obtained as the symmetry
algebra of the Laplace–Dunkl operator associated to the $\mathbb {Z} _2^ n $ root system …

Many and important integrable Hamiltonian systems are 'superintegrable', in the sense that
there is an open subset of their 2 d-dimensional phase space in which all motions are linear …

The analysis of the most general second-order superintegrable system in two dimensions:
the generic 3-parameter model on the 2-sphere is cast in the framework of the Racah …

This article is one of a series that lays the groundwork for a structure and classification
theory of second order superintegrable systems, both classical and quantum, in conformally …

I begin by giving a general discussion of completely integrable Hamiltonian systems in the
setting of contact geometry. We then pass to the particular case of toric contact structures on …

We introduce a family of exactly-solvable two-dimensional Hamiltonians whose wave
functions are given in terms of Laguerre and exceptional Jacobi polynomials. The …

We identify a new superintegrable Hamiltonian in three degrees of freedom, obtained as a
reduction of pure Keplerian motion in six dimensions. The new Hamiltonian is a …

We study the caged anisotropic harmonic oscillator, which is a new example of a
superintegrable or accidentally degenerate Hamiltonian. The potential is that of the …