Related papers: Quantum Integrable Systems on a Classical Integrab…
Constrained Hamiltonian description of the classical limit is utilized in order to derive consistent dynamical equations for hybrid quantum-classical systems. Starting with a compound quantum system in the Hamiltonian formulation conditions…
Calogero-Moser systems are classical and quantum integrable multi-particle dynamics defined for any root system $\Delta$. The {\em quantum} Calogero systems having $1/q^2$ potential and a confining $q^2$ potential and the Sutherland systems…
The key concept discussed in these lectures is the relation between the Hamiltonians of a quantum integrable system and the Casimir elements in the underlying hidden symmetry algebra. (In typical applications the latter is either the…
Classical integrable Hamiltonian systems generated by elements of the Poisson commuting ring of spectral invariants on rational coadjoint orbits of the loop algebra $\wt{\gr{gl}}^{+*}(2,{\bf R})$ are integrated by separation of variables in…
We construct a class of interacting spin Calogero-Moser type systems. They can be regarded as a many particle system with spin degrees of freedom and as an integrable spin chain of Gaudin type. We prove that these Hamiltonian systems are…
We propose in this work a concept of integrability for quantum systems, which corresponds to the concept of noncommutative integrability for systems in classical mechanics. We determine a condition for quantum operators which can be a…
A summary of a recently proposed description of quantum-classical hybrids is presented, which concerns quantum and classical degrees of freedom of a composite object that interact directly with each other. This is based on notions of…
Given a quantum Hamiltonian, we explain how the dynamical properties of the underlying classical system affect the behaviour of quantum eigenstates in the semi-classical limit. We study this problem via the notion of semiclassical measures.…
The classical limit of non-integrable quantum systems is studied. We define non-integrable quantum systems as those which have, as their classical limit, a non-integrable classical system. In order to obtain this limit, the self-induced…
The dynamics of hybrid systems -- i.e. ones in which classical and quantum degrees of freedom co-exist and interact -- feature both diffusion in the classical sector and decoherence in the quantum state. In this article, we will consider…
This note is a review of the recently revealed intriguing connection between integrable quantum spin chains and integrable many-body systems of classical mechanics. The essence of this connection lies in the fact that the spectral problem…
In this paper we demonstrate that there exists a close relationship between quasi-exactly solvable quantum models and two special classes of classical dynamical systems. One of these systems can be considered a natural generalization of the…
Hamiltonian theory of hybrid quantum-classical systems is used to study dynamics of the classical subsystem coupled to different types of quantum systems. It is shown that the qualitative properties of orbits of the classical subsystem…
In this paper we construct certain quantum spin systems on moduli spaces of $G$-connections on a connected oriented finite graph, with $G$ a simply connected compact Lie group. We construct joint eigenfunctions of the commuting quantum…
Quantum systems with a non-conserved probability can be described by means of non-Hermitian Hamiltonians and non-unitary dynamics. In this paper, the case in which the degrees of freedom can be partitioned in two subsets with light and…
We discuss how a standard scattering theory a of multi-particle theory generalises to systems based on Hamiltonians that involve higher-order derivatives in their quantum mechanical formulation. As concrete examples, we consider Hamiltonian…
We study two-dimensional classically integrable field theory with independent boundary condition on each end, and obtain three possible generating functions for integrals of motion when this model is an ultralocal one. Classically…
Hybrid classical-quantum models are computational schemes that investigate the time evolution of systems, where some degrees of freedom are treated classically, while others are described quantum-mechanically. First, we present the…
The classical invariants of a Hamiltonian system are expected to be derivable from the respective quantum spectrum. In fact, semiclassical expressions relate periodic orbits with eigenfunctions and eigenenergies of classical chaotic…
We describe quantum and classical Hamiltonian dynamics in a common Hilbert space framework, that allows the treatment of mixed quantum-classical systems. The analysis of some examples illustrates the possibility of entanglement between…