Related papers: Quantization of classical integrable systems. Part…

In a previous work we have introduced the concept of quasi-integrable quantum system. In the present one we determine sufficient conditions under which, given an integrable classical system, it is possible to construct a quasi-integrable…

The correspondence between the integrability of classical mechanical systems and their quantum counterparts is not a 1-1, although some close correspondencies exist. If a classical mechanical system is integrable with invariants that are…

We give a sufficient condition for quantising integrable systems.

We briefly review the most relevant aspects of complete integrability for classical systems and identify those aspects which should be present in a definition of quantum integrability. We show that a naive extension of classical concepts to…

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…

We discuss the notion of integrability in quantum mechanics. Starting from a review of some definitions commonly used in the literature, we propose a different set of criteria, leading to a classification of models in terms of different…

Integrability in quantum theory has been defined in more than one ways. Recently, Braak suggested a new definition that a quantum system is integrable if the number of parameters required to specify the eigenstates and the number degrees of…

We study the concepts of compatibility and separability and their implications for quantum and classical systems. These concepts are illustrated on a macroscopic model for the singlet state of a quantum system of two entangled spin 1/2 with…

Integrable quantum mechanical systems with magnetic fields are constructed in two-dimensional Euclidean space. The integral of motion is assumed to be a first or second order Hermitian operator. Contrary to the case of purely scalar…

In this paper, we develop the framework for quantum integrable systems on an integrable classical background. We call them hybrid quantum integrable systems (hybrid integrable systems), and we show that they occur naturally in the…

Based on the previously proposed notions of action operators and of quantum integrability, frequency operators are introduced in a fully quantum-mechanical setting. They are conceptually useful because a new formulation can be given to…

An integrable anharmonic oscillator is presumably simulable by a classical computer and therefore by a quantum computer. An integrable anharmonic oscillator whose Hamiltonian is of normal type and quartic in the canonical coordinates is not…

Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function.…

We give a review of concepts related to connection of classical and quantum theories, from the phase space perspective. Quantum theory is described by non-commutative operators of coordinates and momenta, results in values having a certain…

Quantum integrability of classical integrable systems given by quadratic Killing tensors on curved configuration spaces is investigated. It is proven that, using a "minimal" quantization scheme, quantum integrability is insured for a large…

In this paper we give examples of applications of general methods of quantization by symmetrization of classical integrable systems, which have been illustrated in two previous works by the same authors. We consider two classes of systems…

We propose some formulations of the notion of "operational independence" of two subsystems of a larger quantum system and clarify their relation to other independence concepts in the literature. In addition, we indicate why the operational…

The relationship between classical and quantum three one-mode systems interacting in a non-linear way is described. We investigate the integrability of these systems by using the reduction procedure. The reduced coherent states for the…

The formalism of classical and quantum mechanics on phase space leads to symplectic and Heisenberg group representations, respectively. The Wigner functions give a representation of the quantum system using classical variables. The…

In this work we investigate the issue of integrability in a classical model for noninteracting fermionic fields. This model is constructed via classical-quantum correspondence obtained from the semiclassical treatment of the quantum system.…