Related papers: Quantisation ideals of nonabelian integrable syste…
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…
A superintegrable system is, roughly speaking, a system that allows more integrals of motion than degrees of freedom. This review is devoted to finite dimensional classical and quantum superintegrable systems with scalar potentials and…
We consider the problem of defining quantum integrability in systems with finite number of energy levels starting from commuting matrices and construct new general classes of such matrix models with a given number of commuting partners. We…
We propose a new dynamical reflection algebra, distinct from the previous dynamical boundary algebra and semi-dynamical reflection algebra. The associated Yang-Baxter equations, coactions, fusions, and commuting traces are derived. Explicit…
We show that the classical mechanics of an algebraic model are implied by its quantizations. An algebraic model is defined, and the corresponding classical and quantum realizations are given in terms of a spectrum generating algebra.…
We study the dynamical symmetries of a class of two-dimensional superintegrable systems on a 2-sphere, obtained by a procedure based on the Marsden-Weinstein reduction, by considering its shape-invariant intertwining operators. These are…
We present an algebraic formulation of the notion of integrability of dynamical systems, based on a nilpotency property of its flow: it can be explicitly described as a polynomial on its evolution parameter. Such a property is established…
It is noted that the Schrodinger equation with any self-adjoint Hamiltonian is unitary equivalent to a set of non-interacting classical harmonic oscillators and in this sense any quantum dynamics is completely integrable. Higher order…
We introduce two numerical conjugacy invariants for dynamical systems -- the complexity and weak complexity indices -- which are well-suited for the study of "completely integrable" Hamiltonian systems. These invariants can be seen as "slow…
We discuss the dynamical quantum systems which turn out to be bi-unitary with respect to the same alternative Hermitian structures in a infinite-dimensional complex Hilbert space. We give a necessary and sufficient condition so that the…
In this paper we study the problem of quantizing theories defined over a nonclassical configuration space. If one follows the path-integral approach, the first problem one is faced with is the one of definition of the integral over such…
Free noncommutative fields constitute a natural and interesting example of constrained theories with higher derivatives. The quantization methods involving constraints in the higher derivative formalism can be nicely applied to these…
We propose quantum-mechanical systems in which the number of spatial dimensions is promoted to a dynamical quantum variable, making the effective dimension state-dependent. Interestingly, systems of this form can exhibit enhanced symmetries…
The objective of this work is to examine the integrability of Hamiltonian systems in $2D$ spaces with variable curvature of certain types. Based on the differential Galois theory, we announce the necessary conditions of the integrability.…
A completely integrable dynamical system in discrete time is studied by means of algebraic geometry. The system is associated with factorization of a linear operator acting in a direct sum of three linear spaces into a product of three…
The incoherent dynamical properties of open quantum systems are generically attributed to an ongoing correlation between the system and its environment. Here, we propose a novel way to assess the nature of these system-environment…
The complete integrability of a class of dynamical systems with the potential v(q)=q^{-2}+c q^2 is proved.
We discuss extension of soliton theories and integrable systems into noncommutative spaces. In the framework of noncommutative integrable hierarchy, we give infinite conserved quantities and exact soliton solutions for many noncommutative…
We discuss the notion about physical quantities as having values represented by real numbers, and its limiting to describe nature to be understood in relation to our appreciation that the quantum theory is a better theory of natural…
By parametrizing the action integral for the standard Schrodinger equation we present a derivation of the recently proposed method for quantizing a parametrized theory. The reformulation suggests a natural extension from conventional to…