Related papers: Classical and Quantum Superintegrability of St\"ac…
We develop a new method for the construction of one-dimensional integrable Lindblad systems, which describe quantum many body models in contact with a Markovian environment. We find several new models with interesting features, such as…
Two or more quantum systems are said to be in an entangled or non-factorisable state if their joint (supposedly pure) wave-function is not expressible as a product of individual wave functions but is instead a superposition of product…
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…
This work aims to bridge the gap between Dunkl superintegrable systems and the coalgebra symmetry approach to superintegrability, and subsequently to recover known models and construct new ones. In particular, an infinite family of…
Two super-integrable and super-separable classical systems which can be considered as deformations of the harmonic oscillator and the Smorodinsky-Winternitz in two dimensions are studied and identified with motions in spaces of constant…
The paper gives a systematic review of the basic ideas of (non-relativistic) quantum mechanics including all changes that result from previous work of the authors. This shows that the new theory is self-consistent and (in certain sense)…
Quantum systems are notoriously difficult to simulate with classical means. Recently, the idea of using another quantum system - which is experimentally more controllable - as a simulator for the original problem has gained significant…
A quantum system at equilibrium is represented by a corresponding classical system, chosen to reproduce thermodynamic and structural properties. The motivation is to allow application of classical strong coupling theories and molecular…
A recent development of the studies on classical and quasi-classical properties of supersymmetric quantum mechanics in Witten's version is reviewed. First, classical mechanics of a supersymmetric system is considered. Solutions of the…
The full spectrum and eigenfunctions of the quantum version of a nonlinear oscillator defined on an N-dimensional space with nonconstant curvature are rigorously found. Since the underlying curved space generates a position-dependent…
Using semiclassical methods, it is possible to construct very accurate approximations in the short wavelength limit of quantum dynamics that rely exclusively on classical dynamical input. For systems whose classical realization is strongly…
We suggest the notion of perfect integrability for quantum spin chains and conjecture that quantum spin chains are perfectly integrable. We show the perfect integrability for Gaudin models associated to simple Lie algebras of all finite…
A simple quantum generalisation of the Liouville-Arnold criterion of classical integrability is proposed: A system is quantum-integrable if it has an abelian Lie group of Wigner symmetries of dimension equal to the number of degrees of…
A family of maximally superintegrable systems containing the Coulomb atom as a special case is constructed in N-dimensional Euclidean space. Two different sets of N commuting second order operators are found, overlapping in the Hamiltonian…
The goal of this thesis is the search for integrable and superintegrable systems with magnetic field. We formulate the quantum mechanical determining equations for second order integrals of motion in the cylindrical coordinates and we find…
Heisenberg-type higher order symmetries are studied for both classical and quantum mechanical systems separable in cartesian coordinates. A few particular cases of this type of superintegrable systems were already considered in the…
Semiclassical methods are essential in analyzing quantum mechanical systems. Although they generally produce approximate results, relatively rare potentials exist for which these methods are exact. Such intriguing potentials serve as…
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…
Beta-ensembles of random matrices are naturally considered as quantum integrable systems, in particular, due to their relation with conformal field theory, and more recently appeared connection with quantized Painlev\'e Hamiltonians. Here…
The purpose of this work is to present a method based on the factorizations used in one dimensional quantum mechanics in order to find the symmetries of quantum and classical superintegrable systems in higher dimensions. We apply this…