Related papers: Quantum cylindrical integrability in magnetic fiel…
Extension of Feynman's path integral to quantum mechanics of noncommuting spatial coordinates is considered. The corresponding formalism for noncommutative classical dynamics related to quadratic Lagrangians (Hamiltonians) is formulated.…
In this paper, we propose integrable discretizations of a two-dimensional Hamiltonian system with quartic potentials. Using either the method of separation of variables or the method based on bilinear forms, we construct the corresponding…
Integrability of a square billiard is spontaneously broken as it rotates about one of its corners. The system becomes quasi-integrable where the invariant tori are broken with respect to a certain parameter, $\lambda = 2E/\omega^{2}$ where…
The semiclassical interaction of the gravitational with a quantum scalar field is considered, in view of the renormalizability of the associated energy-momentum tensor in a n-dimensional curved spacetime resulting from a quadratic…
We consider the quantum mechanics of a particle on a noncommutative plane. The case of a charged particle in a magnetic field (the Landau problem) with a harmonic oscillator potential is solved. There is a critical point, where the density…
In hybrid classical-quantum theories, the dynamics of the classical system induce the classicality of the quantum system, meaning that such models do not necessarily require a measurement postulate to describe probabilistic measurement…
The relationship (resemblance and/or contrast) between quantum and classical integrability in Ruijsenaars-Schneider systems, which are one parameter deformation of Calogero-Moser systems, is addressed. Many remarkable properties of…
Constructing a classical mechanical system associated with a given quantum mechanical one, entails construction of a classical phase space and a corresponding Hamiltonian function from the available quantum structures and a notion of…
In order to evaluate the Feynman path integral in noncommutative quantum mechanics, we consider properties of a Lagrangian related to a quadratic Hamiltonian with noncommutative spatial coordinates. A quantum-mechanical system with…
We consider the quantum mechanics of an electron confined to move on an infinite cylinder in the presence of a uniform radial magnetic field. This problem is in certain ways very similar to the corresponding problem on the infinite plane.…
Machine learning techniques have achieved impressive results in recent years and the possibility of harnessing the power of quantum physics opens new promising avenues to speed up classical learning methods. Rather than viewing classical…
Quantum bits can be isolated to perform useful information-theoretic tasks, even though physical systems are fundamentally described by very high-dimensional operator algebras. This is because qubits can be consistently embedded into…
We construct the quantum oscillator interacting with a constant magnetic field on complex projective spaces $\DC P^N$, as well as on their non-compact counterparts, i. e. the $N-$dimensional Lobachewski spaces ${\cal L}_N$. We find the…
The superintegrability of a rational harmonic oscillator (non-central harmonic oscillator with rational ratio of frequencies) with non-linear "centrifugal" terms is studied. In the first part, the system is directly studied in the Euclidean…
It is possible to construct a classical, macroscopic system which has a mathematical structure that is exactly the same as that of a quantum mechanical system and which can be put into a state which is identical to quantum mechanical…
The relation between quantum systems associated to root systems and radial parts of Laplace operators on symmetric spaces is established. From this it follows the complete integrability of some quantum systems.
In recent work, we initiated a research program aimed at the systematic investigation of quantum superintegrable systems describing the interaction of two non-relativistic spin-$1/2$ particles in three-dimensional Euclidean space. In that…
We review canonical experiments on systems that have pushed the boundary between the quantum and classical worlds towards much larger scales, and discuss their unique features that enable quantum coherence to survive. Because the types of…
An elementary application of Algorithmic Complexity Theory to the polygonal approximations of curved billiards-integrable and chaotic-unveils the equivalence of this problem to the procedure of quantization of classical systems: the scaling…
A known general class of superintegrable systems on 2D spaces of constant curvature can be defined by potentials separating in (geodesic) polar coordinates. The radial parts of these potentials correspond either to an isotropic harmonic…