Related papers: Quantum cylindrical integrability in magnetic fiel…
We study the dynamics of a classical scalar field that rolls down a linear potential as it interacts bi-quadratically with a quantum field. We explicitly solve the dynamical problem by using the classical-quantum correspondence (CQC).…
We present a general semiclassical theory of the orbital magnetic response of noninteracting electrons confined in two-dimensional potentials. We calculate the magnetic susceptibility of singly-connected and the persistent currents of…
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…
A countable set of quantum superintegrable systems for arbitrary spin is solved explicitly using tools of supersymmetric quantum mechanics. It is shown that these systems (introduced by Pronko, J. Phys. A: Math. Theor. 40 (2007) ) include…
Complementarity was originally introduced as a qualitative concept for the discussion of properties of quantum mechanical objects that are classically incompatible. More recently, complementarity has become a \emph{quantitative} relation…
This work is concerned with suitable choices of tetrad fields and coordinate systems for the Hamiltonian formalism of a spinning particle derived in [E. Barausse, E. Racine, and A. Buonanno, Phys. Rev. D 80, 104025 (2009)]. After…
We refine a method for finding a canonical form for symmetry operators of arbitrary order for the Schroedinger eigenvalue equation on any 2D Riemannian manifold, real or complex, that admits a separation of variables in some orthogonal…
The symmetry studies of Maxwell equations gave new insight on the nature of electromagnetic (EM) field. It has in general case quaternion single structure, consisting of four independent field constituents, which differ with each other by…
Motion of a charged particle in uniform magnetic field has been studied in detail, classically as well as quantum mechanically. However, classical dynamics of a charged particle in non-uniform magnetic field is solvable only for some…
While real Hamiltonian mechanics and Hermitian quantum mechanics can both be cast in the framework of complex canonical equations, their complex generalisations have hitherto been remained tangential. In this paper quaternionic and…
Resonant systems emerge as weakly nonlinear approximations to problems with highly resonant linearized perturbations. Examples include nonlinear Schroedinger equations in harmonic potentials and nonlinear dynamics in Anti-de Sitter…
Quantum entanglement describes superposition states in multi-dimensional systems, at least two partite, which cannot be factorized and are thus non-separable. Non-separable states exist also in classical theories involving vector spaces. In…
A new family of 2-component vector-valued coherent states for the quantum particle motion in an infinite square well potential is presented. They allow a consistent quantization of the classical phase space and observables for a particle in…
Standard (Arnold-Liouville) integrable systems are intimately related to complex rotations. One can define a generalization of these, sharing many of their properties, where complex rotations are replaced by quaternionic ones. Actually this…
A class of two-dimensional superintegrable systems on a constant curvature surface is considered as the natural generalization of some well known one-dimensional factorized systems. By using standard methods to find the shape-invariant…
The famous singlet correlations of a composite quantum system consisting of two spatially separated components exhibit notable features of two kinds. The first kind consists of striking certainty relations: perfect correlation and perfect…
We discuss various descriptions of a quantum particle on noncommutative space in a (possibly non-constant) magnetic field. We have tried to present the basic facts in a unified and synthetic manner, and to clarify the relationship between…
We review various aspects of (infinite) quantum group symmetries in 2D massive quantum field theories. We discuss how these symmetries can be used to exactly solve the integrable models. A possible way for generalizing to three dimensions…
While the dynamics for three-dimensional axially symmetric two-electron quantum dots with parabolic confinement potentials is in general non-separable we have found an exact separability with three quantum numbers for specific values of the…
Quantum mechanics increasingly penetrates modern technologies but, due to its non-deterministic nature seemingly contradicting our classical everyday world, our comprehension often stays elusive. Arguing along the correspondence principle,…