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We analyze the quantum dynamics of the non-relativistic two-dimensional isotropic harmonic oscillator in Heisenberg's picture. Such a system is taken as toy model to analyze some of the various quantum theories that can be built from the…
We characterize quantum limits and semi-classical measures corresponding to sequences of eigenfunctions for systems of coupled quantum harmonic oscillators with arbitrary frequencies. The structure of the set of semi-classical measures…
We study bound states generated by a unique potential minimum in the situation where the system is strongly confined to a bounded region containing the minimum (by imposing Dirichlet boundary conditions). In this case the eigenvalues of the…
Interacting quantum systems evolving from an uncorrelated composite initial state generically develop quantum correlations -- entanglement. As a consequence, a local description of interacting quantum system is impossible as a rule. A…
The spectrum of a quantum system has in general bound, scattering and resonant parts. The Hilbert space includes only the bound and scattering spectra, and discards the resonances. One must therefore enlarge the Hilbert space to a rigged…
We present a symplectic integrator, based on the canonical midpoint rule, for classical spin systems in which each spin is a unit vector in $\mathbb{R}^3$. Unlike splitting methods, it is defined for all Hamiltonians, and is…
We introduce a semiclassical quantization method which is based on a stroboscopic description of the classical and the quantum flows. We show that this approach emerges naturally when one is interested in extracting the energy spectrum…
Systems under holonomic constraints are classified within the generalized Hamiltonian framework as second-class constraints systems. We show that each system of point particles with holonomic constraints has a hidden gauge symmetry which…
We describe quantum and classical Hamiltonian dynamics in a common Hilbert space framework, that allows the treatment of mixed quantum-classical systems. The analysis of some examples illustrates the possibility of entanglement between…
The response of a test particle, both for the free case and under the harmonic oscillator potential, to circularly polarized gravitational waves is investigated in a noncommutative quantum mechanical setting. The system is quantized…
In this work we study the unitary time-evolutions of quantum systems defined on infinite-dimensional separable time-dependent Hilbert spaces. Two possible cases are considered: a quantum system defined on a stochastic interval and another…
In a recent paper a slightly modified version of the Bateman system, originally proposed to describe a damped harmonic oscillator, was proposed. This system is really different from the Bateman's one, in the sense that this latter cannot be…
We consider the usage of dynamical decoupling in quantum metrology, where the joint evolution of system plus environment is described by a Hamiltonian. We demonstrate that by ultra-fast unitary control operations acting locally only on…
Is the dynamical evolution of physical systems objectively a manifestation of information processing by the universe? We find that an affirmative answer has important consequences for the measurement problem. In particular, we calculate the…
Noncommutative oscillators are first-quantized through an abelian Drinfel'd twist deformation of a Hopf algebra and its action on a module. Several important and subtle issues making possible the quantization are solved. The spectrum of the…
Two Dunkl oscillator models are considered: one singular and the other with a 2:1 frequency ratio. These models are defined by Hamiltonians which include the reflection operators in the two variables x and y. The singular or caged Dunkl…
The uniqueness of purifications of quantum states on a system $A$ up to local unitary transformations on a purifying system $B$ is central to quantum information theory. We show that, if the two systems are modelled by commuting von Neumann…
We present a general description of separable states in Quantum Mechanics. In particular, our result gives an easy proof that inseparabitity (or entanglement) is a pure quantum (noncommutative) notion. This implies that distinction between…
Let $\Omega$ be a non-singular syplectic form on some vector space $V$. Denote by $S^{n}_{k}(\Omega)$ the set of all $k$-dimensional planes $s$ in $V$ such that the restriction of $\Omega$ onto $s$ is singular. For the cases when $k=2,n-2$…
The two dimensional set of canonical relations giving rise to minimal uncertainties previously constructed from a q-deformed oscillator algebra is further investigated. We provide a representation for this algebra in terms of a flat…