Related papers: Relativistic pseudo-Gaussian oscillators
A new family of one-dimensional quantum models is proposed in terms of new potentials with a Gaussian asymptotic behavior but approaching to the potential of the harmonic o scillator when $x\to 0$. It is shown that, in the energy basis of…
Geometric models of quantum relativistic rotating oscillators in arbitrary dimensions are defined on backgrounds with deformed anti-de Sitter metrics. It is shown that these models are analytically solvable, deriving the formulas of the…
We introduce a class of interatomic potential models that can be automatically generated from data consisting of the energies and forces experienced by atoms, derived from quantum mechanical calculations. The resulting model does not have a…
The density of states for a particle moving in a random potential with a Gaussian correlator is calculated exactly using the functional integral technique. It is achieved by expressing the functional degrees of freedom in terms of the…
It is shown that in general relativity some static metrics are able to simulate oscillatory motions. Their form depends on two arbitrary real parameters which determine the specific oscillation modes. The conclusion is that these metrics…
A family of relativistic geometric models is defined as a generalization of the actual anti-de Sitter (1+1) model of the relativistic harmonic oscillator. It is shown that all these models lead to the usual harmonic oscillator in the…
The quantum modes of a new family of relativistic oscillators are studied by using the supersymmetry and shape invariance in a version suitable for (1+1) dimensional relativistic systems. In this way one obtains the Rodrigues formulas of…
A family of geometric models of quantum relativistic rotating oscillator is defined by using a set of one-parameter deformations of the static (3+1) de Sitter or anti-de Sitter metrics. It is shown that all these models lead to the usual…
The mathematical description of the quantum harmonic oscillator is essentially based on the Gaussian function. In the case of a quantum oscillator with finite-dimensional Hilbert space, the position space consists in a finite number of…
A finite quantum system evolving unitarily equilibrates in a probabilistic fashion. In the general many-body setting the time-fluctuations of an observable \mathcal{A} are typically exponentially small in the system size. We consider here…
We address quantum systems isospectral to the harmonic oscillator, as those found within the framework of supersymmetric quantum mechanics, as potential resources for continuous variable quantum information. These deformed oscillator…
A finite-dimensional pseudo-unitary framework is set up for describing the dynamics of free elementary particles in a purely relativistic quantum mechanical way. States of any individual particles or antiparticles are defined as suitably…
The solvable quantum mechanical model for the relativistic two-body system composed of spin-1/2 and spin-0 particles is constructed. The model includes the oscillator-type interaction through a combination of Lorentz-vector and -tensor…
Inhomogeneous multidimensional cosmological models with a higher dimensional space-time manifold are investigated under dimensional reduction. In the Einstein conformal frame, small excitations of the scale factors of the internal spaces…
We present a formulation of measurement-based feedback control of a single quantum particle in one spatial dimension. An arbitrary linear combination of the position and momentum of the particle is continuously monitored, and feedback…
The relativistic quantum dynamics of an electrically charged particle subject to the Klein-Gordon oscillator and the Coulomb potential is investigated. By searching for relativistic bound states, a particular quantum effect can be observed:…
In Verlinde's theory of entropic gravity, the internal degrees of freedom are marked by "bits", but the microscopic origin of "bits" is unknown hitherto. To this direction, we adopt the quantum harmonic oscillators to naively model the…
Most approaches towards a quantum theory of gravitation indicate the existence of a minimal length scale of the order of the Planck length. Quantum mechanical models incorporating such an intrinsic length scale call for a deformation of…
We consider theories which explain the flatness of the power spectrum of scalar perturbations in the Universe by conformal invariance, such as conformal rolling model and Galilean Genesis. We show that to the leading {\it non-linear} order,…
The pseudoharmonic oscillator potential is studied in non relativistic quantum mechanics with a generalized uncertainty principle characterized by the existence of a minimal length scale. By using a perturbative approach, we analytically…