相关论文: On a Generalized Oscillator System: Interbasis Exp…

In the present paper it is analyzed a very simple example of pseudoextensive system, the tridimensional system of Linear Coupled Oscillators (OLA Model). The same one constitutes a classical tridimensional system of identical interacting…

The classical nonlinear oscillator, proposed by Mathews and Lakshmanan in 1974 and including a position-dependent mass in the kinetic energy term, is generalized in two different ways by adding an extra term to the potential. The solutions…

In this paper, a generalization of a quadratic manifold approach for the reduction of geometrically nonlinear structural dynamics problems is presented. This generalization is constructed by a linearization of the static force with respect…

The non-linear evolution of one-dimensional perturbations in a three-dimensional expanding Universe is considered. A general Lagrangian scheme is derived, and compared to two previously introduced approximate models. These models are…

Calogero-Moser systems can be generalized for any root system (including the non-crystallographic cases). The algebraic linearization of the generalized Calogero-Moser systems and of their quadratic (resp. quartic) perturbations are…

We study the entanglement dynamics of a system consisting of a large number of coupled harmonic oscillators in various configurations and for different types of nearest neighbour interactions. For a one-dimensional chain we provide compact…

Kuramoto's differential equation describes a synchronization process between several harmonic oscillators. It has been used to model biological phenomena such as the synchronization of heart cells, the circadian rhythm, or brain waves. It…

We carry out a model-theoretic analysis of the Heisenberg algebra. To this end, a geometric structure is associated to the Heisenberg algebra and is shown to be a Zariski geometry. Furthermore, this Zariski geometry is shown to be…

The paper introduces a simple quantum model to calculate in a general way allowed frequencies and energy levels of the anharmonic oscillator. The theoretical basis of the approach has been introduced in two early papers aimed to infer the…

We are dealing in this work with such formal and conceptual extensions of nonrelativistic quantum mechanics (QM) which contain QM with its standard formalism and interpretation as a subtheory. QM is here primarily equivalently reformulated…

A nonlinear model of the quantum harmonic oscillator on two-dimensional spaces of constant curvature is exactly solved. This model depends of a parameter $\la$ that is related with the curvature of the space. Firstly the relation with other…

We consider the Bose-Einstein condensate in a parabolic trap as a macroscopic quantum oscillator and describe, analytically and numerically, its collective modes - a nonlinear generalisation of the (symmetric and antisymmetric)…

We present a comprehensive study of the rational extension of the quantum anisotropic harmonic oscillator (QAHO) potentials with linear and/or quadratic perturbations. For the one-dimensional harmonic oscillator plus imaginary linear…

The nonclassical behaviors of a two-level system coupled to a harmonic oscillator is investigated in the ultrastrong coupling regime. We revisit the variational solution of the ground state and find that the existing solution do not account…

Courses on undergraduate quantum mechanics usually focus on solutions of the Schr\"odinger equation for several simple one-dimensional examples. When the notion of a Hilbert space is introduced only academic examples are used, such as the…

Some particular examples of classical and quantum systems on the lattice are solved with the help of orthogonal polynomials and its connection to continuous models are explored.

We discuss a formalism where a universe is identified with the support of a wave function propagating through space-time. As opposed to classical cosmology, the resulting universe is not a spacelike section of some space-time, but a…

In this paper we present a theoretical analysis of the global dynamics in a triaxial galactic system using a 3D integrable Hamiltonian as a simple representation. We include a thorough discussion on the effect of adding a generic…

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…

Triple systems with low hierarchical structure are common throughout the Universe, including examples such as high-altitude lunar satellites influenced by the Earth, planetary satellites perturbed by the Sun, and stellar binaries affected…