Related papers: Coupled harmonic oscillators and their quantum ent…
We discuss the solutions of the Schroedinger equation for piecewise potentials, given by the harmonic oscillator potential for $\vert x\vert >a$ and an arbitrary function for $\vert x\vert <a$, using elementary methods. The study of this…
We analyze the possible quantum correlations between two coupled dimer systems in the presence of independent losses and driven by a fluctuating field. For the case of the interaction being of a Heisenberg exchange type, we first…
The correlated fermionic many-particle system, near infinite scattering length, reveals an underlying Heisenberg symmetry in one dimension, as compared to an $SO(2,1)$ symmetry in two dimensions. This facilitates an exact map from the…
An explicit solution of the equation for the classical harmonic oscillator with smooth switching of the frequency has been found . A detailed analysis of a quantum harmonic oscillator with such frequency has been done on the base of the…
A linear quantum harmonic oscillator factors into one dimensional oscillators and can be solved using creation and annihilation operators. We consider a spherical analogue. This analogue does not factor. The two dimensional case is…
We develop an approach in solving exactly the problem of three-body oscillators including general quadratic interactions in the coordinates for arbitrary masses and couplings. We introduce a unitary transformation of three independent…
We study the quantum mechanical harmonic oscillator in two and three dimensions, with particular attention to the solutions as represents of their respective symmetry groups: O(2), O(3), and O(2,1). Solving the Schrodinger equation by…
A relativistic quantum harmonic oscillator in 3+1 dimensions is derived from a quaternionic non-relativistic quantum harmonic oscillator. This quaternionic equation also yields the Klein-Gordon wave equation with a covariant (space-time…
We propose a scheme for entangling the motion of two massive objects in a hybrid electromechanical architecture. The entanglement is generated due to the interaction of two mechanical oscillators with a mediating superconducting qubit. We…
We study analytically and numerically the problem of two qubits with fixed coupling irradiated with quantum or classical fields. In the classical case, we derive an effective Hamiltonian, and construct composite pulse sequences leading to a…
Li\'enard-type nonlinear one-dimensional oscillator is quantized using van Roos symmetric ordering recipe for the kinetic-like part of the new derived Hamiltonian. The corresponding Schr\"odinger equation is exactly solved in momuntum space…
Harmonic oscillator in noncommutative two dimensional lattice are investigated. Using the properties of non-differential calculus and its applications to quantum mechanics, we provide the eigenvalues and eigenfunctions of the corresponding…
Quantum entanglement in mechanical systems is not only a key signature of macroscopic quantum effects, but has wide applications in quantum technologies. Here we proposed an effective approach for creating strong steady-state entanglement…
We investigate a system of two coupled harmonic oscillators on the non-commutative plane \RR^2_{\theta} by requiring that the spatial coordinates do not commute. We show that the system can be diagonalized by a suitable transformation, i.e.…
We study the dynamics of an optomechanical system consisting of a single-mode optical field coupled to a mechanical oscillator, where the nonlinear interaction includes both linear and quadratic terms in the oscillator's position. We…
We study a particular form of interaction Hamiltonian between qubits and quantum harmonic oscillators, whose closed system dynamics results in qubit controlled displacement operations. We show how this interaction is realizable in many…
We adopt some basic ideas on quantum-theoretical modeling of tonal attraction and develop them further in an alternative direction. Fitting Gaussian Mixture Models (GMM) to the Krumhansl-Kessler (KK) probe tone profiles for static…
We show that the methods for quantification of system-environment entanglement that were recently developed for interactions that lead to pure decoherence of the system can be straightforwardly generalized to time-dependent Hamiltonians of…
We study many-body properties of quantum harmonic oscillator lattices with disorder. A sufficient condition for dynamical localization, expressed as a zero-velocity Lieb-Robinson bound, is formulated in terms of the decay of the…
It is often conjectured that quantum synchronisation and entanglement are two independent properties which two coupled quantum systems may not exhibit at the same time. However, as both these properties can be understood in terms of the…