Related papers: Quantum forced oscillator via Wigner transform
A harmonic oscillator with time-dependent mass $m(t)$ and a time-dependent (squared) frequency $\omega^2(t)$ occurs in the modelling of several physical systems. It is generally believed that systems, with $m(t)>0$ and $\omega^2(t)>0$…
The symlectic quantum tomography for the general linear quantization is introduced. Using the approach based upon the Wigner function techniques the evolution equation of quantum tomograms is derived for a parametric driven oscillator.
We obtain analytic solutions to various models of dissipation of the quantum harmonic oscillator, employing a simple method in the Wigner function Fourier transform description of the system; and study as an exemplification, the driven open…
We address the problem of determining whether or not a harmonic oscillator has been perturbed by an external force. Quantum detection and estimation theory has been used in devising optimum measurement schemes. Detection probability has…
We introduce a quantum phase space representation for the orientation state of extended quantum objects, using the Euler angles and their conjugate momenta as phase space coordinates. It exhibits the same properties as the standard Wigner…
A q-version of the Fourier transformation and some of its properties are discussed.
The one-dimensional quantum harmonic oscillator problem is examined via the Laplace transform method. The stationary states are determined by requiring definite parity and good behaviour of the eigenfunction at the origin and at infinity.
This paper presents a comprehensive investigation of the problem of a harmonic oscillator with time-depending frequencies in the framework of the Vlasov theory and the Wigner function apparatus for quantum systems in the phase space. A new…
A trapped-ion quantum tunneling rotor (QTR) is in a quantum superposition of two different Wigner crystal orientations. In a QTR system, quantum tunneling drives the coherent transition between the two different Wigner crystal orientations.…
We investigate quantum tunneling in smooth symmetric and asymmetric double-well potentials. Exact solutions for the ground and first excited states are used to study the dynamics. We introduce Wigner's quasi-probability distribution…
We extend the Wigner current vector field (Wigner current) construct to single bosonic mode quantum systems interacting with an environment. In terms of the Wigner function quasiprobability density and associated Wigner current, the open…
We study tunneling of the magnetic moment in a particle that has full rotational freedom. Exact energy levels are obtained and the ground-state magnetic moment is computed for a symmetric rotor. The effect of the mechanical freedom on spin…
In this article we obtained the harmonic oscillator solution for quaternionic quantum mechanics ($\mathbbm{H}$QM) in the real Hilbert space, both in the analytic method and in the algebraic method. The quaternionic solutions have many…
We put forward the concatenation of Quantum Arnold Transformations as a tool to obtain the wave function of a particle subjected to a harmonic potential which is switched on and off successively. This simulates the capture and release…
We elucidate the basic physical mechanisms responsible for the quantum-classical transition in one-dimensional, bounded chaotic systems subject to unconditioned environmental interactions. We show that such a transition occurs due to the…
We revisit dipolar motion of condensate atoms in one-dimensional optical lattices and harmonic magnetic traps including quantum fluctuations within the truncated Wigner approximation. In the strong tunneling limit we reproduce the meanfield…
In this work we present the formal background used to develop the methods used in earlier works to extend the truncated Wigner representation of quantum and atom optics in order to address multi-time problems. The truncated Wigner…
In this paper, we investigate the transformation laws of the Wigner function under changes of reference frames. By employing the coordinate transformation of the wave functions, we derive an integral representation for the transformed…
We investigate a simple forced harmonic oscillator with a natural frequency varying with time. It is shown that the time evolution of such a system can be written in a simplified form with Fresnel integrals, as long as the variation of the…
I briefly review the role of the Wigner function in the study of the quantum-to-classical transition through interaction with the environment (decoherence).