Search results for "HARMONIC OSCILLATOR"
showing 10 items of 109 documents
Competition Between Beta and Double Beta Decay in 48Ca and 96Zr
2000
Highly forbidden beta decays of 48Ca and 96Zr are studied and their relative importance as compared to the double beta decay of these nuclei is evaluated. 48Ca and 96Zr are the only naturally occurring nuclei in which these processes can occur simultaneously. Although usually ordinary beta decay overwhelms double beta decay unless the former is energetically forbidden, in these cases the high degree of forbiddenness and small release of kinetic energy makes the half-lives of these modes comparable to each other.
Shell-model study of the highly forbidden beta decay 48 Ca → 48 Sc
1999
Ordinary β− decay of the 0+ ground state of 48Ca is studied. Partial half-lives for the highly-forbidden transitions to the three lowest-lying states (6+,5+,4+) of 48Sc are calculated by using both the harmonic oscillator and the Woods-Saxon mean-field wave functions. We find the decay to be dominated, as expected, by the unique fourth-forbidden transition to the excited 5+ state of 48Sc. The theoretical beta-decay half-life of 48Ca is found to be 1.1−0.6+0.8·1021 years which is approximately 25 times longer than the measured double-beta-decay half-life of T1/22ν = (4.3−1.1+2.4[stat] ± 1.4[syst])·1019 years.
Dissipation evidence for the quantum damped harmonic oscillator via pseudo-bosons
2011
It is known that a self-adjoint, time-independent hamiltonian can be defined for the quantum damped harmonic oscillator. We show here that the two vacua naturally associated to this operator, when expressed in terms of pseudo-bosonic lowering and raising operators, appear to be non square-integrable. This fact is interpreted as the evidence of the dissipation effect of the classical oscillator at a purely quantum level.
The spiked harmonic oscillatorV(r)=r 2+λr −4 as a challenge to perturbation theory
1991
The standard weak- and strong-coupling perturbation series are interpreted as extreme special cases of expansions obtainable within the framework of Rayleigh-Schroedinger perturbation theory with non-diagonal propagators and unspecified zero-order energies. The formalism of the latter type is then tested by our strongly singular example. It proves suitable for applications in the domain of virtually arbitrary couplings. A few related technicalities and especially the quadruple problem of convergence are also discussed.
Quantization as a consequence of the group law
1982
A method of gemetric quantization which solely makes use of the structure of the symmetry group of the dynamical system is proposed; the classical limit is discussed along similar lines. The method is applied to two examples, the free particle and the harmonic oscillator.
Generalized Conformal Symmetry and Extended Objects from the Free Particle
1998
The algebra of linear and quadratic functions of basic observables on the phase space of either the free particle or the harmonic oscillator possesses a finite-dimensional anomaly. The quantization of these systems outside the critical values of the anomaly leads to a new degree of freedom which shares its internal character with spin, but nevertheless features an infinite number of different states. Both are associated with the transformation properties of wave functions under the Weyl-symplectic group $WSp(6,\Re)$. The physical meaning of this new degree of freedom can be established, with a major scope, only by analysing the quantization of an infinite-dimensional algebra of diffeomorphi…
Confinement of Lévy flights in a parabolic potential and fractional quantum oscillator
2018
We study L\'evy flights confined in a parabolic potential. This has to do with a fractional generalization of an ordinary quantum-mechanical oscillator problem. To solve the spectral problem for the fractional quantum oscillator, we pass to the momentum space, where we apply the variational method. This permits one to obtain approximate analytical expressions for eigenvalues and eigenfunctions with very good accuracy. The latter fact has been checked by a numerical solution to the problem. We point to the realistic physical systems ranging from multiferroics and oxide heterostructures to quantum chaotic excitons, where obtained results can be used.
Control of quantum systems
1999
We propose a new control method for systems whose evolution is described by Schrödinger's equation (quantum dynamics). The goal of the control is to induce modifications of observable quantities — with possible effects at mesoscopic or macroscopic levels — by modifying the potential at the microscopic level. We illustrate the feasibility of the approach on a harmonic oscillator system.
Theoretical analysis of a recent experiment on mesoscopic state superpositions in cavity QED
2005
Quite recently quantum features exhibited by a mesoscopic field interacting with a single Rydberg atom in a microwave cavity has been observed [A. Auffeves et al., Phys. Rev. Lett. 91, 230405 (2003)]. In this paper we theoretically analyze all the phases of this articulated experiment considering from the very beginning cavity losses. Fully applying the theory of quantum open systems, our modelization succeeds in predicting fine aspects of the measured quantity, reaching qualitative and quantitative good agreement with the experimental results. This fact validates our theoretical approach based on the fundamental atom-cavity interaction model and simple mathematical structure of dissipative…
Many-particle dynamics and intershell effects in Wigner molecules
2011
We apply classical molecular dynamics within the velocity Verlet algorithm to examine the formation dynamics of Wigner crystals in two-dimensional harmonic oscillators. Using a large ensemble of initial conditions as well as different freezing mechanisms, we obtain reliable information on the energies and probabilities of stable and metastable configurations, their formation dynamics, and their stability. Wigner-crystal configurations of up to 30 particles are presented and the dynamics of transition processes, e.g., intershell effects, are analyzed.