V. Delgado

Arrival time in quantum mechanics

A self-adjoint operator with dimensions of time is explicitly constructed, and it is shown that its complete and orthonormal set of eigenstates can be used to define consistently a probability distribution of the time of arrival at a spatial point.

Effective mean-field equations for cigar-shaped and disk-shaped Bose-Einstein condensates

By applying the standard adiabatic approximation and using the accurate analytical expression for the corresponding local chemical potential obtained in our previous work [Phys. Rev. A \textbf{75}, 063610 (2007)] we derive an effective 1D equation that governs the axial dynamics of mean-field cigar-shaped condensates with repulsive interatomic interactions, accounting accurately for the contribution from the transverse degrees of freedom. This equation, which is more simple than previous proposals, is also more accurate. Moreover, it allows treating condensates containing an axisymmetric vortex with no additional cost. Our effective equation also has the correct limit in both the quasi-1D mean-field regime and the Thomas-Fermi regime and permits one to derive fully analytical expressions for ground-state properties such as the chemical potential, axial length, axial density profile, and local sound velocity. These analytical expressions remain valid and accurate in between the above two extreme regimes. Following the same procedure we also derive an effective 2D equation that governs the transverse dynamics of mean-field disk-shaped condensates. This equation, which also has the correct limit in both the quasi-2D and the Thomas-Fermi regime, is again more simple and accurate than previous proposals. We have checked the validity of our equations by numerically solving the full 3D Gross-Pitaevskii equation.

Quantum probability distribution of arrival times and probability current density

This paper compares the proposal made in previous papers for a quantum probability distribution of the time of arrival at a certain point with the corresponding proposal based on the probability current density. Quantitative differences between the two formulations are examined analytically and numerically with the aim of establishing conditions under which the proposals might be tested by experiment. It is found that quantum regime conditions produce the biggest differences between the formulations which are otherwise near indistinguishable. These results indicate that in order to discriminate conclusively among the different alternatives, the corresponding experimental test should be performed in the quantum regime and with sufficiently high resolution so as to resolve small quantum effects.

Dynamical evolution of a doubly quantized vortex imprinted in a bose-einstein condensate

The recent experiment by Shin et al. [Phys. Rev. Lett. 93, 160406 (2004)] on the decay of a doubly quantized vortex is analyzed by numerically solving the Gross-Pitaevskii equation. Our results demonstrate that the vortex decay is mainly a consequence of dynamical instability. The monotonic increase observed in the vortex lifetimes is a consequence of the fact that the measured lifetimes incorporate the time it takes for the initial perturbation to reach the central slice. When considered locally, the splitting occurs approximately at the same time in every condensate.

Semiclassical dressed states of two-level quantum systems driven by non-resonant and/or strong laser fields

Analytical expressions for the semiclassical dressed states and corresponding quasienergies are obtained for a two-level quantum system driven by a non-resonant and/or strong laser field in a coherent state. These expressions are of first order in a proper perturbative expansion, and already contain all the relevant physical information on the dynamical and spectroscopic properties displayed by these systems under such particular conditions. The influence of the laser field parameters on transition frequencies, selection rules and line intensities can be easily understood in terms of the quasienergy-level diagram and the allowed transitions between the different semiclassical dressed states.

Comparison of positive flux operators for transition state theory using a solvable model

Several quantum operators representing ‘‘positive flux’’ are compared for the square barrier by examining their ability to reproduce the exact transmittance when traced with the exact microcanonical density operator. They are obtained by means of the ‘‘Weyl rule,’’ the ‘‘Rivier rule,’’ by symmetrizing the product of ‘‘flux’’ and ‘‘positive momentum projection’’ operators, and by a variational technique. Explicit expressions are given for all cases.

PROBABILITY DISTRIBUTION OF ARRIVAL TIMES IN QUANTUM MECHANICS

In a previous paper [V. Delgado and J. G. Muga, Phys. Rev. A 56, 3425 (1997)] we introduced a self-adjoint operator

DOES POSITIVE FLUX PROVIDE A VALID DEFINITION OF TUNNELLING TIMES

\mathcal{T}^(X)

Interaction between an atom and a mesoscopic helicoidal system. Fourier‐transform analysis

whose eigenstates can be used to define consistently a probability distribution of the time of arrival at a given spatial point. In the present work we show that the probability distribution previously proposed can be well understood on classical grounds in the sense that it is given by the expectation value of a certain positive-definite operator

Extension of the Thomas-Fermi approximation for trapped Bose-Einstein condensates with an arbitrary number of atoms

{J}^{(+)}(X)