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I. L. Egusquiza

Publications and source records attributed to I. L. Egusquiza.

At least 55 records · Page 3Linked to original sources
arXiv2002

A measurement-based approach to quantum arrival times

For a quantum-mechanically spread-out particle we investigate a method for determining its arrival time at a specific location. The procedure is based on the emission of a first photon from a two-level system moving into a laser-illuminated region. The resulting temporal distribution is explicitly calculated for the one-dimensional case and compared with axiomatically proposed expressions. As a main result we show that by means of a deconvolution one obtains the well known quantum mechanical probability flux of the particle at the location as a limiting distribution.

quant-ph↗
arXiv2002

Bounds and enhancements for the Hartman effect

The time of passage of the transmitted wave packet in a tunneling collision of a quantum particle with a square potential barrier becomes independent of the barrier width in a range of barrier thickness. This is the Hartman effect, which has been frequently associated with ``superluminality''. A fundamental limitation on the effect is set by non-relativistic ``causality conditions''. We demonstrate first that the causality conditions impose more restrictive bounds on the negative time delays (time advancements) when no bound states are present. These restrictive bounds are in agreement with a naive, and generally false, causality argument based on the positivity of the ``extrapolated phase time'', one of the quantities proposed to characterize the duration of the barrier's traversal. Nevertheless, square wells may in fact lead to much larger advancements than square barriers. We point out that close to thresholds of new bound states the time advancement increases considerably, while, at the same time, the transmission probability is large, which facilitates the possible observation of the enhanced time advancement.

quant-ph↗
arXiv2001

Asymptotic behaviour of the probability density in one dimension

We demonstrate that the probability density of a quantum state moving freely in one dimension may decay faster than 1/t. Inverse quadratic and cubic dependences are illustrated with analytically solvable examples. Decays faster than 1/t allow the existence of dwell times and delay times.

quant-ph↗
arXiv2001

Quantum times of arrival for multiparticle states

Using the concept of crossing state and the formalism of second quantization, we propose a prescription for computing the density of arrivals of particles for multiparticle states, both in the free and the interacting case. The densities thus computed are positive, covariant in time for time independent hamiltonians, normalized to the total number of arrivals, and related to the flux. We investigate the behaviour of this prescriptions for bosons and fermions, finding boson enhancement and fermion depletion of arrivals.

quant-ph↗
arXiv2001

Generalizations of Kijowski's time-of-arrival distribution for interaction potentials

Several proposals for a time-of-arrival distribution of ensembles of independent quantum particles subject to an external interaction potential are compared making use of the ``crossing state'' concept. It is shown that only one of them has the properties expected for a classical distribution in the classical limit. The comparison is illustrated numerically with a collision of a Gaussian wave packet with an opaque square barrier.

quant-ph↗
arXiv2000

Comment on "Measurement of time of arrival in quantum mechanics"

The analysis of the model quantum clocks proposed by Aharonov et al. [Phys. Rev. A 57 (1998) 4130 - quant-ph/9709031] requires considering evanescent components, previously ignored. We also clarify the meaning of the operational time of arrival distribution which had been investigated.

quant-ph↗
arXiv2000

Model for the arrival-time distribution in fluorescence time-of-flight experiments

An operational arrival-time distribution is defined as the distribution of detection times of the first photons emitted by two level atoms in resonance with a perpendicular laser beam in a time of flight experiment. For ultracold Cesium atoms the simulations are in excellent agreement with the theoretical ideal time-of-arrival distribution of Kijowski.

quant-ph↗
arXiv2000

Effect of classically forbidden momenta in one dimensional quantum scattering

The transmitted wave that results from a collision of a wave packet which is initially to the left of a potential barrier depends in general on the amplitudes of negative momenta of the initial state. The exact form of this dependence is shown and the importance of this classically forbidden effect is illustrated with numerical examples. Special care is taken to account properly for bound states.

quant-ph↗
arXiv2000

Sources of quantum waves

Due to the space and time dependence of the wave function in the time dependent Schroedinger equation, different boundary conditions are possible. The equation is usually solved as an ``initial value problem'', by fixing the value of the wave function in all space at a given instant. We compare this standard approach to "source boundary conditions'' that fix the wave at all times in a given region, in particular at a point in one dimension. In contrast to the well-known physical interpretation of the initial-value-problem approach, the interpretation of the source approach has remained unclear, since it introduces negative energy components, even for ``free motion'', and a time-dependent norm. This work provides physical meaning to the source method by finding the link with equivalent initial value problems.

quant-ph↗
arXiv2000

Consistent histories, the quantum Zeno effect, and time of arrival

We present a decomposition of the general quantum mechanical evolution operator, that corresponds to the path decomposition expansion, and interpret its constituents in terms of the quantum Zeno effect (QZE). This decomposition is applied to a finite dimensional example and to the case of a free particle in the real line, where the possibility of boundary conditions more general than those hitherto considered in the literature is shown. We reinterpret the assignment of consistent probabilities to different regions of spacetime in terms of the QZE. The comparison of the approach of consistent histories to the problem of time of arrival with the solution provided by the probability distribution of Kijowski shows the strength of the latter point of view.

quant-ph↗
arXiv1999

Time-of-arrival distributions from position-momentum and energy-time joint measurements

The position-momentum quasi-distribution obtained from an Arthurs and Kelly joint measurement model is used to obtain indirectly an ``operational'' time-of-arrival (TOA) distribution following a quantization procedure proposed by Kochański and Wódkiewicz [Phys. Rev. A 60, 2689 (1999)]. This TOA distribution is not time covariant. The procedure is generalized by using other phase-space quasi-distributions, and sufficient conditions are provided for time covariance that limit the possible phase-space quasi-distributions essentially to the Wigner function, which, however, provides a non-positive TOA quasi-distribution. These problems are remedied with a different quantization procedure which, on the other hand, does not guarantee normalization. Finally an Arthurs and Kelly measurement model for TOA and energy (valid also for arbitrary conjugate variables when one of the variables is bounded from below) is worked out. The marginal TOA distribution so obtained, a distorted version of Kijowski's distribution, is time covariant, positive, and normalized.

quant-ph↗
arXiv1999

Free motion time-of-arrival operator and probability distribution

We reappraise and clarify the contradictory statements found in the literature concerning the time-of-arrival operator introduced by Aharonov and Bohm in Phys. Rev. {\bf 122}, 1649 (1961). We use Naimark's dilation theorem to reproduce the generalized decomposition of unity (or POVM) from any self-adjoint extension of the operator, emphasizing a natural one, which arises from the analogy with the momentum operator on the half-line. General time operators are set within a unifying perspective. It is shown that they are not in general related to the time of arrival, even though they may have the same form.

quant-ph↗
arXiv1999

Time-of-arrival distribution for arbitrary potentials and Wigner's time-energy uncertainty relation

A realization of the concept of "crossing state" invoked, but not implemented, by Wigner, allows to advance in two important aspects of the time of arrival in quantum mechanics: (i) For free motion, we find that the limitations described by Aharonov et al. in Phys. Rev. A 57, 4130 (1998) for the time-of-arrival uncertainty at low energies for certain mesurement models are in fact already present in the intrinsic time-of-arrival distribution of Kijowski; (ii) We have also found a covariant generalization of this distribution for arbitrary potentials and positions.

quant-ph↗
arXiv1997

On the Entropy and the Density Matrix of Cosmological Perturbations

We look at the transition to the semiclassical behaviour and the decoherence process for the inhomogeneous perturbations in the inflationary universe. Two different decoherence mechanisms appear: one dynamical, accompanied with a negligible, if at all, entropy gain, and the other, effectively irreversible dephasing, due to a rapid variation in time of the off-diagonal density matrix elements in the post-inflationary epoch. We thus settle the discrepancies in the entropy content of perturbations evaluated by different authors.

gr-qc↗
arXiv1996

Planetoid String Solutions in 3 + 1 Axisymmetric Spacetimes

The string propagation equations in axisymmetric spacetimes are exactly solved by quadratures for a planetoid Ansatz. This is a straight non-oscillating string, radially disposed, which rotates uniformly around the symmetry axis of the spacetime. In Schwarzschild black holes, the string stays outside the horizon pointing towards the origin. In de Sitter spacetime the planetoid rotates around its center. We quantize semiclassically these solutions and analyze the spin/(mass$^2$) (Regge) relation for the planetoids, which turns out to be non-linear.

hep-th↗
arXiv1995

Strings Next To and Inside Black Holes

The string equations of motion and constraints are solved near the horizon and near the singularity of a Schwarzschild black hole. In a conformal gauge such that $τ= 0$ ($τ$ = worldsheet time coordinate) corresponds to the horizon ($r=1$) or to the black hole singularity ($r=0$), the string coordinates express in power series in $τ$ near the horizon and in power series in $τ^{1/5}$ around $r=0$. We compute the string invariant size and the string energy-momentum tensor. Near the horizon both are finite and analytic. Near the black hole singularity, the string size, the string energy and the transverse pressures (in the angular directions) tend to infinity as $r^{-1}$. To leading order near $r=0$, the string behaves as two dimensional radiation. This two spatial dimensions are describing the $S^2$ sphere in the Schwarzschild manifold.

hep-th↗