Search

The question of how long a particle takes to pass through a potential barrier is still a controversial topic in quantum mechanics. Arguably, the main theoretical problem in obtaining estimates for measurable times is the fact that previously defined time operators, that remained within the borders of standard quantum mechanics, present some kind of pathology. Recently, a time operator acting on an additional Hilbert space has been shown to support both Hermiticity and canonical relation with an energy observable. The theory is built in a framework which treats space and time as symmetrically as possible, in the nonrelativistic regime. In this work, we use this formalism to derive a closed analytic expression for the traversal time of a quantum particle impinging on a constant-potential barrier. We test our theory in the specific experimental scenario of a realization by Rafagni et al [Appl. Phys. Lett. {\bf 58}, 774 (1991)]. The proposed approach displays a much better performance in comparison with the B\"uttiker-Landauer and the phase-time approximations., Comment: 6 pages, 1 figure

There is no doubt about the fact that entanglement and nonlocality are distinct resources. It is acknowledged that a clear illustration of this point is the difference between maximally entangled states and states that maximally violate a Bell inequality. We give strong evidence that this anomaly may be an artefact of the measures that have been used to quantify nonlocality. By reasoning that the numeric value of a Bell function is akin to a witness rather than a quantifier, we define a measure of nonlocality and show that, for pairs of qutrits and of four-level systems, maximal entanglement does correspond to maximal nonlocality in the same scenario that gave rise to the discrepancy.

We propose a scheme to investigate the time scale of wave-function collapse by using polarization-entangled photon pairs. The setup is similar to those employed to study quantum correlations, but in the present case, synchronization is essential at all stages. We find that it is possible to discriminate between the scenarios of instantaneous collapse and finite-time reduction via a large number of double measurements of polarization. The quantities to be recorded present distinct behaviors in each scenario, the deviations being small but distinguishable from pure statistical fluctuations. The connection between the presented formalism and the theory of weak measurements is discussed as well as the possible consequences for experimental tests of nonlocality.

An effective description of microscopic measurements is given, in which the precise moment of probing is not determined. Within this scenario we propose a scheme that relies on an "attempt" to make a forbidden simultaneous measurement of two incompatible observables. Although bound to failure in what concerns this goal, the process can lead to information on a possible non-vanishing time scale $\delta t$ involved in the collapsing of the wave function, even if the duration $\Delta t$ of the individual measurements is much larger than $\delta t$., Comment: 5 pages

We derive a semiclassical approximation for the coherent state propagator using a path integral formulation in which the intermediate coherent states can have arbitrary widths. Our semiclassical formula involves complex trajectories of the smoothed Hamiltonian H(q,p,b)= where b, the width of the coherent state vertical bar z>, is a free function that can be chosen conveniently. The generality of this formalism enables us to derive a semiclassical approximation which contains, as particular cases, other similar approximations known in the literature, providing a natural link between them. We present numerical results showing that the semiclassical propagation can be very sensitive to the choice of b and we suggest an energy dependent value b=b{sub E} that results in considerable improvement over other choices. This value for the width will be generally different from the widths {sigma}{sup '} or {sigma}{sup ''} of the initial and final states vertical ba z{sup '}> and vertical bar z{sup ''}>.