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We put forward several inherently quantum characteristics of the dwell time, and propose an operational method to detect them. The quantum dwell time is pointed out to be a conserved quantity, totally bypassing Paulis theorem. Furthermore, the quantum dwell time in a region for one dimensional motion is doubly degenerate. In presence of a potential barrier, the dwell time becomes bounded, unlike the classical quantity. By using off-resonance coupling to a laser we propose an operational method to measure the absorption by a complex potential, and thereby the average time spent by an incoming atom in the laser region.
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We examine the connection between the dwell time of a quantum particle in a region of space and flux-flux correlations at the boundaries. It is shown that the first and second moments of a flux-flux correlation function which generalizes a previous proposal by Pollak and Miller [E. Pollak and W. H. Miller, Phys. Rev. Lett. {bf 53}, 115 (1984)], agree with the corresponding moments of the dwell-time distribution, whereas the third and higher moments do not. We also discuss operational approaches and approximations to measure the flux-flux correlation function and thus the second moment of the dwell time, which is shown to be characteristically quantum, and larger than the corresponding classical moment even for freely moving particles.
The general and explicit relation between the phase time and the dwell time for quantum tunneling of a relativistically propagating particle is investigated and quantified. In analogy with previously obtained non-relativistic results, it is shown that the group delay can be described in terms of the dwell time and a self-interference delay. Lessons concerning the phenomenology of the relativistic tunneling are drawn.
In a recent review paper [{em Phys. Reports} {bf 214} (1992) 339] we proposed, within conventional quantum mechanics, new definitions for the sub-barrier tunnelling and reflection times. Aims of the present paper are: (i) presenting and analysing the results of various numerical calculations (based on our equations) on the penetration and return times $<tau_{, rm Pen}>$, $<tau_{, rm Ret}>$, during tunnelling {em inside} a rectangular potential barrier, for various penetration depths $x_{rm f}$; (ii) putting forth and discussing suitable definitions, besides of the mean values, also of the {em variances} (or dispersions) ${rm D} , {tau_{rm T}}$ and ${rm D} , {tau_{, rm R}}$ for the time durations of transmission and reflection processes; (iii) mentioning, moreover, that our definition $<tau_{rm T}>$ for the average transmission time results to constitute an {em improvement} of the ordinary dwell--time ${ove tau}^{rm Dw}$ formula: (iv) commenting, at last, on the basis of our {em new} numerical results, upon some recent criticism by C.R.Leavens. We stress that our numerical evaluations {em confirm} that our approach implied, and implies, the existence of the {em Hartman effect}: an effect that in these days (due to the theoretical connections between tunnelling and evanescent--wave propagation) is receiving ---at Cologne, Berkeley, Florence and Vienna--- indirect, but quite interesting, experimental verifications. Eventually, we briefly analyze some other definitions of tunnelling times.
In this paper we focus our attention on a particle that follows a unidirectional quantum walk, an alternative version of the nowadays widespread discrete-time quantum walk on a line. Here the walker at each time step can either remain in place or move in a fixed direction, e.g., rightward or upward. While both formulations are essentially equivalent, the present approach leads to consider Discrete Fourier Transforms, which eventually results in obtaining explicit expressions for the wave functions in terms of finite sums, and allows the use of efficient algorithms based on the Fast Fourier Transform. The wave functions here obtained govern the probability of finding the particle at any given location, but determine as well the exit-time probability of the walker from a fixed interval, which is also analyzed.
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.
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