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Register a new userRelation between phase and dwell times for quantum tunneling of a relativistically propagating particle
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Authors
Alex E. Bernardini
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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.
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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.
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.
The transit times are obtained for a symmetrized (two identical bosons) and an antisymmetrized (two identical fermions) quantum colliding configuration. Considering two identical particles symmetrically impinging on a one-dimensional barrier, we demonstrate that the phase time and the dwell time give connected results where, however, the exact position of the scattered particles is explicitly determined by the phase time (group delay). For the antisymmetrized wave function configuration, an unusual effect of {em accelerated} transmission is clearly identified in a simultaneous tunneling of two identical fermions.
Characteristic quantities such as the penetration and preformation probabilities, assault frequency and tunneling times in the tunneling description of alpha decay of heavy nuclei are explored to reveal their sensitivity to neutron numbers in the vicinity of the magic neutron number $N$ = 126. Using realistic nuclear potentials, the sensitivity of these quantities to the parameters of the theoretical approach is also tested. An investigation of the region from $N=116$ to $N=132$ in Po nuclei reveals that the tunneling $alpha$ particle spends the least amount of time with an $N=126$ magic daughter nucleus. The shell closure at $N=126$ seems to affect the behaviour of the dwell times of the tunneling alpha particles and this occurs through the influence of the $Q$-values involved.
The stationary phase method is often employed for computing tunneling {em phase} times of analytically-continuous {em gaussian} or infinite-bandwidth step pulses which collide with a potential barrier. The indiscriminate utilization of this method without considering the barrier boundary effects leads to some misconceptions in the interpretation of the phase times. After reexamining the above barrier diffusion problem where we notice the wave packet collision necessarily leads to the possibility of multiple reflected and transmitted wave packets, we study the phase times for tunneling/reflecting particles in a framework where an idea of multiple wave packet decomposition is recovered. To partially overcome the analytical incongruities which rise up when tunneling phase time expressions are obtained, we present a theoretical exercise involving a symmetrical collision between two identical wave packets and a one dimensional squared potential barrier where the scattered wave packets can be recomposed by summing the amplitudes of simultaneously reflected and transmitted waves.
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