Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userMore About Tunnelling Times, the Dwell Time, and the ``Hartman Effect
59
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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.
rate research
Read More
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 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 barriers 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.
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.
In this paper we examine critically and in detail some existing definitions for the tunnelling times, namely: the phase-time; the centroid-based times; the Buttiker and Landauer times; the Larmor times; the complex (path-integral and Bohm) times; the dwell time, and finally the generalized (Olkhovsky and Recami) dwell time, by adding also some numerical evaluations. Then, we pass to examine the equivalence between quantum tunnelling and photon tunnelling (evanescent waves propagation), with particular attention to tunnelling with Superluminal group-velocities (Hartman effect). At last, in an Appendix, we add a bird-eye view of all the experimental sectors of physics in which Superluminal motions seem to appear.
We analyse a little known aspect of the Klein paradox. A Klein-Gordon boson appears to be able to cross a supercritical rectangular barrier without being reflected, while spending there a negative amount of time. The transmission mechanism is demonstrably acausal, yet an attempt to construct the corresponding causal solution of the Klein-Gordon equation fails. We relate the causal solution to a divergent multiple-reflections series, and show that the problem is remedied for a smooth barrier, where pair production at the energy equal to a half of the barriers height is enhanced yet remains finite.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
