14 research outputs found
Tunneling Time Distribution by means of Nelson's Quantum Mechanics and Wave-Particle Duality
We calculate a tunneling time distribution by means of Nelson's quantum
mechanics and investigate its statistical properties. The relationship between
the average and deviation of tunneling time suggests the exsistence of
``wave-particle duality'' in the tunneling phenomena.Comment: 14 pages including 11 figures, the text has been revise
Anomalous Diffusion in Infinite Horizon Billiards
We consider the long time dependence for the moments of displacement < |r|^q
> of infinite horizon billiards, given a bounded initial distribution of
particles. For a variety of billiard models we find ~ t^g(q) (up to
factors of log t). The time exponent, g(q), is piecewise linear and equal to
q/2 for q2. We discuss the lack of dependence of this result
on the initial distribution of particles and resolve apparent discrepancies
between this time dependence and a prior result. The lack of dependence on
initial distribution follows from a remarkable scaling result that we obtain
for the time evolution of the distribution function of the angle of a
particle's velocity vector.Comment: 11 pages, 7 figures Submitted to Physical Review
The Exact Correspondence between Phase Times and Dwell Times in a Symmetrical Quantum Tunneling Configuration
The general and explicit relation between the phase time and the dwell time
for quantum tunneling or scattering is investigated. Considering a symmetrical
collision of two identical wave packets with an one-dimensional barrier, here
we demonstrate that these two distinct transit time definitions give connected
results where, however, the phase time (group delay) accurately describes the
exact position of the scattered particles. The analytical difficulties that
arise when the stationary phase method is employed for obtaining phase
(traversal) times are all overcome. Multiple wave packet decomposition allows
us to recover the exact position of the reflected and transmitted waves in
terms of the phase time, which, in addition to the exact relation between the
phase time and the dwell time, leads to right interpretation for both of them.Comment: 11 pages, 2 figure
Small Corrections to the Tunneling Phase Time Formulation
After reexamining the above barrier diffusion problem where we notice that
the wave packet collision implies the existence of {\em multiple} reflected and
transmitted wave packets, we analyze the way of obtaining phase times for
tunneling/reflecting particles in a particular colliding configuration where
the idea of multiple peak decomposition is recovered. To partially overcome the
analytical incongruities which frequently rise up when the stationary phase
method is adopted for computing the (tunneling) phase time expressions, we
present a theoretical exercise involving a symmetrical collision between two
identical wave packets and a unidimensional squared potential barrier where the
scattered wave packets can be recomposed by summing the amplitudes of
simultaneously reflected and transmitted wave components so that the conditions
for applying the stationary phase principle are totally recovered. Lessons
concerning the use of the stationary phase method are drawn.Comment: 14 pages, 3 figure
Dwell-time distributions in quantum mechanics
Some fundamental and formal aspects of the quantum dwell time are reviewed,
examples for free motion and scattering off a potential barrier are provided,
as well as extensions of the concept. We also examine the connection between
the dwell time of a quantum particle in a region of space and flux-flux
correlations at the boundaries, as well as 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.Comment: To appear in "Time in Quantum Mechanics, Vol. 2", Springer 2009, ed.
by J. G. Muga, A. Ruschhaupt and A. del Camp