Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Mysteries, Puzzles, and Paradoxes in Quantum Mechanics

Tunneling as a stochastic process

Anedio Ranfagni, R. Ruggeri, A. Agresti

Published Jan 1, 1999• 0 citations
Publisher

Abstract

An alternative model for tunneling processes, based on the capability of the telegrapher’s equation to describe stochastic processes, is able to account for delay time results of an optical experiment at the microwave scale, where superluminal behaviors have been evidenced.
DOI
10.1063/1.57886

Related papers

Stochastic model for tunneling processes: The question of superluminal behavior

Anedio Ranfagni, Daniela Mugnai

A stochastic model for tunneling processes that is based on a close correspondence between quantum relativistic and telegrapher's equations is proposed along the lines of a procedure similar to the one already adopted by Kac [Rocky Mountain J. Math 4, 497 (1974)]. It is hypothesized that reversals of motion imply the inversion of the (imaginary) time rather than of the space, as in the ordinary allowed processes. In this way, superluminal behavior can be predicted in limiting cases. The plausibility of the superluminal motions observed is then discussed on the basis of a signal analysis along the lines of the Sommerfeld-Brillouin criterion which has been suitably modified.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Jul 1, 1995•31 citations

Experimental evidence of tunneling as a stochastic process

Anedio Ranfagni, R. Ruggeri, Carlo Susini +2 more

A model for tunneling based on stochastic processes proves to be capable of interpreting the results of two experiments at the microwave scale. The first of these consisted of measuring the penetration time in a subcutoff waveguide; the second one, in measuring the shift of a beam in a frustrated total reflection. Said shift which is a measurement of the traversal time of the barrier. In both cases, a peak in the real-time component was evidenced, as predicted by the theoretical model.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Jan 24, 2001•23 citations

Tunneling as a stochastic process: A path-integral model for microwave experiments

Anedio Ranfagni, R. Ruggeri, Daniela Mugnai +3 more

Delay time results obtained in microwave experiments at frequencies above and below the cutoff frequency of different waveguide sections are interpreted on the basis of wave propagation in the presence of dissipative effects. Kac's original suggestion was the starting point for the formulation of a stochastic model, which has now been substantially improved, also in relation to the transition-elements theory of Feynman-Hibbs. In this way, an approach to the problem is provided, which is completely distinct from the ones formulated elsewhere.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Jun 27, 2003•8 citations

Real-time analysis of the telegrapher’s equation for tunneling processes

Anedio Ranfagni, Daniela Mugnai, Maria Angela Vitali

Based on a close analogy with an RLC circuit, a model for interpreting delay times in forbidden regimes (tunneling) is formulated, avoiding the analytical continuation into imaginary time. In this way, a reasonable description of experimental data, which were previously reported for a waveguide propagation below the cutoff frequency at approximately 9.5 GHz, is obtained.

Physical Review E•May 28, 2004•5 citations

Anomalous delay in wave propagation and tunneling: A transition-elements analysis of the traversal time

A. Agresti, Paolo Levi Sandri, C. Ranfagni +2 more

An alternative model for near-field propagation and optical tunneling is proposed following the lines of the path-integral method developed by Feynman, and in particular by using a transition-elements analysis. Such a model was able to account for the frequency dependency of delay-time results of an experiment involving microwave propagation in the near field using two horn antennas [A. Ranfagni et al., Phys. Rev. E 66, 036111 (2002)]. Furthermore, this approach is also capable of interpreting delay-time results as a function of the barrier width in a frustrated total internal reflection experiment performed at the microwave scale and in the optical region.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Dec 30, 2002•12 citations

Superluminal processes and signal velocity in tunneling simulation

Daniela Mugnai, Anedio Ranfagni, R. Ruggeri +2 more

Physics Letters A•Dec 1, 1995•35 citations
A stochastic model for tunneling processes that is based on a close correspondence between quantum relativistic and telegrapher's equations is proposed along the lines of a procedure similar to the one already adopted by Kac [Rocky Mountain J. Math 4, 497 (1974)]. It is hypothesized that reversals of motion imply the inversion of the (imaginary) time rather than of the space, as in the ordinary allowed processes. In this way, superluminal behavior can be predicted in limiting cases. The plausibility of the superluminal motions observed is then discussed on the basis of a signal analysis along the lines of the Sommerfeld-Brillouin criterion which has been suitably modified.
Delay time results obtained in microwave experiments at frequencies above and below the cutoff frequency of different waveguide sections are interpreted on the basis of wave propagation in the presence of dissipative effects. Kac's original suggestion was the starting point for the formulation of a stochastic model, which has now been substantially improved, also in relation to the transition-elements theory of Feynman-Hibbs. In this way, an approach to the problem is provided, which is completely distinct from the ones formulated elsewhere.
An alternative model for near-field propagation and optical tunneling is proposed following the lines of the path-integral method developed by Feynman, and in particular by using a transition-elements analysis. Such a model was able to account for the frequency dependency of delay-time results of an experiment involving microwave propagation in the near field using two horn antennas [A. Ranfagni et al., Phys. Rev. E 66, 036111 (2002)]. Furthermore, this approach is also capable of interpreting delay-time results as a function of the barrier width in a frustrated total internal reflection experiment performed at the microwave scale and in the optical region.