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

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Experimental evidence of tunneling as a stochastic process

Anedio Ranfagni, R. Ruggeri, Carlo Susini, A. Agresti, Paolo Levi Sandri

Published Jan 24, 2001• 23 citations
Publisher

Abstract

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.

DOI
10.1103/physreve.63.025102

Related papers

Tunneling as a stochastic process

Anedio Ranfagni, R. Ruggeri, A. Agresti

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.

Mysteries, Puzzles, and Paradoxes in Quantum Mechanics•Jan 1, 1999•0 citations

Path-integral treatment of optical and microwave tunneling

Paolo Moretti, Anedio Ranfagni, Paolo Levi Sandri

A model based on a statistical method, as deduced from a path-integral treatment of the Brownian motion proposed by Feynman and Hibbs in 1965, demonstrates to be capable of interpreting the results of delay time measurements in frustrated total internal reflection experiments at an optical and microwave scale. A plausible description of the trajectories followed by the system inside the tunneling region, the air gap between the two dielectric prisms, is given.

Physical Review E•Jun 27, 2007•3 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

Universal tunneling time for all fields

G. Nimtz, A.A. Stahlhofen

Tunneling is an outstanding physical process. The observation that particles surmount a high barrier in spite of the fact that they don't have the necessary energy can not be explained by classical physics. However, this so called tunneling became allowed by quantum mechanics. Experimental tunneling studies with different photonic barriers from microwave frequencies up to ultraviolet frequencies point towards a universal tunneling time [1, 2]. Tunneling can be described by virtual, that is, by unobservable particles [3]. In the case of tunneling there is a virtual particle between the real incident and the real transmitted particles. Tunneling modes are solutions of the Schrödinger and of the Helmholtz equations. The most prominent example of the occurrence of tunneling modes in optics is frustrated total internal reflection (FTIR) at double prisms. In 1949 Sommerfeld [4] pointed out that this optical phenomenon represents the analogy of quantum mechanical particle tunneling. Recent experimental and theoretical data confirmed the conjecture that the tunneling process is characterized by a universal tunneling time presumably independent of the kind of field. The observed tunneling processes proceeded at a time of the order of magnitude of the reciprocal frequency of the wave packets.

arXiv:0709.0921•Annalen der Physik•Apr 16, 2008•21 citations

Delay-time measurements in narrowed waveguides as a test of tunneling

Anedio Ranfagni, Daniela Mugnai, Pasquale Fabeni +1 more

Delay-time measurements with a microwave setup, where a step narrowing in the waveguide simulates a quantum mechanical potential barrier, have been performed even beyond the cutoff. This allows experimental measurements in a very accessible temporal range of the order of nanoseconds. The results, interpreted as tunneling times, are compared with the existing quantum mechanical models, translated into the electromagnetic framework.

Applied Physics Letters•Feb 18, 1991•148 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
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.
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.
Tunneling is an outstanding physical process. The observation that particles surmount a high barrier in spite of the fact that they don't have the necessary energy can not be explained by classical physics. However, this so called tunneling became allowed by quantum mechanics. Experimental tunneling studies with different photonic barriers from microwave frequencies up to ultraviolet frequencies point towards a universal tunneling time [1, 2]. Tunneling can be described by virtual, that is, by unobservable particles [3]. In the case of tunneling there is a virtual particle between the real incident and the real transmitted particles. Tunneling modes are solutions of the Schrödinger and of the Helmholtz equations. The most prominent example of the occurrence of tunneling modes in optics is frustrated total internal reflection (FTIR) at double prisms. In 1949 Sommerfeld [4] pointed out that this optical phenomenon represents the analogy of quantum mechanical particle tunneling. Recent experimental and theoretical data confirmed the conjecture that the tunneling process is characterized by a universal tunneling time presumably independent of the kind of field. The observed tunneling processes proceeded at a time of the order of magnitude of the reciprocal frequency of the wave packets.
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.