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The Hartman effect refers to the rather paradoxical result that the time spent by a quantum mechanical particle or a photon to tunnel through an opaque potential barrier becomes independent of barrier width for long barriers. Such an…

Quantum Physics · Physics 2022-10-19 Stefano Longhi

We investigate the tunneling time of a wave packet propagating through a non-Hermitian potential $V_{r} - iV_{i}$ in space-fractional quantum mechanics. By applying the stationary phase method, we derive a closed-form expression for the…

Quantum Physics · Physics 2025-04-08 Mohammad Umar , Vibhav Narayan Singh , Bhabani Prasad Mandal

We study the nature of tunneling phase time for various quantum mechanical structures such as networks and rings having potential barriers in their arms. We find the generic presence of Hartman effect, with superluminal velocities as a…

Quantum Physics · Physics 2007-05-23 Swarnali Bandopadhyay , A. M. Jayannavar

Quantum tunneling is considered from the point of view of local realism. It is concluded that a quantum object tunneling through a potential barrier cannot be interpreted as a point-like particle because such an interpretation generates a…

Quantum Physics · Physics 2021-03-23 A. Yu. Samarin

We calculate the time taken by a wave packet to travel through a classically forbidden region of space in space fractional quantum mechanics. We obtain the close form expression of tunneling time from a rectangular barrier by stationary…

Quantum Physics · Physics 2019-08-06 Mohammad Hasan , Bhabani Prasad Mandal

Quantum tunneling, a phenomenon which has no counterpart in classical physics, is the quantum-mechanical process by which a microscopic particle can transition through a potential barrier even when the energy of the incident particle is…

Mesoscale and Nanoscale Physics · Physics 2020-02-04 Raul J. Martin-Palma

A unified approach to the time analysis of tunnelling of nonrelativistic particles is presented, in which Time is regarded as a quantum-mechanical observable, canonically conjugated to Energy. The validity of the Hartman effect…

Quantum Physics · Physics 2009-11-07 Vladislav S. Olkhovsky , Erasmo Recami , Jacek Jakiel

Tunneling is an iconic concept that captures the peculiarity of quantum dynamics but, despite its ubiquity, questions remain. We focus on strong-field tunneling, which is vital to all attosecond science. We find an unexpected optical…

Quantum Physics · Physics 2025-04-22 Anne Weber , Margarita Khokhlova , Emilio Pisanty

We consider the time delay of massive, non-relativistic, one-dimensional particles due to a tunneling potential. In this setting the well-known Hartman effect asserts that often the sub-ensemble of particles going through the tunnel seems…

Quantum Physics · Physics 2009-07-13 J. Kiukas , A. Ruschhaupt , R. F. Werner

We study the relativistic quantum mechanical problem of a Dirac particle tunneling through two successive electrostatic barriers. Our aim is to study the emergence of the so-called \emph{Generalized Hartman Effect}, an effect observed in…

Quantum Physics · Physics 2011-11-10 José T. Lunardi , Luiz A. Manzoni

This is an analysis of some aspects of an old but still controversial topic, superluminal quantum tunneling. Some features of quantum tunneling described in literature, such as definition of the tunneling time and a frequency range of a…

Quantum Physics · Physics 2020-09-15 Moses Fayngold

We elaborate an interpretation of quantum physics founded on the hypothesis that quantum particles are conceptual entities playing the role of communication vehicles between material entities composed of ordinary matter which function as…

Quantum Physics · Physics 2011-05-13 Diederik Aerts

Quantum particles interacting with potential barriers are ubiquitous in physics, and the question of how much time they spend inside classically forbidden regions has attracted interest for many decades. Recent developments of new…

Quantum Physics · Physics 2021-07-06 Seyedmohammad Yusofsani , Miroslav Kolesik

In the First Part of this paper [that was submitted for pub. in 1991 and appeared in print in Phys. Reports 214 (1992) 339] we critically review the main theoretical definitions and calculations of the sub-barrier tunnelling and reflection…

Condensed Matter · Physics 2007-09-17 Vladislav S. Olkhovsky , Erasmo Recami

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…

Quantum Physics · Physics 2013-05-29 J. G. Muga , I. L. Egusquiza , J. A. Damborenea , F. Delgado

Integrating out virtual quantum fluctuations in an originally local quantum field theory results in an effective theory which is non-local. In this Letter we argue that tunneling of the 3rd kind - where particles traverse a barrier by…

Quantum Physics · Physics 2013-04-10 Simon A. Gardiner , Holger Gies , Joerg Jaeckel , Chris J. Wallace

This paper develops a geometrodynamic extension of Bohmian mechanics to describe quantum tunneling through a potential barrier, treating particle trajectories as geodesics in an Alcubierre-type spacetime. The model provides analytical…

Quantum Physics · Physics 2025-11-27 Said Lantigua , Jonas Maziero

By using techniques developed in quantum cosmology, it is found that a tunneling particle spends purely imaginary time on a barrier region. The {\it imaginary} time is associated with the stochastic acausal behaviour of a state, while the…

Quantum Physics · Physics 2008-04-03 Zhong Chao Wu

We introduce the concept of partial and full tunneling processes to explain the seemingly contradictory non-zero and vanishing tunneling times often reported in the literature. Our analysis starts by considering the traversal time of a…

Quantum Physics · Physics 2024-01-09 Philip Caesar M. Flores , Dean Alvin L. Pablico , Eric A. Galapon

The celebrated Hartman effect, according to which, the tunneling time through a opaque barrier is independent of the width of the barrier for a sufficiently thick barrier, is not well understood theoretically and experimentally till today.…

Quantum Physics · Physics 2021-07-20 Mohammad Hasan , Vibhav Narayan Singh , Bhabani Prasad Mandal
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