Related papers: Hartman effect from layered $PT$-symmetric system
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.…
We calculate the time taken by a wave packet to tunnel through a series of complex barrier potentials using stationary phase method to show its saturation (Hartman-Fletcher effect) with number of barriers in various situations. We…
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…
With reference to a particle tunneling through two successive barriers, it seems to have been generally accepted that the tunneling time does not depend on the separation distance between the barriers. This phenomenon has been called the…
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…
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…
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…
We calculate the time taken by a wave packet to travel through a classically forbidden locally periodic rectangular potential in space fractional quantum mechanics (SFQM). We obtain the close form expression of tunneling time from such a…
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…
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…
The mechanism of superluminal traversal time through a potential well or potential barrier is investigated from the viewpoint of interference between multiple finite wave packets, due to the multiple reflections inside the well or barrier.…
In this paper we calculate the analytic expression of the phase time for the scattering of an electron off a complex square barrier. As is well known the (negative) imaginary part of the potential takes into account, phenomenologically, the…
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…
In this work we study the behaviour of Wigner phase delay time for tunneling in the reflection mode. Our system consists of a circular loop connected to a single wire of semi-infinite length in the presence of Aharonov-Bohm flux. We…
I show that the MacColl-Hartman effect, namely, the saturation of the group delay time of sub-barrier quantum tunneling as a function of the barrier width, comes from the saturating behavior of a more fundamental concept - the phase of the…
We study the phenomenon of one-dimensional non-resonant tunnelling through two successive potential barriers, separated by an intermediate free region R, by analyzing the relevant solutions to the Schroedinger equation. We find that the…
Tunneling delay times of wavepackets in quantum mechanical penetration of rectangular barriers have long been known to show a perplexing independence with respect to the width of the barrier. This also has relevence to the transmission of…
The phenomenon of quantum tunneling remains a fascinating and enigmatic one, defying classical notions of particle behavior. This paper presents a novel theoretical investigation of the tunneling phenomenon, from the viewpoint of Hartman…
We use the method of Laplace transformation to determine the dynamics of a wave packet that passes a barrier by tunneling. We investigate the transmitted wave packet and find that it can be resolved into a sequence of subsequent wave…
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…