Related papers: Superluminal effects for quantum tunneling through…
We investigate the tunnelling zone V0 < E < V0+m for a one-dimensional potential within the Dirac equation. We find the appearance of superluminal transit times akin to the Hartman effect.
The tunneling effect of a periodic potential with an asymmetric twin barrier per period is calculated using the instanton method. The model is derived from the Hamiltonian of a small ferromagnetic particle in an external magnetic field…
Two rectangular models described by the one-dimensional Schroedinger equation with sharply localized potentials are suggested. The potentials have a multi-layer thin structure being composed from adjacent barriers and wells. Their peculiar…
Time-dependent analytical solutions to Schr\"{o}dinger's equation with quantum shutter initial conditions are used to investigate the issue of the tunneling time of forerunners in rectangular potential barriers. By using a time-frequency…
Quantum mechanical tunneling across smooth double barrier potentials modeled using Gaussian functions, is analyzed numerically and by using the WKB approximation. The transmission probability, resonances as a function of incident particle…
Experiments have shown that individual photons penetrate an optical tunnel barrier with an effective group velocity considerably greater than the vacuum speed of light. The experiments were conducted with a two-photon parametric…
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 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…
We show that a short-range strong repulsive (contact) interaction between the particles in the barrier may change the statistics of two-particle tunnelling. In the case of a resonance of a width $\Gamma$, the effect would be observed if the…
It is shown that in the case of the one-particle one-dimensional scattering problem for a given time-independent potential, for each state of the whole quantum ensemble of identically prepared particles, there is an unique pair of…
Others have solved the Schr\"odinger equation for a one-dimensional model having a square potential barrier in free-space by requiring an incident and a reflected wave in the semi-infinite pre-barrier region, two opposing waves in the…
In the Hartle-Hawking ``no boundary'' approach to quantum cosmology, a real tunneling geometry is a configuration that represents a transition from a compact Riemannian spacetime to a Lorentzian universe. I complete an earlier proof that in…
We show that scattering a quantum particle on a one-dimensional potential barrier as well as scattering the electromagnetic wave on a quasi-one-dimensional layered structure (both represent scattering problems with one 'source' and two…
Experiments done in the early 1990's produced a surprising result: that single photons pass through a photonic tunnel barrier with a group velocity faster than the vacuum speed of light. Subsequent experiments with classical pulses have…
We consider a phase-coherent system of two parallel quantum wires that are coupled via a tunneling barrier of finite length. The usual perturbative treatment of tunneling fails in this case, even in the diffusive limit, once the length L of…
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…
We study the tunnelling trough a potential barrier of the system of two quantum correlated particles. The system is considered in one dimension. The interaction with the barrier and between particles is approximated by $\delta$-potentials.…
The particle approach to one-dimensional potential scattering is applied to non relativistic tunnelling between two, three and four identical barriers. We demonstrate as expected that the infinite sum of particle contributions yield the…
Starting with the equivalence of the rest energy of a particle to an amount of the radiant energy characterized by a frequency, in addition to the usual relativistic transformation rules leading to the wave-particle duality, we investigate…
Time dependence for barrier penetration is considered in the phase space. An asymptotic phase-space propagator for nonrelativistic scattering on a one - dimensional barrier is constructed. The propagator has a form universal for various…