FTL Travel under the Quantum Harmonic Resonance Framework (QHRF

Europhysics Letters (EPL), 2005

An explicit expression is obtained for the phase-time corresponding to tunneling of a (non-relativistic) particle through two rectangular barriers, both in the case of resonant and in the case of non-resonant tunneling. It is shown that the behavior of the transmission coefficient and of the tunneling phase-time near a resonance is given by expressions with "Breit-Wigner type" denominators. By contrast, it is shown that, when the tunneling probability is low (but not negligible), the non-resonant tunneling time depends on the barrier width and on the distance between the barriers only in a very weak (exponentially decreasing) way: This can imply in various cases, as well known, the highly superluminal tunneling associated with the so-called "generalized Hartman Effect": but we are now able to improve and modify the mathematical description of such an effect, and to compare more in detail our results with the experimental data for non-resonant tunneling of photons. Finally, as a second example, the tunneling phase-time is calculated, and compared with the available experimental results, in the case of the quantum-mechanical tunneling of neutrons through two barrier-filters at the resonance energy of the set-up. Our analysis appears to explain satisfactorily both sets of experiments.

Research Advances in Quantum Dynamics, 2016

The physics of dynamic resonant tunneling is investigated. First, the resonant tunneling effect through an opaque barrier via a delta-function well is illustrated. Then, it is shown that, even in the adiabatic regime, where the dynamics can be governed by an analytic solution, the particle can be activated to higher energies. If the well varies quickly enough that the particle cannot escape from the well during the energetic elevation, the activation can be enhanced, as was anticipated by Azbel. However, and this is the main result of this work, the quasi-bound state of the well can even "reduce" the activation. In fact, because the resonant energy of the well matches twice the incoming particle's energy, and if the contribution to the wave function from both parts destructively interferes, then the particle cannot dwell in the well and activation is suppressed. This effect can be utilized in frequency-controlled transistors, and it is even speculated that it may explain the reason that humans can distinguish between tens of thousands of different odors with merely few hundreds of odor receptors. Lastly, the short time dynamics of a very fast perturbative well is also discussed.

Physical Review A, 2003

Physics Letters B, 1985

In asymmetric double-well potentaals, it can be tacatly assumed that a wave functmn m the hagher-energy well (false vacuum) wall always tunnel to the lower well, gwen enough Ume However, m general this as not true Whether a state can sxgmficantly tunnel to the true vacuum is a very sensatave functton of the shape of the potentaal We dlustrate tlus vath analytac and numerical examples Thus, ff there as not dlsslpalaon or coupling to other modes, a wave functmn may not tunnel

The phenomenon of one-dimensional non-resonant tunnelling is analyzed through two or more successive (opaque) potential barriers, separated by intermediate free regions R, just by exploiting the relevant solutions to the Schroedinger equation. The total traversal time has been shown by us to be independent not only of the barrier widths (the so-called 'Hartman effect'), but also of the R-widths: so that the effective group velocity in the regions R, between two successive barriers, can be regarded as practically infinite. Such a prediction has been theoretically confirmed and generalized (as well as interpreted in terms of 'super-oscillations') by Aharonov et al. A recent experiment by Longhi et al. supported the predictions by considering two successive gratings in an optical fibre, that is, by having recourse to two 'classical barriers' (which allow simulating the tunnelling, due to the known formal identity between the Schro¨dinger and the Helmholtz equation). journal of modern optics, 15 april-10 may 2004 vol. 51, no. 6-7, 913-923 914 E. Recami 916 E. Recami

In this work we discuss how the occurrence of resonant tunneling through a one-dimensional (1D) double barrier involves some interesting phenomena which have so far been overlooked. The effect of an externally applied electric field is considered, and it is shown that with fully symmetrical barriers it leads to weaker resonances than otherwise possible. Furthermore, the time required for resonance to be fully established is discussed, and it is shown that, depending on the barrier transmission coefficients and experimental conditions, it can be exceedingly long, thus contributing to a reduction of resonance effects on the usual experimental time scale. We alsa show that resonant tunneling under the usual experimental conditions implies carrier trapping, hence a buildup of space charge available for modifying the potential-energy barrier. Different current behaviors then result from the inherent feedback mechanism. The effects of temperature an the measured current are finally discussed.

Physical Review Letters, 2015

We present the first experimental observation of resonance-assisted tunneling, a wave phenomenon, where regular-to-chaotic tunneling is strongly enhanced by the presence of a classical nonlinear resonance chain. For this we use a microwave cavity made of oxygen free copper with the shape of a desymmetrized cosine billiard designed with a large nonlinear resonance chain in the regular region. It is opened in a region, where only chaotic dynamics takes place, such that the tunneling rate of a regular mode to the chaotic region increases the line width of the mode. Resonance-assisted tunneling is demonstrated by (i) a parametric variation and (ii) the characteristic plateau and peak structure towards the semiclassical limit.

Physical Review A, 1997

We consider an analytic solution of the time-dependent Schrödinger equation with the initial condition (x,0)ϭexp(ikx) along ϪϱϽxϽ0 to investigate the time evolution for xϾ0 of the wave function in a double-barrier resonant structure at resonance. For typical parameters of the structure we find that the singleresonance approximation is valid from a few tenths of the corresponding lifetime onward. Very short times require the contribution of many far away resonances. The buildup time along the internal region takes a few lifetimes. At birth the transmitted wave front is blurred; however, for long times it becomes well defined and moves with classical velocity yielding a delay time Ϸ2ប/⌫ as in the stationary-phase treatment.

Quantum tunnelling or tunneling (see spelling differences) refers to the quantum mechanical phenomenon where a particle tunnels through a barrier that it classically could not surmount. This plays an essential role in several physical phenomena, such as the nuclear fusion that occurs in main sequence stars like the Sun. It has important applications to modern devices such as the tunnel diode, quantum computing, and the scanning tunnelling microscope. The effect was predicted in the early 20th century and its acceptance, as a general physical phenomenon, came mid-century. Tunnelling is often explained using the Heisenberg uncertainty principle and the wave-particle duality of matter. Pure quantum mechanical concepts are central to the phenomenon, so quantum tunnelling is one of the novel implications of quantum mechanics.

Physical Review B, 1984

In this work we discuss how the occurrence of resonant tunneling through a one-dimensional (1D) double barrier involves some interesting phenomena which have so far been overlooked. The effect of an externally applied electric field is considered, and it is shown that with fully symmetrical barriers it leads to weaker resonances than otherwise possible. Furthermore, the time required for resonance to be fully established is discussed, and it is shown that, depending on the barrier transmission coefficients and experimental conditions, it can be exceedingly long, thus contributing to a reduction of resonance effects on the usual experimental time scale. We alsa show that resonant tunneling under the usual experimental conditions implies carrier trapping, hence a buildup of space charge available for modifying the potential-energy barrier. Different current behaviors then result from the inherent feedback mechanism. The effects of temperature an the measured current are finally discussed.