Tunneling Time Distribution by means of Nelson's Quantum Mechanics and Wave-Particle Duality

We discuss the propagation of wave packets through interacting environments. Such environments generally modify the dispersion relation or shape of the wave function. To study such effects in detail, we define the distribution function P_{X}(T), which describes the arrival time T of a packet at a detector located at point X. We calculate P_{X}(T) for wave packets traveling through a tunneling barrier and find that our results actually explain recent experiments. We compare ou...

We analyze the effects of inelastic scattering on the tunneling time theoretically, using generalized Nelson's quantum mechanics. This generalization enables us to describe quantum system with optical potential and channel couplings in a real time stochastic approach, which seems to give us a new insight into quantum mechanics beyond Copenhagen interpretation.

We propose a general expression for the probability distribution of real-valued tunneling times of a localized particle, as measured by the Salecker-Wigner-Peres quantum clock. This general expression is used to obtain the distribution of times for the scattering of a particle through a static rectangular barrier and for the tunneling decay of an initially bound state after the sudden deformation of the potential, the latter case being relevant to understand tunneling times i...

Tunneling, transport of particles through classically forbidden regions, is a pure quantum phenomenon. It governs numerous phenomena ranging from single-molecule electronics to donor-acceptor transition reactions. The main problem is the absence of a universal method to compute tunneling time. This problem has been attacked in various ways in the literature. Here, in the present work, we show that a statistical approach to the problem, motivated by the imaginary nature of tim...

In this article, we propose a resolution to the paradox of apparent superluminal velocities for tunneling particles, by a careful treatment of temporal observables in quantum theory and through a precise application of the duality between particles and waves. To this end, we employ a new method for constructing probabilities associated to quantum time measurements that provides an explicit link between the tunneling time of particles and the associated quantum fields. We demo...

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 experimental techniques revived the issue and ignited a debate with often contradictory results. This motivates the present study of an exactly solvable model for quantum tunneling induced by a strong field. We show that the tunneling dynamics can d...

There remains the old question of how long a quantum particle takes to tunnel through a potential barrier higher than its incident kinetic energy. In this article a solution of the question is proposed on the basis of a realistic explanation of quantum mechanics. The explanation implies that the tunneling particle has a certain chance to borrow enough energy from self-interference to high-jump over the barrier. The root-mean-square velocity and the effective tunneling time of...

A simple model of a quantum clock is applied to the old and controversial problem of how long a particle takes to tunnel through a quantum barrier. The model I employ has the advantage of yielding sensible results for energy eigenstates, and does not require the use of time-dependant wave packets. Although the treatment does not forbid superluminal tunneling velocities, there is no implication of faster-than-light signaling because only the transit duration is measurable, not...

The phenomenon of quantum tunneling is reviewed and an overview of applying approximate methods for studying this effect is given. An approach to a time-dependent formalism is proposed in one dimension and generalized to higher dimensions. Some physical examples involving the resulting wavefunction which is determined are presented.

In this paper we examine critically and in detail some existing definitions for the tunnelling times, namely: the phase-time; the centroid-based times; the Buttiker and Landauer times; the Larmor times; the complex (path-integral and Bohm) times; the dwell time, and finally the generalized (Olkhovsky and Recami) dwell time, by adding also some numerical evaluations. Then, we pass to examine the equivalence between quantum tunnelling and "photon tunnelling" (evanescent waves p...