Quantum Mechanics as a Classical Theory XIII: The Tunnel Effect

We consider in what sense quantum tunnelling is associated with non-classical probabilistic behaviour. We use the Wigner function quasi-probability description of quantum states. We give a definition of tunnelling that allows us to say whether in a given scenario there is tunnelling or not. We prove that this can only happen if either the Wigner function is negative and/or a certain measurement operator which we call the tunnelling rate operator has a negative Wigner function...

A compact analysis of development and prospects in the study of the tunnelling evolution is given. A new systematization of various approaches to defining tunnelling times in the light of time as a quantum mechanical observable is proposed. The problem of superluminal group velocities, without violations of special relativity, is also taken in account. Then a particular attention is devoted to the presentation of new results on the analogy between particle and photon tunnelli...

We follow up the work, where in light of the Picard-Lefschetz thimble approach, we split up the real-time path integral into two parts: the initial density matrix part which can be represented via an ensemble of initial conditions, and the dynamic part of the path integral which corresponds to the integration over field variables at all later times. This turns the path integral into a two-stage problem where, for each initial condition, there exits one and only one critical p...

As a serious attempt for constructing a new foundation for describing micro-incidents from a local causal standpoint, I explained before that each micro-entity can be assumed to be composed of a probability field joined to a particle (called a particle-field or PF system) which is endowed with energy, having an objective character. In this essay, some odd quantum phenomena including the tunneling effect, the measurement problem and the EPR theorem are reexamined in detail fro...

A semiclassical method of complex trajectories for the calculation of the tunneling exponent in systems with many degrees of freedom is further developed. It is supplemented with an easily implementable technique, which enables one to single out the physically relevant trajectory from the whole set of complex classical trajectories. The method is applied to semiclassical transitions of a bound system through a potential barrier. We find that the properties of physically relev...

Recent developments in elementary quantum mechanics have seen a number of extraordinary claims regarding quantum behaviour, and even questioning internal consistency of the theory. These are, we argue, different disguises of what Feynman described as quantum theory's "only mystery".

We develop a new variant of the wave-packet analysis and solve the tunneling time problem for one particle. Our approach suggests an individual asymptotic description of the quantum subensembles of transmitted and reflected particles both at the final and initial stage of tunneling. We find the initial states of both subensembles, which are non-orthogonal. The latter reflects ultimately the fact that at the initial stage of tunneling it is impossible to predict whether a part...

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 {\it generalized Hartman effect}. In this letter, we point out a lack of mathematical rigour in the reasoning by which this effect was deduced about ten years ago. A mathematically rigorous treatment shows us that the tunneling time does inde...

The concepts of quantile position, trajectory, and velocity are defined. For a tunneling quantum mechanical wave packet, it is proved that its quantile position always stays behind that of a free wave packet with the same initial parameters. In quantum mechanics the quantile trajectories are mathematically identical to Bohm's trajectories. A generalization to three dimensions is given.

We consider simple models of tunneling of an object with intrinsic degrees of freedom. This important problem was not extensively studied until now, in spite of numerous applications in various areas of physics and astrophysics. We show possibilities of enhancement for the probability of tunneling due to the presence of intrinsic degrees of freedom split by weak external fields or by polarizability of the slow composite object.