Tunneling through a parabolic barrier viewed from Wigner phase space

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 initial state preparations and local potential barriers. It is manifestly causal and includes time-lag effects and quantum spreading. Specific features of quantum dynamics which disappear in the standard semi-classical approximation are reveal...

Asymptotic time evolution of a wave packet describing a non-relativistic particle incident on a potential barrier is considered, using the Wigner phase-space distribution. The distortion of the trasmitted wave packet is determined by two time-like parameters, given by the energy derivative of the complex transmission amplitude. The result is consistent with various definitions of the tunneling time (e.g. the B\"{u}ttiker-Landauer time, the complex time and Wigner's phase time...

Quantum mechanics predicts an exponentially small probability that a particle with energy greater than the height of a potential barrier will nevertheless reflect from the barrier in violation of classical expectations. This process can be regarded as tunneling in momentum space, leading to a simple derivation of the reflection probability.

In this paper, I present a mapping between representation of some quantum phenomena in one dimension and behavior of a classical time-dependent harmonic oscillator. For the first time, it is demonstrated that quantum tunneling can be described in terms of classical physics without invoking violations of the energy conservation law at any time instance. A formula is presented that generates a wide class of potential barrier shapes with the desirable reflection (transmission) c...

In this paper we review the basic results concerning the Wigner transform and then we completely solve the quantum forced harmonic/inverted oscillator in such a framework; eventually, the tunnel effect for the forced inverted oscillator is discussed.

We emphasize the fact the evolution of quantum states in the inverted oscillator (IO) is reduced to classical equations of motion, stressing that the corresponding tunnelling and reflexion coefficients addressed in the literature are calculated by considering only classically trajectories. The Wigner function formalism is employed to describe the IO classical dynamics, subsequently leading to the introduction of the Ambiguity function lying in the so-called Reciprocal phase s...

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...

The problem of wave packet tunneling from a parabolic potential well through a barrier represented by a power potential is considered in the case when the barrier height is much greater than the oscillator ground state energy, and the difference between the average energy of the packet and the nearest oscillator eigenvalue is sufficiently small. The universal Poisson distribution of the partial tunneling rates from the oscillator energy levels is discovered. The explicit expr...

We investigate quantum tunneling in smooth symmetric and asymmetric double-well potentials. Exact solutions for the ground and first excited states are used to study the dynamics. We introduce Wigner's quasi-probability distribution function to highlight and visualize the non-classical nature of spatial correlations arising in tunneling.

In this continuation paper we will address the problem of tunneling. We will show how to settle this phenomenon within our classical interpretation. It will be shown that, rigorously speaking, there is no tunnel effect at all.