Quantum Tunneling in the Wigner Representation

Abstract

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 revealed. The propagator may be applied to calculation of the final momentum and coordinate distributions, for particles transmitted through or reflected from the potential barrier, as well as for elucidating the tunneling time problem.

18 pages, LATEX, no figures

References in corpus (6)

• How much time does a tunneling particle spend in the barrier region?
• Wigner Functional Approach to Quantum Field Dynamics
• Analytical properties of scattering amplitudes in one-dimensional quantum theory
• Complex-time path-integral formalism for quantum tunneling
• Semiclassical Scattering in Yang-Mills Theory
• On the concept of the tunneling time

Cited by in corpus (6)

• Time-of-arrival distribution for arbitrary potentials and Wigner's time-energy uncertainty relation
• Semiclassical propagation of Wigner functions
• Tunnelling necessitates negative Wigner function
• Time-of-arrival probabilities and quantum measurements: II Application to tunneling times
• The Response Field and the Saddle Points of Quantum Mechanical Path Integrals
• Salecker-Wigner-Peres quantum clock applied to strong-field tunnel ionization