Existence and nonexistence of an intrinsic tunneling time

TL;DR

This paper investigates the concept of tunneling time in quantum mechanics, showing that near the energy continuum's branch point, tunneling time depends on wave packet width, challenging the notion of an intrinsic tunneling time.

Contribution

The authors define a tunneling time using a time operator and analyze its dependence on energy and wave packet properties, revealing the nonexistence of an intrinsic tunneling time.

Findings

Tunneling time is affected by resonances and branch points.

Near the branch point, tunneling time depends on wave packet width.

No intrinsic tunneling time exists near the energy continuum edge.

Abstract

Using a time operator, we define a tunneling time for a particle going through a barrier. This tunneling time is the average of the phase time introduced by other authors. In addition to the delay time caused by the resonances over the barrier, the present tunneling time is also affected by the branch point at the edge of the energy continuum. We find that when the particle energy is near the branch point, the tunneling time becomes strongly dependent on the width of the incoming wave packet, which implies that there is no intrinsic tunneling time. This effect is related to the quantum uncertainty in the particle's momentum.