Imaginary past of a quantum particle moving on imaginary time

Abstract

The analytical continuation of classical equations of motion to complex times suggests that a tunnelling particle spends in the barrier an imaginary duration $i|\mathcal{T}|$. Does this mean that it takes a finite time to tunnel, or should tunnelling be seen as an instantaneous process? It is well known that examination of the adiabatic limit in a small additional AC field points towards $|\mathcal{T}|$ being the time it takes to traverse the barrier. However, this is only half the story. We probe the transmitted particle's history, and find that it "remembers" very little of the field's past behaviour, as if the transit time were close to zero. The ensuing contradiction suggests that the question is ill-posed, and we explain why.

9 pages, 4 figures

References in corpus (6)

• Experimental evidence for Wigner's tunneling time
• Unified time analysis of photon and (nonrelativistic) particle Tunnelling, and the Superluminal group-velocity problem
• An even simpler understanding of quantum weak values
• The Salecker-Wigner-Peres clock, Feynman paths, and a tunnelling time that should not exist
• Speed-up and slow-down of a quantum particle
• Quantum measurements and delays in scattering by zero-range potentials