Traversal-time wave-function analysis of resonance and nonresonance tunneling

Attosecond chronoscopy of photoemission

“…Accounts of this debate can be found in a large number of reviews (see de Carvalho and Nussenzveig, 2002;Hauge and Støvneng, 1989;Landauer and Martin, 1994;Olkhovsky et al, 2004;Winful, 2006;Muga et al, 2007;Choi and Jordan, 2013). As a well-defined operator whose eigenvalue would correspond to the travel time through the classically forbidden region could not be identified, unconventional operational descriptions have been put forward, such as complex travel time based on a Feynman path integral formulation (Sokolovski et al, 1994) or contextual values replacing conventional eigenvalues of a self-adjoined operators for so-called weak measurements (Choi and Jordan, 2013). Closely related is the notion of a Larmor clock (Baz', 1967a,b;Büttiker, 1983) which yields, in general, two different precession times which can be interpreted in special cases as the real and imaginary parts of a complex time (Sokolovski et al, 1994).…”

“…As a well-defined operator whose eigenvalue would correspond to the travel time through the classically forbidden region could not be identified, unconventional operational descriptions have been put forward, such as complex travel time based on a Feynman path integral formulation (Sokolovski et al, 1994) or contextual values replacing conventional eigenvalues of a self-adjoined operators for so-called weak measurements (Choi and Jordan, 2013). Closely related is the notion of a Larmor clock (Baz', 1967a,b;Büttiker, 1983) which yields, in general, two different precession times which can be interpreted in special cases as the real and imaginary parts of a complex time (Sokolovski et al, 1994). The Larmor clock exploiting the expectation value of the spin projection as "hand" can be viewed as a realization of a quantum clock (Landauer and Martin, 1994).…”

Beyond the Schrödinger Equation: Quantum Motion with Traversal Time Control

“…Z2`e xp͓2͑k 2 k 0 ͒ 2 ͞Dk 2 2 ik 2 t͞2M 1 ikx͔ dk (10) from some t I , when it is to the left of the region of interest V, to such t F by which it will have crossed V. We ask next for the duration spent by the wave packet in the region. Setting C I ͑x͒ C͑x, t I ͒ in Eq.…”

Parabolic Connection Formulae in Quantum Mechanics

“…Note in this respect that recent advances [7] in understanding the nature of tunnelling times for rectangular barriers were just possible due to the known structure of tunnelling states for such simple barriers. However, while being simple from the standpoint of mathematical description, rectangular barriers represent an extreme quantum case, which makes the physical analysis of tunnelling very difficult [8]. Further progress in this field requires a detailed investigation of tunnelling states for smooth potential barriers which have a continuous connection onto the classical regime.…”