Jump time and passage time: the duration of a quantum transition
| dc.creator | Schulman, L. S. | |
| dc.date | 2001-03-27 | |
| dc.date.accessioned | 2026-07-07T06:01:50Z | |
| dc.date.available | 2026-07-07T06:01:50Z | |
| dc.description | Under unitary evolution, systems move gradually from state to state. An unstable atom has amplitude in its original state after many lifetimes ($τ_L$). But in the laboratory, transitions seem to go instantaneously, as suggested by the term "quantum jump." The problem studied here is whether the "jump" can be assigned a duration, in theory and in experiment. Two characteristic times are defined, jump time ($τ_J$) and passage time ($τ_P$). Both use Zeno time, $τ_Z$, defined in terms of $H$ and its initial state as $τ_Z \equiv \hbar/\sqrt{<ψ| (H-E_ψ)^2 |ψ>}$, with $E_ψ\equiv <ψ|H|ψ>$. $τ_J$ is defined in terms of the time needed to slow (à la the quantum Zeno effect) the decay: $τ_J \equiv τ_Z^2/τ_L$. It appears in several contexts. It is related to tunneling time in barrier penetration. Its inverse is the bandwidth of the Hamiltonian, in a time-energy uncertainty principle. $τ_J$ is also an indicator of the duration of the quadratic decay regime in both experiment and in numerical calculations (cf. Fig.~2 of PRA 57,1509 (1998).) The passage time, $τ_P$, arises from unitary evolution sans interpretation. It is based on a bound of Fleming (Nuov. Cim. 16 A, 232 (1973)): for any $H$ and $ψ$ a system cannot evolve to a state orthogonal to $ψ$ for $t< τ_P \equiv πτ_Z/2$. By including apparatus in $H$, $τ_P$ limits the observation of decay according to the quantum measurement ideas proposed in "Time's Arrows and Quantum Measurement," Cambridge U. Press, 1997, thereby allowing an experimental test of these ideas. | |
| dc.description | To appear in: Time in Quantum Mechanics, edited by J. G. Muga, R. Sala Mayato, and I. L. Egusquiza. Springer-Verlag | |
| dc.identifier | https://arxiv.org/abs/quant-ph/0103151 | |
| dc.identifier | http://arxiv.org/abs/quant-ph/0103151 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/89401 | |
| dc.subject | Quantum Physics | |
| dc.title | Jump time and passage time: the duration of a quantum transition | |
| dc.type | text |