Superadiabatic tracking of quantum evolution

The adiabatic quantum evolution of a two-state system without energy-level crossings is an example of the Stokes phenomenon. In the latter, a small (subdominant) exponential is an asymptotic expansion appears when a Stokes line is crossed; truncating the dominant asymptotic series at its least term causes the multiplier of the subdominant term to rise in a smooth, compact and universal manner across the Stokes line. In quantum evolution this corresponds to a smooth transition, universal in form, between 'superadiabatic' basis states (high-order WKB approximate solutions of the time-dependent Schrodinger equation). The authors give a numerical demonstration of this previously predicted universality by constructing, for two Hamiltonians, the superadiabatic quantum bases asymptotic to the actual evolving state. Universality when a Stokes line is crossed is seen in the changing probability that the system makes a transition away from the superadiabatic state, and occurs at that order of superadiabatic approximation corresponding to truncating the asymptotic series at its least term.