Atop-the-barrier localization in periodically driven double wells: A minimization of information entropic sums in conjugate spaces

摘要

The spatio-temporal localization of a systemin the presence of an oscillating electric field for a symmetric double-well potential is examined via numerical simulations of the time-dependent Schrodinger equation. For an initial state with equal probability densities in both the wells, stabilized localization atop the barrier can be achieved on a periodic high-frequency driving. The barrier localization is characterized using Shannon information entropies in position and momentum spaces, defined as S-p = - integral vertical bar psi vertical bar(2) In vertical bar psi vertical bar(2) dx and S-gamma = - integral vertical bar phi vertical bar(2) In vertical bar phi vertical bar(2) dp, where psi and phi refer to position and momentum space wave functions, respectively. The information entropy sum, S-rho + S-gamma, goes through a minimum indicating the formation of the barrier-localized state, when the peak intensity of the oscillating field is reached. The generalized uncertainty via the Bialynicki-Birula-Mycielski inequality (S-rho + S-gamma >= 1 + ln pi) is saturated upon this minimization. This serves as a signature of the formation of the barrier-atop localized state, in terms of Shannon entropies of measurable densities.