External-field-modified entropic exchange in confined quantum systems: static versus time-dependent electric fields

We review how external electric fields reshape the information content of spatially confined atoms, and we contrast the response to a uniform static field with that to a monochromatic, time-dependent laser field. The central quantities are the Shannon entropies in position and momentum space, Sr and Sp, and their sum ST = Sr +Sp, which obeys the BBM bound. Using the confined hydrogen atom (CHA) and the particle in a spherical box (PISB), its tight confinement limit, as reference systems, we first show that the field-free total entropy of the CHA depends non-monotonically on the confining radius whereas that of the PISB is strictly scale invariant. We then present Stark maps of the entropies for the ten lowest m = 0 levels at the confining radius of 6 a.u. The ground-state polarizability is reduced from the free-atom value 4.5 a.u. to 4.06 a.u. in the CHA but is 46.8 a.u. in the PISB, and the entropic response of the two systems differs correspondingly.