Rydberg atom A** states perturbed by the force field of a neutral atom B are examined. The problem is reduced to studying the wave functions of the composite system and elucidating their fundamental differences from the Rydberg wave functions. The wave function of the Rydberg atom A**-atom B system is constructed using the finite-radius potential method with consideration for the short- and long-range interactions of the weakly bound Rydberg electron with the perturbing particle. The Na**-He system is considered as an example.
The authors study nonrelativistic particles and waves in N dimensions in a time-dependent potential V(r/l(t))/(l(t)) 2 , which describes a force field that expands and weakens as the scale factor l increases. If l 2 is a quadratic function of time, then, in a reference frame expanding with the system and employing clocks recalibrated to read a scaled time that depends on l(t), the classical and quantum evolutions can be described by a conservative Hamiltonian differing from the original one by an 'inertial' term quadratic in the position variables. The quantal 'expanding modes' form a complete set whose energies decrease and which carry current outwards from the centre of expansion. Non-equilibrium statistical ensembles can be constructed, expanding with the force field.
We show how a candidate mean-field amplitude can be constructed from the exact wave function of an externally forced
N-Boson system. The construction makes use of subsidiary
(N−1)-particle states which are propagated in time in addition to the true
N-particle state, but does not involve spontaneous breaking of the
U(1) symmetry associated with particle number conservation. Provided the flow in Fock space possesses a property which we call maximum stiffness, or
t-coherence, the candidate amplitude actually satisfies the time-dependent Gross-Pitaevskii equation, and then serves as macroscopic wave function of the forced
N-particle system. The general procedure is illustrated in detail by numerical calculations performed for the model of a driven bosonic Josephson junction, which allows one to keep track of all contributions which usually are subject to uncontrolled assumptions. These calculations indicate that macroscopic wave functions can persist even under conditions of strong forcing, but are rapidly destroyed upon entering a regime of chaotic dynamics. Our results provide a foundation for future attempts to manipulate, and actively control, macroscopic wave functions by means of purposefully designed force protocols.