RESONANCE AND REVIVALS I. QUANTUM ROTOR AND INFINITE-WELL DYNAMICS

Author Institution: Department of Physics, University of Arkansas, Fayetteville, AR 72701; Microelectronics-Photonics, University of Arkansas, Fayetteville, AR 72701Space-time structure of exploding quantum wave packets exhibit a resonate beating phenomena. Such "super-beats" were called "revivals" by J. H. Eberly in connection with numerical studies of Jaynes-Cummings models of atom-in-cavity quantum electrodynamics. The term revival refers to the ability of an initial localized wave packet to dramatically "un-explode" after a period of decoherent quiescence and then more-or-less repeat the process. Analogous revival dynamics can be seen most clearly in a simple 1D rotor or Bohr-ring atomic model, and this provides what is perhaps the clearest understanding so far of the underlying wave mechanics. In this model the main revival and its multitude of sub-revivals repeat perfectly. For this model it is possible predict the space-time location of each revival peak and rank its coherence using a Farey-sum formula so named after a geologist who studied tidal resonance in the early 1800's. Moreover, it is possible to calculate the phases of individual revival peaks using overlapping Cyclic (Cn) group character tables. The resulting interference patterns clearly exhibit all factors of each integer n below a certain Farey-threshold determined by spatial width of the initial packet. A subsequent talk will discuss the revivals observed in Morse oscillator vibrational potential models

RESONANCE AND REVIVALS II. MORSE OSCILLATOR AND DOUBLE MORSE WELL DYNAMICS

Author Institution: Microelectronics-Photonics Program, University of Arkansas, Fayetteville, AR 72701; Department of Physics, University of Arkansas, Fayetteville, AR 72701Analytical solutions for the Morse oscillator are applied to investigate the quantum resonance and revivals that occur in position and momentum spaces. The anharmonicity of this oscillator appears to cause interesting space-time phenomena that includes relatively simple Farey-sum revival structure. Furthermore, a simple sum of two Morse oscillators leads to a double Morse well whose geometric symmetry provides a quasi-analytical solution. The resonant beats and revivals of wavepacket propagation involve quantum tunneling between the double Morse wells and mode dynamics local to each well. Such quantum dynamic systems may have applications for quantum information processing and quantum computing

EFFECTS OF SUPERFINE STRUCTURE LEVEL-CLUSTER CROSSING ON AMPLITUDE AND PHASE REVIVAL DYNAMICS: COMPARING TETRAHEDRAL AND OCTAHEDRAL SPHERICAL ROTORS WITH ICOSAHEDRAL ROTORS

Author Institution: Department of Physics, University of Arkansas, Fayetteville, AR; 72701Quantum revivals or "super-beats" are predicted to occur when angularly localized symmetric tops states are free to evolve. Similar types of dynamics are expected to involve spherical top superfine and superhyperfine level clusters that are labeled by induced representations of octahedral or tetrahedral symmetries for $XY_4$, $XY_6$, and related molecules. A considerably more complicated set of effects are expected for the icosahedral molecule $C_ {60}$ and its related isotopomers. An important difference for icosahedral symmetry is that its superfine splitting ratios are most-irrational (Golden-ratio) fractions that preclude perfect Poincare recurrence of quantum phase while the octahedral splitting ratios are rational