Poster: Mapping parameter dependence for tunneling and entanglement dynamics in the kicked top

We study the Quantum Kicked Top (QKT) as a function of nonlinearity K. Using adiabatic evolution of the parameter, we uncover the phenomenon even when the original spectrum is recovered the states have been shuffled(also termed exotic quantum holonomy). Further, we use measures of spectral bunching and averaged inverse participation ratios across phase-space to identify K values that yield unusual many-body quantum dynamics. In particular, for the 4 qubit QKT we find unusual dynamics for both linear entropy and tunneling at non-obvious K values 4π/3, 2π, ~2.76π, 4π corresponding to sharply-defined local minima in K for spectral bunching. We also see differing K-periodicities for the 4 qubit QKT with the period of 4π for the linear entropy, 8π for measures of tunneling and spectral bunching, and 16π for the adiabatically unrave led spectrum itself. Finally, we show that with increasing number of qubits n, the density of these local minima increases along with the K period, nonlinearly accelerating the number of K values with these degeneracies. We discuss the N → infinity limit.