RESUMO
Within the de Broglie-Bohm theory, we numerically study a generic two-dimensional anharmonic oscillator including cubic and quartic interactions in addition to a bilinear coupling term. Our analysis of the quantum velocity fields and trajectories reveals the emergence of dynamical vortices. In their vicinity, fingerprints of chaotic behavior such as unpredictability and sensitivity to initial conditions are detected. The simultaneous presence of the off-diagonal -kxy and nonlinear terms leads to robust quantum chaos very analogous to its classical version.
RESUMO
The q-exponential form eqx≡[1+(1-q)x]1/(1-q)(e1x=ex) is obtained by optimizing the nonadditive entropy Sq≡k1-∑ipiqq-1 (with S1=SBG≡-k∑ipilnpi, where BG stands for Boltzmann-Gibbs) under simple constraints, and emerges in wide classes of natural, artificial and social complex systems. However, in experiments, observations and numerical calculations, it rarely appears in its pure mathematical form. It appears instead exhibiting crossovers to, or mixed with, other similar forms. We first discuss departures from q-exponentials within crossover statistics, or by linearly combining them, or by linearly combining the corresponding q-entropies. Then, we discuss departures originated by double-index nonadditive entropies containing Sq as particular case.