Chaos in Laser-matter Interactions

2-torus action-angle variables amplitude approximation atom attractor background modes broadband Casperson cavity chaotic behavior chaotic regime classical model computed consider correlations corresponding curve defined dependence on initial dimension discrete mapping discussed distribution dynamics eigenvalues equations of motion ergodic hypothesis example experimental field Fourier frequency function Hamiltonian systems Hénon-Heiles homogeneously broadened implies initial conditions instability integrable iterates kicked pendulum laser Lett limit cycle linear logistic map Lorenz model Lyapunov exponent Maxwell-Bloch equations molecule nonlinear numerical experiments obtained one-dimensional optical bistability oscillation parameter period doubling period doubling route perturbation phase space Phys Poincare power spectrum predicted pumped mode quantum chaos quantum mechanically quantum-mechanical quasiperiodic random resonance overlap route to chaos Schrödinger equation separatrices sequence shown in Figure shows single-mode SMHBL solution spectra stable fixed point steady-state stochastic excitation surface of section theorem theory trajectories transformation transition two-state values variables vector vibrational Xn+1