We study the nonequilibrium dynamics of relaxation and dressing of a mobile impurity with velocity $v$, suddenly immersed, or quenched, into a zero-temperature homogeneous Bose-Einstein condensate. A many-body generalization of Weisskopf-Wigner theory is implemented to obtain the impurity fidelity, reduced density matrix and entanglement entropy. The dynamics depends crucially on the Mach number $\beta =v/c$, with $c$ the speed of sound of superfluid phonons, and features many different timescales. Quantum Zeno behavior at early time is followed by nonequilibrium dynamics determined by Cerenkov emission of long-wavelength phonons for $\beta >1$ with a relaxation rate ${\mathrm{\Gamma }}_p\propto {(\beta -1)}^3$. The polaron dressing dynamics slows down as $\beta \to 1$ and is characterized by power laws $t^{-\alpha }$ with exponents $\alpha =3/2,1/2,2$ for $\beta >1,=1,<1,$ respectively. The asymptotic entanglement entropy features a sharp discontinuity, and the residue features a cusp at $\beta =1$. These nonequilibrium features suggest universal dynamical critical phenomena near $\beta \simeq 1$ and are a direct consequence of the linear dispersion relation of long-wavelength superfluid phonons. We conjecture on the emergence of an asymptotic dynamical attractor with $\beta \le 1$.

The dynamics of multidimensional wave packet motion on nonadiabatically coupled electronic potential surfaces is explored by numerically exact time¿dependent quantum mechanics and by the time¿dependent Hartree grid (TDHG) approximation. Excellent agreement is found between the TDHG and the exact evolution of the wave packet; in particular, the approximation yields accurate total cross sections for electronic absorption, excitation profiles for resonance Raman scattering, and partial cross sections for photofragmentation in a two degree of freedom model of direct dissociation (which is qualitatively related to experimentally observed processes in methyl halides and ICN).@ American Institute of PhysicsThis work was supported by a grant from the National Science Foundation, the Petroleum Research Fund, the Alfred P. Sloan Foundation, and the Camille and Henry Dreyfus Foundation. J. C.-M. gratefully acknowledges a grant from the Ministerio de Educacion y Ciencia of SpainPeer Reviewe