Propagation and interaction of ultrashort electromagnetic pulses in nonlinear media with a quadratic-cubic nonlinearity

Propagation of extremely short unipolar pulses of electromagnetic field ("videopulses") is considered in the framework of a model in which the material medium is represented by anharmonic oscillators (approximating bound electrons) with quadratic and cubic nonlinearities. Two families of exact analytical solutions (with positive or negative polarity) are found for the moving solitary pulses. Direct simulations demonstrate that the pulses are very robust against perturbations. Two unipolar pulses collide nearly elastically, while collisions between pulses with opposite polarities and a small relative velocity are inelastic, leading to emission of radiation and generation of a small-amplitude additional pulse.Comment: 12 pages, 10 figure

Eigenstate Structure in Graphs and Disordered Lattices

We study wave function structure for quantum graphs in the chaotic and disordered regime, using measures such as the wave function intensity distribution and the inverse participation ratio. The result is much less ergodicity than expected from random matrix theory, even though the spectral statistics are in agreement with random matrix predictions. Instead, analytical calculations based on short-time semiclassical behavior correctly describe the eigenstate structure.Comment: 4 pages, including 2 figure

The Hypertriton in Effective Field Theory

Doublet Lambda d scattering and the hypertriton are studied in the framework of an effective field theory for large scattering lengths. As in the triton case, consistent renormalization requires a one-parameter three-body force at leading order whose renormalization group evolution is governed by a limit cycle. Constraining unknown parameters from symmetry considerations and the measured binding energy of the hypertriton, we calculate the low-energy phase shifts for doublet Lambda d scattering. For the low-energy parameters, we find a_{Lambda d}=(16.8^{+4.4}_{-2.4}) fm and r_{Lambda d}=(2.3 +/- 0.3) fm, where the errors are due to the uncertainty in the hypertriton binding energy. Since the hypertriton is extremely shallow, low-energy three-body observables in this channel are very insensitive to the exact values of the Lambda N low-energy parameters.Comment: 16 pages, revtex4, 5 ps figures, reference added, typos in appendix A correcte