Collective atomic recoil motion in short-pulse multi-matter-optical wave mixing

An analytical perturbation theory of short-pulse, matter-wave superradiant scatterings is presented. We show that Bragg resonant enhancement is incapacitated and both positive and negative order scatterings contribute equally. We further show that propagation gain is small and scattering events primarily occur at the end of the condensate where the generated field has maximum strength, thereby explaining the apparent ``asymmetry" in the scattered components with respect to the condensate center. In addition, the generated field travels near the speed of light in a vacuum, resulting in significant spontaneous emission when the one-photon detuning is not sufficiently large. Finally, we show that when the excitation rate increases, the generated-field front-edge-steepening and peak forward-shifting effects are due to depletion of the ground state matter wave.Comment: This manuscript was submitted for publication in Nov., 200

Bosonization and entanglement spectrum for one-dimensional polar bosons on disordered lattices

The extended Bose-Hubbard model subjected to a disordered potential is predicted to display a rich phase diagram. In the case of uniform random disorder one finds two insulating quantum phases -- the Mott-insulator and the Haldane insulator -- in addition to a superfluid and a Bose glass phase. In the case of a quasiperiodic potential further phases are found, eg the incommensurate density wave, adiabatically connected to the Haldane insulator. For the case of weak random disorder we determine the phase boundaries using a perturbative bosonization approach. We then calculate the entanglement spectrum for both types of disorder, showing that it provides a good indication of the various phases.Comment: Submitted to NJ

Rank-frequency relation for Chinese characters

We show that the Zipf's law for Chinese characters perfectly holds for sufficiently short texts (few thousand different characters). The scenario of its validity is similar to the Zipf's law for words in short English texts. For long Chinese texts (or for mixtures of short Chinese texts), rank-frequency relations for Chinese characters display a two-layer, hierarchic structure that combines a Zipfian power-law regime for frequent characters (first layer) with an exponential-like regime for less frequent characters (second layer). For these two layers we provide different (though related) theoretical descriptions that include the range of low-frequency characters (hapax legomena). The comparative analysis of rank-frequency relations for Chinese characters versus English words illustrates the extent to which the characters play for Chinese writers the same role as the words for those writing within alphabetical systems.Comment: To appear in European Physical Journal B (EPJ B), 2014 (22 pages, 7 figures