Intersecting branes and Supersymmetry

We consider intersecting M-brane solutions of supergravity in eleven dimensions. Supersymmetry turns out to be a powerful tool in obtaining such solutions and their generalizations.Comment: 6 pages, Latex, Presented at Supersymmetry and Quantum Field Theory, International Seminar dedicated to the memory of D. V. Volkov, Kharkov, 199

Aspects of Superembeddings

Some aspects of the geometry of superembeddings and its application to supersymmetric extended objects are discussed. In particular, the embeddings of (3|16) and (6|16) dimensional superspaces into (11|32) dimensional superspace, corresponding to supermembranes and superfivebranes in eleven dimensions, are treated in some detail.Comment: 13 pages, Latex, Contribution to Supersymmetry and Quantum Field Theory, International Seminar dedicated to the memory of D. V. Volkov (Kharkov, 1997), some clarifications are mad

Off-diagonal correlations of the Calogero-Sutherland model

We study correlation functions of the Calogero-Sutherland model in the whole range of the interaction parameter. Using the replica method we obtain analytical expressions for the long-distance asymptotics of the one-body density matrix in addition to the previously derived asymptotics of the pair-distribution function [D.M. Gangardt and A. Kamenev, Nucl. Phys. B, 610, 578 (2001)]. The leading analytic and non-analytic terms in the short-distance expansion of the one-body density matrix are discussed. Exact numerical results for these correlation functions are obtained using Monte Carlo techniques for all distances. The momentum distribution and static structure factor are calculated. The potential and kinetic energies are obtained using the Hellmann-Feynman theorem. Perfect agreement is found between the analytical expressions and numerical data. These results allow for the description of physical regimes of the Calogero-Sutherland model. The zero temperature phase diagram is found to be of a crossover type and includes quasi-condensation, quasi-crystallization and quasi-supersolid regimes.Comment: 17 pages, 7 figure

Soliton absorption spectroscopy

We analyze optical soliton propagation in the presence of weak absorption lines with much narrower linewidths as compared to the soliton spectrum width using the novel perturbation analysis technique based on an integral representation in the spectral domain. The stable soliton acquires spectral modulation that follows the associated index of refraction of the absorber. The model can be applied to ordinary soliton propagation and to an absorber inside a passively modelocked laser. In the latter case, a comparison with water vapor absorption in a femtosecond Cr:ZnSe laser yields a very good agreement with experiment. Compared to the conventional absorption measurement in a cell of the same length, the signal is increased by an order of magnitude. The obtained analytical expressions allow further improving of the sensitivity and spectroscopic accuracy making the soliton absorption spectroscopy a promising novel measurement technique.Comment: 9 pages, 7 figures