Exponential martingales and changes of measure for counting processes

We give sufficient criteria for the Dol\'eans-Dade exponential of a stochastic integral with respect to a counting process local martingale to be a true martingale. The criteria are adapted particularly to the case of counting processes and are sufficiently weak to be useful and verifiable, as we illustrate by several examples. In particular, the criteria allow for the construction of for example nonexplosive Hawkes processes as well as counting processes with stochastic intensities depending on diffusion processes

Testing quantum correlations in a confined atomic cloud by scattering fast atoms

We suggest measuring one-particle density matrix of a trapped ultracold atomic cloud by scattering fast atoms in a pure momentum state off the cloud. The lowest-order probability of the inelastic process, resulting in a pair of outcoming fast atoms for each incoming one, turns out to be given by a Fourier transform of the density matrix. Accordingly, important information about quantum correlations can be deduced directly from the differential scattering cross-section. A possible design of the atomic detector is also discussed.Comment: 5 RevTex pages, no figures, submitted to PR

Spinor condensates and light scattering from Bose-Einstein condensates

These notes discuss two aspects of the physics of atomic Bose-Einstein condensates: optical properties and spinor condensates. The first topic includes light scattering experiments which probe the excitations of a condensate in both the free-particle and phonon regime. At higher light intensity, a new form of superradiance and phase-coherent matter wave amplification were observed. We also discuss properties of spinor condensates and describe studies of ground--state spin domain structures and dynamical studies which revealed metastable excited states and quantum tunneling.Comment: 58 pages, 33 figures, to appear in Proceedings of Les Houches 1999 Summer School, Session LXXI

Synthesis of a new aza-14-crown-4 with di(α-pyridyl)-substituted bispidine subunit and the crystal structure of its complex with CoCl2

The aza-14-crown-4 with the di(α-pyridyl)-substituted bispidine subunit (L) and its cationanion complex with cobalt(II) chloride of composition [Co(L)(H2O)][CoCl4] (I) have been synthesized. The structure of compound L has been proved by IR spectroscopy, NMR, and mass spectrometry. X-ray crystallography has demonstrated that the L molecule in the complex is an NNNN-tetradentate chelating ligand, and the crown ether moiety is not directly bound to the metal cation. In the cationic moiety of the complex, the Co(1) atom has an octahedral environment, and the Co(2) polyhedron in the anionic moiety is a tetrahedron. The cationic and anionic moieties of complex I are linked by the bridging chlorine atom. © 2013 Pleiades Publishing, Ltd

Synthesis of a new aza-14-crown-4 with di(α-pyridyl)-substituted bispidine subunit and the crystal structure of its complex with CoCl2

The aza-14-crown-4 with the di(α-pyridyl)-substituted bispidine subunit (L) and its cationanion complex with cobalt(II) chloride of composition [Co(L)(H2O)][CoCl4] (I) have been synthesized. The structure of compound L has been proved by IR spectroscopy, NMR, and mass spectrometry. X-ray crystallography has demonstrated that the L molecule in the complex is an NNNN-tetradentate chelating ligand, and the crown ether moiety is not directly bound to the metal cation. In the cationic moiety of the complex, the Co(1) atom has an octahedral environment, and the Co(2) polyhedron in the anionic moiety is a tetrahedron. The cationic and anionic moieties of complex I are linked by the bridging chlorine atom. © 2013 Pleiades Publishing, Ltd