Distribution of velocities in an avalanche

For a driven elastic object near depinning, we derive from first principles the distribution of instantaneous velocities in an avalanche. We prove that above the upper critical dimension, d >= d_uc, the n-times distribution of the center-of-mass velocity is equivalent to the prediction from the ABBM stochastic equation. Our method allows to compute space and time dependence from an instanton equation. We extend the calculation beyond mean field, to lowest order in epsilon=d_uc-d.Comment: 4 pages, 2 figure

Frequency modulation and pulse compression by coherent multimode molecular motion

We study beating of a probe field with a time-varying susceptibility in a coherently prepared Raman medium. We consider the general case of an arbitrary variation of susceptibility, which corresponds to a superposition of an arbitrary number of excited Raman transitions. We derive a general analytical solution and conservation relations for this process. We show that the interference between Raman polarizations may substantially affect frequency modulation and pulse compression for the probe field.Comment: 4 pages, 4 figure

Electron Redistribution of Aromatic Ligands in (Arene)Cr(CO)\u3csub\u3e3\u3c/sub\u3e Complexes. Structural (Bond-Length) Changes as Quantitative Measures

Arene ligands experience significant ring expansion upon coordination with chromium tricarbonyl, as established by precise X-ray crystallographic analyses of various (η6-arene)Cr(CO)3 complexes. Such changes in ligand structures result from the charge (electron) redistribution, Ar+−Cr-, upon arene coordination, since they are closely related to those found in the intermolecular 1:1 complexes of the corresponding series of arenes with nitrosonium cation (NO+). The latter are prototypical examples of charge-transfer complexes as described by Mulliken. As such, they show enhanced degrees of charge (electron) transfer that approach unity, which is confirmed by quantitative comparison with the structural changes measured in the one-electron (oxidative) transformation of electron-rich arene donors (Ar) to the cation-radicals (Ar•+). Such a charge redistribution thus readily accounts for the enhanced reactivity to nucleophilic attack of the arene ligand in various ArCr(CO)3 complexes and related transition-metal/arene analogues

Novel (Heteromolecular) π-Complexes of Aromatic Cation Radicals. Isolation and Structural Characterization

Extensive (electron) delocalization in the novel heteromolecular π-complex of the hindered naphthalene cation radical (OMN+•) with naphthalene (NAP) accompanies the pronounced charge-transfer absorption band at ∼1100 nm in the near-IR. X-ray crystallography establishes the viability of the unusual “club sandwich” structure despite the repulsive electrostatic forces inherent to the dicationic unit

Freezing Transition in Decaying Burgers Turbulence and Random Matrix Dualities

We reveal a phase transition with decreasing viscosity $\nu$ at \nu=\nu_c>0 in one-dimensional decaying Burgers turbulence with a power-law correlated random profile of Gaussian-distributed initial velocities \sim|x-x'|^{-2}. The low-viscosity phase exhibits non-Gaussian one-point probability density of velocities, continuously dependent on \nu, reflecting a spontaneous one step replica symmetry breaking (RSB) in the associated statistical mechanics problem. We obtain the low orders cumulants analytically. Our results, which are checked numerically, are based on combining insights in the mechanism of the freezing transition in random logarithmic potentials with an extension of duality relations discovered recently in Random Matrix Theory. They are essentially non mean-field in nature as also demonstrated by the shock size distribution computed numerically and different from the short range correlated Kida model, itself well described by a mean field one step RSB ansatz. We also provide some insights for the finite viscosity behaviour of velocities in the latter model.Comment: Published version, essentially restructured & misprints corrected. 6 pages, 5 figure