On two conjectures concerning convex curves

We recall two basic conjectures on the developables of convex projective curves, prove one of them and disprove the other in the firdt nontrivial case of curves in RP^3. Namely, we show that i) the tangent developable surface of any convex curve in RP^3 has 'degree' 4 and ii) construct an example of 4 tangent lines to a convex curve in RP^3 such that no real line intersects all four of them.Comment: AMSTEX, 15 pages, 3 eps pictures. to appear in Int. J. Mat

Time-reversal violating generation of static magnetic and electric fields and a problem of electric dipole moment measurement

It is shown that in the experiments for search of the EDM of an electron (atom, molecule) the T-odd magnetic moment induced by an electric field and the T-odd electric dipole moment induced by a magnetic field will be also measured. It is discussed how to distinguish these contributions.Comment: Latex, 5 pages with 1 Postscript figur

Some relations for one-part double Hurwitz numbers

In this very short note we slightly generalize some relations for one-part double Hurwitz numbers from math.AG/0209282.Comment: 3 page

Complete transfer of populations from a single state to a pre-selected superposition of states using Piecewise Adiabatic Passage

We develop a method for executing robust and selective transfer of populations between a single level and pre-selected superpositions of energy eigenstates. Viewed in the frequency domain, our method amounts to executing a series of simultaneous adiabatic passages into each component of the target superposition state. Viewed in {the} time domain, the method works by accumulating the wavefunction of the target wave packet as it revisits the Franck Condon region, in what amounts to an extension of the Piecewise Adiabatic Passage technique [ Shapiro et.al., Phys. Rev. Lett. 99, 033002 (2007)] to the multi-state regime. The viability of the method is verified by performing numerical tests for the Na_2 molecule.Comment: 8 pages, 4 figure

Incomplete Photonic Bandgap as Inferred from the Speckle Pattern of Scattered Light Waves

Motivated by recent experiments on intensity correlations of the waves transmitted through disordered media, we demonstrate that the speckle pattern from disordered photonic crystal with incomplete band-gap represents a sensitive tool for determination the stop-band width. We establish the quantitative relation between this width and the {\em angualar anisotropy} of the intensity correlation function.Comment: 6 pages, 3 figure

A possibility for precise Weinberg angle measurement in centrosymmetric crystals with axis

We demonstrate that parity nonconserving interaction due to the nuclear weak charge Q_W leads to nonlinear magnetoelectric effect in centrosymmetric paramagnetic crystals. It is shown that the effect exists only in crystals with special symmetry axis k. Kinematically, the correlation (correction to energy) has the form H_PNC ~ Q_W (E,[B,k])(B,k), where B and E are the external magnetic and electric fields. This gives rise to magnetic induction M_PNC ~ Q_W {k(B,[k,E]) + [k,E](B,k)}. To be specific we consider rare-earth trifluorides and, in particular, dysprosium trifluoride which looks the most suitable for experiment. We estimate the optimal temperature for the experiment to be of a few kelvin. For the magnetic field B = 1 T and the electric field E = 10 kV/cm, the expected magnetic induction is 4 \pi M_PNC = 0.5 * 10^-11 G, six orders of magnitude larger than the best sensitivity currently under discussion. Dysprosium has several stable isotopes, and so, comparison of the effects for different isotopes provides possibility for precise measurement of the Weinberg angle.Comment: 7 pages, 1 figure, 2 tables; version 2 - added discussion of neutron distribution uncertaint

Intensity Fluctuations in Closed and Open Systems

We consider the intensity pattern, generated by a monochromatic source, in a disordered cavity coupled to the environment. For weak coupling, and when the source frequency is tuned to a resonance, the intensity distribution is close to Porter-Thomas distribution. When the coupling increases, gradually crosses over to the Rayleigh distribution. The joint probability distribution for intensities at two different points is also discussed.Comment: 11 pages, LATEX, no figure

Crossover Between Universality Classes in the Statistics of Rare Events in Disordered Conductors

The crossover from orthogonal to the unitary universality classes in the distribution of the anomalously localized states (ALS) in two-dimensional disordered conductors is traced as a function of magnetic field. We demonstrate that the microscopic origin of the crossover is the change in the symmetry of the underlying disorder configurations, that are responsible for ALS. These disorder configurations are of weak magnitude (compared to the Fermi energy) and of small size (compared to the mean free path). We find their shape explicitly by means of the direct optimal fluctuation method.Comment: 7 pages including 2 figure