Creating solitons by means of spin-orbit coupling

This mini-review collects theoretical results predicting the creation of matter-wave solitons by the pseudo-spinor system of Gross-Pitaevskii equations (GPEs) with the self-attractive cubic nonlinearity and linear first-order-derivative terms accounting for the spin-orbit coupling (SOC). In one dimension (1D), the so predicted bright solitons are similar to their well-known counterparts supported by the GPE in the absence of SOC. Completely novel results were recently obtained for 2D and 3D systems: SOC suppresses the collapse instability of the multidimensional GPE, creating fully stable 2D ground-state solitons and metastable 3D ones of two types: semi-vortices (SVs), with vorticities m = 1 in one spin component and m = 0 in the other, and mixed modes (MMs), with m = 0 and m = (+/-)1 present in both components. With the Galilean invariance broken by SOC, moving solitons exist up to a certain critical velocity, suffering delocalization above it. The newest result predicts stable 2D "quantum droplets" of the MM type in the presence of the Lee-Huang-Yang corrections to the GPE system, induced by quantum fluctuations around the mean-field states, in the case when the inter-component attraction dominates over the self-repulsion in each component.Comment: a slightly shortened version will be published as an invited mini-review (perspective) in EP

Network Flow Optimization for Restoration of Images

The network flow optimization approach is offered for restoration of grayscale and color images corrupted by noise. The Ising models are used as a statistical background of the proposed method. The new multiresolution network flow minimum cut algorithm, which is especially efficient in identification of the maximum a posteriori estimates of corrupted images, is presented. The algorithm is able to compute the MAP estimates of large size images and can be used in a concurrent mode. We also describe the efficient solutions of the problem of integer minimization of two energy functions for the Ising models of gray-scale and color images

Nonlinear Model of non-Debye Relaxation

We present a simple nonlinear relaxation equation which contains the Debye equation as a particular case. The suggested relaxation equation results in power-law decay of fluctuations. This equation contains a parameter defining the frequency dependence of the dielectric permittivity similarly to the well-known one-parameter phenomenological equations of Cole-Cole, Davidson-Cole and Kohlrausch-Williams-Watts. Unlike these models, the obtained dielectric permittivity (i) obeys to the Kramers-Kronig relation; (ii) has proper behaviour at large frequency; (iii) its imaginary part, conductivity, shows a power-law frequency dependence \sigma ~ \omega^n where n<1 corresponds to empirical Jonscher's universal relaxation law while n>1 is also observed in several experiments. The nonlinear equation proposed may be useful in various fields of relaxation theory

Results from HARP and their implications for neutrino physics

Recent results from the HARP experiment on the measurements of the double-differential production cross-section of pions in proton interactions with beryllium, carbon and tantalum targets are presented. These results are relevant for a detailed understanding of neutrino flux in accelerator neutrino experiments MiniBooNE/SciBooNE, for a better prediction of atmospheric neutrino fluxes as well as for an optimization of a future neutrino factory design.Comment: Presented at the XLIInd Rencontres de Moriond on Electroweak Interactions and Unified Theorie