Galilean Lee Model of the Delta Function Potential

The scattering cross section associated with a two dimensional delta function has recently been the object of considerable study. It is shown here that this problem can be put into a field theoretical framework by the construction of an appropriate Galilean covariant theory. The Lee model with a standard Yukawa interaction is shown to provide such a realization. The usual results for delta function scattering are then obtained in the case that a stable particle exists in the scattering channel provided that a certain limit is taken in the relevant parameter space. In the more general case in which no such limit is taken finite corrections to the cross section are obtained which (unlike the pure delta function case) depend on the coupling constant of the model.Comment: 7 pages, latex, no figure

Scalar and vector meson exchange in V->P0P0gamma decays

The scalar contributions to the radiative decays of light vector mesons into a pair of neutral pseudoscalars, $V\to P^0P^0\gamma$, are studied within the framework of the Linear Sigma Model. This model has the advantage of incorporating not only the scalar resonances in an explicit way but also the constraints required by chiral symmetry. The experimental data on $\phi\to\pi^0\pi^0\gamma$, $\phi\to\pi^0\eta\gamma$, $\rho\to\pi^0\pi^0\gamma$ and $\omega\to\pi^0\pi^0\gamma$ are satisfactorily accommodated in our framework. Theoretical predictions for $\phi\to K^0\bar K^0\gamma$, $\rho\to\pi^0\eta\gamma$, $\omega\to\pi^0\eta\gamma$ and the ratio $\phi\to f_0\gamma/a_0\gamma$ are also given.Comment: 42 pages, 11 figures. A new paragraph explaining the seminal contribution of Ref. [19] is adde

Possible persistent current in a ring made of the perfect crystalline insulator

A mesoscopic conducting ring pierced by magnetic flux is known to support the persistent electron current. Here we propose possibility of the persistent current in the ring made of the perfect crystalline insulator. We consider a ring-shaped lattice of one-dimensional "atoms" with a single energy level. We express the Bloch states in the lattice as a linear combination of atomic orbitals. The discrete energy level splits into the energy band which serves as a simple model of the valence band. We show that the insulating ring (with the valence band fully filled by electrons) supports a nonzero persistent current, because each atomic orbital overlaps with its own tail when making one loop around the ring. In the tight-binding limit only the neighboring orbitals overlap. In that limit the persistent current at full filling becomes zero which is a standard result.Comment: Conference proceedings. Accepted for publication in Physica

Anyons, group theory and planar physics

Relativistic and nonrelativistic anyons are described in a unified formalism by means of the coadjoint orbits of the symmetry groups in the free case as well as when there is an interaction with a constant electromagnetic field. To deal with interactions we introduce the extended Poincar\'e and Galilei Maxwell groups.Comment: 22 pages, journal reference added, bibliography update

Hopf instantons, Chern-Simons vortices, and Heisenberg ferromagnets

The dimensional reduction of the three-dimensional fermion-Chern-Simons model (related to Hopf maps) of Adam et el. is shown to be equivalent to (i) either the static, fixed--chirality sector of our non-relativistic spinor-Chern-Simons model in 2+1 dimensions, (ii) or a particular Heisenberg ferromagnet in the plane.Comment: 4 pages, Plain Tex, no figure

Cross-section and polarization of neutrino-produced τ\tau's made simple

Practical formulae are derived for the cross-section and polarization of the $\tau$ lepton produced in deep-inelastic neutrino-nucleon scattering in the frame of the simple quark-parton model.Comment: 10 pages, no figure

Estimating the number of change-points in a two-dimensional segmentation model without penalization

In computational biology, numerous recent studies have been dedicated to the analysis of the chromatin structure within the cell by two-dimensional segmentation methods. Motivated by this application, we consider the problem of retrieving the diagonal blocks in a matrix of observations. The theoretical properties of the least-squares estimators of both the boundaries and the number of blocks proposed by L\'evy-Leduc et al. [2014] are investigated. More precisely, the contribution of the paper is to establish the consistency of these estimators. A surprising consequence of our results is that, contrary to the onedimensional case, a penalty is not needed for retrieving the true number of diagonal blocks. Finally, the results are illustrated on synthetic data.Comment: 30 pages, 8 figure

Sub-ballistic behavior in quantum systems with L\'evy noise

We investigate the quantum walk and the quantum kicked rotor in resonance subjected to noise with a L\'evy waiting time distribution. We find that both systems have a sub-ballistic wave function spreading as shown by a power-law tail of the standard deviation.Comment: 4 pages, 4 figure