Reality property of discrete Wronski map with imaginary step

For a set of quasi-exponentials with real exponents, we consider the discrete Wronskian (also known as Casorati determinant) with pure imaginary step 2h. We prove that if the coefficients of the discrete Wronskian are real and for every its roots the imaginary part is at most |h|, then the complex span of this set of quasi-exponentials has a basis consisting of quasi-exponentials with real coefficients. This result is a generalization of the statement of the B. and M. Shapiro conjecture on spaces of polynomials. The proof is based on the Bethe ansatz for the XXX model.Comment: Latex, 9 page

Limits of Gaudin algebras, quantization of bending flows, Jucys--Murphy elements and Gelfand--Tsetlin bases

Gaudin algebras form a family of maximal commutative subalgebras in the tensor product of $n$ copies of the universal enveloping algebra U(\g) of a semisimple Lie algebra \g. This family is parameterized by collections of pairwise distinct complex numbers $z_1,...,z_n$. We obtain some new commutative subalgebras in U(\g)^{\otimes n} as limit cases of Gaudin subalgebras. These commutative subalgebras turn to be related to the hamiltonians of bending flows and to the Gelfand--Tsetlin bases. We use this to prove the simplicity of spectrum in the Gaudin model for some new cases.Comment: 11 pages, references adde

Unusual magnetoelectric effect in paramagnetic rare-earth langasite

Violation of time reversal and spatial inversion symmetries has profound consequences for elementary particles and cosmology. Spontaneous breaking of these symmetries at phase transitions gives rise to unconventional physical phenomena in condensed matter systems, such as ferroelectricity induced by magnetic spirals, electromagnons, non-reciprocal propagation of light and spin waves, and the linear magnetoelectric (ME) effect - the electric polarization proportional to the applied magnetic field and the magnetization induced by the electric field. Here, we report the experimental study of the holmium-doped langasite, Ho$_{x}$La$_{3-x}$Ga$_5$SiO$_{14}$, showing a puzzling combination of linear and highly non-linear ME responses in the disordered paramagnetic state: its electric polarization grows linearly with the magnetic field but oscillates many times upon rotation of the magnetic field vector. We propose a simple phenomenological Hamiltonian describing this unusual behavior and derive it microscopically using the coupling of magnetic multipoles of the rare-earth ions to the electric field.Comment: 8 pages, 3 figure

BPS States in Omega Background and Integrability

We reconsider string and domain wall central charges in N=2 supersymmetric gauge theories in four dimensions in presence of the Omega background in the Nekrasov-Shatashvili (NS) limit. Existence of these charges entails presence of the corresponding topological defects in the theory - vortices and domain walls. In spirit of the 4d/2d duality we discuss the worldsheet low energy effective theory living on the BPS vortex in N=2 Supersymmetric Quantum Chromodynamics (SQCD). We discuss some aspects of the brane realization of the dualities between various quantum integrable models. A chain of such dualities enables us to check the AGT correspondence in the NS limit.Comment: 48 pages, 10 figures, minor changes, references added, typos correcte

How close can one approach the Dirac point in graphene experimentally?

The above question is frequently asked by theorists who are interested in graphene as a model system, especially in context of relativistic quantum physics. We offer an experimental answer by describing electron transport in suspended devices with carrier mobilities of several 10^6 cm^2V^-1s^-1 and with the onset of Landau quantization occurring in fields below 5 mT. The observed charge inhomogeneity is as low as \approx10^8 cm^-2, allowing a neutral state with a few charge carriers per entire micron-scale device. Above liquid helium temperatures, the electronic properties of such devices are intrinsic, being governed by thermal excitations only. This yields that the Dirac point can be approached within 1 meV, a limit currently set by the remaining charge inhomogeneity. No sign of an insulating state is observed down to 1 K, which establishes the upper limit on a possible bandgap

Observation of the Cabibbo-suppressed decay Xi_c+ -> p K- pi+

We report the first observation of the Cabibbo-suppressed charm baryon decay Xi_c+ -> p K- pi+. We observe 150 +- 22 events for the signal. The data were accumulated using the SELEX spectrometer during the 1996-1997 fixed target run at Fermilab, chiefly from a 600 GeV/c Sigma- beam. The branching fractions of the decay relative to the Cabibbo-favored Xi_c+ -> Sigma+ K- pi+ and Xi_c+ -> X- pi+ pi+ are measured to be B(Xi_c+ -> p K- pi+)/B(Xi_c+ -> Sigma+ K- pi+) = 0.22 +- 0.06 +- 0.03 and B(Xi_c+ -> p K- pi+)/B(Xi_c+ -> X- pi+ pi+) = 0.20 +- 0.04 +- 0.02, respectively.Comment: 5 pages, RevTeX, 3 figures (postscript), Submitted to Phys. Rev. Let

Study of Gluon versus Quark Fragmentation in Υ→ggγ\Upsilon\to gg\gamma and e+e−→qqˉγe^{+}e^{-}\to q\bar{q}\gamma Events at \sqrt{s}=10 GeV

Using data collected with the CLEO II detector at the Cornell Electron Storage Ring, we determine the ratio R(chrg) for the mean charged multiplicity observed in Upsilon(1S)->gggamma events, to the mean charged multiplicity observed in e+e- -> qqbar gamma events. We find R(chrg)=1.04+/-0.02+/-0.05 for jet-jet masses less than 7 GeV.Comment: 15 pages, postscript file also available through http://w4.lns.cornell.edu/public/CLN