Correlation Kernels for Discrete Symplectic and Orthogonal Ensembles

In [49] H. Widom derived formulae expressing correlation functions of orthogonal and symplectic ensembles of random matrices in terms of orthogonal polynomials. We obtain similar results for discrete ensembles with rational discrete logarithmic derivative, and compute explicitly correlation kernels associated to the classical Meixner and Charlier orthogonal polynomials.     

On the Quasi-linear Elliptic PDE {-\nabla \cdot ( \nabla{u}/ \sqrt{1-| \nabla{u} |^2}) = 4 \pi \sum_k a_k \delta_{s_k}} in Physics and Geometry

It is shown that for each finite number N of Dirac measures ${\delta_{s_n}}$ supported at points ${s_n \in {\mathbb R}^3}$ with given amplitudes ${a_n \in {\mathbb R} \backslash\{0\}}$ there exists a unique real-valued function ${u \in C^{0, 1}({\mathbb R}^3)}$ , vanishing at infinity, which distributionally solves the quasi-linear elliptic partial differential equation of divergence form ${-\nabla \cdot ( \nabla{u}/ \sqrt{1-| \nabla{u} |^2}) = 4 \pi \sum_{n=1}^N a_n \delta_{s_n}}$ . Moreover, ${u \in C^{\omega}({\mathbb R}^3\backslash \{s_n\}_{n=1}^N)}$ . The result can be interpreted in at least two ways: (a) for any number N of point charges of arbitrary magnitude and sign at prescribed locations s _n in three-dimensional Euclidean space there exists a unique electrostatic field which satisfies the Maxwell-Born-Infeld field equations smoothly away from the point charges and vanishes as |s| ?? ??; (b) for any number N of integral mean curvatures assigned to locations ${s_n \in {\mathbb R}^3 \subset{\mathbb R}^{1, 3}}$ there exists a unique asymptotically flat, almost everywhere space-like maximal slice with point defects of Minkowski spacetime ${{\mathbb R}^{1, 3}}$ , having lightcone singularities over the s _n but being smooth otherwise, and whose height function vanishes as |s| ?? ??. No struts between the point singularities ever occur.     

CUPID-0: the first array of enriched scintillating bolometers for 0$$\nu \beta \beta $$ decay investigations

The CUPID-0 detector hosted at the Laboratori Nazionali del Gran Sasso, Italy, is the first large array of enriched scintillating cryogenic detectors for the investigation of \(^{82}\)Se neutrinoless double-beta decay (\(0\nu \beta \beta \)). CUPID-0 aims at measuring a background index in the region of interest (RoI) for \(0\nu \beta \beta \) at the level of 10\(^{-3}\) counts/(keV kg years), the lowest value ever measured using cryogenic detectors. CUPID-0 operates an array of Zn\(^{82}\)Se scintillating bolometers coupled with bolometric light detectors, with a state of the art technology for background suppression and thorough protocols and procedures for the detector preparation and construction. In this paper, the different phases of the detector design and construction will be presented, from the material selection (for the absorber production) to the new and innovative detector structure. The successful construction of the detector lead to promising preliminary detector performance which is discussed here.     

Flavored surface defects in 4d $$\mathcal{N}=1$$ N = 1 SCFTs

We discuss supersymmetric surface defects in compactifications of six-dimensional minimal conformal matter of types SU(3) and SO(8) to four dimensions. The relevant field theories in four dimensions are \(\mathcal{N}=1\) quiver gauge theories with SU(3) and SU(4) gauge groups, respectively. The defects are engineered by giving space-time-dependent vacuum expectation values to baryonic operators. We find evidence that in the case of SU(3) minimal conformal matter, the defects carry SU(2) flavor symmetry which is not a symmetry of the four-dimensional model. The simplest case of a model in this class is SU(3) SQCD with nine flavors, and thus the results suggest that this admits natural surface defects with SU(2) flavor symmetry. We analyze the defects using the superconformal index and derive analytic difference operators introducing the defects into the index computation. The duality properties of the four-dimensional theories imply that the index of the models is a kernel function for such difference operators. In turn, checking the kernel property constitutes an independent check of the dualities and the dictionary between six- dimensional compactifications and four-dimensional models.

     

The decay of theT=1 isospin triplet inA=12 systems: IV. The energy dependence of the asymmetry coefficients\alpha _{\beta ^ \mp } of the beta-ray angular distribution in aligned12B and12N and the induced pseudotensor interaction

The asymmetry parameters \(\alpha _{\beta ^ \mp } \) of the beta-ray emitted from aligned¹²B and¹²N are evaluated as a function of the energy. The agreement with experimental differential data is excellent for both \(\alpha _{\beta ^ - } \) (W) and \(\alpha _{\beta ^ + } \) (W). This work confirms, using available nuclear model information, that no induced pseudotensor (IPT) interaction is required for a correct theoretical interpretation of the data. An upper limit for the IPT coupling constantf _T is determined from a simultaneous fit of \(\alpha _{\beta ^ - } \) (W) and \(\alpha _{\beta ^ + } \) (W).     

The optical Airy transform and its application in generating and controlling the Airy beam

We propose an optical Airy transform in this paper, and obtain the analytical expressions for the Airy transform of fundamental Gaussian beams and finite energy Airy beams. The setup for performing the optical Airy transform is presented. The Airy transform for Gaussian beams and finite energy Airy beams are theoretically calculated and analyzed. Our results show that the Airy beam can be conveniently generated and controlled through the optical Airy transform of the Gaussian beam. The optical Airy transform also can be used to directly modulate the beam parameters of the incident Airy beam, and it can transform the incident Airy beam into the Gaussian beam.     

Invariant-mass distributions for the pp \rightarrow pp \eta reaction at Q = 10 MeV

Proton-proton and proton- $ \eta$ invariant-mass distributions and the total cross-section for the pp $ \rightarrow$ pp $ \eta$ reaction have been determined near the threshold at an excess energy of Q = 10 MeV. The experiment has been conducted using the COSY-11 detector setup and the cooler synchrotron COSY. The determined invariant-mass spectra reveal significant enhancements in the region of low proton-proton relative momenta, similarly as observed previously at higher excess energies of Q = 15.5 MeV and Q = 40 MeV.     

Cut-and-join operators and $ \mathcal{N} = 4 $ super Yang-Mills

We show which multi-trace structures are compatible with the symmetrisation of local operators in \( \mathcal{N} = 4 \) super Yang-Mills when they are organised into representations of the global symmetry group. Cut-and-join operators give the non-planar expansion of correlation functions of these operators in the free theory. Using these techniques we find the 1/N corrections to the quarter-BPS operators which remain protected at weak coupling. We also present a new way of counting these chiral ring operators using the Weyl group S _N .     

Elliptic and triangular flow in event-by-event D=3+1 viscous hydrodynamics

We present results for the elliptic and triangular flow coefficients v(2) and v(3) in Au+Au collisions at √s=200 AGeV using event-by-event D=3+1 viscous hydrodynamic simulations. We study the effect of initial state fluctuations and finite viscosities on the flow coefficients v(2) and v(3) as functions of transverse momentum and pseudorapidity. Fluctuations are essential to reproduce the measured centrality dependence of elliptic flow. We argue that simultaneous measurements of v(2) and v(3) can determine η/s more precisely.     

The 4PI effective action for $\phi^4$ theory

In the symplectic Lagrangian framework we in a new fashion embed an irreducible massive vector-tensor theory into a gauge invariant system, which has become reducible, by extending the configuration space to include an additional pair of scalar and vector fields, which give the desired Wess-Zumino action. A comparison with the BFT Hamiltonian embedding approach is also given.Received: 13 January 2004, Published online: 16 March 2004     

An $${n = \left( {1,1} \right)}$$ Super-Toda Model Based on OSp $$1|{\kern 1pt} 4$$

We show that a Hamiltonian reduction of affine Lie superalgebras having bosonic simple roots (such as OSp ) does produce supersymmetric Toda models, with superconformal symmetry being nonlinearly realized for those fields of the Toda system which are related to the bosonic simple roots of the superalgebra. A fermionic b-c system of conformal spin is a natural ingredient of such models.     

The atomic structure of the 1/3\langle 2\overline 1 \overline 1 0\rangle superdislocation core and prismatic slip in Ti3Al

The structure of the core of a $1/6\langle 2\overline 1 \overline 1 0\rangle $ superpartial dislocation in the prism plane of the D0₁₉ superlattice is studied by computer simulation. Atomic interaction potentials for Ti₃Al are derived with the embedded atom method. The core of the superpartial dislocation is found to have three different configurations (of I′, I, and II types) in nonequivalent prism planes $\{ 0\overline 1 10\} $ . For screw and edge dislocations, the core is planar in type-I′ prism planes and nonplanar in prism planes of type I and II. Results of simulation are compared with experimental data for the superdislocation mobility in Ti₃Al.     

The Nondynamical r-Matrix Structure of the Elliptic Ruijsenaars-Schneider Model with N = 2

We demonstrate that in a certain gauge the elliptic Ruijsenaars-Schneider model with N = 2 admits a nondynamical r-matrix structure and the corresponding classical rmatrix is the same as that of its nonrelativistic counterpart (CalogereMoser model) in the same gauge. The relation between our (classical) Lax operator and the Lax operator given by Ruijsenaars is also obtained.     

Search for double- \beta decays of 96Ru and 104Ru by ultra-low background HPGe \gamma spectrometry

A search for double- $ \beta$ processes in ⁹⁶Ru and ¹⁰⁴Ru was realized in the underground Gran Sasso National Laboratories of the INFN (Italy) with the help of ultra-low background HPGe $ \gamma$ spectrometry. After 158h of data taking with 473g ruthenium sample, new improved limits on double-beta processes in ⁹⁶Ru have been established on the level of 10¹⁸-10¹⁹yr. For the first time the double-beta decay of ¹⁰⁴Ru to the 2⁺ ₁ excited level of ¹⁰⁴Pd has been restricted as T _1/2 > 3.5×10¹⁹ yr.     

The \gamma \gamma \to Z Z process and the search for virtual SUSY effects at a \gamma \gamma Collider

We study the helicity amplitudes of the process in the Standard Model at high energy. These amplitudes receive contributions from the W and charged quark and lepton loops, analogous to those encountered in the cases studied before. But also receives contributions from the Higgs s-channel poles involving the effective Higgs- vertex. At energies , the amplitudes in all three processes are mainly helicity-conserving and almost purely imaginary; which renders them a very useful tool in searching for New Physics. As an example, a SUSY case is studied, and the signatures due to the virtual effects induced by a chargino-, charged slepton- or a lightest stop-loop in , are explored. These signatures, combined with the analogous ones in and , should help identifying the nature of possible New Physics particles. Received: 3 September 1999 / Published online: 3 February 2000