Picard-Fuchs Equation for Glueball Superfield for the SO(N) Gauge Group

In this paper, by using the factorization equation of the N = 2 supersymmetric gauge theory, we study N = 1 theory in Argyres-Douglas points. We suppose that all monopoles become massive. We derive general Picard-Fuchs equations for glueball superfields. These equations are hypergeometric equations and have regular singular points corresponding to Argyres-Douglas points. Furthermore, we obtain the solution of these differential equations.     

Entanglement in quantum spin chains, symmetry classes of random matrices, and conformal field theory

We compute the entropy of entanglement between the first N spins and the rest of the system in the ground states of a general class of quantum spin chains. We show that under certain conditions the entropy can be expressed in terms of averages over ensembles of random matrices. These averages can be evaluated, allowing us to prove that at critical points the entropy grows like kappalog(2N+kappa as N-->infinity, where kappa and kappa are determined explicitly. In an important class of systems, kappa is equal to one-third of the central charge of an associated Virasoro algebra. Our expression for kappa therefore provides an explicit formula for the central charge.     

Quantum electrodynamics in 2 + 1 dimensions, confinement, and the stability of U(1) spin liquids

Compact quantum electrodynamics in 2 + 1 dimensions often arises as an effective theory for a Mott insulator, with the Dirac fermions representing the low-energy spinons. An important and controversial issue in this context is whether a deconfinement transition takes place. We perform a renormalization group analysis to show that deconfinement occurs when N > Nc = 36/pi3 approximately to 1.161, where N is the number of fermion replica. For N < Nc, however, there are two stable fixed points separated by a line containing a unstable nontrivial fixed point: a fixed point corresponding to the scaling limit of the noncompact theory, and another one governing the scaling behavior of the compact theory. The string tension associated with the confining interspinon potential is shown to exhibit a universal jump as N --> Nc-. Our results imply the stability of a spin liquid at the physical value N = 2 for Mott insulators.     

Black hole/string transition for the small Schwarzschild black hole of AdS 5 × S5 and critical unitary matrix models

In this paper we discuss the black hole–string transition of the small Schwarzschild black hole of AdS ₅×S⁵ using the AdS/CFT correspondence at finite temperature. The finite temperature gauge theory effective action, at weak and strong coupling, can be expressed entirely in terms of constant Polyakov lines which are SU(N) matrices. In showing this we have taken into account that there are no Nambu–Goldstone modes associated with the fact that the 10-dimensional black hole solution sits at a point in S⁵. We show that the phase of the gauge theory in which the eigenvalue spectrum has a gap corresponds to supergravity saddle points in the bulk theory. We identify the third order N=∞ phase transition with the black hole–string transition. This singularity can be resolved using a double scaling limit in the transition region where the large N expansion is organized in terms of powers of N^-2/3. The N=∞ transition now becomes a smooth crossover in terms of a renormalized string coupling constant, reflecting the physics of large but finite N. Multiply wound Polyakov lines condense in the crossover region. We also discuss the implications of our results for the resolution of the singularity of the lorenztian section of the small Schwarzschild black hole.     

Achromatic wave plates for optical pickup units fabricated by use of imprint lithography

We report achromatic form-birefringence wave plates for optical pickup units. Material dispersion and structure dispersion are balanced in a rigorous multilayer design. A trilayer grating using SiN(x)/SiO(y)N(z)/SiO2 provides easily accessible process control points and relaxed fabrication tolerance. We demonstrate precise patterning by using nanoimprint lithography on UV-curable polymers, alleviating a major fabrication challenge. The achromatic wave plates exhibit 90+/-3 degrees retardance and >95% transmittance as measured by a Mueller matrix method at wavelengths of 640-800 nm.     

Discrete Structure of Some Schlesinger Systems on the Riemann Sphere

In the present work we investigate the group structure of the Schlesinger transformations for isomonodromic deformations of the Fuchsian differential equations. We perform these transformations as isomorphisms between the moduli spaces of the logarithmic sl(N)-connections with fixed eigenvalues of the residues at singular points. We give a geometrical interpretation of the Schlesinger transformations and perform our calculations using the techniques of the modifications of bundles with connections, or, the Hecke correspondences for the loop group SL(N)C(z).     

Asymptotics and Dimensional Dependence of the Number of Critical Points of Random Holomorphic Sections

We prove two conjectures from [DSZ2,DSZ3] concerning the expected number of critical points of random holomorphic sections of a positive line bundle. We show that, on average, the critical points of minimal Morse index are the most plentiful for holomorphic sections of \({\mathcal {O}(N) \to \mathbb {CP}^m}\) and, in an asymptotic sense, for those of line bundles over general Kähler manifolds. We calculate the expected number of these critical points for the respective cases and use these to obtain growth rates and asymptotic bounds for the total expected number of critical points in these cases. This line of research was motivated by landscape problems in string theory and spin glasses.     

正交光栅干涉仪对二维分立点物体成像

本文将正交光栅干涉仪的条纹箱分离,获得两个方向上的条纹箱.对于由N个分立点组成的物体,从两个条纹箱可以得到由N~2个点组成的像.其中N个点是物的格实像点,N(N—1)个是交叉项点.将光栅干涉仪绕其对称轴转过一角度,得到第二个像.与第一个像相比,N(N—1)个交叉项点的空间位置发生了变化,而N个真实像点未变.因此,将这两个像相乘,即能消除交叉项点而获得真实像点.利用这一方法,给出了实验结果.     

Biaxial nematic phase in model bent-core systems

We determine the bifurcation phase diagrams with isotropic (I), uniaxial (N(U)) and biaxial (N(B)) nematic phases for model bent-core mesogens using Onsager-type theory. The molecules comprise two or three Gay-Berne interacting ellipsoids of uniaxial and biaxial shape and a transverse central dipole. The Landau point is found to turn into an I-N(B) line for the three-center model with a large dipole moment. For the biaxial ellipsoids, a line of Landau points is observed even in the absence of the dipoles.     

Magnetothermal transport in the spin-1/2 chains of copper pyrazine dinitrate

We present experiments on the thermal transport in the spin-1/2 chain compound copper pyrazine dinitrate Cu(C4H4N2)(NO3)2. The heat conductivity shows a surprisingly strong dependence on the applied magnetic field B, characterized at low temperatures by two main features. The first one appearing at low B is a characteristic dip located at muBB approximately kBT, that may arise from umklapp scattering. The second one is a plateaulike feature in the quantum critical regime, muB|B - Bc| < kBT, where Bc is the saturation field at T=0. The latter feature clearly points towards a momentum and field-independent mean free path of the spin excitations, contrary to theoretical expectations.     

Many-body exceptional points in colliding condensates

ABSTRACT

Exceptional points describe the coalescence of the eigenmodes of a non-Hermitian matrix. When an exceptional point occurs in the unitary evolution of a many-body system, it generically leads to a dynamical instability with a finite wavevector [N. Bernier et al., Phys. Rev. Lett. 113, 065303 (2014)]. Here, we study exceptional points in the context of the counterflow instability of colliding Bose–Einstein condensates. We show that the instability of this system is due to an exceptional point in the Bogoliubov spectrum. We further clarify the connection of this effect to the Landau criterion of superfluidity and to the scattering of classical particles. We propose an experimental set-up to directly probe this exceptional point, and demonstrate its feasibility with the aid of numerical calculations. Our work fosters the observation of exceptional points in nonequilibrium many-body quantum systems.     

Analysis of the Dispersion Characteristic Features of Radio Channels Using a Chirp Ionosonde

We show that stationary points of the dispersion characteristics of ionospheric HF radio channels can appear due to the effect of irregularities with scales l 2-5 km and relative variations N/N 10^-3 of electron density. These stationary points can give rise to peaks of the impulse characteristics of wideband HF radio channels. Analytical formulas for estimation of the position, height, and duration of a peak are obtained. We develop and test experimentally methods for determination of the impulse characteristics of ionospheric HF radio channels with various operating frequencies and passbands using chirp-ionosonde signals as well as methods for estimation of the parameters l and N/N of ionospheric irregularities.     

Phase transitions in the distribution of the Andreev conductance of superconductor-metal junctions with multiple transverse modes

We compute analytically the full distribution of Andreev conductance G(NS) of a metal-superconductor interface with a large number N(c) of transverse modes, using a random matrix approach. The probability distribution P(G(NS),N(c) in the limit of large N(c) displays a Gaussian behavior near the average value =(2-√2)N(c) and asymmetric power-law tails in the two limits of very small and very large G(NS). In addition, we find a novel third regime sandwiched between the central Gaussian peak and the power-law tail for large G(NS). Weakly nonanalytic points separate these four regimes-these are shown to be consequences of three phase transitions in an associated Coulomb gas problem.     

Determination of the strong coupling constant using available experimental data

We determine the strong coupling constant α s up to 4-loop in perturbative QCD.Testing QCD requires the measurement of α s over ranges of energy scales.In this analysis,the value of α s is determined from the unpolarized structure functions data points by minimizing the χ 2 function between the theory result and experimental data.Using perturbative QCD calculations from threshold corrections,we obtain α s (M 2 Z ) = 0.1139±0.0020 at N 3 LO which is in good agreement with the very recently results from the inclusive jet cross section in pp collisions at√ s=1.96 TeV.     

Dipolar spin correlations in classical pyrochlore magnets

We study spin correlations for the highly frustrated classical pyrochlore lattice antiferromagnets with O(N) symmetry in the limit T-->0. We conjecture that a local constraint obeyed by the extensively degenerate ground states dictates a dipolar form for the asymptotic spin correlations, at all N not equal 2 for which the system is paramagnetic down to T=0. We verify this conjecture in the cases N=1 and N=3 by simulations and to all orders in the 1/N expansion about the solvable N=infinity limit. Remarkably, the N=infinity formulas are an excellent fit, at all distances, to the correlators at N=3 and even at N=1. Thus we obtain a simple analytical expression also for the correlations of the equivalent models of spin ice and cubic water ice, Ic.     

Phase diagram of optimal paths

We show that by choosing appropriate distributions of the randomness the search for optimal paths links diverse problems of disordered media, such as directed percolation, invasion percolation, and directed and nondirected spanning polymers. We also introduce a simple and efficient algorithm, which solves the d-dimensional model numerically in O(N(1+df/d)) steps, where df is the fractal dimension of the path. Using extensive simulations in two dimensions, we identify the phase boundaries of the directed polymer universality class. A new strong-disorder phase occurs where the optimum paths are self-affine with parameter-dependent scaling exponents. Furthermore, the phase diagram contains directed and nondirected percolation as well as the directed random walk models at specific points and lines.     

The massless supersymmetric ladder with L rungs

We show that in the massless N=1$N=1$ supersymmetric Wess–Zumino theory it is possible to devise a computational strategy by which the x-space calculation of the ladder 4-point correlators can be carried out without introducing any regularization. As an application we derive a representation valid at all loop orders in terms of conformal invariant integrals. We obtain an explicit expression of the 3-loop ladder diagram for collinear external points.     

Determination of the backbone torsion psi angle by tensor correlation of chemical shift anisotropy and heteronuclear dipole-dipole interaction

We demonstrate that the backbone torsion psi angle of a uniformly labeled residue can be determined accurately by correlating the chemical shift anisotropy of the carbonyl carbon and the 13C-1H heteronuclear dipole-dipole interaction of the alpha carbon. To obtain the highest sensitivity for the psi angle determination, the following conditions are desired: (i) the recoupling pulse sequences for the CSA and the heteronuclear dipolar interactions are gamma encoded, in which the spatial parts of m=2 are selected; (ii) the homonuclear polarization transfer is based on the scalar spin-spin coupling. Experimental data were obtained for [U-13C, 15N]-alanine and N-acetyl-[U-13C, 15N]-d,l-valine under magic-angle spinning at 25kHz. Only three data points are required for the measurements and the dihedral angles determined are in excellent agreement with the diffraction data.     

Current noise in the vicinity of the 2D superconductor-insulator quantum critical point

Systems near to quantum critical points show universal scaling in response to external probes. We consider whether this scaling is reflected in their out-of-equilibrium fluctuations. We study current noise in the metallic state at the z=1 quantum critical point between a superconductor and an insulator in two dimensions. Using a Boltzmann-Langevin approach within a 1/N expansion, we show that the current noise obeys a universal scaling form S_{j}=TPhi[T/T_{eff}(E)], with T_{eff} proportional, variantsqrt[E]. This treatment recovers Johnson noise in thermal equilibrium and S_{j} proportional, variantsqrt[E] at strong electric fields. The latter differs significantly from both the shot noise in conventional metals (diffusive Fermi liquids) and the free carrier result, due to strong correlations between the critical bosonic excitations. Current-noise measurements could therefore help clarify the physics of the destruction of superconductivity in thin film superconductors.