The quantum Weyl group and the universal quantumR-matrix for affine lie algebraA1(1)

The universal quantumR-matrix is obtained in the case of the affine Kac-Moody Lie algebra sl(2).     

The Bogoliubov inner product in quantum statistics

A natural Riemannian geometry is defined on the state space of a finite quantum system by means of the Bogoliubov scalar product which is infinitesimally induced by the (nonsymmetric) relative entropy functional. The basic geometrical quantities, including sectional curvatures, are computed for a two-level quantum system. It is found that the real density matrices form a totally geodesic submanifold and the von Neumann entropy is a monotone function of the scalar curvature. Furthermore, we establish information inequalities extending the Cramér-Rao inequality of classical statistics. These are based on a very general new form of the logarithmic derivative.This work was supported by the Hungarian National Foundation for Scientific Research, grant No. 1900. Authors' e-mail addresses are: H1128PET@ella.hu and TOTH@zodiac.rutgers.edu.     

Fermionic stochastic differential equations and the index of Fredholm operators

The index of a Fredholm operator associated to a-summable Fredholm module is expressed in terms of the vacuum expectation value of a unitary operator-valued stochastic process which satisfies a stochastic differential equation with unbounded coefficients driven by fermion noise.     

The algebra of differential operators on the circle and W KP (q)

Radul has recently introduced a map from the Lie algebra of differential operators on the circle of W _n . In this Letter, we extend this map to W _KP ^(q) , a recently introduced one-parameter deformation of W_KP - the second Hamiltonian structure of the KP hierarchy. We use this to give a short proof that W is the algebra of additional symmetries of the KP equation.     

Long-range order in a simple model of interacting fermions

We consider a model of spinless fermions on a lattice, interacting through a nearest neighbor repulsion. In the half-filled band case and for dimensionsd 2, we rigorously prove that there is long-range order in some domain of the parameters=(k _B T)^–1 andt/U, wheret is the hopping amplitude of the particles,U the strength of their repulsion, and the inverse temperature. Our technique is based on the usual Peierls argument of classical statistical mechanics but fails for the groundstate. We discuss the specific difficulties introduced by the Fermi statistics.Work supported in part by U.S. NSF grant PHY 90-19433-A02.     

Time-asymptotic boson states from infinite mean field quantum systems coupled to the boson gas

By means of cocycle techniques in a recent paper, the global dynamics of mean field-boson couplings has been studied. Here, by restricting to the bosonic system the infinite time limit (t ) for very general initial states, one obtains time-asymptotic states on the bosonicC ^*-Weyl algebra, in which one partially rediscovers the collective ordering of the infinite mean field lattice.     

Quasi-classical limit of Toda hierarchy andW-infinity symmetries

Previous results on quasi-classical limit of the KP hierarchy and itsW-infinity symmetries are extended to the Toda hierarchy. The Planck constant now emerges as the spacing unit of difference operators in the Lax formalism. Basic notions, such as dressing operators, Baker-Akhiezer functions, and tau function, are redefined.W _{1 +} symmetries of the Toda hierarchy are realized by suitable rescaling of the Date-Jimbo-Kashiara-Miwa vertex operators. These symmetries are contracted tow _{1 +} symmetries of the dispersionless hierarchy through their action on the tau function.     

Properties of sol-gel dip-coated zinc oxide thin films

Zinc oxide (ZnO) films were deposited on glass substrates by the sol-gel dip coating method using acrylamide route. The films were characterized by X-ray diffraction studies which indicated wurtzite structure. Optical absorption measurements indicated band gap in the range 3.17-3.32 eV. XPS studies indicated the formation of ZnO. The resistivity of the films were in the range 1000-10,000 ohm cm.     

Optical and photocatalytic properties of nanocrystalline TiO2 synthesised by solid-state chemical reaction

Nanoparticulate TiO₂ is of interest for a variety of technological applications, including optically transparent UV-filters and photocatalysts for the destruction of chemical waste. The successful use of nanoparticulate TiO₂ in such applications requires an understanding of how the synthesis conditions effect the optical and photocatalytic properties. In this study, we have investigated the effect of heat treatment temperature on the properties of nanoparticulate TiO₂ powders that were synthesised by solid-state chemical reaction of anhydrous TiOSO₄ with Na₂CO₃. It was found that the photocatalytic activity increased with the heat treatment temperature up to a maximum at 600 °C and thereafter declined. In contrast, the optical transparency decreased monotonically with the heat treatment temperature. These results indicate that solid-state chemical reaction can be used to prepare powders of nanoparticulate TiO₂ with properties that are optimised for use as either optically transparent UV-filters or photocatalysts.     

Raman spectroscopy of the BC3 phase obtained under high pressure and high temperature

A direct transformation of the g‐BC₃ phase to a new diamond‐like d‐BC₃ phase was observed in a diamond‐anvil cell (DAC) at high temperature, 2033 ± 241 K, and high pressure, 50 GPa. Analysis of the peak positions of the d‐BC₃, B₄C, α‐boron, and the boron‐doped diamond leads to the conclusion that the positions of the peaks of the d‐BC₃ are more similar to the peak pattern of the boron‐doped diamond rather than that of boron carbide, α‐boron. Copyright © 2007 John Wiley & Sons, Ltd.