Continued fractions and fermionic representations for characters of M(p,p′) minimal models

We present fermionic sum representations of the characters _{, s} ^{(p, p)} of the minimal M(p,p) models for all relatively prime integers p>p for some allowed values of r and s. Our starting point is biomial (q-binomial) identities derived from a truncation of the state counting equations of the XXZ spin 1/2 chain of anisotropy –=–cos((p/p)). We use the Takahashi-Suzuki method to express the allowed values of r (and s) in terms of the continued fraction decomposition of {p/p} (and p/p), where {x} stands for the fractional part of x. These values are, in fact, the dimensions of the Hermitian irreducible representations of SU _q- (2) (and SU _q+ (2)) with q–=exp(i{p/p}) (and q+=exp(i(p/p))). We also establish the duality relation M(p,p) M(p–p,p) and discuss the action of the Andrews-Bailey transformation in the space of minimal models. Many new identities of the Rogers-Ramanujan type are presented.Dedicated to Prof. Vladimir Rittenberg on his 60th birthday     

Induced modules for vertex operator algebras

For a vertex operator algebraV and a vertex operator subalgebraV which is invariant under an automorphismg ofV of finite order, we introduce ag-twisted induction functor from the category ofg-twistedV-modules to the category ofg-twistedV-modules. This functor satisfies the Frobenius reciprocity and transitivity. The results are illustrated withV being theg-invariants in simpleV orV beingg-rational.The first author was supported by NSF grant DMS-9303374 and a research grant from the Committee on Research, UC Santa Cruz.The second author was supported by NSF grant DMS-9401389.     

A Monomial Basis for the Virasoro Minimal Series M(p,p′) : The Case 1<p′/p<2

Quadratic relations are given explicitly in two cases of chiral conformal field theory, and monomial bases of the representation spaces are constructed by using the Fourier components of the intertwiners. The first case is the (2,1) primary fields for the (p,p)-minimal series M_r,s (1rp–1,1sp–1) for the Virasoro algebra where 1<p/p<2. We restrict ourselves to the case p3, for which the (2,1) primary field exists. The second case is the intertwiners corresponding to the two-dimensional representation for the level k integrable highest weight modules V() (0k) for the affine Lie algebra      

Some critical exponent inequalities for percolation

For a large class of independent (site or bond, short- or long-range) percolation models, we show the following: (1) If the percolation densityP (p) is discontinuous atp _c , then the critical exponent (defined by the divergence of expected cluster size, nP _n (p) (P _c –P)^– asp p _c ) must satisfy 2. (2) or (defined analogously to, but asp p _c ) and [P _n (p _c ) (n ^–1–1/) asn ] must satisfy, 2(1 – 1/). These inequalities for improve the previously known bound 1(Aizenman and Newman), since 2 (Aizenman and Barsky). Additionally, result 1may be useful, in standardd-dimensional percolation, for proving rigorously (ind>2) that, as expected,P _x has no discontinuity atp _c .     

Algebras for flavor quantum numbers

It is shown that the flavor quantum numbers of the basic elementary particles, leptons and quarks, as well as hadrons (with quarks as constituents), can be described withSU(2)×U(1) type of algebras. To treat simultaneously leptons and quarks (hadrons), we introduce the grace quantum number,G, in place ofL (the total lepton quantum number) andB (the baryon quantum number). The formalism developed here requires the basic elementary particles to come in even numbers. For the case of four basic particles we have quantum numbers denoted asQ, X, andY and their duals denoted asQ, X, andY. For the four leptonsQ is the ordinary charge, while —Y andY areL (the muon lepton number) andL _e (the electron lepton number), respectively. For the four quarksQ is the ordinary charge,Y the ordinary hypercharge, whileX, a new quantum number, is simply theX charge, which, however, can be related to charmC.     

Analysis of intermediate structures of spectral emission in pre-equilibrium nuclear reactions in the microscopic approach

The quasi-particle-phonon model of pre-equilibrium decay (QP Ph M PED) is proposed. Within this model, intermediate states are specified by the number of quasi-particles, quasi-holes and phonons. In describing nuclear relaxation we consider two types of internuclear transitions with the change in exciton number byN _ex=0, ±2 and number of phononN _ph=±1. The mixed densities of intermediate states(N _ex,N _ph,E) have been determined. An analysis has been made of the structure of the hard part of the emission spectrum in the⁶⁰Ni(p,p) and¹²⁰Sn(p,p) reaction at _p=62 MeV. This analysis suggests the importance of taking into account the transitions withN _ph=+1, along with the transitions withN _ex= +2.     

Direct observation of the second-order Stark effect of theX-B transition in molecular iodine

The second-order Stark shift of the components of the hyperfine structure of the transition¹ _g ⁺ ( = 0,j = 13, 15) ³ _ou ⁺ ( = 43,j = 12, 16) (of molecular iodine have been studied by means of saturated absorption spectroscopy in an external cell with the I₂ vapour located in an electric field. The anisotropic polarizabilities of the upper and lower levels together with the difference between the isotropic polarizabilities of the levels of the transition have been obtained.     

Natural boundaries for area-preserving twist maps

We consider KAM invariant curves for generalizations of the standard map of the form (x, y)=(x+y, y+f(x)), wheref(x) is an odd trigonometric polynomial. We study numerically their analytic properties by a Padé approximant method applied to the function which conjugates the dynamics to a rotation +. In the complex plane, natural boundaries of different shapes are found. In the complex plane the analyticity region appears to be a strip bounded by a natural boundary, whose width tends linearly to 0 as tends to the critical value.     

Sensitivity of approximate formulas for determining optical constants of thin films

The sensitivity of approximate formulas for determining the optical constants of thin films using measurement of reflectancesR and transmittancesT at normal incidence have been investigated theoretically. The ranges of refractive indexn, absorption indexk,2nk (=₂) andn ²–k ²(=₁) within relative errors of 5%, 10%, and 20% may be obtained. Selected signs of (₁)⁺ or (₁)^– have been determined. Validity of the condition n₀ A=n _s A has been also evaluated (A=1–R –T andA=1–R–T).     

Analytical electron microscopy study of diffusion-bonded multiphase system

This study presents diffusion experiments of NiAl coupled with pure Ni (Ni/NiAl). The couple produces the Ni₃Al-based intermetallic phase ( phase) as an intermediate layer at the interface during diffusion annealing. Analytical electron microscopy is used to examine microstructural features, crystallographic orientation and compositional variations across the interface. Interdiffusivities are measured from the compositional variations. It is shown that the growing behavior of the phase changes between higher and lower annealing temperatures. The growth kinetics of the phase is also discussed.     

Möbius function for the set of acyclic directed backbone graphs

Consider a two-rooted graphG, the edges of which are directed in such a way that there are no cycles and every edge belongs to some self-avoiding walk from rootu to rootv which follows the direction of the edges. Au-v backbone ofG is a subgraph formed by taking the union of any subset of directed self-avoiding walks fromu tov. Let _uv be the set of all such backbones ofG partially ordered by set-inclusion. We prove the conjecture of Bhatti and Essam that the Möbius function of this set is given, for acyclicb,b _uv withbb, by(b,b)=(–1) ^c-c , wherec andc are the respective cycle ranks ofb andb. The significance of this result in percolation theory is reviewed together with previous results for other sets of subgraphs.     

Quantum-resolved fluorescence excitation spectra of SnO free radical

TheA ¹ –X ^{1 +} system of SnO is studied by laser- induced fluorescence excitation spectroscopy using isotopically enriched tin Sn¹¹⁶. The rotational structure analysis has been carried out for 6-0, 5-0, 2-0 bands. All these spectra were well resolved only with few perturbed lines in 2-0 band. Rotational constantsB ₂,B ₅,B ₆ and henceB _e , _{e e} have been obtained for the Sn¹¹⁶O molecule. An extension of perturbation study on 4-0 band has been made showing the maximum perturbation occurs at different J values for different isotopes.     

Vector two-point functions in maximally symmetric spaces

We obtain massive and massless vector two-point functions in maximally symmetric spaces (and vacua) of any number of dimensions. These include de Sitter space and anti-de Sitter space, and their Euclidean analogsS ⁿ andH ⁿ. Our method is based on a simple way of constructing every possible maximally symmetric bitensorT _a...bc...d(x, x) which carries tangent-space indicesa...b atx andc...d atx.     

Effect of plastic deformation on precipitation in Al-30 wt.% Zn alloy aged at 200 °C

The electron microscopic investigation of an Al-30 wt.% Zn alloy reveals that the plastic deformation of quenched samples substantionally modifies the phase transformation processes examined in the alloy aged at 200°C. Whereas the growth kinetics of metastable precipitates and associated solute diffusion are unaffected by cold rolling the alloy specimens from 9% up to 97·5% reduction in thickness, the rate of all observed transformations is enhanced considerably by prior plastic deformation. A corresponding increase of stored strain energy within the lattice provides namely an additional driving force for the establishment of a new precipitate/matrix interface of higher surface energy on the transformation of a metastable precipitate into a more stable one. The sizes of transforming transition precipitates consequently diminish with an increase of cold work and the respective transformations are thus accelerated.High dislocation density in heavily cold worked alloy also reduces the nucleation barrier for a heterogeneous nucleation on dislocations. The formation of platelike coherent_coh precipitates with internal cubic structure on dislocations is observed followed by the transformation of_coh into spheroidical semicoherent precipitates. The non-uniform distribution of stresses and strains in cold rolled specimens leads to the development of deformation bands in the higher strained regions of even lightly deformed alloy. The direct precipitation of equilibrium precipitates in deformation bands is already observed immediately after cold work analogously to the -allotriomorph formation at grain boundaries.     

A solution spectrum of the nonlinear Schrödinger equation. II

It was shown in a previous communication that the nonlinear Schrödinger equation exhibits a spectrum of eigenfunctions of the form = _k,A _k (coshkx) ^–k and = _k B _k (coshkx) ^–k–1sinhkx, and the corresponding eigenvalues of the energy are related to a band structure with a characteristic energy gap as a significant feature. In the present paper, it is shown that a further spectrum exists exhibiting the general structure = _k=0 A _k(cosh kx)^–k–1/2and = _k=0 B_k(cosh kx)^–k–3/2sinhkx and yielding also a band structure. An extension of the solution spectrum to a nonlinear Klein-Gordon equation and a nonlinear Dirac equation does not imply essential difficulties, and the corresponding characteristic band structure has to be related to a mass spectrum.     

Kinetic equation in the kinetic region of the dilute and nonuniform electron plasma

Mori's scaling method is used to derive the kinetic equation for a dilute, nonuniform electron plasma in the kinetic region where the space-time cutoff (b, t _c) satisfies _Dbl _f , _D t _{c f} , with _D the Debye length, _D ^–1= _p the plasma frequency, andl _f and _f the mean free path and time, respectively. The kinetic equation takes account of the nonuniformity of the order ofl _f and _D for the single-and the two-particle distribution function, respectively. Thus the Vlasov term associated with the two-particle distribution function is retained. This kinetic equation is deduced from the kinetic equation in the coherent region obtained by Morita, Mori, and Tokuyama, where the space-time cutoff of the coherent region satisfies _Dbr ₀, _Dt _{c 0}, withr ₀ the Landau length and ₀ the corresponding time scale.     

Correlations of Spin States for Icosahedral Double Group

The irreducible bases of the icosahedral double groups I and I_h are explicitly presented in their respective group spaces. Applying these bases to the spin states |j, , we obtain a simple formula for combining the spin states into the symmetry-adapted bases which belong to a given row of given irreducible representations of I and I_h.     

Enhancement of conductance fluctuations in two-dimensional mesoscopic electron systems with valley structures

Conductance fluctuations are studied in twodimensional mesoscopic electron system with a two-hold valley degeneracy (n _v =2), which corresponds to the inversion layer of Si-MOSFET formed in (1,0,0) plane. It is shown that the intervalley scattering modifies conductance fluctuations depending on the ratio, Min { _c , _T }/ _v , where _v = ( – 2)/2 and _c , _T , and are, respectively, system traversal time, thermal diffusion time, intervalley scattering time and total life time of electrons. Conductance fluctuations are no longer universal and vary from G _univ 0.862·e ²/h to {ie223-5} at low temperatures even for isotropic systems. The conductance fluctuations increase with decreasing system size, increasing electron density and increasing intervalley scattering time. The effect of intervalley scattering is essentially the same as that of intersubband scattering as previously reported. At finite temperatures where _{T c} , the intervalley scattering modifies the fluctuations through the change in the energy correlation range to results in the reduction of the conductance fluctuations. In Si-MOSFET formed in (1, 1, 1) plane, wheren _v =6, more enhanced fluctuations are expected. Experimental studies are desired on theoretically predicted points.     

Microwave dielectric properties of Ti4+/MgO and Ni2+/MgO

The dielectric properties of titanium-doped magnesium oxide (Ti/MgO) and nickel-doped magnesium oxide (Ni/MgO) single crystals have been measured in the range of temperature from 300 to 450 K at the microwave frequency of 9.31 GHz. For both crystals the dielectric properties are found similar. From the conductivity data, the activation energy in the measured temperature region has been estimated to be 0.15 eV. The values of the temperature dependence (–1)^–1(+2)^–1 (/T) _p have been calculated. The data confirms the Bosmann and Havinga postulate that, for materials in which the dielectric constant; is less than 20 the temperature dependence should be positive.     

S0-S1 two photon absorption dynamics of organic dye solutions

The two-photon absorption cross-sections and excited-state absorption cross-sections of the dyes rhodamine 6G, methylene blue and fuchsin dissolved in methanol, and of the dyes safranine T, 1,3,3,1,3,3-hexamethylindocarbocyanine iodide (HMICI) and 1,3,1,3-tetramethyl-2,2-dioxopyrimidi-6,6-carbocyanine hydrogen sulphate (PYC) dissolved in hexafluoroisopropanol (HFIP) are determined. The excitation is achieved with picosecond light pulses of a passively mode-locked Nd-glass laser (_L = 1.054m). The influence of amplified spontaneous emission on the two-photon absorption dynamics is analysed.