Some comments on the solvable chiral potts model

We present a simple proof of the conjecture produced by Baxter, Perk and Au-Yang on the structure of the normalization factorR(p, q, r) corresponding to their new solution of the star-triangle equation related with the generalized Fermat curve. Some important properties of the underlying curvex ^N y ^N+x ^N+y ^N+1/k ²=0 for theN=3 state case are also established. Particularly, we calculate exactly its matrix of theb-periods for some normalized basis of holomorphic differentials. We also show that associated four-dimensional theta function may be decomposed into a sum containing 12 terms, each term being the product of four one-dimensional theta functions. We also derive Picard-Fuchs equations for the periods of holomorphic differentials of the same curve. The remarkable appearance of the hypergeometric functions in our answers seems to be closely related with an expression for the groundstate energy per site, obtained for the superintegrable case by Albertini, Perk, and McCoy and independently by Baxter, although for a moment the connection is not clear.     

Non-radiative energy transfer from Sm3+→Nd3+ in sodium borate glass

A study of energy transfer from optically excited Sm³⁺ to Nd³⁺ in borate glass has been performed. Contrary to the observations made by Cabezas and DeShazer, the Sm³⁺ → Nd³⁺ energy transfer has been observed as non-radiative. Energy transfer probabilities (P_da) and transfer efficiencies (η_T) have been calculated from our measurements of donor fluorescence intensity and decay times. The mechanism governing the transfer is electrostatic dipole-dipole in nature, contrary to the conclusions made by Nakazawa and Shionoya. At low acceptor (Nd³⁺) concentrations a linear dependence of P_da on acceptor concentration (C) has been observed which suggests the migration of excitation energy among donors. At high acceptor (Nd³⁺) concentration a plot of P_da vs (C_o + C)², where C_o is donor ion concentration, presents a linear dependence which is consistent with the Fong-Drestler theory of dipole-dipole energy transfer mechanism and interaction of one donor (Sm³⁺) with two acceptors (Nd³⁺).     

The forgotten 1D2 level of charmonium

The standard “charmonium” picture predicts four C=+1 states (³P₀, ³P₁, ³P₂, 2 ¹S₀) between ψ and ψ′. If these are identified with the four experimentally observed levels, serious difficulties arise. We remark that a ,,forgotten” ¹D₂ level (J^PC=2^?) is likely to be around 3.5 GeV. It may be identified with χ(2.45) or χ(3.50), avoiding the above above difficulties. The 2 ¹S₀ level has then yet to be discovered.     

Mathematics of noncanonical quantum theory

The Weyl relatione ^?isQ e ^itP e ^isQ =e ^it(P+sI) is generalized so as to hold for noncanonical couples (P,Q) implying the commutation relationi[P,Q]=C whereC is arbitrary bounded self-adjoint. It is shown that if 0 is not in the closure of the numerical range ofC then bothP andQ are spectrally continuous and neither bounded from below nor above. The dynamical equations in noncanonical theory are established. It is shown thatH (which is no longer given by correspondence) cannot be bounded from below (above) ifC≦0 (C≧0),C≠0.     

Quantum efficiency of non-radiative energy transfer from Eu3+ → Pr3+ in calibo glass

Study of energy transfer from optically excited Eu³⁺ to Pr³⁺ has been carried out in calibo glass. Probabilities (P_da) and efficiencies (η_T) of energy transfer from Eu³⁺ to Pr³⁺ have been calculated from the life time and emission intensity of Eu³⁺ + Pr³⁺. At low acceptor concentrations, P_da varies linearly with C_a showing migration of energy among donors. At high acceptor concentrations, P_da depends linearly on (C_a + C_d)², which is consistent with Fong and Diestler theory of dipole-dipole mechanism of energy transfer. At low temperatures the probability and the efficiency decrease due to increase in the emission intensity and life time, which suggests that at room temperature the energy is transferred to lattice by donor lowering life time and intensity. At high temperatures no emission from higher levels of donor is obtained which suggests blurring out of energy levels in glassy matrix.     

Instantons, Poisson Structures and Generalized Kähler Geometry

Using the idea of a generalized Kähler structure, we construct bihermitian metrics on CP² and CP¹×CP¹, and show that any such structure on a compact 4-manifold M defines one on the moduli space of anti-self-dual connections on a fixed principal bundle over M. We highlight the role of holomorphic Poisson structures in all these constructions.     

Gauge Theoretical Construction of Non-compact Calabi-Yau Manifolds

We construct the non-compact Calabi-Yau manifolds interpreted as the complex line bundles over the Hermitian symmetric spaces. These manifolds are the various generalizations of the complex line bundle over CP^N−1. Imposing an F-term constraint on the line bundle over CP^N−1, we obtain the line bundle over the complex quadric surface Q^N−2. On the other hand, when we promote the U(1) gauge symmetry in CP^N−1 to the non-abelian gauge group U(M), the line bundle over the Grassmann manifold is obtained. We construct the non-compact Calabi-Yau manifolds with isometries of exceptional groups, which we have not discussed in the previous papers. Each of these manifolds contains the resolution parameter which controls the size of the base manifold, and the conical singularity appears when the parameter vanishes.     

Low-energy e4 compton scattering of spin-12 targets without C,P and T invariances

We have studied the low-energy e⁴ Compton scattering on $\text{spin}\text{-}\text{1}\text{2}$ targets without assuming C, P and T invariances. It is shown that the scattering amplitude has a term ω³ ln ω (ω is the energy of incident photon in the lab frame), whose coefficient is determined entirely by the charge, mass, magnetic dipole moment, and electric dipole moment of the target. To derive the result, we calculate the second-order (in ω) terms of the e² Compton scattering amplitudes. When the electric dipole moment (whose existence violates P and T but conserves PT) is set to zero, the result reduces to that obtained before by Lin assuming C, P and T invariances.     

Quantum Hall effect in higher dimensions

Following recent work on the quantum Hall effect on S⁴, we solve the Landau problem on the complex projective spaces $\text{C}\text{P}{}^{\mathrm{k}}$ and discuss quantum Hall states for such spaces. Unlike the case of S⁴, a finite spatial density can be obtained with a finite number of internal states for each particle. We treat the case of $\text{C}\text{P}{}^2$ in some detail considering both Abelian and nonAbelian background fields. The wavefunctions are obtained and incompressibility of the Hall states is shown. The case of $\text{C}\text{P}{}^3$ is related to the case of S⁴.     

Pressure derivatives of bulk and shear modulus of rare gas solids

Expressions for the isothermal bulk and shear modulus and also their first and second order pressure derivatives for rare gas solids are derived by a simple method considering the different interactions i.e. modified variable induce dipoles, short range overlap repulsion and the vibrational contribution. The derived relations for dK_T/dP, dC_S/dP, dC′₄₄/dP, d²K_T/dP², d²C_S/dP² and d²C′₄₄/dP² are used to compute the numerical values of these constants at P=0 for Ne, Ar, Kr and Xe.     

On the interaction of excited alkali atoms with rare gas targets in scattering processes

A model potential calculation has been applied to evaluate scattering experiments for Na and K in the groundstate and the resonance state interacting with Ar. The model potential has only two free parameters which are determined by a best fit of the interatomic potentials to experimental results. Satisfactory agreement between calculated and experimental results is found for the differential cross sections in the groundstate and the excited state, for satellites in theK(4P),K(5P) and Na(3P) line profile, for the van der Waals constantsC ⁽⁶⁾ andC ⁽⁸⁾, the alkali ion-rare gas interaction and the vibrational energy levels of the Na-Ar molecule. As maior advantages we point out that for a given pair of atoms all these calculated data are given with one single pair of values for the free parameters and that with this set also the interatomic potentials for the higher alkali states (specifically up to 5f for Na and K) are obtained.     

Poincaré subalgebras in so(4, 2) and sl(5, R)

Injective homomorphisms ε which map the Poincaré Lie algebra P into so(4, 2)=C are considered. Two mappings ε₁ and ε₂ are said to be Int-equivalent iff there exists an inner automorphism ρⁱⁿ_c> of C such that ε₁=ρⁱⁿ_cε₂. The set of all ε splits into four Int- equivalence classes. Mappings in different classes are equivalent with respect to non-inner automorphisms of C. A corresponding theorem holds for homomorphisms of P into sl (5, R). These algebraic properties give strong limitations for those integrable representations of P which can be found by restriction of integrable representations of so(4, 2) and of sl(5, R) to ε(P). Physical applications of the results are discussed.     

The elastic behaviour of the ternary zincblende structure semiconductor CuGe2P3

A single crystal has been grown of CuGe₂P₃, a ternary semiconductor with a zincblende structure in which the copper and germanium atoms are randomly distributed on the cation sites. The second order elastic constants measured by the ultrasonic pulse echo overlap technique (C₁₁ = 13.66, C₁₂ = 6.17, C₄₄ = 6.66 and bulk modulus B = 8.67 in units of 10¹⁰Nm^?2 at 291 K) are closely similar to those of GaP and conform well to Keyes' correlation for zincblende structure crystals. The hydrostatic pressure derivatives of the second order elastic constants ($\text{?C}{}_{11}\text{?P}\text{= 4.40}$, $\text{?C}{}_{12}\text{?P}\text{= 3.9}$, $\text{?C}{}_{44}\text{?P}\text{= 0.93}$ and $\text{?B}\text{?P}\text{= 4.07}$) and the third order elastic constants (C₁₁₁ = ? 8.45, C₁₁₂ = ? 3.49, C₁₂₃ = ? 1.13, C₁₄₄ = ? 2.82, C₁₅₅ = ? 1.44 and C₄₅₆ = ? 0.69 in units of 10¹¹Nm^?2) also resemble those of GaP: even the anharmonicity of the long wavelength acoustic modes of this ternary semiconductor resembles that of its binary “parent” compound. The positive signs of the hydrostatic pressure derivatives and the negative signs of the third order elastic constants show that the acoustic modes at the long wavelength limit stiffen under pressure, an effect which is quantified here by computation of the mode Grüneisen parameters, which are all positive. The harmonic and anharmonic force constants, obtained in the valence force field model, fit well into the pattern shown by related zincblende structure compounds: the ratio ($\text{β}\text{α}$) for bond bending (β) to stretching (α) force constants is greater than 4:1; the dominating anharmonic force constant is γ: most of the anharmonicity is associated with nearest neighbour atoms. Analysis of the temperature dependence of the elastic constants on the basis of a simple anharmonic model again emphasises the similarity between the elastic behaviour of CuGe₂P₃ and GaP. The thermal expansion of CuGe₂P₃ varies almost linearly with temperature between 291 K and 1000 K, the linear coefficient of thermal expansion α being 8.21 ± 0.02 × 10^?6 °C^?1. The similar lattice parameters and elastic behaviour of CuGe₂P₃ and GaP indicate that semiconducting devices made of epitaxial deposits of CuGe₂P₃ on a GaP substrate should prove to be almost strain-free.     

Jahn-Teller effect for the 3A2-term

The first detection of the zero-phonon line (ZPL) structure in the absorption spectrum for an optical transition between the ³T₁ and ³A₂-terms (λ = 1.3–1.5 μm) is reported for CdS:Ni crystals. An analysis of the structure shows that its occurrence is due to the weak vibronic coupling of the ³A₂-state with trigonal pseudolocal vibrations of energy hω = 22 cm⁻¹, i.e. the dynamic Jahn-Teller (JT) effect is observed. The energy of the JT coupling is E_JT = 13 cm⁻¹. With E_JT < hω, a weak JT coupling takes place. Besides the ZPL, the absorption spectrum also involves other lines of vibronic nature which can be treated as dielectric local vibration modes. An axial pressure (P) is shown to lead to a change in the magnitude of E_JT: for P ∥ C(C being the optical axis of the crystal), E_JT increases, and for P ⊥ C, it decreases.     

High sensitivity CW-cavity ring down spectroscopy of CO2 near 1.35 μm (II): New observations and line intensities modeling

In a previous contribution [Kassi S, Song KF, Campargue A. High sensitivity CW-cavity ring down spectroscopy of ¹²CO₂ near 1.35 μm (I): line positions. JQSRT 110 (2009) 1801-1814], the line positions analysis of the high sensitivity absorption spectrum of carbon dioxide has been reported in the 7123-7793 cm⁻¹ region. In this second contribution, the spectral region investigated by CW-cavity ring down spectroscopy has been extended up to 7917 cm⁻¹. It added about 400 lines to our previous list of about 2500 transitions. These additional lines include transitions belonging to six newly observed ¹²C¹⁶O₂ bands for which we provide the spectroscopic parameters. Over the whole 7123-7917 cm⁻¹ region, the accurate intensities of about 2900 lines belonging to four isotopologues (¹²C¹⁶O₂, ¹³C¹⁶O₂, ¹⁶O¹²C¹⁸O and ¹⁶O¹²C¹⁷O) were retrieved with an average accuracy of 3%. Intensity values range between 1.2×10⁻²⁹ and 4.1×10⁻²⁵ cm/mol. Compared to the present version of the carbon dioxide spectroscopic databank recently adopted for the HITRAN database, important deviations were evidenced for some weak bands of the main isotopologue. The CW-CRDS intensity data relative to a total of 46 ¹²C¹⁶O₂ bands together with selected intensity information available in the literature for nine bands have been fitted simultaneously using the effective operators approach. The ΔP=11 set of the ¹²C¹⁶O₂ effective dipole moment parameters has been refined leading to a much better agreement with the measured intensity values. In addition, the ΔP=10 effective dipole moment parameters of the ¹⁶O¹²C¹⁸O minor isotopologue were determined for the first time. The obtained results will help to improve the carbon dioxide spectroscopic databank (CDSD).     

Lifting classes of principal bundles

Given a principal G-bundle P over X, we define a particularly suitable equivalence relation between liftings of P with respect to a group morphism σ:M→G. Supposing that σ has a central kernel C, we obtain a free operation of H¹(X$\text{C}$) (with coefficients in the sheaf of C-valued functions) on the set of lifting classes of P, which is natural under change of groups and base spaces. It is simply transitive, if in addition σ is an epimorphism; otherwise we classify its orbits by sections in the associated bundle P × _G(G/σM).For $\text{C=}\text{Z}{}_{\mathrm{n}}$ we relate the lifting classes to similar classes of n-th roots of associated line bundles. In the differentiable case and for an epimorphism σ with discrete kernel, there is a natural lifting of partial principal connections in each of these lifting classes. Finally, we indicate some applications to geometric quantization.     

Carbon clusters near the step of Rh surface: implication for the initial stage of graphene nucleation

To understand the initial nucleation of graphene by chemical vapor deposition along metal step, carbon clusters (N = 1 ～ 24) near Rh (4 3 3) stepwise surface were systemically explored by first-principles calculations. Carbon chains are always more stable than carbon rings on stepped metal surface. Starting from C₆, carbon chains prefer two-end passivation on the metal step. A structural transition of carbon clusters from one-dimensional sp chains to two-dimensional s p ² networks are found at C₁₀, which corresponds to the nucleation size at a wide range of chemical potentials. According to these theoretical results, we proposed that appropriately controlling the chemical potential may be helpful for observing the four stable carbon clusters along metal step and improving the quality of graphene.     

Spectroscopic modifications of Pippard relations: Tricritical phase transition in NH4Cl

We study here the Pippard relations modified spectroscopically for the NH₄Cl crystal. By relating the specific heat C_P to the frequency shift (1/ν)(∂ν/∂T)_P for the disorder-allowed Raman modes of ν₇ (93 cm⁻¹) and ν₅ (144 cm⁻¹) in NH₄Cl close to the tricritical point (P=1.6 kbar, T_C=257 K), we show that the first Pippard relation is valid for this crystalline system.     

Observation of the HeI 33 P polarization after medium energy He+ — Ne collisions with impact parameter selection

A quasi coincident method selective to impact parameters has been employed to determine four out of five possible density matrix elements of the Hel 3³ P excited term after He⁺(1s)+Ne(2p ⁶)→HeI(3³ P)+Ne⁺(?) collision processes for the He⁺ energies from 10 to 355 keV.     

Local conserved currents for CPN σ-models

We present a new method to derive an infinite series of conserved local charges for the two-dimensional CP^N σ-models. The generating relation for the conservation laws is a couple of first-order nonlinear differential equations. The method displays transparently the connection of the local charges with nonlocal dynamical charges of CP^N models previously found.