Quantum rotors with regular frustration and the quantum Lifshitz point

We have discussed the zero-temperature quantum phase transition in n-component quantum rotor Hamiltonian in the presence of regular frustration in the interaction. The phase diagram consists of ferromagnetic, helical and quantum paramagnetic phase, where the ferro-para and the helical-para phase boundary meets at a multicritical point called a (d,m) quantum Lifshitz point where (d,m) indicates that the m of the d spatial dimensions incorporate frustration. We have studied the Hamiltonian in the vicinity of the quantum Lifshitz point in the spherical limit and also studied the renormalisation group flow behaviour using standard momentum space renormalisation technique (for finite n). In the spherical limit ()one finds that the helical phase does not exist in the presence of any nonvanishing quantum fluctuation for m =d though the quantum Lifshitz point exists for all d > 1+m/2, and the upper critical dimensionality is given by d _u = 3 +m/2. The scaling behaviour in the neighbourhood of a quantum Lifshitz point in d dimensions is consistent with the behaviour near the classical Lifshitz point in (d+z) dimensions. The dynamical exponent of the quantum Hamiltonian z is unity in the case of anisotropic Lifshitz point (d>m) whereas z=2 in the case of isotropic Lifshitz point (d=m). We have evaluated all the exponents using the renormalisation flow equations along-with the scaling relations near the quantum Lifshitz point. We have also obtained the exponents in the spherical limit (). It has also been shown that the exponents in the spherical model are all related to those of the corresponding Gaussian model by Fisher renormalisation. Received: 23 December 1997 / Received in final form: 6 January 1998 / Accepted: 7 January 1998     

Regular Basis and R-Matrices for the ^(su)(n)k Knizhnik–Zamolodchikov Equation

Dynamical R-matrix relations are derived for the group-valued chiral vertex operators in the SU(n) WZNW model from the KZ equation for a general four-point function including two step operators. They fit the exchange relations of the U _q (sl _n ) covariant quantum matrix algebra derived previously by solving the dynamical Yang–Baxter equation. As a byproduct, we extend the regular basis introduced earlier for SU(2) chiral fields to SU(n) step operators and display the corresponding triangular matrix representation of the braid group.     

Microphase separation at two length scales

The possibility of microphase separation at two different length scales in monodisperse AB block copolymer melts consisting of a homopolymer A block and either a linear alternating AB copolymer block (poly(A)_m-block-poly(B-alt -A)_n) or an AB comb copolymer block poly(A)_m-block-poly(A-graft-B)_n, is investigated. An analysis of the structure factor reveals that in the parameter space of n and m three different cases can be distinguished: I) The structure factor has only one minimum corresponding to the short length scale (i.e. the characteristic length of the repeating unit of the alternating or comb block). II) The structure factor has only one minimum corresponding to the long length scale (the characteristic length of the blocks). III) Two minima are present leading to a competition between microphase separation at the short and the long length scale. Depending on the choice of n and m, one of these three possibilities will occur. Received 25 August 2000     

Non-Maxwellian Electron Velocity Distribution Resulting from Electron-SF6 Attachment Collisions

A model reaction system is considered consisting of a heat bath of argon atoms (c) and small concentrations of SF₆-molecules (m) and electrons (e) (number densities: n_e ? n_m ? n_c). Within the model the time behaviour of the electron velocity distribution function is studied under the influence of elastic electron-argon collisions and electron SF₆ attachment collisions. On the basis of the distribution function time-dependent macroscopic quantities (kinetic electron temperature. nonequilibrium rate constant of the attachment reaction) are calculated.     

Block persistence

We define a block persistence probability p _l (t) as the probability that the order parameter integrated on a block of linear size l has never changed sign since the initial time in a phase-ordering process at finite temperature T<T _c . We argue that in the scaling limit of large blocks, where z is the growth exponent (), is the global (magnetization) persistence exponent and f(x) decays with the local (single spin) exponent for large x. This scaling is demonstrated at zero temperature for the diffusion equation and the large-n model, and generically it can be used to determine easily from simulations of coarsening models. We also argue that and the scaling function do not depend on temperature, leading to a definition of at finite temperature, whereas the local persistence probability decays exponentially due to thermal fluctuations. These ideas are applied to the study of persistence for conserved models. We illustrate our discussions by extensive numerical results. We also comment on the relation between this method and an alternative definition of at finite temperature recently introduced by Derrida [Phys. Rev. E 55, 3705 (1997)]. Received: 25 February 1998 / Revised: 24 July 1998 / Accepted: 27 July 1998     

Carbon clusters for absolute mass measurements at ISOLTRAP

The cyclotron frequencies of singly charged carbon clusters C_n ⁺ (n ≥ 2) were measured with the Penning-trap mass spectrometer ISOLTRAP at ISOLDE/CERN. The present limit of mass accuracy δm/m = 1.2 ^. 10^-8 and the extent of the mass-dependent systematic shift (δm/m)_sys = 1.7(0.6) ^. 10^-10/u ^. (m - m _ref) of the setup were investigated for the first time. In addition, absolute mass measurements by use of pure clusters of the most abundant carbon isotope ¹²C are now possible at ISOLTRAP. Received: 21 March 2002 / Accepted: 16 May 2002 / Published online: 31 October 2002 RID="a" ID="a"Present address: CERN, CH-1211 Geneva 23, Switzerland; e-mail: klaus.blaum@cern.ch     

Chiral SU(4) × SU(4) breaking: masses and decay constants of charmed hadrons

The (4, 4*) ⊕ (4*, 4) model of broken chiral SU (4) × SU (4) symmetry has been used to calculate the third-order coupling constants involving charmed and ordinary pseudoscalar mesons. These coupling constants are exploited to derive some interesting new relations among the masses and decay constants of these charmed particles. Using the known masses and decay constants as inputs, we exploit these relations to predict:F _D = −1·41F _π ,F _F = −1·13F _π ,F _D/F_F = 1·25,m(D _s) = 1·43 GeV,m(F _s) = 1·39 GeV andm(K _s) = 1·02 GeV.     

On bilocal gauge field theory

The nonlocal gauge group of unitary integral operators U _n (∞) is considered. Gluons in the nonlocal version of QCD are described by the bilocal gauge fields (BGF). The Higgs effect for BGF are discussed. It is shown that the local SU(n) gauge theory can be treated as a local limit of spontaneously broken U _n(∞)/SU(n) BGF theory.     

Reaction kinetics in polymer melts

We study the reaction kinetics of end-functionalized polymer chains dispersed in an unreactive polymer melt. Starting from an infinite hierarchy of coupled equations for many-chain correlation functions, a closed equation is derived for the 2nd order rate constant k after postulating simple physical bounds. Our results generalize previous 2-chain treatments (valid in dilute reactants limit) by Doi [#!doi:inter2!#], de Gennes [#!gennes:polreactionsiandii!#], and Friedman and O'Shaughnessy [#!ben:interdil_all_aip!#], to arbitrary initial reactive group density n₀ and local chemical reactivity Q. Simple mean field (MF) kinetics apply at short times, .For high Q, a transition occurs to diffusion-controlled (DC) kinetics with (where x_t is rms monomer displacement in time t) leading to a density decay . If n₀ exceeds the chain overlap threshold, this behavior is followed by a regime where during which k has the same power law dependence in time, , but possibly different numerical coefficient. For unentangled melts this gives while for entangled cases one or more of the successive regimes ,t ^-3/8 and t ^-3/4 may be realized depending on the magnitudes of Q and n₀. Kinetics at times longer than the longest polymer relaxation time are always MF. If a DC regime has developed before then the long time rate constant is where R is the coil radius. We propose measuring the above kinetics in a model experiment where radical end groups are generated by photolysis. Received: 2 June 1998 / Revised: 9 July 1998 / Accepted: 10 July 1998     

Photofragmentation of hydrated iron ions Fe(HO) () at 532, 355 and 266 nm

Photofragmentation of Fe(H₂O)n ⁺ clusters (n =1-9) is investigated at three different wavelengths, 532, 355 and 266 nm. Two fragmentation pathways are observed depending essentially on the photon energy, but also on the parent size n. The fragmentation products belong to two ion families, Fe(H₂O)m ⁺ and FeOH(H₂O)m ⁺ , which correspond to dehydration and intracluster dehydrogenation reactions respectively. The ion yields are studied as a function of the laser fluence in order to determine the number of photons implied in the photofragmentation process. This allows us to estimate that the D[(H₂O)_n-1Fe^+-(H₂O)] bond energy is ranging between 0.44 eV and 0.55 eV for .Photon absorption cross sections are also derived from the fluence experiments, and two different behaviors are observed: i) At 355 nm, far away from any transition, progressive solvation of the metal ion results in an increasing absorption cross section from n =2 to n =9. This can be attributed to a forbidden transition of bare , which becomes progressively allowed because of the interaction with more and more water ligands. ii) At 266 nm, close to several allowed transitions of bare , a distinct maximum is observed for the absorption of ion. It may be attributed to a change in the spin multiplicity when switching from and on one hand to Fe(H₂O) on the other. Received: 11 November 1997 / Revised: 18 February 1998 / Accepted: 22 April 1998     

Predictions of geometrical structures and ionization potentials for small barium clusters Ba

The geometrical structure of ground state Ba_n clusters (n =2-14) has been predicted from various types of calculations including two ab initio approaches used for the smaller sizes namely HF+MP2( n =2-6), DFT (LSDA)( n =2-6, 9) and one model approach HF+pairwise dispersion used for all sizes investigated here. The lowest energy configurations as well as some isomers have been investigated. The sizes n =4, 7 and 13 are predicted to be the relatively more stable ones and they correspond to the three compact structures: the tetrahedron, the pentagonal bipyramid and the icosahedron. The growth behavior from Ba₇ to Ba₁₃ appears to be characterized by the addition of atoms around a pentagonal bipyramid leading to the icosahedral structure of Ba₁₃ which is consistent with the observed size-distribution of barium clusters. Values for vertical ionization potentials calculated for n =2-5 at the CI level are seen to be in quite good agreement with recent measures. Received: 14 May 1997 / Received in final form: 2 February 1998 / Accepted: 27 February 1998     

Breaking of the SO(n) symmetry with vector and adjoint higgses

The spontaneous symmetry breaking of SO(n) is investigated by studying the most general quartic SO(n)-invariant Higgs potential with two multiplets of scalars belonging to a vector and to an adjoint representation. In the most general cases largest residual symmetry is found to be SU(l), SU(l-1), SO(l), SO(l-1) or SO(n-2) wherel is the rank of SO(n). In particular, the breaking of SO(n) into SU(n ₁)×SU(n ₂) is found to occur only in special cases.     

Light Quark Hadron Mass Scale

With a symmetry procedure based on Noether's theorem, the field equation of motion is obtained from the Dirac Hamiltonian H(D_μ) of a massless quark interacting with a gluon. The equation of motion is the Yang-Mills equation with external current which is spin-dependent and follows from the group algebra. In addition to the pure gauge solution we find a gauge covariant solution which follows from current conservation and sets the mass scale m₀/M = g². This gluon field is due to the density of dipole moments squared and represents four harmonic oscillators with quadratic constraints; the gluon can be written as a string potential or as a 1/x potential with a sharp cutoff. The chiral symmetry group G^spin × G^D gives the light quark hadron degenerate multiplet mass spectrum in terms of m₀[SU(2) × SU(2)] with the spinorial decomposition and the multipole breaks into dipoles. Scaling from atomic lengths it is found that g = em₀/nM for light quarks is the quark charge e/3 renormalized by m₀/M and g is magnetic. Thus quarks occur at the ends of spinning magnetic strings with dipole lengths ∼m₀⁻¹. The mass scale is that of a degenerate magnetic multipole with charge n = 3, 4… .     

Chiral symmetry breaking and condensates in the rishon model

The rishon model is studied in the limit g_c → 0, α → 0 when its global flavour symmetry is SU(6) × SU(6) × U(1) analogous to six massless flavour QCD. Recently it was shown that the ad hoc breaking SU(6) × SU(6) → SU(3) × SU(3) allows the anomaly constraint to be satisfied. In this paper this is shown to be but one of several successful patterns of chiral symmetry breaking. The condensates required to perform these breakings are fully discussed. A plausibility argument based on single gauge boson exchange is presented which determines the condensate uniquely to be 〈(v_LV_L)³〉 corresponding to the original breaking above. The same argument applies to QCD, which is argued to differ in its chiral behaviour due to the large intrinsic masses of the quarks. The implications of the above condensate and pattern of chiral symmetry breaking for the rishon model include the prediction of integer charged colour octet fermions, a naive mass formula m_e = 2m_u ? m_d, new insight into the parity-violating condensate 〈(v_Lv_L)²(v_Rv_R)〉 and the prediction of 52 new pseudos whose masses are estimated.     

Cooperativity in a spin transition ferrous polymer: Interacting domain model, thermodynamic, optical and EPR study

A new thermodynamic model is proposed in order to account for the high spin low spin conversion in metal-organic polymers. The model, based on the idea that the spin conversion occurs in interacting domains of like-spin metal ions, allows to explain most of the important features of various types of spin conversion. The sine qua non condition of the existence of spin transitions with hysteresis is obtained. In the case of very large cooperativity, the model predicts unusual behaviour of the spin conversion system due to a low-temperature metastable high spin state. Existence of such a state is interesting in the context of the light induced excited spin state trapping recently observed in some ferrous compounds. The model is applied to interpret the spin transition in polycrystalline ferrous polymer [Fe _1-y Cu _y (Htrz)₂ trz] (BF ₄) with y = 0.00, 0.01 and 0.10, detected by differential scanning calorimetry, optical reflectivity and electron paramagnetic resonance. The domain size and the interaction energy between the domains are estimated as, respectively, n = 11 and for the y = 0 compound. As the copper content is growing, n and tend to decrease, resulting in transformations of the shape of hysteresis loop which becomes less steep, narrows and shifts to lower temperatures. The electron paramagnetic resonance gives further evidence of the presence of like-spin domains. Received 27 November 1998 and Received in final form 19 April 1999     

No-scale supersymmetric GUTs

We construct locally supersymmetric GUTs in which radiative corrections determine all the mass scales which are hierarchically smaller than the Planck mass: $\text{m}{}_{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}\text{=}\text{O}\text{(m}{}_{\mathrm{<mtext>W</mtext>}}\text{) =}\text{exp}\text{(}\text{?}\text{O}\text{(1)}\text{α}{}_{\mathrm{<mtext>t</mtext>}}\text{)m}{}_{\mathrm{<mtext>p</mtext>}}$, etc. Such no-scale GUTs are based on a hidden sector with a flat potential guaranteed by SU(1, 1) conformal invariance. This is extended to include observable chiral fields in an SU(n, 1)/SU(n) × U(1) structure reminiscent of N ? 5 extended supergravity theories. Tree-level supersymmetry breaking is present only for the gravitino, and for the light gaugino masses through non-minimal kinetic terms reminiscent of N?4 extended supergravity theories. Radiative corrections generate squark and slepton masses which are phenomenologically acceptable, and the right value of m_W is obtained if m_t ≈ 50 GeV in the simplest such model.     

Canonical Structure and Symmetries of the Schlesinger Equations

The Schlesinger equations S _(n,m) describe monodromy preserving deformations of order m Fuchsian systems with n + 1 poles. They can be considered as a family of commuting time-dependent Hamiltonian systems on the direct product of n copies of m × m matrix algebras equipped with the standard linear Poisson bracket. In this paper we present a new canonical Hamiltonian formulation of the general Schlesinger equations S _(n,m) for all n, m and we compute the action of the symmetries of the Schlesinger equations in these coordinates.     

The n = 0 replica limit of U(n) and models

Recently the replica limit n = 0 of the U(n) and models have attracted interest since they describe the Anderson localization behaviour in the band-centre of a two-sublattice model. For n ≠ 0 the theories can be decomposed into one with symmetry U(1) and one for SU(n) and . This does not no longer hold for n = 0. We show how the beta-functions and zeta-functions for operators without derivatives can be obtained in this limit from those of SU(n) and and draw consequences for these functions in this limit.     

Spherical averaged jellium model with norm-conserving pseudopotentials

The effect of non-local norm-conserving pseudo-potentials on the static and dynamic properties of Na_n and Li_n cluster with n=6,8 is investigated in the frame of self-consistent LDA calculations with spherically averaged ionic density (SAPS model). A comparison with previous calculations which use local pseudo-potentials as well with uniform averaged non-local pseudo-jellium calculation has been carried out. A better quantitative agreement with experiments has been found in the calculation of the photoresponse cross-section with respect to either simple jellium or pseudo-jellium model, even in very small clusters, where deviations from sphericity are not negligible. Received: 3 March 1998 / Received in final form and Accepted: 2 June 1998