Weakly Non-Ergodic Statistical Physics

For weakly non ergodic systems, the probability density function of a time average observable is where is the value of the observable when the system is in state j=1,…L. p _j ^eq is the probability that a member of an ensemble of systems occupies state j in equilibrium. For a particle undergoing a fractional diffusion process in a binding force field, with thermal detailed balance conditions, p _j ^eq is Boltzmann’s canonical probability. Within the unbiased sub-diffusive continuous time random walk model, the exponent 0<α<1 is the anomalous diffusion exponent 〈x ²〉∼t ^α found for free boundary conditions. When α→1 ergodic statistical mechanics is recovered . We briefly discuss possible physical applications in single particle experiments.     

Random Walk Weakly Attracted to a Wall

We consider a random walk X _n in ℤ₊, starting at X ₀=x≥0, with transition probabilities

NLO contributions to <Emphasis Type="Italic">B</Emphasis>→<Emphasis Type="Italic">KK</Emphasis><Superscript>*</Superscript> decays in the pQCD approach

We calculate the important next-to-leading-order (NLO) contributions to the B→KK ^* decays from the vertex corrections, the quark loops, and the magnetic penguins in the perturbative QCD (pQCD) factorization approach. The pQCD predictions for the CP-averaged branching ratios are , , and Br(B ⁰→K ⁺ K ^*−+K ⁻ K ^*+)≈1.3×10⁻⁷, which agree well with both the experimental upper limits and the predictions based on the QCD factorization approach. Furthermore, the CP violating asymmetries of the considered decay modes are also evaluated. The NLO pQCD predictions for and decays are and .     

Study of Z pair production and anomalous couplingsin e + e- collisions at $\sqrt{s}$ between 190 GeV and 209 GeV

A study of Z-boson pair production in e ⁺ e^- annihilation at center-of-mass energies between 190 GeV and 209 GeV is reported. Final states containing only leptons, ( and ), quark and lepton pairs, ( , ) and only hadrons ( ) are considered. In all states with at least one Z boson decaying hadronically, lifetime, lepton and event-shape tags are used to separate pairs from final states. Limits on anomalous ZZ and ZZZ couplings are derived from the measured cross sections and from event kinematics using an optimal observable method. Limits on low scale gravity with large extra dimensions are derived from the cross sections and their dependence on polar angle.Received: 14 July 2003, Published online: 18 December 2003     

Study of spin and decay-plane correlations of W bosons in the e + e$^-\rightarrow$ W + W- process at LEP

Data collected at LEP at centre-of-mass energies GeV are used to study correlations of the spin of W bosons using events. Spin correlations are favoured by data, and found to agree with the Standard Model predictions. In addition, correlations between the W-boson decay planes are studied in and events. Decay-plane correlations are measured to be consistent with the Standard Model predictions.Received: 26 October 2004, Revised: 15 January 2005, Published online: 3 March 2005     

On the Best Constant in the Moser-Onofri-Aubin Inequality

Let S ² be the 2-dimensional unit sphere and let J _α denote the nonlinear functional on the Sobolev space H ¹(S ²) defined by

Preparation,structure and properties of La<Subscript>0.67</Subscript>Pb<Subscript>0.33</Subscript>(Mn<Subscript>1-x</Subscript>Co<Subscript>x</Subscript>)O<Subscript>3-δ</Subscript>

La_0.67Pb_0.33(Mn_1-xCo_x)O_3-δ ceramics with x=0, 0.01, 0.03, 0.06, 0.1 and 0.15 have been prepared in a two-step procedure. Precursor gels were made by the wet chemical malic acid method. The gels were calcined and then converted into ceramics by heat treatment at 950 °C and 1000 °C in air. X-ray diffraction showed that the compounds were phase pure. The crystal structure symmetry of the compounds was confirmed to be rhombohedral (space group R3̄c) for the whole investigated range of x. All compounds undergo a paramagnetic–ferromagnetic phase transition between 335 K and 225 K. The basic magnetic characteristics such as the Curie temperature , the paramagnetic Curie temperature θ, the effective magnetic moment and the saturated magnetization decrease with increasing Co doping. The ferromagnetic transition is accompanied by an anomaly in the electrical resistance for all compounds. The high-temperature insulator–metal transitions () do not coincide with the relevant . A large magnetoresistance peak of about 15% was observed for all compounds at . PACS 72.80.Ga; 75.47.Lx; 75.60.Ej     

Search for charged Higgs bosons at LEP in general two Higgs doublet models

A search for pair-produced charged Higgs bosons was performed in the data collected by the DELPHI detector at LEP II at centre-of-mass energies from 189 GeV to 209 GeV. Five different final states, , , , and were considered, accounting for the major expected decays in type I and type II Two Higgs Doublet Models. No significant excess of data compared to the expected Standard Model processes was observed. The existence of a charged Higgs boson with mass lower than 76.7 GeV/c² (type I) or 74.4 GeV/c² (type II) is excluded at the 95% confidence level, for a wide range of the model parameters. Model independent cross-section limits have also been calculated.Received: 30 September 2003, Revised: 12 February 2004, Published online: 8 April 2004     

Inhomogeneous contact processes on trees

We consider an inhomogeneous contact process on a tree of degreek, where the infection rate at any site isλ, the death rate at any site in isδ (with 0 <δ ⩽ 1) and that at any site in is 1. Denote by the critical value for thehomogeneous model (i.e.,δ=1) on and byϑ(δ, λ) the survival probability of the inhomogeneous model on . We prove that whenk > 4, if , a subtree embedded in , with 1 ⩽σ ⩽ √k, then three existsδ _c ^σ strictly between ( ) and 1 such that ( ) whenδ >δ _c ^σ andϑ(δ, λ _c( ) > 0 whenδ <δ _c ^σ ; ifS={o}, the origin of , then for anyδ ε (0, 1).     

New gauge bosons from the littlest Higgs modeland the process $e^{ + }e^{-}\rightarrow t\bar{t}$

In the context of the littlest Higgs (LH) model, we study the process . We find that the new gauge bosons Z _H and B _H can produce significant correction effects on this process, which can be further enhanced by suitably polarized beams. In most of the parameter space preferred by the electroweak precision data, the absolute value of the relative correction parameter is larger than 5 %. As long as and the absolute value of the relative correction parameter is larger than . With reasonable values of the parameters of the LH model, the possible signals of the new gauge bosons B _H and Z _H can be detected via the process in the future LC experiments with the CM energy . B _H exchange and Z _H exchange can generate significantly corrections to the forward-backward asymmetry only in a small part of the parameter space.Received: 29 October 2004, Revised: 29 November 2004, Published online: 15 February 2005     

Correlation Functions of Harish-Chandra Integrals over the Orthogonal and the Symplectic Groups

The Harish-Chandra correlation functions, i.e. integrals over compact groups of invariant monomials with the weight exp tr (X Ω Y Ω ^† ) are computed for the orthogonal and symplectic groups. We proceed in two steps. First, the integral over the compact group is recast into a Gaussian integral over strictly upper triangular complex matrices (with some additional symmetries), supplemented by a summation over the Weyl group. This result follows from the study of loop equations in an associated two-matrix integral and may be viewed as the adequate version of Duistermaat–Heckman’s theorem for our correlation function integrals. Secondly, the Gaussian integration over triangular matrices is carried out and leads to compact determinantal expressions.     

Condensation of the Roots of Real Random Polynomials on the Real Axis

We introduce a family of real random polynomials of degree n whose coefficients a _k are symmetric independent Gaussian variables with variance , indexed by a real α≥0. We compute exactly the mean number of real roots 〈N _n 〉 for large n. As α is varied, one finds three different phases. First, for 0≤α<1, one finds that . For 1<α<2, there is an intermediate phase where 〈N _n 〉 grows algebraically with a continuously varying exponent, . And finally for α>2, one finds a third phase where 〈N _n 〉∼n. This family of real random polynomials thus exhibits a condensation of their roots on the real line in the sense that, for large n, a finite fraction of their roots 〈N _n 〉/n are real. This condensation occurs via a localization of the real roots around the values , 1≪k≤n.     

An Algebraic Derivation of the Eigenspaces Associated with an Ising-Like Spectrum of the Superintegrable Chiral Potts Model

In terms of the loop algebra and the algebraic Bethe-ansatz method, we derive the invariant subspace associated with a given Ising-like spectrum consisting of 2 ^r eigenvalues of the diagonal-to-diagonal transfer matrix of the superintegrable chiral Potts (SCP) model with arbitrary inhomogeneous parameters. We show that every regular Bethe eigenstate of the τ ₂-model leads to an Ising-like spectrum and is an eigenvector of the SCP transfer matrix which is given by the product of two diagonal-to-diagonal transfer matrices with a constraint on the spectral parameters. We also show in a sector that the τ ₂-model commutes with the loop algebra, , and every regular Bethe state of the τ ₂-model is of highest weight. Thus, from physical assumptions such as the completeness of the Bethe ansatz, it follows in the sector that every regular Bethe state of the τ ₂-model generates an -degenerate eigenspace and it gives the invariant subspace, i.e. the direct sum of the eigenspaces associated with the Ising-like spectrum.     

Search for anomalous weak dipole moments of the $\tau$ lepton

The anomalous weak dipole moments of the lepton are measured in a data sample collected by ALEPH from 1990 to 1995 corresponding to an integrated luminosity of 155 pb^-1. Tau leptons produced in the reaction at energies close to the mass are studied using their semileptonic decays to , , or . The real and imaginary components of both the anomalous weak magnetic dipole moment and the CP-violating anomalous weak electric dipole moment, , , and , are measured simultaneously by means of a likelihood fit built from the full differential cross section. No evidence of new physics is found. The following bounds are obtained (95% CL): , , , and .Received: 25 September 2002, Published online: 29 August 2003     

Determining resonance parameters of heavy Higgs bosonsat a future linear collider

This study investigates the potential of an Electron-Positron Linear Collider for measuring resonance parameters of Higgs bosons beyond the mass range studied so far. The analysis is based on the reconstruction of events from the Higgs-strahlung process . It is shown that the total width , the mass m_H and the event rate N can be measured from the mass spectrum in a model independent way. Also, the branching ratios BR ^H_WW and BR ^H_ZZ can be measured, assuming these are the only relevant Higgs decay modes. The simulation includes realistic detector effects and all relevant Standard Model background processes. Results are given for m_H = 200-320 GeV assuming fb^-1 integrated luminosity at a collision energy GeV.Received: 13 February 2004, Revised: 14 April 2004, Published online: 18 May 2004     

Asymptotic Behavior of Inflated Lattice Polygons

We study the inflated phase of two dimensional lattice polygons with fixed perimeter N and variable area, associating a weight exp [pA−Jb] to a polygon with area A and b bends. For convex and column-convex polygons, we calculate the average area for positive values of the pressure. For large pressures, the area has the asymptotic behaviour , where , and ρ<1. The constant K(J) is found to be the same for both types of polygons. We argue that self-avoiding polygons should exhibit the same asymptotic behavior. For self-avoiding polygons, our predictions are in good agreement with exact enumeration data for J=0 and Monte Carlo simulations for J≠0. We also study polygons where self-intersections are allowed, verifying numerically that the asymptotic behavior described above continues to hold.     

Non-Lifshitz Tails at the Spectral Bottom of Some Random Operators

In this paper we continue with the investigation of the behavior of the integrated density of states of random operators of the form H _ω =−∇ ρ _ω ∇. In the present work we are interested in its behavior at 0, the bottom of the spectrum of H _ω . We prove that it converges exponentially fast to the integrated density of states of some periodic operator . Being periodic, cannot exhibit a Lifshitz behaviour. This result relates to the result of S.M. Kozlov (Russ. Math. Surv. 34(4):168–169, 1979) and improves it. Research partially supported by the Research Unity 01/UR/ 15-01 projects.     

(1+1)-Dirac Particle with Position-Dependent Mass in Complexified Lorentz Scalar Interactions: Effectively $\mathcal{PT}$ -Symmetric

The effect of the built-in supersymmetric quantum mechanical language on the spectrum of the (1+1)-Dirac equation, with position-dependent mass (PDM) and complexified Lorentz scalar interactions, is re-emphasized. The signature of the “quasi-parity” on the Dirac particles’ spectra is also studied. A Dirac particle with PDM and complexified scalar interactions of the form S(z)=S(x−ib) (an inversely linear plus linear, leading to a symmetric oscillator model), and S(x)=S _r (x)+iS _i (x) (a -symmetric Scarf II model) are considered. Moreover, a first-order intertwining differential operator and an η-weak-pseudo-Hermiticity generator are presented and a complexified -symmetric periodic-type model is used as an illustrative example.     

Absence of symmetry breaking for systems of rotors with random interactions

We prove that Gibbs states for the Hamiltonian , with thes _x varying on theN-dimensional unit sphere, obtained with nonrandom boundary conditions (in a suitable sense), are almost surely rotationally invariant if withJ _xy i.i.d. bounded random variables with zero average, 1 in one dimension, and 2 in two dimensions.     

Real Roots of Random Polynomials and Zero Crossing Properties of Diffusion Equation

We study various statistical properties of real roots of three different classes of random polynomials which recently attracted a vivid interest in the context of probability theory and quantum chaos. We first focus on gap probabilities on the real axis, i.e. the probability that these polynomials have no real root in a given interval. For generalized Kac polynomials, indexed by an integer d, of large degree n, one finds that the probability of no real root in the interval [0,1] decays as a power law n ^−θ(d) where θ(d)>0 is the persistence exponent of the diffusion equation with random initial conditions in spatial dimension d. For n≫1 even, the probability that they have no real root on the full real axis decays like n ^{−2(θ(2)+θ(d))}. For Weyl polynomials and Binomial polynomials, this probability decays respectively like and where θ _∞ is such that in large dimension d. We also show that the probability that such polynomials have exactly k roots on a given interval [a,b] has a scaling form given by where N _ab is the mean number of real roots in [a,b] and a universal scaling function. We develop a simple Mean Field (MF) theory reproducing qualitatively these scaling behaviors, and improve systematically this MF approach using the method of persistence with partial survival, which in some cases yields exact results. Finally, we show that the probability density function of the largest absolute value of the real roots has a universal algebraic tail with exponent −2. These analytical results are confirmed by detailed numerical computations. Some of these results were announced in a recent letter (Schehr and Majumdar in Phys. Rev. Lett. 99:060603, 2007).