Inelastic scattering and elastic amplitude in Ising field theory in a weak magnetic field at T>T_c. Perturbative analysis

Two-particle scattering in Ising field theory in a weak magnetic field h is studied in the regime T>T_c, using perturbation theory in h^2. We calculate explicitly the cross-section of the process 2->3 to the order h^2. To this order, the corresponding cross-section dominates the total cross-section (the probability of all inelastic processes) at all energies E. We show that at high energies the h^2 term in the total cross-section grows as 16 G_3 h^2 log(E) where G_3 is exactly the third moment of the Euclidean spin-spin correlation function. Going beyond the leading order, we argue that at small h^2 the probability of the 2->2 process decays as E^(-16G_3 h^2) as E->infinity.Comment: 20 pages, 3 figures; typos correcte

Optical characterization of homogeneous and heterogeneous intralipid-based samples

Different scattering processes take place when photons propagate inside turbid media. Many powerful experimental techniques exploiting these processes have been developed and applied over the years in a large variety of situations from fundamental and applied research to industrial applications. In the present paper, we intend to take advantage of Static Light Scattering (SLS), Dynamic Light Scattering (DLS), and Time-Resolved Transmittance (TRT) for investigating all the different scattering regimes by using scattering suspensions in a very large range of scatterer concentrations. The suspensions were prepared using Intralipid 20%, a material largely employed in studies of the optical properties of turbid media, with concentrations from 10-5% to 50%. By the analysis of the angular and temporal dependence of the scattered light, a more reliable description of the scattering process occurring in these samples can be obtained. TRT measurements allowed us to obtain information on the reduced scattering coefficient, an important parameter largely used in the description of the optical properties of turbid media. TRT was also employed for the detection of inclusions embedded in Intralipid suspensions, by using a properly designed data analysis. The present study allowed us to better elucidate the dependence of scattering properties of Intralipid suspensions in a very large concentration range and the occurrence of the different scattering processes involved in the propagation of light in turbid media for the first time to our knowledge. In so doing, the complementary contribution of SLS, DLS, and TRT in the characterization of turbid media from an optical and structural point of view is strongly evidenced

Boundary form factors of the sinh-Gordon model with Dirichlet boundary conditions at the self-dual point

In this manuscript we present a detailed investigation of the form factors of boundary fields of the sinh-Gordon model with a particular type of Dirichlet boundary condition, corresponding to zero value of the sinh-Gordon field at the boundary, at the self-dual point. We follow for this the boundary form factor program recently proposed by Z. Bajnok, L. Palla and G. Takaks in hep-th/0603171, extending the analysis of the boundary sinh-Gordon model initiated there. The main result of the paper is a conjecture for the structure of all n-particle form factors of two particular boundary operators in terms of elementary symmetric polynomials in certain functions of the rapidity variables. In addition, form factors of boundary "descendant" fields have been constructedComment: 14 pages LaTex. Version to appear in J. Phys.

Interface localization near criticality

The theory of interface localization in near-critical planar systems at phase coexistence is formulated from first principles. We show that mutual delocalization of two interfaces, amounting to interfacial wetting, occurs when the bulk correlation length crit- ical exponent \u3bd is larger than or equal to 1. Interaction with a boundary or defect line involves an additional scale and a dependence of the localization strength on the distance from criticality. The implications are particularly rich in the boundary case, where de- localization proceeds through different renormalization patterns sharing the feature that the boundary field becomes irrelevant in the delocalized regime. The boundary delocal- ization (wetting) transition is shown to be continuous, with surface specific heat and layer thickness exponents which can take values that we determine

A statistical analysis of the characteristics of pigmented skin lesions using epiluminescence microscopy

Due to the fact that not all pigmented skin lesions (PSL) can be diagnosed solely by their clinical appearance, additional criteria are required to optimize the clinical diagnosis of atypical nevus and melanoma. Epiluminescence microscopy is a non-invasive in vivo examination that often helps to improved the accuracy of clinical diagnosis of such lesions. Years of experience have indicated some differential epiluminescent patterns for benign and malignant PSI, but there is some controversy about certain borderline lesions for which histological examination is always necessary. In our study we performed a statistical analysis of data concerning 183 PSI, to determine characteristics significantly associated with these lesions allowing identification of epiluminescent criteria suggestive of atypical nevus and malignant melanoma. Using he chi-quadro test and stepwise regression logistic model, we identified the following epiluminescent pattern as a risk factor for atypical nevus and malignant melanoma: irregular pigment network, presence of capillaries, irregular and abrupt ending of overall pigmentation, irregular brown globules and irregular shape and size of black dots

Haldane Gapped Spin Chains: Exact Low Temperature Expansions of Correlation Functions

We study both the static and dynamic properties of gapped, one-dimensional, Heisenberg, anti-ferromagnetic, spin chains at finite temperature through an analysis of the O(3) non-linear sigma model. Exploiting the integrability of this theory, we are able to compute an exact low temperature expansion of the finite temperature correlators. We do so using a truncated `form-factor' expansion and so provide evidence that this technique can be successfully extended to finite temperature. As a direct test, we compute the static zero-field susceptibility and obtain an exact match to the susceptibility derived from the low temperature expansion of the exact free energy. We also study transport properties, computing both the spin conductance and the NMR-relaxation rate, 1/T_1. We find these quantities to show ballistic behaviour. In particular, the computed spin conductance exhibits a non-zero Drude weight at finite temperature and zero applied field. The physics thus described differs from the spin diffusion reported by Takigawa et al. from experiments on the Haldane gap material, AgVP_2S_6.Comment: 51 pages, 5 figure

Universal Ratios in the 2-D Tricritical Ising Model

We consider the universality class of the two-dimensional Tricritical Ising Model. The scaling form of the free-energy naturally leads to the definition of universal ratios of critical amplitudes which may have experimental relevance. We compute these universal ratios by a combined use of results coming from Perturbed Conformal Field Theory, Integrable Quantum Field Theory and numerical methods.Comment: 4 pages, LATEX fil

Finite Temperature Dynamical Correlations in Massive Integrable Quantum Field Theories

We consider the finite-temperature frequency and momentum dependent two-point functions of local operators in integrable quantum field theories. We focus on the case where the zero temperature correlation function is dominated by a delta-function line arising from the coherent propagation of single particle modes. Our specific examples are the two-point function of spin fields in the disordered phase of the quantum Ising and the O(3) nonlinear sigma models. We employ a Lehmann representation in terms of the known exact zero-temperature form factors to carry out a low-temperature expansion of two-point functions. We present two different but equivalent methods of regularizing the divergences present in the Lehmann expansion: one directly regulates the integral expressions of the squares of matrix elements in the infinite volume whereas the other operates through subtracting divergences in a large, finite volume. Our central results are that the temperature broadening of the line shape exhibits a pronounced asymmetry and a shift of the maximum upwards in energy ("temperature dependent gap"). The field theory results presented here describe the scaling limits of the dynamical structure factor in the quantum Ising and integer spin Heisenberg chains. We discuss the relevance of our results for the analysis of inelastic neutron scattering experiments on gapped spin chain systems such as CsNiCl3 and YBaNiO5.Comment: 54 pages, 10 figure