Change in the surface density of immobilized enzyme molecules due to photoelectron processes in a silicon substrate

The work was supported by the Russian Foundation for Basic Research, projects no. 16-08-00524

On the thermodynamic limit of form factors in the massless XXZ Heisenberg chain

We consider the problem of computing form factors of the massless XXZ Heisenberg spin-1/2 chain in a magnetic field in the (thermodynamic) limit where the size M of the chain becomes large. For that purpose, we take the particular example of the matrix element of the third component of spin between the ground state and an excited state with one particle and one hole located at the opposite ends of the Fermi interval (umklapp-type term). We exhibit its power-law decrease in terms of the size of the chain M, and compute the corresponding exponent and amplitude. As a consequence, we show that this form factor is directly related to the amplitude of the leading oscillating term in the long-distance asymptotic expansion of the two-point correlation function of the third component of spin.Comment: 28 page

Time-dependent correlation function of the Jordan-Wigner operator as a Fredholm determinant

We calculate a correlation function of the Jordan-Wigner operator in a class of free-fermion models formulated on an infinite one-dimensional lattice. We represent this function in terms of the determinant of an integrable Fredholm operator, convenient for analytic and numerical investigations. By using Wick's theorem, we avoid the form-factor summation customarily used in literature for treating similar problems.Comment: references added, introduction and conclusion modified, version accepted for publication in J. Stat. Mec

Kinetics of photo-stimulated adsorption of enzyme molecules onto n- and p-type silicon

The work was supported by the German-Russian Interdisciplinary Science Center (G-RISC) funded by the German Federal Foreign Office via the German Academic Exchange Service (DAAD), Project No. P-2018a-10

Form factor approach to dynamical correlation functions in critical models

We develop a form factor approach to the study of dynamical correlation functions of quantum integrable models in the critical regime. As an example, we consider the quantum non-linear Schr\"odinger model. We derive long-distance/long-time asymptotic behavior of various two-point functions of this model. We also compute edge exponents and amplitudes characterizing the power-law behavior of dynamical response functions on the particle/hole excitation thresholds. These last results confirm predictions based on the non-linear Luttinger liquid method. Our results rely on a first principles derivation, based on the microscopic analysis of the model, without invoking, at any stage, some correspondence with a continuous field theory. Furthermore, our approach only makes use of certain general properties of the model, so that it should be applicable, with possibly minor modifications, to a wide class of (not necessarily integrable) gapless one dimensional Hamiltonians.Comment: 33 page

Mid-infrared Variability from the Spitzer Deep Wide-field Survey

We use the multi-epoch, mid-infrared Spitzer Deep Wide-Field Survey to investigate the variability of objects in 8.1 deg^2 of the NOAO Deep Wide Field Survey Boötes field. We perform a Difference Image Analysis of the four available epochs between 2004 and 2008, focusing on the deeper 3.6 and 4.5 μm bands. Out of 474, 179 analyzed sources, 1.1% meet our standard variability selection criteria that the two light curves are strongly correlated (r > 0.8) and that their joint variance (σ_(12)) exceeds that for all sources with the same magnitude by 2σ. We then examine the mid-IR colors of the variable sources and match them with X-ray sources from the XBoötes survey, radio catalogs, 24 μm selected active galactic nucleus (AGN) candidates, and spectroscopically identified AGNs from the AGN and Galaxy Evolution Survey (AGES). Based on their mid-IR colors, most of the variable sources are AGNs (76%), with smaller contributions from stars (11%), galaxies (6%), and unclassified objects, although most of the stellar, galaxy, and unclassified sources are false positives. For our standard selection criteria, 11%-12% of the mid-IR counterparts to X-ray sources, 24 μm AGN candidates, and spectroscopically identified AGNs show variability. The exact fractions depend on both the search depth and the selection criteria. For example, 12% of the 1131 known z>1 AGNs in the field and 14%-17% of the known AGNs with well-measured fluxes in all four Infrared Array Camera bands meet our standard selection criteria. The mid-IR AGN variability can be well described by a single power-law structure function with an index of γ ≈ 0.5 at both 3.6 and 4.5 μm, and an amplitude of S _0 ≃ 0.1 mag on rest-frame timescales of 2 yr. The variability amplitude is higher for shorter rest-frame wavelengths and lower luminosities

Domain wall partition functions and KP

We observe that the partition function of the six vertex model on a finite square lattice with domain wall boundary conditions is (a restriction of) a KP tau function and express it as an expectation value of charged free fermions (up to an overall normalization).Comment: 16 pages, LaTeX2

Algebraic Bethe ansatz approach to the asymptotic behavior of correlation functions

We describe a method to derive, from first principles, the long-distance asymptotic behavior of correlation functions of integrable models in the framework of the algebraic Bethe ansatz. We apply this approach to the longitudinal spin- spin correlation function of the XXZ Heisenberg spin-1/2 chain (with magnetic field) in the disordered regime as well as to the density-density correlation func- tion of the interacting one-dimensional Bose gas. At leading order, the results confirm the Luttinger liquid and conformal field theory predictions.Comment: 78 page

On correlation functions of integrable models associated to the six-vertex R-matrix

We derive an analog of the master equation obtained recently for correlation functions of the XXZ chain for a wide class of quantum integrable systems described by the R-matrix of the six-vertex model, including in particular continuum models. This generalized master equation allows us to obtain multiple integral representations for the correlation functions of these models. We apply this method to derive the density-density correlation functions of the quantum non-linear Schrodinger model.Comment: 21 page