Long-distance asymptotics of temperature correlators of the impenetrable Bose gas

The inverse scattering method is applied to the integrable nonlinear system describing temperature correlators of the impenetrable bosons in one space dimension. The corresponding matrix Riemann problems are constructed for two-point as well as for multi-point correlators. Long-distance asymptotics of two-point correlators is calculated.     

Measurement of high-order current correlators

The feasibility of measuring high-order current correlators by means of a linear detector is analyzed. Two different types of measurements are considered: measurement of fluctuation power spectrum and measurement of unequal-time current correlators at fixed points in time. In both cases, formally exact expressions in terms of Keldysh time-ordered electron current operators are derived for the detector output. An explicit time ordering is found for the current correlators under the expectation operator used in measurements of high-order unequal-time current correlators. The situation when a detector measures current correlators at different points of a conductor is considered.     

TFT construction of RCFT correlators IV:: Structure constants and correlation functions

We compute the fundamental correlation functions in two-dimensional rational conformal field theory, from which all other correlators can be obtained by sewing: the correlators of three bulk fields on the sphere, one bulk and one boundary field on the disk, three boundary fields on the disk, and one bulk field on the cross cap. We also consider conformal defects and calculate the correlators of three defect fields on the sphere and of one defect field on the cross cap.Each of these correlators is presented as the product of a structure constant and the appropriate conformal two- or three-point block. The structure constants are expressed as invariants of ribbon graphs in three-manifolds.     

Factorial correlators: angular scaling within QCD jets

Factorial correlators measure the amount of dynamical correlation in the multiplicity between two separated phase-space windows. We present the analytical derivation of factorial correlators for a QCD jet described at the double logarithmic (DL) accuracy. We obtain a new angular scaling property for properly normalized correlators between two solid-angle cells or two rings around the jet axis. Normalized QCD factorial correlators scale with the angular distance and are independent of the window size. Scaling violations are expected beyond the DL approximation, in particular from the subjet structure. Experimental tests are feasible, and thus would be welcome. Received: 12 January 2001 / Published online: 7 September 2001     

Quantum Harmonic Oscillator Systems with Disorder

We study many-body properties of quantum harmonic oscillator lattices with disorder. A sufficient condition for dynamical localization, expressed as a zero-velocity Lieb-Robinson bound, is formulated in terms of the decay of the eigenfunction correlators for an effective one-particle Hamiltonian. We show how state-of-the-art techniques for proving Anderson localization can be used to prove that these properties hold in a number of standard models. We also derive bounds on the static and dynamic correlation functions at both zero and positive temperature in terms of one-particle eigenfunction correlators. In particular, we show that static correlations decay exponentially fast if the corresponding effective one-particle Hamiltonian exhibits localization at low energies, regardless of whether there is a gap in the spectrum above the ground state or not. Our results apply to finite as well as to infinite oscillator systems. The eigenfunction correlators that appear are more general than those previously studied in the literature. In particular, we must allow for functions of the Hamiltonian that have a singularity at the bottom of the spectrum. We prove exponential bounds for such correlators for some of the standard models.     

Subtracted dispersion relations for in-medium meson correlators in QCD sum rules

We analyze subtracted dispersion relations for meson correlators at finite baryon density and temperature. Such relations are needed for QCD sum rules. We point out the importance of scattering terms, as well as finite, well-defined subtraction constants. Both are necessary for consistency, in particular for the equality of the longitudinal and transverse correlators in the limit of vanishing three-momentum of mesons relative to the medium. We present detailed calculations in various mesonic channels for the case of the Fermi gas of nucleons.     

Heavy quarkonia survival in potential model

We investigate the quarkonia correlators in QCD with no light quarks within a potential model with different screened potentials. Our results for the temperature dependence of the charmonium and bottomonium correlators are qualitatively consistent with existing and preliminary lattice results. We identify however, a much richer structure in the correlators than the one seen on the lattice.Arrival of the final proofs: 3 March 2005PACS: 11.15.Ha, 11.10.Wx, 12.38.Mh, 25.75.Nq     

Spatial and temporal hadron correlators below and above the chiral phase transition

Hadronic correlation functions at finite temperature in QCD, with four flavours of dynamical quarks, have been analyzed both above and below the chiral symmetry restoration temperature. We have used both point and extended sources for spatial as well as temporal correlators. The effect of periodic temporal boundary conditions for the valence quarks on the spatial meson correlators has also been investigated. All our results are consistent with the existence of individual quarks at high temperatures. A measurement of the residual interaction between the quarks is presented.     

Parity effects in eigenvalue correlators, parametric and crossover correlators in random matrix models: Application to mesoscopic systems

This paper summarizes some work that I have been doing on eigenvalue correlators of random matrix models which show some interesting behavior. First we consider matrix models with gaps in their spectrum or density of eigenvalues. The density-density correlators of these models depend on whether N, where N is the size of the matrix, takes even or odd values. The fact that this dependence persists in the large N thermodynamic limit is an unusual property and may have consequences in the study of one electron effects in mesoscopic systems. Secondly, we study the parametric and cross correlators of the Harish Chandra-Itzykson-Zuber matrix model. The analytic expressions determine how the correlators change as a parameter (e.g. the strength of a perturbation in the Hamiltonian of the chaotic system or external magnetic field on a sample of material) is varied. The results are relevant for the conductance fluctuations in disordered mesoscopic systems.     

Calculating particle correlators with the account of detector efficiency

The formulae for m-order correlators K _m of a given particle observable (e.g., energy, transverse momentum or a conserved discrete quantum number) accounting for the track reconstruction efficiencies in a real detector are presented. The calculation of second- to fourth-order correlators is considered in some detail. Similar to the case of an ideal detector, the correlators can be expressed through the event-by-event fluctuation measures of the observable single event mean, the pseudocorrelators (determined by the pseudo-central moments of the observable distribution) and their cross terms. It allows one to avoid the combinatorics and essentially reduce the computer time when calculating the higher-order correlators in high multiplicity events. Compared with the case of ideal detector, this reduction is somewhat smaller due to the increased number of pseudocorrelators and additional calculations of the moments of the distribution of the track weights. For a constant track reconstruction efficiency, the correlator formulae reduce to those for an ideal detector. However, in real experiments the efficiencies are usually essentially dependent on particle momenta and may lead to substantial corrections of momentum correlators on the level of tens of percent.     

Time Ordering and Counting Statistics

The basic quantum mechanical relation between fluctuations of transported charge and current correlators is discussed. It is found that, as a rule, the correlators are to be time-ordered in an unusual way. Instances where the difference with the conventional ordering matters are illustrated by means of a simple scattering model. We apply the results to resolve a discrepancy concerning the third cumulant of charge transport across a tunnel junction.     

A virtual pipe rig for testing acoustic leak detection correlators: Proof of concept

Acoustic correlators have been used for many years to locate and detect leaks in buried water distribution pipes. Currently, the only way to compare different correlators directly is in the field. This can be problematic as it may be difficult to present exactly the same conditions to each correlator. In recent years, the way in which leak noise propagates in buried water pipes has been determined, and this has enabled the development of a virtual pipe whose behaviour can be simulated in the computer. By coupling the filtering properties of the pipe with electrodynamic shakers, a proof-of-concept virtual pipe test-rig has been developed that will allow different correlators to be compared directly in laboratory conditions. Different situations, such as pipe material and size, and measurement positions, as well as leak strength can be simulated. The theoretical basis of the test-rig and details of the proof-of-concept system are discussed in this paper. It is shown that careful consideration of the dynamics of the shakers is vital if the system is to faithfully model situations that are found in the field.     

The properties of conformal blocks,the AGT hypothesis,and knot polynomials

Various properties of correlators of the two-dimensional conformal field theory are discussed. Specifically, their relation to the partition function of the four-dimensional supersymmetric theory is analyzed. In addition to being of interest in its own right, this relation is of practical importance. For example, it is much easier to calculate the known expressions for the partition function of supersymmetric theory than to calculate directly the expressions for correlators in conformal theory. The examined representation of conformal theory correlators as a matrix model serves the same purpose. The integral form of these correlators allows one to generalize the obtained results for the Virasoro algebra to more complicated cases of the W algebra or the quantum Virasoro algebra. This provides an opportunity to examine more complex configurations in conformal field theory. The three-dimensional Chern–Simons theory is discussed in the second part of the present review. The current interest in this theory stems largely from its relation to the mathematical knot theory (a rather well-developed area of mathematics known since the 17th century). The primary objective of this theory is to develop an algorithm that allows one to distinguish different knots (closed loops in three-dimensional space). The basic way to do this is by constructing the so-called knot invariants.     

Fisher-Hartwig conjecture and the correlators in the inpenetrable Bose gas

We apply the theorems from the theory of Toeplitz determinants to calculate the asymptotics of various correlators including the exponential ones in the inpenetrable one-dimensional Bose gas system. The known correlators in the free-fermion system are also used to test the generalized Fisher-Hartwig conjecture.     

OPE and sum rules for correlators of pseudoscalar and axial currents

We study the operator product expansion (OPE) and quark-hadron duality for two-and three-point correlators of the axial (A) and pseudoscalar (P) currents of the light quarks. In the chiral limit, these correlators are often dominated by nonperturbative power corrections leading to subtleties of quark-hadron duality relations and of the extraction of properties of light pseudoscalars. For the two-point correlators, we show the sum rule for 〈PP〉 to be sensitive to the excited light pseudoscalar. For the three-point correlators, we derive the Ward identities which provide the normalization of the pion electromagnetic form factor at zero momentum transfer. For large momentum transfer, we demonstrate the way the correct behavior of the pion form factor in agreement with perturbative QCD emerges from condensate terms in the OPE for the 〈PV P〉 and 〈AV P〉 correlators. The local-duality sum rule for 〈AV A〉 is shown to lead to the pion form factor with the required properties for all values of the momentum transfer. The text was submitted by the authors in English. On leave from Institute of Nuclear Physics, Moscow State University, Moscow, Russia.     

Generating Function of Correlators in the sl2 Gaudin Model

An exponential generating function of correlators is calculated explicitly for the sl2 Gaudin model (degenerated quantum integrable XXX spin chain). The calculation relies on the Gauss decomposition for the SL(2) loop group. A new explicit expression for the correlators is derived from the generating function, from which the determinant formulas for the norms of Bethe eigenfunctions due to Richardson and Gaudin are obtained.     

Dual field formulation of quantum integrable models

Equal time correlators are studied in completely integrable models. The main example is the quantum non-linear Schrödinger equation. Introduction of an auxiliary Fock space permits us to represent the generating functional of correlators in the form of a determinant of the integral operator.     

Effect of long-range correlation on scaling behavior of normalized factorial moments for the first-order phase transition

Within the framework of Ginzburg–Landau theory, the effect of multiplicity correlation between the dynamical multiplicity fluctuations is analyzed for a first-order phase transition from quark–gluon plasma to hadrons.Normalized factorial correlators are used to study the correlated dynamical fluctuations. A scaling behavior is found among the factorial correlators, and an approximate universal exponent, which is weakly dependent on the details of the phase transition, is obtained.     

Engineering implementation of a hybrid optical correlator using SLMs

Optical correlators have been widely used for such applications as automatic target identification, invariant pattern recognition and machine vision. In hybrid optical correlators, Spatial light modulators (SLMs) are used to dynamically update the input and the filter. However, implementation is difficult because of the interference of “ghost” images; rigorous requirements for filter registration, accurate and effective filter sizing and complex valued filtering functions. This paper proposes some practical approaches to handle these issues and provides engineering details of how to build a hybrid optical correlator, where a SLM serves as an updateable intensity filter for real-time pattern recognition.