Temperature Correlation Functions Research Articles

A comment on finite temperature correlations in integrable QFT

I discuss and extend the recent proposal of Leclair and Mussardo for finite temperature correlation functions in integrable QFTs. I give further justification for its validity in the case of one-point functions of conserved quantities. I also argue that the proposal is not correct for two- (and higher-) point functions, and give some counterexamples to justify that claim.

Finite Temperature Correlation Functions of One-dimensional Interacting Electron Systems

The well-known bosonisation method of one-dimensional electron systems is extended to finite temperatures. As an example, the correlation functions of the non-interacting case are explicitly calculated. The presentation is pedagogical and is intended to be accessible to graduate students or physicists who are not experts in this field.

Integral equations for correlation functions of a quantum one-dimensional Bose gas

The large time and long distance behavior of the temperature correlation functions of the quantum one-dimensional Bose gas is considered. We obtain integral equations, which solutions describe the asymptotics. These equations are closely related to the thermodynamic Bethe Ansatz equations. In the low temperature limit the solutions of these equations are given in terms of observables of the model.

Finite temperature correlation functions in integrable QFT

Finite temperature correlation functions in integrable quantum field theories are formulated only in terms of the usual, temperature-independent form factors, and certain thermodynamic filling fractions which are determined from the thermodynamic Bethe ansatz. Explicit expressions are given for the one- and two-point functions.

On the Riemann-Hilbert approach to asymptotic analysis of the correlation functions of the quantum nonlinear schrödinger equation: Interacting fermion case

We consider the local field dynamic temperature correlation function of the quantum nonlinear Schrödinger equation with a finite coupling constant. This correlation function admits a Fredholm determinant representation. The related operator-valued Riemann-Hilbert problem is used to analyze the leading term of the large time and distance asymptotic expansion of the correlation function.

Dynamics of the classical two dimensional XY ferromagnet at low temperatures: a memory function approach

The spin dynamics of two dimensional XY ferromagnet are reexamined at low temperatures in the framework of the Mori continued fraction formalism using the Gaussian approximation. In this formalism, the terms on denominators for the Laplace transform of the relaxation function R(t) are related to the frequency moments<img src="http:/img/fbpe/bjp/v28n4/sd6.gif" alt="sd6.gif (174 bytes)" align="absmiddle"> of the relaxation shape function R(q,w). In the Gaussian approximation scheme, we truncate the continued fraction for R(t) on the second stage. Adopting this approximation, we calculated up to the sixth moment. The moments are writing in terms the static spin correlation functions. In the estimation of the fourth and sixth moment at finite temperature, the four and six-spin correlation functions may be approximated by a sum of products of appropriate pair correlation functions(mode-mode decoupling). In this work we calculated the static spin correlation functions for the expressions to the fourth and sixth moments, needed in the study of the dynamics.

Computing CMB anisotropy in compact hyperbolic spaces

The measurements of CMB anisotropy have opened up a window for probing the global topology of the universe on length scales comparable to and beyond the Hubble radius. For compact topologies, the two main effects on the CMB are: (i) the breaking of statistical isotropy in characteristic patterns determined by the photon geodesic structure of the manifold and (ii) an infrared cut-off in the power spectrum of perturbations imposed by the finite spatial extent. We present a completely general scheme using the regularized method of images for calculating CMB anisotropy in models with non-trivial topology, and apply it to the computationally challenging compact hyperbolic topologies. This new technique eliminates the need for the difficult task of spatial eigenmode decomposition on these spaces. We estimate a Bayesian probability for a selection of models by confronting the theoretical pixel-pixel temperature correlation function with the COBE-DMR data. Our results demonstrate that strong constraints on compactness arise: if the universe is small compared to the `horizon' size, correlations appear in the maps that are irreconcilable with the observations. If the universe is of comparable size, the likelihood function is very dependent upon orientation of the manifold with respect to the sky. While most orientations may be strongly ruled out, it sometimes happens that for a specific orientation the predicted correlation patterns are preferred over the conventional infinite models.

Temperature correlators in the one-dimensional Hubbard model in the strong coupling limit

We consider the one-dimensional Hubbard model with infinitely strong repulsion. The two-point dynamical temperature correlation functions are calculated. They are represented as Fredholm determinants of linear integrable integral operators.

Critical phenomena in finite-size system with Gaussian direct correlation function. 1. Pair correlation function and shift of critical temperature

Critical phenomena in finite-size system with Gaussian direct correlation function. 1. Pair correlation function and shift of critical temperature

Long-Ranged Correlations in Bounded Nonequilibrium Fluids

In a recent paper, Liu and Oppenheim [J. Stat. Phys.86:179 (1997)] solve the fluctuating heat diffusion equation for a bounded system with a temperature gradient. This note demonstrates that, contrary to their claims, their solution for the temperature correlation function is indeed long-ranged and reduces to that of Garcia et al.[J. Stat. Phys.47:209 (1987)].

Correlators of the phase model

We introduce the phase model on a lattice and solve it using the algebraic Bethe ansatz. Time-dependent temperature correlation functions of phase operators and the “darkness formation probability” are calculated in the thermodynamical limit. These results can be used to construct integrable equations for the correlation functions and to calculate their asymptotics.

Critical behavior and the Néel temperature of quantum quasi-two-dimensional Heisenberg antiferromagnets

The nonlinear sigma-model and its generalization on N-component spins, the O(N) model, are considered to describe thermodynamics of a quantum quasi-two-dimensional (quasi-2D) Heisenberg antiferromagnet. A comparison with standard spin-wave approaches is performed. The sublattice magnetization, Neel temperature and spin correlation function are calculated to first order of the 1/N-expansion. A description of crossover from a 2D-like to 3D regime of sublattice magnetization temperature dependence is obtained. The values of the critical exponents derived are \beta =0.36, \eta =0.09. An account of the corrections to the standard logarithmic term of the spin-wave theory modifies considerably the value of the Neel temperature. The thermodynamic quantities calculated are universal functions of the renormalized interlayer coupling parameter. The renormalization of interlayer coupling parameter turns out to be considerably temperature dependent. A good agreement with experimental data on La2CuO4 is obtained. The application of the approach used to the case of a ferromagnet is discussed.

Perturbation growth and cosmic microwave background anisotropies in the stringlike matter-dominated universe.

The growth of small perturbations and the temperature correlation function of cosmic background radiation induced by the perturbations in the isotropic and homogeneous universe with arbitrary spatial curvature, filled with nonrelativistic and so-called stringlike matter (cosmic strings, textures or time-varying cosmological constant) are calculated. It is shown that both magnitudes are insensitive to the eventual existence of the stringlike matter in the universe. The widespread opinion that the stringlike matter-dominated universe suppresses the growth of perturbations is questioned. \textcopyright{} 1996 The American Physical Society.

Two-Point Correlations in the [ITAL]COBE[/ITAL] DMR Four-Year Anisotropy Maps

The two-point temperature correlation function is evaluated from the 4 yr COBE DMR microwave anisotropy maps. We examine the two-point function, which is the Legendre transform of the angular power spectrum, and show that the data are statistically consistent from channel to channel and frequency to frequency. The most likely quadrupole normalization is computed for a scale-invariant power-law spectrum of CMB anisotropy, using a variety of data combinations. For a given data set, the normalization inferred from the two-point data is consistent with that inferred by other methods. The smallest and largest normalizations deduced from any data combination are 16.4 and 19.6 μK, respectively, with a value ~18 μK generally preferred.

Integrable differential equations for temperature correlation functions of the XXO Heisenberg chain

It is shown that the two-point time-dependent temperature correlators of the XXO Heisenberg spin chain satisfy a system of classical equations in the distance between correlating spins and time. This system is an integrable lattice version of the nonlinear Schrodinger equation. Bibliography: 17 titles.

Analytic approach to the polarization of the cosmic microwave background in flat and open universes.

We develop an analytic method and approximations to compute the polarization induced in the cosmic microwave background radiation on a wide range of angular scales by anisotropic Thomson scattering in the presence of adiabatic scalar (energy-density) linear fluctuations. The formalism is an extension to the polarized case of the analytic approach recently developed by Hu and Sugiyama to evaluate the (unpolarized) temperature correlation function. The analytic approach helps to highlight the dependence of potentially measurable polarization properties of the cosmic microwave background radiation upon various parameters of the cosmological model. We show, for instance, that the ratio between the multipoles of the temperature and polarization correlation functions depends very sensitively upon the value of ${\mathrm{\ensuremath{\Omega}}}_{0}$, the matter density in units of the critical, in an open universe.

Temperature quench echoes in proteins

Temperature quench echoes are analyzed in terms of the temperature–temperature correlation function in the harmonic approximation, and the resulting expressions are compared with molecular dynamics simulations. The relationship between the time dependence of the echo depth and the density of states is demonstrated for harmonic systems. For a protein, which has significant anharmonicity, the time dependence is dominated by relaxation effects that originate from dephasing of the periodic motions. A simple relaxation model is shown to provide a good description of the results observed in the simulations.

Velocity reassignment echoes in proteins

A new echo phenomenon in proteins, a generalization of so-called temperature quench echoes, is introduced and shown to reveal, through molecular dynamics simulations, periodic motions (normal modes) in proteins with phase coherence times of about one picosecond. The echoes are induced through reassignments of Cartesian velocities to protein atoms at times t=0 and t=τ (0&amp;lt;τ≤1 ps) and appear as two sharp (widths of about 5 fs) features in the kinetic and potential energy at t=3τ/2 and t=2τ. The velocities, assigned at t=0 and at t=τ to each atom, need to be correlated, but can otherwise be random. The echo at 3τ/2 can be induced without any change in the temperature of the protein. Skeletal motions involving angular and stretch motions contribute principally to the echo effect. Electrostatic interactions do not affect the echoes. The echoes in the temperature are described, in the framework of the harmonic approximation, in terms of the equilibrium temperature–temperature correlation function. The velocity reassignments induce the echoes through the generation of phase coherence of protein modes. Phase relaxation due to anharmonic interactions, lead to a dependence of the echo depths on the time interval τ between velocity replacements which can be accounted for by phase diffusion or by Langevin oscillators. The echo effect can provide a sensitive probe for the study of non-diffusive energy transport in proteins.

Cosmic Strings and Cosmic Variance

By using a simple analytical model based on counting random multiple impulses inflicted on photons by a network of cosmic strings we show how to construct the general q-point temperature correlation function of the Cosmic Microwave Background radiation. Our analysis is sensible specially for large angular scales where the Kaiser-Stebbins effect is dominant. Then we concentrate our study on the four-point function and in particular on its zero-lag limit, namely, the excess kurtosis parameter, for which we obtain a predicted value of $\sim 10^{-2}$. In addition, we estimate the cosmic variance for the kurtosis due to a Gaussian fluctuation field, showing its dependence on the primordial spectral index of density fluctuations $n$ and finding agreement with previous published results for the particular case of a flat Harrison-Zel'dovich spectrum. Our value for the kurtosis compares well with previous analyses but falls below the threshold imposed by the cosmic variance when commonly accepted parameters from string simulations are considered. In particular the non-Gaussian signal is found to be inversely proportional to the scaling number of defects, as could be expected by the central limit theorem.

Contribution to the Three-Point Function of the Cosmic Microwave Background from the Rees-Sciama Effect

view Abstract Citations (43) References (27) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Contribution to the Three-Point Function of the Cosmic Microwave Background from the Rees-Sciama Effect Mollerach, Silvia ; Gangui, Alejandro ; Lucchin, Francesco ; Matarrese, Sabino Abstract We compute the contribution to the three-point temperature correlation function of the cosmic microwave background coming from the nonlinear evolution of Gaussian initial perturbations, as described by the Rees-Sciama (or integrated Sachs-Wolfe) effect. By expressing the collapsed three-point function in terms of multipole amplitudes, we are able to calculate its expectation value for any power spectrum and for any experimental setting on large angular scales. We also give an analytical expression for the rms collapsed three-point function arising from the cosmic variance of a Gaussian fluctuation field. In the case of COBE DMR, we find that the predicted signal is ∼3 orders of magnitude below that expected from the cosmic variance. Publication: The Astrophysical Journal Pub Date: November 1995 DOI: 10.1086/176363 arXiv: arXiv:astro-ph/9503115 Bibcode: 1995ApJ...453....1M Keywords: COSMOLOGY: COSMIC MICROWAVE BACKGROUND; GALAXIES: CLUSTERS: GENERAL; Astrophysics E-Print: uuencoded compressed postscript, 10 pages text, 2 pages figures full text sources arXiv | ADS |