Quenched ising model within two-site cluster approximation

We calculate the static and dynamic single-particle correlation functions in one-dimensional (1D) trapped Bose gases and discuss experimental measurements that can directly probe such correlation functions. Using a quantized hydrodynamic theory for the low energy excitations, we calculate both the static and dynamic single-particle correlation functions for a 1D Bose gas that is a phase-fluctuating quasi-condensate. For the static (equal-time) correlation function, our approximations and results are equivalent to those of Petrov, Shlyapnikov and Walraven. The Fourier transform of the static single-particle correlation function gives the momentum distribution, which can be measured using Doppler-sensitive Bragg scattering experiments on a highly elongated Bose gas. We show how a two-photon Raman out-coupling experiment can measure the characteristic features of the dynamic or time-dependent single-particle correlation function of a 1D Bose quasi-condensate.

Self-diffusion in a 2D lattice gas with lateral interactions

We develop a general approach to calculating ``nonuniversal'' prefactors in static and dynamic correlation functions of one-dimensional (1D) quantum liquids at zero temperature by relating them to the finite-size scaling of certain matrix elements (form factors). This represents a powerful tool for extracting data valid in the thermodynamic limit from finite-size effects. As the main application, we consider weakly interacting spinless fermions with an arbitrary pair interaction potential, for which we perturbatively calculate certain prefactors in static and dynamic correlation functions. We also evaluate prefactors of the long-distance behavior of correlation functions nonperturbatively for the exactly solvable Lieb-Liniger model of 1D bosons.

In this paper, we theoretically explore the effect of temperature on the Wigner crystallization in a semiconductor based electron quantum wire. The electrons are free to move along the axis of wire and their transverse motion is assumed to be confined by a (2D) harmonic potential. The dynamics of electron correlations is included within the self-consistent mean-field approximation of Hasegawa and Shimizu. Numerical results are reported for static structure factor and pair correlation function of the quantum wire at finite temperature and some selected values of electron number density. The formation of Wigner crystal in the quantum wire at finite temperature is predicted by a strong peak in the static structure factor and pronounced oscillations in the pair-correlation function at sufficiently low electron density.

Amorphous cell studies of polyglycolic, poly( l-lactic), poly( l, d-lactic) and poly(glycolic/ l-lactic) acids

This paper is an attempt towards developing a theory of the self-motion of atoms in monatomic classical fluids, based on a simplified Liouville equation and on a knowledge of the interaction potential $V(r)$ and the static pair correlation function $g(r)$. A nonlinear integral equation for the velocity autocorrelation function $\ensuremath{\Phi}(t)$ is derived which under certain approximations can be written as $\frac{d\ensuremath{\Phi}(t)}{\mathrm{dt}}+\ensuremath{\int}{0}^{t}K(t\ensuremath{-}{t}^{\ensuremath{'}})\ensuremath{\Phi}({t}^{\ensuremath{'}})d{t}^{\ensuremath{'}}=0$ where the kernel $K(t)$ is an implicit function of $\ensuremath{\Phi}(t)$. An expression for $K(t)$ in terms of $V(r)$ and $g(r)$ has been given. Explicit numerical calculations for the "memory" function $K(t)$ have been made for liquid argon at $T=85.9\ifmmode^\circ\else\textdegree\fi{}$K, and the results have been compared with those obtained by Rahman from his machine computations.

Molecular dynamics simulations are performed for a supercooled simple liquid with changing the system size from N=108 to 10(4) to examine possible finite-size effects. Although almost no systematic deviation is detected in the static pair correlation functions, it is demonstrated that the structural alpha relaxation in a small system becomes considerably slower than that in larger systems for temperatures below T(c) at which the size of the cooperative particle motions becomes comparable to the unit cell length of the small system. The discrepancy increases with decreasing temperature.

The static and dynamic properties of a dilute binary macroion mixture, where a small amount of large and highly charged spheres is immersed in a system of small spheres, are theoretically discussed. From light scattering experiments on such systems, the self-diffusion of the large spheres within the system of small spheres is essentially determined. Such systems have recently been studied by Phillies, using suspensions of highly charged polystyrene spheres. Modelling the elements of the memory function matrix by single exponentials, relating the k-dependent amplitudes and relaxation rates to the moments of the one-particle propagators, compact analytic expressions are derived for the normalized mean squared displacements and long-time self-diffusion coefficients. The moments are calculated from a generalized Smoluchowski equation and are given by integrals over the static correlation functions. Using the so-called two-component macrofluid model to calculate the static correlation functions, analytic expressions of the static partial total correlation functions in k-space are derived within the mean-spherical approximation for the binary mixture. Because of the strong dilution of the mixture, a rescaling procedure has to be used. This rescaling procedure is a simple generalization of that given by Hansen and Hayter for the one-component macroion fluid. Comparison of the theoretically calculated long-time self-diffusion of the large spheres with the experimental results of Phillies was quite satisfactory. Also, calculations of the two self-diffusion coefficients as functions of the diameter ratio and salt concentration have been performed, as well as of the normalized mean squared displacements.Key wordsColloidal suspensionself-diffusionBrownian motion

A real-space dynamic renormalization-group scheme is used to evaluate static and dynamic correlation functions for a kinetic Ising model on a two-dimensional square lattice. The critical exponents obtained from the correlation functions calculated using this method satisfy the proper static and dynamic scaling relations and are in excellent agreement with known values.

We characterize the steady-state static and dynamic properties in a broad class of mass transport processes on a periodic hypercubic lattice of volume Ld , where both the mass and center-of-mass (CoM) remain conserved and the detailed balance is violated in the bulk; we specifically consider the models in the d = 1 and 2 dimensions. Using a microscopic approach, we exactly determine the decay (or growth) exponents for various dynamic and static correlation functions. We show that despite constrained dynamics due to CoM conservation (CoMC), the density relaxation is indeed diffusive. However, the fluctuation properties are strikingly different from those in diffusive systems with a single (mass) conservation law as dynamic and static fluctuations are more suppressed in systems with CoMC, resulting in an extreme (‘class-I’) hyperuniformity in certain cases. In the thermodynamic limit, the steady-state variance ⟨ Q 2 ( T ) ⟩ c of time-integrated bond current Q ( T ) across a bond in the time interval T exhibits the following long-time behavior: ⟨ Q 2 ( T ) ⟩ c ≃ A 1 T + A 2 + A 3 T − d / 2 . The exponents governing the small-frequency behavior of the power spectra S J ( f ) ≃ A 1 + Const . f ψ J for bond current are exactly determined as ψ J = 3 / 2 and 2 in d = 1 and 2 dimensions, respectively; the corresponding unequal-time current-current correlation function decay as t − 5 / 2 and t −3 as a function of time t in d = 1 and 2 dimensions, respectively. Remarkably, depending on the dimensions and microscopic details, the prefactor A 1 can vanish, causing the variance to eventually saturate, implying a class-I ‘dynamic hyperuniformity’. We also compute the static structure factor S(q), which varies as the square of the wave number q in the small-q limit, i.e. S ( q ) ∼ q 2 , implying a class-I spatial hyperuniformity.

The usual spin-wave theory, when applied to the calculation of rotationally invariant averages in the Heisenberg model, permits exact calculation of static and dynamical correlation functions in one dimension. The results are also believed to be exact in two dimensions, although this has not been show rigorously here. The one-dimensional ferromagnet in the hydrodynamic regime and the two-dimensional ferromagnet at all wave vectors do not satisfy the dynamical scaling hypothesis. There is no characteristic exponent in these cases. The present results contradict the prediction of the mode-coupling theory.

First results of massive Monte Carlo simulations of the d=3 Ising spin glass with ± J bond distribution, performed on a fast special purpose computer, are discussed. Equilibrium static and dynamic correlation functions have been recorded for temperatures T/J=1.10 to 2.00. A qualitative change in the behavior of the system, and the best fits for the spin glass correlation length and relaxation time favor a continuous phase transition at Tc/J≊1.20±0.05. We find no evidence for the Tc=0 freezing picture.

The dynamical properties of liquid caesium near the melting point are investigated within the generalized collective-modes approach in a Markovian approximation. The generalized thermodynamic quantities and spectra of collective modes have been obtained for the five-variables description of longitudinal fluctuations. As the basis variables, three conserved and two nonconserved quantities have been used: the number density, longitudinal momentum, and energy density; and the first time derivatives of the longitudinal momentum and the energy density. All of the static and dynamic correlation functions were calculated directly from molecular dynamics simulations for 500 particles over 165 000 time steps, avoiding any fitting parameters. A comparison with the experimental data and results of previous molecular dynamics simulations is made.

We consider the quantum nonlinear Schr\"odinger equation in one space and one time dimension. We are interested in the non-free-fermionic case. We consider static temperature-dependent correlation functions. The determinant representation for correlation functions simplifies in the small mass limit of the Bose particle. In this limit we describe the correlation functions by the vacuum expectation value of a boson-valued solution for Maxwell-Bloch differential equation. We evaluate long-distance asymptotics of correlation functions in the small mass limit.

The lattice dynamics of low-frequency rigid-plane modes in metallic (graphene multilayers, GML) and in insulating (hexagonal boron-nitride multilayers, BNML) layered crystals is investigated. The frequencies of shearing and compression (stretching) modes depend on the layer number ${\EuScript N}$ and are presented in the form of fan diagrams. The results for GML and BNML are very similar. In both cases only the interactions (van der Waals and Coulomb) between nearest-neighbor planes are effective, while the interactions between more distant planes are screened. A comparison with recent Raman scattering results on low-frequency shear modes in GML [Tan {\it et al.}, arXiv:1106.1146v1 (2011)] is made. Relations with the low-lying rigid-plane phonon dispersions in the bulk materials are established. Master curves which connect the fan diagram frequencies for any given ${\EuScript N}$ are derived. Static and dynamic thermal correlation functions for rigid-layer shear and compression modes are calculated. The results might be of use for the interpretation of friction force experiments on multilayer crystals.