Mapping a Homopolymer onto a Model Fluid

We describe a linear homopolymer using a Grand Canonical ensemble formalism, a statistical representation that is very convenient for formal manipulations. We investigate the properties of a system where only next neighbor interactions and an external, confining, field are present, and then show how a general pair interaction can be introduced perturbatively, making use of a Mayer expansion. Through a diagrammatic analysis, we shall show how constitutive equations derived for the polymeric system are equivalent to the Ornstein-Zernike and P.Y. equations for a simple fluid, and find the implications of such a mapping for the simple situation of Van der Waals mean field model for the fluid.Comment: 12 pages, 3 figure

Solution of the Percus-Yevick equation for hard discs

We solve the Percus-Yevick equation in two dimensions by reducing it to a set of simple integral equations. We numerically obtain both the pair correlation function and the equation of state for a hard disc fluid and find good agreement with available Monte-Carlo calculations. The present method of resolution may be generalized to any even dimension.Comment: 9 pages, 3 figure

Classification of minimal actions of a compact Kac algebra with amenable dual

We show the uniqueness of minimal actions of a compact Kac algebra with amenable dual on the AFD factor of type II$_1$. This particularly implies the uniqueness of minimal actions of a compact group. Our main tools are a Rohlin type theorem, the 2-cohomology vanishing theorem, and the Evans-Kishimoto type intertwining argument.Comment: 68 pages, Introduction rewritten; minor correction

Evolution of collision numbers for a chaotic gas dynamics

We put forward a conjecture of recurrence for a gas of hard spheres that collide elastically in a finite volume. The dynamics consists of a sequence of instantaneous binary collisions. We study how the numbers of collisions of different pairs of particles grow as functions of time. We observe that these numbers can be represented as a time-integral of a function on the phase space. Assuming the results of the ergodic theory apply, we describe the evolution of the numbers by an effective Langevin dynamics. We use the facts that hold for these dynamics with probability one, in order to establish properties of a single trajectory of the system. We find that for any triplet of particles there will be an infinite sequence of moments of time, when the numbers of collisions of all three different pairs of the triplet will be equal. Moreover, any value of difference of collision numbers of pairs in the triplet will repeat indefinitely. On the other hand, for larger number of pairs there is but a finite number of repetitions. Thus the ergodic theory produces a limitation on the dynamics.Comment: 4 pages, published versio

Liquid Transport Due to Light Scattering

Using experiments and theory, we show that light scattering by inhomogeneities in the index of refraction of a fluid can drive a large-scale flow. The experiment uses a near-critical, phase-separated liquid, which experiences large fluctuations in its index of refraction. A laser beam traversing the liquid produces a large-scale deformation of the interface and can cause a liquid jet to form. We demonstrate that the deformation is produced by a scattering-induced flow by obtaining good agreements between the measured deformations and those calculated assuming this mechanism.Comment: 4 pages, 5 figures, submitted to Physical Review Letters v2: Edited based on comments from referee

Quantum criticality around metal-insulator transitions of strongly correlated electrons

Quantum criticality of metal-insulator transitions in correlated electron systems is shownto belong to an unconventional universality class with violation of Ginzburg-Landau-Wilson(GLW) scheme formulated for symmetry breaking transitions. This unconventionality arises from an emergent character of the quantum critical point, which appears at the marginal point between the Ising-type symmetry breaking at nonzero temperatures and the topological transition of the Fermi surface at zero temperature. We show that Hartree-Fock approximations of an extended Hubbard model on square latticesare capable of such metal-insulator transitions with unusual criticality under a preexisting symmetry breaking. The obtained universality is consistent with the scaling theory formulated for Mott transition and with a number of numerical results beyond the mean-field level, implying that the preexisting symmetry breaking is not necessarily required for the emergence of this unconventional universality. Examinations of fluctuation effects indicate that the obtained critical exponents remain essentially exact beyond the mean-field level. Detailed analyses on the criticality, containing diverging carrier density fluctuations around the marginal quantum critical point, are presented from microscopic calculations and reveal the nature as quantum critical "opalescence". Analyses on crossovers between GLW type at nonzero temperature and topological type at zero temperature show that the critical exponents observed in (V,Cr)2O3 and kappa-ET-type organic conductor provide us with evidences for the existence of the present marginal quantum criticality.Comment: 24 pages, 19 figure

Orbit equivalence rigidity for ergodic actions of the mapping class group

We establish orbit equivalence rigidity for any ergodic, essentially free and measure-preserving action on a standard Borel space with a finite positive measure of the mapping class group for a compact orientable surface with higher complexity. We prove similar rigidity results for a finite direct product of mapping class groups as well.Comment: 11 pages, title changed, a part of contents remove

Solution of the Percus-Yevick equation for hard hyperspheres in even dimensions

We solve the Percus-Yevick equation in even dimensions by reducing it to a set of simple integro-differential equations. This work generalizes an approach we developed previously for hard discs. We numerically obtain both the pair correlation function and the virial coefficients for a fluid of hyper-spheres in dimensions $d=4,6$ and 8, and find good agreement with available exact results and Monte-Carlo simulations. This paper confirms the alternating character of the virial series for $d \ge 6$, and provides the first evidence for an alternating character for $d=4$. Moreover, we show that this sign alternation is due to the existence of a branch point on the negative real axis. It is this branch point that determines the radius of convergence of the virial series, whose value we determine explicitly for $d=4,6,8$. Our results complement, and are consistent with, a recent study in odd dimensions [R.D. Rohrmann et al., J. Chem. Phys. 129, 014510 (2008)].Comment: Accepted for publication in J. Chem. Phys. (11 pages, 6 figures

Working memory subsystems and task complexity in young boys with Fragile X syndrome: Working memory in boys with FXS

Working memory problems have been targeted as core deficits in individuals with Fragile X syndrome (FXS); however, there have been few studies that have examined working memory in young boys with FXS, and even fewer studies that have studied the working memory performance of young boys with FXS across different degrees of complexity. The purpose of this study was to investigate the phonological loop and visual–spatial working memory in young boys with FXS, in comparison to mental age-matched typical boys, and to examine the impact of complexity of the working memory tasks on performance

Implementation of the Hierarchical Reference Theory for simple one-component fluids

Combining renormalization group theoretical ideas with the integral equation approach to fluid structure and thermodynamics, the Hierarchical Reference Theory is known to be successful even in the vicinity of the critical point and for sub-critical temperatures. We here present a software package independent of earlier programs for the application of this theory to simple fluids composed of particles interacting via spherically symmetrical pair potentials, restricting ourselves to hard sphere reference systems. Using the hard-core Yukawa potential with z=1.8/sigma for illustration, we discuss our implementation and the results it yields, paying special attention to the core condition and emphasizing the decoupling assumption's role.Comment: RevTeX, 16 pages, 2 figures. Minor changes, published versio