Comment on "Constant stress and pressure rheology of colloidal suspensions"

This is a comment on the recent letter by Wang and Brady on "Constant stress and pressure rheology of colloidal suspensions", Phys. Rev. Lett. 115, 158301 (2015).Comment: 1 page; under review -> v2: publishe

Topological Field Theories and Geometry of Batalin-Vilkovisky Algebras

The algebraic and geometric structures of deformations are analyzed concerning topological field theories of Schwarz type by means of the Batalin-Vilkovisky formalism. Deformations of the Chern-Simons-BF theory in three dimensions induces the Courant algebroid structure on the target space as a sigma model. Deformations of BF theories in $n$ dimensions are also analyzed. Two dimensional deformed BF theory induces the Poisson structure and three dimensional deformed BF theory induces the Courant algebroid structure on the target space as a sigma model. The deformations of BF theories in $n$ dimensions induce the structures of Batalin-Vilkovisky algebras on the target space.Comment: 25 page

Graphical Classification of Global SO(n) Invariants and Independent General Invariants

This paper treats some basic points in general relativity and in its perturbative analysis. Firstly a systematic classification of global SO(n) invariants, which appear in the weak-field expansion of n-dimensional gravitational theories, is presented. Through the analysis, we explain the following points: a) a graphical representation is introduced to express invariants clearly; b) every graph of invariants is specified by a set of indices; c) a number, called weight, is assigned to each invariant. It expresses the symmetry with respect to the suffix-permutation within an invariant. Interesting relations among the weights of invariants are given. Those relations show the consistency and the completeness of the present classification; d) some reduction procedures are introduced in graphs for the purpose of classifying them. Secondly the above result is applied to the proof of the independence of general invariants with the mass-dimension $M^6$ for the general geometry in a general space dimension. We take a graphical representation for general invariants too. Finally all relations depending on each space-dimension are systematically obtained for 2, 4 and 6 dimensions.Comment: LaTex, epsf, 60 pages, many figure

AKSZ-BV Formalism and Courant Algebroid-induced Topological Field Theories

We give a detailed exposition of the Alexandrov-Kontsevich-Schwarz- Zaboronsky superfield formalism using the language of graded manifolds. As a main illustarting example, to every Courant algebroid structure we associate canonically a three-dimensional topological sigma-model. Using the AKSZ formalism, we construct the Batalin-Vilkovisky master action for the model.Comment: 13 pages, based on lectures at Rencontres mathematiques de Glanon 200

Vortex-lattice melting in two-dimensional superconductors in intermediate fields

To examine the field dependence of the vortex lattice melting transition in two-dimensional (2D) superconductors, Monte Carlo simulations of the 2D Ginzburg-Landau (GL) model are performed by extending the conventional lowest Landau level (LL) approximation to include several {\it higher} LL modes of the superconducting order parameter with LL indices up to six. It is found that a nearly vertical melting line in lower fields, which is familiar within the elastic theory, is reached just by including higher LL modes with LL indices less than five, and that the first order character of the melting transition in higher fields is significantly weakened with decreasing the field. Nevertheless, a genuine crossover to the consecutive continuous melting picture intervened by a hexatic liquid is not found within the use of the GL model.Comment: 6 pages, 7 figures. To appear in Phys. Rev.

QP-Structures of Degree 3 and 4D Topological Field Theory

A A BV algebra and a QP-structure of degree 3 is formulated. A QP-structure of degree 3 gives rise to Lie algebroids up to homotopy and its algebraic and geometric structure is analyzed. A new algebroid is constructed, which derives a new topological field theory in 4 dimensions by the AKSZ construction.Comment: 17 pages, Some errors and typos have been correcte

Effect of in-plane line defects on field-tuned superconductor-insulator transition behavior in homogeneous thin film

Field-tuned superconductor-insulator transition (FSIT) behavior in 2D isotropic and homogeneous thin films is usually accompanied by a nonvanishing critical resistance at low $T$. It is shown that, in a 2D film including line defects paralle to each other but with random positions perpendicular to them, the (apparent) critical resistance in low $T$ limit vanishes, as in the 1D quantum superconducting (SC) transition, under a current parallel to the line defects. This 1D-like critical resistive behavior is more clearly seen in systems with weaker point disorder and may be useful in clarifying whether the true origin of FSIT behavior in the parent superconductor is the glass fluctuation or the quantum SC fluctuation. As a by-product of the present calculation, it is also pointed out that, in 2D films with line-like defects with a long but {\it finite} correlation length parallel to the lines, a quantum metallic behavior intervening the insulating and SC ones appears in the resistivity curves.Comment: 16 pages, 14 figure

Mode-Coupling Theory as a Mean-Field Description of the Glass Transition

Mode-coupling theory (MCT) is conjectured to be a mean-field description of dynamics of the structural glass transition and the replica theory to be its thermodynamic counterpart. However, the relationship between the two theories remains controversial and quantitative comparison is lacking. In this Letter, we investigate MCT for monatomic hard sphere fluids at arbitrary dimensions above three and compare the results with replica theory. We find grave discrepancies between the predictions of two theories. While MCT describes the nonergodic parameter quantitatively better than the replica theory in three dimension, it predicts a completely different dimension dependence of the dynamical transition point. We find it to be due to the pathological behavior of the nonergodic parameters derived from MCT, which exhibit negative tails in real space at high dimensions.Comment: 5 pages, to appear in Phys. Rev. Lett.: Typos have been correcte

Theoretical Description of Nearly Discontinuous Transition in Superconductors with Paramagnetic Depairing

Based on a theoretical argument and Monte Carlo simulations of a Ginzburg-Landau model derived microscopically, it is argued that, in type-II superconductors where {\it both} the paramagnetic {\it and} orbital depairings are important, a strong first-order transition (FOT) at $H_{c2}$ expected in the mean field (MF) approximation never occurs in real systems and changes due to the fluctuation into a crossover. The present result explains why a {\it nearly} discontinuous crossover at $H_{c2}$ with {\it no} intrinsic hysteresis is observed only in a clean superconducting material with a singlet pairing and a high condensation energy such as CeCoIn$_5$.Comment: Publication version. See cond-mat/0306060 regarding a corresponding long pape

Thermodynamics and Structural Properties of the High Density Gaussian Core Model

We numerically study thermodynamic and structural properties of the one-component Gaussian core model (GCM) at very high densities. The solid-fluid phase boundary is carefully determined. We find that the density dependence of both the freezing and melting temperatures obey the asymptotic relation, $\log T_f$, $\log T_m \propto -\rho^{2/3}$, where $\rho$ is the number density, which is consistent with Stillinger's conjecture. Thermodynamic quantities such as the energy and pressure and the structural functions such as the static structure factor are also investigated in the fluid phase for a wide range of temperature above the phase boundary. We compare the numerical results with the prediction of the liquid theory with the random phase approximation (RPA). At high temperatures, the results are in almost perfect agreement with RPA for a wide range of density, as it has been already shown in the previous studies. In the low temperature regime close to the phase boundary line, although RPA fails to describe the structure factors and the radial distribution functions at the length scales of the interparticle distance, it successfully predicts their behaviors at shorter length scales. RPA also predicts thermodynamic quantities such as the energy, pressure, and the temperature at which the thermal expansion coefficient becomes negative, almost perfectly. Striking ability of RPA to predict thermodynamic quantities even at high densities and low temperatures is understood in terms of the decoupling of the length scales which dictate thermodynamic quantities from the interparticle distance which dominates the peak structures of the static structure factor due to the softness of the Gaussian core potential.Comment: 10 pages, 10 figure