Effective medium super-cell approximation for interacting disordered systems: an alternative real-space derivation of generalized dynamical cluster approximation

Two challenges in mechanics of granular media are taken up in this paper: (i) development of adequate numerical discrete element models of topologically disordered granular assemblies, and (ii) calculation of macroscopic elastic moduli of such materials using effective medium theories. Consideration of the first one leads to an adaptation of a spring-network (Kirkwood) model of solid-state physics to disordered systems, which is developed in the context of planar Delaunay networks. The model employs two linear springs: a normal one along an edge connecting two neighboring vertices (grain centers) which accounts for normal interactions between the grains, as well as an angular one which accounts for angle changes between two edges incident onto the same vertex; edges remain straight and grain rotations do not appear. This model is then used to predict elastic moduli of two-phase granular materials—random mixtures of soft and stiff grains —for high coordination numbers. It is found here that an effective Poisson’s ratio, νeff, of such a mixture is a convex function of the volume fraction, so that νeff may become negative when the individual Poisson’s ratios of both phases are both positive. Additionally, the usefulness of three effective medium theories—perfect disks, symmetric ellipses, and asymmetric ellipses—is tested.

Download Full-text

Generalizated effective-medium approximation for hopping transport in topologically disordered systems

Philosophical Magazine B ◽

10.1080/13642810108205780 ◽

2001 ◽

Vol 81 (9) ◽

pp. 915-924 ◽

Cited By ~ 7

Author(s):

Carl Ganter ◽

Walter Schirmacher

Keyword(s):

Disordered Systems ◽

Effective Medium ◽

Effective Medium Approximation ◽

Hopping Transport

Download Full-text

Disorder induced lifetime effects in binary disordered systems: A first principles formalism and an application to disordered graphene

International Journal of Modern Physics B ◽

10.1142/s0217979217502186 ◽

2017 ◽

Vol 31 (29) ◽

pp. 1750218 ◽

Cited By ~ 1

Author(s):

Banasree Sadhukhan ◽

Subhadeep Bandyopadhyay ◽

Arabinda Nayak ◽

Abhijit Mookerjee

Keyword(s):

Green Function ◽

First Principles ◽

Disordered Systems ◽

Random Distribution ◽

Real Space ◽

Recursion Method ◽

Resonant States ◽

Graphene Lattice ◽

Lifetime Effects ◽

Local Defects

In this work, the conducting properties of graphene lattice with a particular concentration of defect (5% and 10%) has been studied. The real space block recursion method introduced by Haydock et al. has been used in presence of the random distribution of defects in graphene. This Green function based method is found to be more powerful than the usual reciprocal based methods which need artificial periodicity. Different resonant states appear because of the presence of topological and local defects are studied within the framework of Green function.

Download Full-text

Mottness collapse and statistical quantum criticality

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2010.0188 ◽

2011 ◽

Vol 369 (1941) ◽

pp. 1599-1625 ◽

Cited By ~ 28

Author(s):

J. Zaanen ◽

B. J. Overbosch

Keyword(s):

Scale Invariance ◽

Quantum Dynamics ◽

Cuprate Superconductors ◽

Quantum Criticality ◽

Cluster Approximation ◽

Integral Formalism ◽

Model Sets ◽

Sign Structure ◽

Normal Fermi ◽

Dynamical Cluster Approximation

We put forward here the case that the anomalous electron states found in cuprate superconductors and related systems are rooted in a deeply non-classical fermion sign structure. The collapse of Mottness, as advocated by Phillips and supported by recent dynamical cluster approximation results on the Hubbard model, sets the necessary microscopic conditions. The crucial insight is due to Weng, who demonstrated that, in the presence of Mottness, the fundamental workings of quantum statistics change, and we will elaborate on the effects of this Weng statistics with an emphasis on characterizing it further using numerical methods. The pseudo-gap physics of the underdoped regime appears as a consequence of the altered statistics and the profound question is how to connect this by a continuous quantum phase transition to the overdoped regime ruled by normal Fermi–Dirac statistics. Proof of principle follows from Ceperley’s constrained path integral formalism, in which states can be explicitly constructed showing a merger of Fermi–Dirac sign structure and scale invariance of the quantum dynamics.

Download Full-text