scholarly journals Condensation of achiral simple currents in topological lattice models: Hamiltonian study of topological symmetry breaking

2011 ◽  
Vol 84 (12) ◽  
Author(s):  
F. J. Burnell ◽  
Steven H. Simon ◽  
J. K. Slingerland
Keyword(s):  
Symmetry Breaking ◽  
Lattice Models ◽  
Topological Lattice ◽  
Simple Currents

scholarly journals Phase transitions in topological lattice models via topological symmetry breaking

2012 ◽  
Vol 14 (1) ◽  
pp. 015004 ◽  
Author(s):  
F J Burnell ◽  
Steven H Simon ◽  
J K Slingerland
Keyword(s):  
Phase Transitions ◽  
Symmetry Breaking ◽  
Lattice Models ◽  
Topological Lattice

scholarly journals TOPOLOGICAL LATTICE MODELS IN FOUR DIMENSIONS

1992 ◽  
Vol 07 (30) ◽  
pp. 2799-2810 ◽  
Author(s):  
HIROSI OOGURI
Keyword(s):  
Partition Function ◽  
Piecewise Linear ◽  
Lattice Models ◽  
Closed Surface ◽  
Statistical Weight ◽  
Four Dimensions ◽  
Angular Momenta ◽  
Topological Lattice ◽  
Wilson Operator ◽  
Dimensional Version

We define a lattice statistical model on a triangulated manifold in four dimensions associated to a group G. When G= SU (2), the statistical weight is constructed from the 15j-symbol as well as the 6j-symbol for recombination of angular momenta, and the model may be regarded as the four-dimensional version of the Ponzano-Regge model. We show that the partition function of the model is invariant under the Alexander moves of the simplicial complex, thus it depends only on the piecewise linear topology of the manifold. For an orientable manifold, the model is related to the so-called BF model. The q-analog of the model is also constructed, and it is argued that its partition function is invariant under the Alexander moves. It is discussed how to realize the 't Hooft operator in these models associated to a closed surface in four dimensions as well as the Wilson operator associated to a closed loop. Correlation functions of these operators in the q-deformed version of the model would define a new type of invariants of knots and links in four dimensions.

scholarly journals Extended Bloch theorem for topological lattice models with open boundaries

2019 ◽  
Vol 99 (8) ◽  
Author(s):  
Flore K. Kunst ◽  
Guido van Miert ◽  
Emil J. Bergholtz
Keyword(s):  
Lattice Models ◽  
Open Boundaries ◽  
Bloch Theorem ◽  
Topological Lattice

scholarly journals Three-dimensional topological lattice models with surface anyons

2013 ◽  
Vol 87 (4) ◽  
Author(s):  
C. W. von Keyserlingk ◽  
F. J. Burnell ◽  
S. H. Simon
Keyword(s):  
Three Dimensional ◽  
Lattice Models ◽  
Topological Lattice

Symmetry breaking in convergent-beam diffraction

1989 ◽  
Vol 47 ◽  
pp. 480-481
Author(s):  
D.J. Eaglesham
Keyword(s):  
Symmetry Breaking ◽  
Point Group ◽  
X Ray Diffraction ◽  
Multiple Diffraction ◽  
Space Groups ◽  
Atomic Displacements ◽  
Small Probe ◽  
Phase Sensitive ◽  
Convergent Beam

Convergent Beam Electron Diffraction is now almost routinely used in the determination of the point- and space-groups of crystalline samples. In addition to its small-probe capability, CBED is also postulated to be more sensitive than X-ray diffraction in determining crystal symmetries. Multiple diffraction is phase-sensitive, so that the distinction between centro- and non-centro-symmetric space groups should be trivial in CBED: in addition, the stronger scattering of electrons may give a general increase in sensitivity to small atomic displacements. However, the sensitivity of CBED symmetry to the crystal point group has rarely been quantified, and CBED is also subject to symmetry-breaking due to local strains and inhomogeneities. The purpose of this paper is to classify the various types of symmetry-breaking, present calculations of the sensitivity, and illustrate symmetry-breaking by surface strains.CBED symmetry determinations usually proceed by determining the diffraction group along various zone axes, and hence finding the point group. The diffraction group can be found using either the intensity distribution in the discs

Centrosome Aurora A gradient ensures single polarity axis in C. elegans embryos

2020 ◽  
Vol 48 (3) ◽  
pp. 1243-1253 ◽  
Author(s):  
Sukriti Kapoor ◽  
Sachin Kotak
Keyword(s):  
Symmetry Breaking ◽  
Cell Fate ◽  
Cell Cortex ◽  
Axis Formation ◽  
Aurora A Kinase ◽  
Aurora A ◽  
C Elegans ◽  
Cell Embryo ◽  
Polarity Establishment

Cellular asymmetries are vital for generating cell fate diversity during development and in stem cells. In the newly fertilized Caenorhabditis elegans embryo, centrosomes are responsible for polarity establishment, i.e. anterior–posterior body axis formation. The signal for polarity originates from the centrosomes and is transmitted to the cell cortex, where it disassembles the actomyosin network. This event leads to symmetry breaking and the establishment of distinct domains of evolutionarily conserved PAR proteins. However, the identity of an essential component that localizes to the centrosomes and promotes symmetry breaking was unknown. Recent work has uncovered that the loss of Aurora A kinase (AIR-1 in C. elegans and hereafter referred to as Aurora A) in the one-cell embryo disrupts stereotypical actomyosin-based cortical flows that occur at the time of polarity establishment. This misregulation of actomyosin flow dynamics results in the occurrence of two polarity axes. Notably, the role of Aurora A in ensuring a single polarity axis is independent of its well-established function in centrosome maturation. The mechanism by which Aurora A directs symmetry breaking is likely through direct regulation of Rho-dependent contractility. In this mini-review, we will discuss the unconventional role of Aurora A kinase in polarity establishment in C. elegans embryos and propose a refined model of centrosome-dependent symmetry breaking.

A Symmetry-Breaking Theory of False Pop Out

2011 ◽  
Author(s):  
Kimberley D. Orsten ◽  
Mary C. Portillo ◽  
James R. Pomerantz
Keyword(s):  
Symmetry Breaking
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