scholarly journals Phase transitions in three-dimensional topological lattice models with surface anyons

2013 ◽  
Vol 88 (23) ◽  
Author(s):  
F. J. Burnell ◽  
C. W. von Keyserlingk ◽  
S. H. Simon
Keyword(s):  
Phase Transitions ◽  
Three Dimensional ◽  
Lattice Models ◽  
Topological Lattice

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 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

scholarly journals Crystal–liquid phase transitions in three-dimensional complex plasma under microgravity conditions

2018 ◽  
Vol 946 ◽  
pp. 012144 ◽  
Author(s):  
V N Naumkin ◽  
A M Lipaev ◽  
V I Molotkov ◽  
D I Zhukhovitskii ◽  
A D Usachev ◽  
...  
Keyword(s):  
Phase Transitions ◽  
Liquid Phase ◽  
Three Dimensional ◽  
Complex Plasma ◽  
Microgravity Conditions

scholarly journals Vortex states in an acoustic Weyl crystal with a topological lattice defect

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Qiang Wang ◽  
Yong Ge ◽  
Hong-xiang Sun ◽  
Haoran Xue ◽  
Ding Jia ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Lattice Defect ◽  
Three Dimensional ◽  
Surface States ◽  
Real Space ◽  
Lattice Defects ◽  
One Dimensional ◽  
Topological Features ◽  
Topological Lattice

AbstractCrystalline materials can host topological lattice defects that are robust against local deformations, and such defects can interact in interesting ways with the topological features of the underlying band structure. We design and implement a three dimensional acoustic Weyl metamaterial hosting robust modes bound to a one-dimensional topological lattice defect. The modes are related to topological features of the bulk bands, and carry nonzero orbital angular momentum locked to the direction of propagation. They span a range of axial wavenumbers defined by the projections of two bulk Weyl points to a one-dimensional subspace, in a manner analogous to the formation of Fermi arc surface states. We use acoustic experiments to probe their dispersion relation, orbital angular momentum locked waveguiding, and ability to emit acoustic vortices into free space. These results point to new possibilities for creating and exploiting topological modes in three-dimensional structures through the interplay between band topology in momentum space and topological lattice defects in real space.

scholarly journals Fractional Diffusion Equations for Lattice and Continuum: Grünwald-Letnikov Differences and Derivatives Approach

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Vasily E. Tarasov
Keyword(s):  
Fractional Derivatives ◽  
Three Dimensional ◽  
Lattice Models ◽  
Fractional Diffusion ◽  
Lattice Diffusion ◽  
Diffusion Equations ◽  
Difference Operators ◽  
Fractional Diffusion Equations ◽  
Nonlocal Media ◽  
Derivatives Of

Fractional diffusion equations for three-dimensional lattice models based on fractional-order differences of the Grünwald-Letnikov type are suggested. These lattice fractional diffusion equations contain difference operators that describe long-range jumps from one lattice site to another. In continuum limit, the suggested lattice diffusion equations with noninteger order differences give the diffusion equations with the Grünwald-Letnikov fractional derivatives for continuum. We propose a consistent derivation of the fractional diffusion equation with the fractional derivatives of Grünwald-Letnikov type. The suggested lattice diffusion equations can be considered as a new microstructural basis of space-fractional diffusion in nonlocal media.

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