Topological kinematic constraints: dislocations and the glide principle

Abstract

Topological defects play an important role in physics of elastic media and liquid crystals. Their kinematics is determined by constraints of topological origin. An example is the glide motion of dislocations which has been extensively studied by metallurgists. In a recent theoretical study dealing with quantum dualities associated with the quantum melting of solids it was argued that these kinematic constraints play a central role in defining the quantum field theories of relevance to the description of quantum liquid crystalline states of the nematic type. This forms the motivation to analyze more thoroughly the climb constraints underlying the glide motions. In the setting of continuum field theory the climb constraint is equivalent to the condition that the density of constituent particles is vanishing and we derive a mathematical definition of this constraint which has a universal status. This makes possible to study the kinematics of dislocations in arbitrary space-time dimensions and as an example we analyze the restricted climb associated with edge dislocations in 3+1D. Very generally, it can be shown that the climb constraint is equivalent to the condition that dislocations do not communicate with compressional stresses at long distances. However, the formalism makes possible to address the full non-linear theory of relevance to short distance behaviors where violations of the constraint become possible.

Quantum Smectic as a Dislocation Higgs Phase

“…The kinematics of dislocations is unusual because of the ''glide constraint'', the fact that dislocations only propagate in the direction of their Burgers vectors [15], implying that the spacelike components of the dislocation currents form symmetric tensors J x y ÿ J y x 0 [9,18]. A ramification is that dislocations only carry shear, and no compressional gauge charge.…”

“…A ramification is that dislocations only carry shear, and no compressional gauge charge. The effect is that only shear rigidity is destroyed by the dislocation condensate, while it still carries sound [9,18]. Glide plays an especially interesting role in the quantum smectic: although the dislocations form a (2 1)D condensate, the Burgers vectors are oriented in the liquid direction and only in this direction ''diamagnetic'' currents occur, screening the shear stress.…”

Detecting hidden spatial and spatio-temporal structures in glasses and complex physical systems by multiresolution network clustering

“…Other theories seek a similar measures of structure. Amongst many others, these approaches include spin glass type analysis [24], theories of topological defects and kinetic constraints [14,13,29,30,31], and numerous ingenious approaches summarized in excellent reviews, e.g., [19,32,33]. Formally, as demonstrated in [34], a growing static length scale is associated with the diverging relaxation times in supercooled liquids.…”

“…We apply field theoretic ideas introduced by [113]. In particular, we next follow the procedure of [30,111,112] and write the corresponding action of the system in a manner similar to that of the energy of an anisotropic solid in (D + 1) dimensions. We will label the time direction as the α = 0 direction and denote all spatial Cartesian coordinates by α = 1, 2, ..., D. Fig.…”

“…In the continuum limit, expanding the energy to harmonic order about any local minima (inherent state), the action reads [111,30],…”