386 research outputs found
An elastoplastic theory of dislocations as a physical field theory with torsion
We consider a static theory of dislocations with moment stress in an
anisotropic or isotropic elastoplastical material as a T(3)-gauge theory. We
obtain Yang-Mills type field equations which express the force and the moment
equilibrium. Additionally, we discuss several constitutive laws between the
dislocation density and the moment stress. For a straight screw dislocation, we
find the stress field which is modified near the dislocation core due to the
appearance of moment stress. For the first time, we calculate the localized
moment stress, the Nye tensor, the elastoplastic energy and the modified
Peach-Koehler force of a screw dislocation in this framework. Moreover, we
discuss the straightforward analogy between a screw dislocation and a magnetic
vortex. The dislocation theory in solids is also considered as a
three-dimensional effective theory of gravity.Comment: 38 pages, 6 figures, RevTe
Aharonov-Bohm Effect and Disclinations in an Elastic Medium
In this work we investigate quasiparticles in the background of defects in
solids using the geometric theory of defects. We use the parallel transport
matrix to study the Aharonov-Bohm effect in this background. For quasiparticles
moving in this effective medium we demonstrate an effect similar to the
gravitational Aharonov- Bohm effect. We analyze this effect in an elastic
medium with one and defects.Comment: 6 pages, Revtex
Volterra Distortions, Spinning Strings, and Cosmic Defects
Cosmic strings, as topological spacetime defects, show striking resemblance
to defects in solid continua: distortions, which can be classified into
disclinations and dislocations, are line-like defects characterized by a delta
function-valued curvature and torsion distribution giving rise to rotational
and translational holonomy. We exploit this analogy and investigate how
distortions can be adapted in a systematic manner from solid state systems to
Einstein-Cartan gravity. As distortions are efficiently described within the
framework of a SO(3) {\rlap{\supset}\times}} T(3) gauge theory of solid
continua with line defects, we are led in a straightforward way to a Poincar\'e
gauge approach to gravity which is a natural framework for introducing the
notion of distorted spacetimes. Constructing all ten possible distorted
spacetimes, we recover, inter alia, the well-known exterior spacetime of a
spin-polarized cosmic string as a special case of such a geometry. In a second
step, we search for matter distributions which, in Einstein-Cartan gravity, act
as sources of distorted spacetimes. The resulting solutions, appropriately
matched to the distorted vacua, are cylindrically symmetric and are interpreted
as spin-polarized cosmic strings and cosmic dislocations.Comment: 24 pages, LaTeX, 9 eps figures; remarks on energy conditions added,
discussion extended, version to be published in Class. Quantum Gra
Probing non-Riemannian spacetime geometry
The equations of motion for matter in non-Riemannian spacetimes are derived
via a multipole method. It is found that only test bodies with microstructure
couple to the non-Riemannian spacetime geometry. Consequently it is impossible
to detect spacetime torsion with the satellite experiment Gravity Probe B,
contrary to some recent claims in the literature.Comment: 8 pages, 1 figure, matches published version including the erratum in
Phys. Lett. A 373 (2009) 160
The Inverse Variational Problem for Autoparallels
We study the problem of the existence of a local quantum scalar field theory
in a general affine metric space that in the semiclassical approximation would
lead to the autoparallel motion of wave packets, thus providing a deviation of
the spinless particle trajectory from the geodesics in the presence of torsion.
The problem is shown to be equivalent to the inverse problem of the calculus of
variations for the autoparallel motion with additional conditions that the
action (if it exists) has to be invariant under time reparametrizations and
general coordinate transformations, while depending analytically on the torsion
tensor. The problem is proved to have no solution for a generic torsion in
four-dimensional spacetime. A solution exists only if the contracted torsion
tensor is a gradient of a scalar field. The corresponding field theory
describes coupling of matter to the dilaton field.Comment: 13 pages, plain Latex, no figure
The Einsteinian T(3)-Gauge Approach and the Stress Tensor of the Screw Dislocation in the Second Order: Avoiding the Cut-off at the Core
A translational gauge approach of the Einstein type is proposed for obtaining
the stresses that are due to non-singular screw dislocation. The stress
distribution of second order around the screw dislocation is classically known
for the hollow circular cylinder with traction-free external and internal
boundaries. The inner boundary surrounds the dislocation's core, which is not
captured by the conventional solution. The present gauge approach enables us to
continue the classically known quadratic stresses inside the core. The gauge
equation is chosen in the Hilbert--Einstein form, and it plays the role of
non-conventional incompatibility law. The stress function method is used, and
it leads to the modified stress potential given by two constituents: the
conventional one, say, the `background' and a short-ranged gauge contribution.
The latter just causes additional stresses, which are localized. The asymptotic
properties of the resulting stresses are studied. Since the gauge contributions
are short-ranged, the background stress field dominates sufficiently far from
the core. The outer cylinder's boundary is traction-free. At sufficiently
moderate distances, the second order stresses acquire regular continuation
within the core region, and the cut-off at the core does not occur. Expressions
for the asymptotically far stresses provide self-consistently new length scales
dependent on the elastic parameters. These lengths could characterize an
exteriority of the dislocation core region.Comment: 34 pages, LaTe
Non-singular screw dislocations as the Coulomb gas with smoothed out coupling and the renormalization of the shear modulus
A field theory is developed for a thermodynamical description of array of
parallel non-singular screw dislocations in elastic cylinder. The partition
function of the system is considered in the functional integral form.
Self-energy of the dislocation cores is chosen in the form suggested by the
gauge-translational model of non-singular screw dislocation. It is shown that
the system of the dislocations is equivalent to the two-dimensional Coulomb
gas. The coupling potential is prevented from a short-distance divergency since
the core energies are taken into account. Two-point correlation functions of
the stress components are obtained. Renormalization of the shear modulus caused
by the presence of the dislocations is studied in the approximation of
non-interacting dislocation dipoles. It is demonstrated that the finite size of
the dislocation cores results in a modification of the renormalization law.Comment: 20 pages, LaTe
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