434 research outputs found
Brownian motion of Massive Particle in a Space with Curvature and Torsion and Crystals with Defects
We develop a theory of Brownian motion of a massive particle, including the
effects of inertia (Kramers' problem), in spaces with curvature and torsion.
This is done by invoking the recently discovered generalized equivalence
principle, according to which the equations of motion of a point particle in
such spaces can be obtained from the Newton equation in euclidean space by
means of a nonholonomic mapping. By this principle, the known Langevin equation
in euclidean space goes over into the correct Langevin equation in the Cartan
space. This, in turn, serves to derive the Kubo and Fokker-Planck equations
satisfied by the particle distribution as a function of time in such a space.
The theory can be applied to classical diffusion processes in crystals with
defects.Comment: LaTeX, http://www.physik.fu-berlin.de/kleinert.htm
A gauge theoretic approach to elasticity with microrotations
We formulate elasticity theory with microrotations using the framework of
gauge theories, which has been developed and successfully applied in various
areas of gravitation and cosmology. Following this approach, we demonstrate the
existence of particle-like solutions. Mathematically this is due to the fact
that our equations of motion are of Sine-Gordon type and thus have soliton type
solutions. Similar to Skyrmions and Kinks in classical field theory, we can
show explicitly that these solutions have a topological origin.Comment: 15 pages, 1 figure; revised and extended version, one extra page;
revised and extended versio
On the incompatibility of strains and its application to mesoscopic studies of plasticity
Structural transitions are invariably affected by lattice distortions. If the
body is to remain crack-free, the strain field cannot be arbitrary but has to
satisfy the Saint-Venant compatibility constraint. Equivalently, an
incompatibility constraint consistent with the actual dislocation network has
to be satisfied in media with dislocations. This constraint can be incorporated
into strain-based free energy functionals to study the influence of
dislocations on phase stability. We provide a systematic analysis of this
constraint in three dimensions and show how three incompatibility equations
accommodate an arbitrary dislocation density. This approach allows the internal
stress field to be calculated for an anisotropic material with spatially
inhomogeneous microstructure and distribution of dislocations by minimizing the
free energy. This is illustrated by calculating the stress field of an edge
dislocation and comparing it with that of an edge dislocation in an infinite
isotropic medium. We outline how this procedure can be utilized to study the
interaction of plasticity with polarization and magnetization.Comment: 6 pages, 2 figures; will appear in Phys. Rev.
Riemann-Cartan Space-times of G\"odel Type
A class of Riemann-Cartan G\"odel-type space-times are examined in the light
of the equivalence problem techniques. The conditions for local space-time
homogeneity are derived, generalizing previous works on Riemannian G\"odel-type
space-times. The equivalence of Riemann-Cartan G\"odel-type space-times of this
class is studied. It is shown that they admit a five-dimensional group of
affine-isometries and are characterized by three essential parameters : identical triads () correspond to locally
equivalent manifolds. The algebraic types of the irreducible parts of the
curvature and torsion tensors are also presented.Comment: 24 pages, LaTeX fil
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
First-principles calculation of intrinsic defect formation volumes in silicon
We present an extensive first-principles study of the pressure dependence of
the formation enthalpies of all the know vacancy and self-interstitial
configurations in silicon, in each charge state from -2 through +2. The neutral
vacancy is found to have a formation volume that varies markedly with pressure,
leading to a remarkably large negative value (-0.68 atomic volumes) for the
zero-pressure formation volume of a Frenkel pair (V + I). The interaction of
volume and charge was examined, leading to pressure--Fermi level stability
diagrams of the defects. Finally, we quantify the anisotropic nature of the
lattice relaxation around the neutral defects.Comment: 9 pages, 9 figure
Nonholonomic Mapping Principle for Classical Mechanics in Spaces with Curvature and Torsion. New Covariant Conservation Law for Energy-Momentum Tensor
The lecture explains the geometric basis for the recently-discovered
nonholonomic mapping principle which specifies certain laws of nature in
spacetimes with curvature and torsion from those in flat spacetime, thus
replacing and extending Einstein's equivalence principle. An important
consequence is a new action principle for determining the equation of motion of
a free spinless point particle in such spacetimes. Surprisingly, this equation
contains a torsion force, although the action involves only the metric. This
force changes geodesic into autoparallel trajectories, which are a direct
manifestation of inertia. The geometric origin of the torsion force is a
closure failure of parallelograms. The torsion force changes the covariant
conservation law of the energy-momentum tensor whose new form is derived.Comment: Corrected typos. Author Information under
http://www.physik.fu-berlin.de/~kleinert/institution.html . Paper also at
http://www.physik.fu-berlin.de/~kleinert/kleiner_re261/preprint.htm
Defect-induced incompatibility of elastic strains: dislocations within the Landau theory of martensitic phase transformations
In dislocation-free martensites the components of the elastic strain tensor
are constrained by the Saint-Venant compatibility condition which guarantees
continuity of the body during external loading. However, in dislocated
materials the plastic part of the distortion tensor introduces a displacement
mismatch that is removed by elastic relaxation. The elastic strains are then no
longer compatible in the sense of the Saint-Venant law and the ensuing
incompatibility tensor is shown to be proportional to the gradients of the Nye
dislocation density tensor. We demonstrate that the presence of this
incompatibility gives rise to an additional long-range contribution in the
inhomogeneous part of the Landau energy functional and to the corresponding
stress fields. Competition amongst the local and long-range interactions
results in frustration in the evolving order parameter (elastic) texture. We
show how the Peach-Koehler forces and stress fields for any distribution of
dislocations in arbitrarily anisotropic media can be calculated and employed in
a Fokker-Planck dynamics for the dislocation density. This approach represents
a self-consistent scheme that yields the evolutions of both the order parameter
field and the continuous dislocation density. We illustrate our method by
studying the effects of dislocations on microstructure, particularly twinned
domain walls, in an Fe-Pd alloy undergoing a martensitic transformation.Comment: 24 pages, submitted to Phys. Rev. B (changes from v1 include mainly
incorporation of discrete slip systems; densities of crystal dislocations are
now tracked explicitly
Dislocation-Mediated Melting: The One-Component Plasma Limit
The melting parameter of a classical one-component plasma is
estimated using a relation between melting temperature, density, shear modulus,
and crystal coordination number that follows from our model of
dislocation-mediated melting. We obtain in good agreement
with the results of numerous Monte-Carlo calculations.Comment: 8 pages, LaTe
Disclinations, dislocations and continuous defects: a reappraisal
Disclinations, first observed in mesomorphic phases, are relevant to a number
of ill-ordered condensed matter media, with continuous symmetries or frustrated
order. They also appear in polycrystals at the edges of grain boundaries. They
are of limited interest in solid single crystals, where, owing to their large
elastic stresses, they mostly appear in close pairs of opposite signs. The
relaxation mechanisms associated with a disclination in its creation, motion,
change of shape, involve an interplay with continuous or quantized dislocations
and/or continuous disclinations. These are attached to the disclinations or are
akin to Nye's dislocation densities, well suited here. The notion of 'extended
Volterra process' takes these relaxation processes into account and covers
different situations where this interplay takes place. These concepts are
illustrated by applications in amorphous solids, mesomorphic phases and
frustrated media in their curved habit space. The powerful topological theory
of line defects only considers defects stable against relaxation processes
compatible with the structure considered. It can be seen as a simplified case
of the approach considered here, well suited for media of high plasticity
or/and complex structures. Topological stability cannot guarantee energetic
stability and sometimes cannot distinguish finer details of structure of
defects.Comment: 72 pages, 36 figure
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