2,608 research outputs found
Plane waves in a relativistic homogeneous and isotropic elastic continuum
Propagation of gravitational and acoustic plane waves in a flat universe
filled with a general relativistic, homogeneous and isotropic, spatially flat
continuum is studied. The continuum is described by analogues of
nonrelativistic characteristics, namely energy per particle, pressure and Lame
coefficients, and considered in the comoving proper-time gauge. For all modes
with the given wave covector, differential equations governing the time
dependence of the amplitudes are derived. In particular, longitudinal acoustic
waves are described, in analogy with the nonrelativistic theory, by two coupled
first-order equations. As an example, plane waves in a stiff ultrarigid
continuum are considered.Comment: 12 pages, 1 figure; section 4 extended, minor changes elsewhere,
author adde
Exact Description of Rotational Waves in an Elastic Solid
Conventional descriptions of transverse waves in an elastic solid are limited
by an assumption of infinitesimally small gradients of rotation. By assuming a
linear response to variations in orientation, we derive an exact description of
a restricted class of rotational waves in an ideal isotropic elastic solid. The
result is a nonlinear equation expressed in terms of Dirac bispinors. This
result provides a simple classical interpretation of relativistic quantum
mechanical dynamics. We construct a Lagrangian of the form L=-E+U+K=0, where E
is the total energy, U is the potential energy, and K is the kinetic energy.Comment: 9 pages; Added references in revisio
Magnetic bubble refraction and quasibreathers in inhomogeneous antiferromagnets
The dynamics of magnetic bubble solitons in a two-dimensional isotropic
antiferromagnetic spin lattice is studied, in the case where the exchange
integral J(x,y) is position dependent. In the near continuum regime, this
system is described by the relativistic O(3) sigma model on a spacetime with a
spatially inhomogeneous metric, determined by J. The geodesic approximation is
used to describe low energy soliton dynamics in this system: n-soliton motion
is approximated by geodesic motion in the moduli space of static n-solitons,
equipped with the L^2 metric. Explicit formulae for this metric for various
natural choices of J(x,y) are obtained. From these it is shown that single
soliton trajectories experience refraction, with 1/J analogous to the
refractive index, and that this refraction effect allows the construction of
simple bubble lenses and bubble guides. The case where J has a disk
inhomogeneity (taking the value J_1 outside a disk, and J_2<J_1 inside) is
considered in detail. It is argued that, for sufficiently large J_1/J_2 this
type of antiferromagnet supports approximate quasibreathers: two or more
coincident bubbles confined within the disk which spin internally while their
shape undergoes periodic oscillations with a generically incommensurate period.Comment: Conference proceedings paper for talk given at Nonlinear Physics
Theory and Experiment IV, Gallipoli, Italy, June 200
Rotational elasticity
We consider an infinite 3-dimensional elastic continuum whose material points
experience no displacements, only rotations. This framework is a special case
of the Cosserat theory of elasticity. Rotations of material points are
described mathematically by attaching to each geometric point an orthonormal
basis which gives a field of orthonormal bases called the coframe. As the
dynamical variables (unknowns) of our theory we choose the coframe and a
density. We write down the general dynamic variational functional for our
rotational theory of elasticity, assuming our material to be physically linear
but the kinematic model geometrically nonlinear. Allowing geometric
nonlinearity is natural when dealing with rotations because rotations in
dimension 3 are inherently nonlinear (rotations about different axes do not
commute) and because there is no reason to exclude from our study large
rotations such as full turns. The main result of the paper is an explicit
construction of a class of time-dependent solutions which we call plane wave
solutions; these are travelling waves of rotations. The existence of such
explicit closed form solutions is a nontrivial fact given that our system of
Euler-Lagrange equations is highly nonlinear. In the last section we consider a
special case of our rotational theory of elasticity which in the stationary
setting (harmonic time dependence and arbitrary dependence on spatial
coordinates) turns out to be equivalent to a pair of massless Dirac equations
Electromagnetic Response of Layered Superconductors with Broken Lattice Inversion Symmetry
We investigate the macroscopic effects of charge density waves (CDW) and
superconductivity in layered superconducting systems with broken lattice
inversion symmetry (allowing for piezoelectricity) such as two dimensional (2D)
transition metal dichalcogenides (TMD). We work with the low temperature time
dependent Ginzburg-Landau theory and study the coupling of lattice distortions
and low energy CDW collective modes to the superconducting order parameter in
the presence of electromagnetic fields. We show that superconductivity and
piezoelectricity can coexist in these singular metals. Furthermore, our study
indicates the nature of the quantum phase transition between a commensurate CDW
phase and the stripe phase that has been observed as a function of applied
pressure.Comment: 9 pages, 1 figure. Final version. Accepted in Phys.Rev.
Motion of Quantized Vortices as Elementary Objects
The general local, nondissipative equations of motion for a quantized vortex
moving in an uncharged laboratory superfluid are derived from a relativistic,
co-ordinate invariant framework, having vortices as its elementary objects in
the form of stable topological excitations. This derivation is carried out for
a pure superfluid with isotropic gap at the absolute zero of temperature, on
the level of a hydrodynamic, collective co-ordinate description. In the
formalism, we use as fundamental ingredients that particle number as well as
vorticity are conserved, and that the fluid is perfect. No assumptions are
involved as regards the dynamical behaviour of the order parameter. The
interaction of the vortex with the background fluid, representing the Magnus
force, and with itself via phonons, giving rise to the hydrodynamic vortex
mass, are separated. For a description of the motion of the vortex in a dense
laboratory superfluid like helium II, two limits have to be considered: The
nonrelativistic limit for the superfluid background is taken, and the motion of
the vortex is restricted to velocities much less than the speed of sound. The
canonical structure of vortex motion in terms of the collective co-ordinate is
used for the quantization of this motion.Comment: 25 pages, 4 figures, published versio
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