25 research outputs found
A new approach to quantum backflow
We derive some rigorous results concerning the backflow operator introduced
by Bracken and Melloy. We show that it is linear bounded, self adjoint, and not
compact. Thus the question is underlined whether the backflow constant is an
eigenvalue of the backflow operator. From the position representation of the
backflow operator we obtain a more efficient method to determine the backflow
constant. Finally, detailed position probability flow properties of a numerical
approximation to the (perhaps improper) wave function of maximal backflow are
displayed.Comment: 12 pages, 8 figure
The gauge theory of dislocations: a nonuniformly moving screw dislocation
We investigate the nonuniform motion of a straight screw dislocation in
infinite media in the framework of the translational gauge theory of
dislocations. The equations of motion are derived for an arbitrary moving screw
dislocation. The fields of the elastic velocity, elastic distortion,
dislocation density and dislocation current surrounding the arbitrarily moving
screw dislocation are derived explicitely in the form of integral
representations. We calculate the radiation fields and the fields depending on
the dislocation velocities.Comment: 12 page
The gauge theory of dislocations: static solutions of screw and edge dislocations
We investigate the T(3)-gauge theory of static dislocations in continuous
solids. We use the most general linear constitutive relations bilinear in the
elastic distortion tensor and dislocation density tensor for the force and
pseudomoment stresses of an isotropic solid. The constitutive relations contain
six material parameters. In this theory both the force and pseudomoment
stresses are asymmetric. The theory possesses four characteristic lengths l1,
l2, l3 and l4 which are given explicitely. We first derive the
three-dimensional Green tensor of the master equation for the force stresses in
the translational gauge theory of dislocations. We then investigate the
situation of generalized plane strain (anti-plane strain and plane strain).
Using the stress function method, we find modified stress functions for screw
and edge dislocations. The solution of the screw dislocation is given in terms
of one independent length l1=l4. For the problem of an edge dislocation, only
two characteristic lengths l2 and l3 arise with one of them being the same
l2=l1 as for the screw dislocation. Thus, this theory possesses only two
independent lengths for generalized plane strain. If the two lengths l2 and l3
of an edge dislocation are equal, we obtain an edge dislocation which is the
gauge theoretical version of a modified Volterra edge dislocation. In the case
of symmetric stresses we recover well known results obtained earlier.Comment: 33 pages, 17 figure