4,178 research outputs found
Three-Dimensional Billiards with Time Machine
Self-collision of a non-relativistic classical point-like body, or particle,
in the spacetime containing closed time-like curves (time-machine spacetime) is
considered. A point-like body (particle) is an idealization of a small ideal
elastic billiard ball. The known model of a time machine is used containing a
wormhole leading to the past. If the body enters one of the mouths of the
wormhole, it emerges from another mouth in an earlier time so that both the
particle and its "incarnation" coexist during some time and may collide. Such
self-collisions are considered in the case when the size of the body is much
less than the radius of the mouth, and the latter is much less than the
distance between the mouths. Three-dimensional configurations of trajectories
with a self-collision are presented. Their dynamics is investigated in detail.
Configurations corresponding to multiple wormhole traversals are discussed. It
is shown that, for each world line describing self-collision of a particle,
dynamically equivalent configurations exist in which the particle collides not
with itself but with an identical particle having a closed trajectory (Jinnee
of Time Machine).Comment: 20 pages (LATEX), 5 figures (EPS
Lattice Gauge Theory Sum Rule for the Shear Channel
An exact expression is derived for the thermal correlator of
shear stress in SU() lattice gauge theory. I remove a logarithmic
divergence by taking a suitable linear combination of the shear correlator and
the correlator of the energy density. The operator product expansion shows that
the same linear combination has a finite limit when . It
follows that the vacuum-subtracted shear spectral function vanishes at large
frequencies at least as fast as and obeys a sum rule. The
trace anomaly makes a potential contribution to the spectral sum rule which
remains to be fully calculated, but which I estimate to be numerically small
for . By contrast with the bulk channel, the shear channel
spectral density is then overall enhanced as compared to the spectral density
in vacuo.Comment: 11 pages, no figure
Two-dimensional algebro-geometric difference operators
A generalized inverse problem for a two-dimensional difference operator is
introduced. A new construction of the algebro-geometric difference operators of
two types first considered by I.M.Krichever and S.P.Novikov is proposedComment: 11 pages; added references, enlarged introduction, rewritten abstrac
Distribution of averages in a correlated Gaussian medium as a tool for the estimation of the cluster distribution on size
Calculation of the distribution of the average value of a Gaussian random
field in a finite domain is carried out for different cases. The results of the
calculation demonstrate a strong dependence of the width of the distribution on
the spatial correlations of the field. Comparison with the simulation results
for the distribution of the size of the cluster indicates that the distribution
of an average field could serve as a useful tool for the estimation of the
asymptotic behavior of the distribution of the size of the clusters for "deep"
clusters where value of the field on each site is much greater than the rms
disorder.Comment: 15 pages, 6 figures, RevTe
Topological Phenomena in the Real Periodic Sine-Gordon Theory
The set of real finite-gap Sine-Gordon solutions corresponding to a fixed
spectral curve consists of several connected components. A simple explicit
description of these components obtained by the authors recently is used to
study the consequences of this property. In particular this description allows
to calculate the topological charge of solutions (the averaging of the
-derivative of the potential) and to show that the averaging of other
standard conservation laws is the same for all components.Comment: LaTeX, 18 pages, 3 figure
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