15,911 research outputs found
The Periodic Standing-Wave Approximation: Overview and Three Dimensional Scalar Models
The periodic standing-wave method for binary inspiral computes the exact
numerical solution for periodic binary motion with standing gravitational
waves, and uses it as an approximation to slow binary inspiral with outgoing
waves. Important features of this method presented here are: (i) the
mathematical nature of the ``mixed'' partial differential equations to be
solved, (ii) the meaning of standing waves in the method, (iii) computational
difficulties, and (iv) the ``effective linearity'' that ultimately justifies
the approximation. The method is applied to three dimensional nonlinear scalar
model problems, and the numerical results are used to demonstrate extraction of
the outgoing solution from the standing-wave solution, and the role of
effective linearity.Comment: 13 pages RevTeX, 5 figures. New version. A revised form of the
nonlinearity produces better result
Phantom field fluctuation induced Higgs effect
Symmetry breaking solutions are investigated in the limit for
the ground state of a system consisting of a Lorentz-scalar, N component
``phantom'' field and an O(N) singlet. The most general form of O(N) x Z_2
invariant quartic interaction is considered. The non-perturbatively
renormalised solution demonstrates the possibility for Z_2 symmetry breaking
induced by phantom fluctuations. It becomes also evident that the strength of
the ``internal'' dynamics of the N-component field tunes away the ratio of the
Higgs condensate and the Higgs mass from its perturbative (nearly tree-level)
expression.Comment: 9 pages, uses elsart.cls, version to appear in Phys. Lett.
An Algorithm for Gluinos on the Lattice
L\"uscher's local bosonic algorithm for Monte Carlo simulations of quantum
field theories with fermions is applied to the simulation of a possibly
supersymmetric Yang-Mills theory with a Majorana fermion in the adjoint
representation. Combined with a correction step in a two-step polynomial
approximation scheme, the obtained algorithm seems to be promising and could be
competitive with more conventional algorithms based on discretized classical
(``molecular dynamics'') equations of motion. The application of the considered
polynomial approximation scheme to optimized hopping parameter expansions is
also discussed.Comment: latex2e, 23 pages, 4 figures with epsfig. Section 5 is rewritten,
more data are added and the discussion is extende
Many Masses on One Stroke: Economic Computation of Quark Propagators
The computational effort in the calculation of Wilson fermion quark
propagators in Lattice Quantum Chromodynamics can be considerably reduced by
exploiting the Wilson fermion matrix structure in inversion algorithms based on
the non-symmetric Lanczos process. We consider two such methods: QMR (quasi
minimal residual) and BCG (biconjugate gradients). Based on the decomposition
of the Wilson mass matrix, using QMR, one can carry
out inversions on a {\em whole} trajectory of masses simultaneously, merely at
the computational expense of a single propagator computation. In other words,
one has to compute the propagator corresponding to the lightest mass only,
while all the heavier masses are given for free, at the price of extra storage.
Moreover, the symmetry can be used to cut
the computational effort in QMR and BCG by a factor of two. We show that both
methods then become---in the critical regime of small quark
masses---competitive to BiCGStab and significantly better than the standard MR
method, with optimal relaxation factor, and CG as applied to the normal
equations.Comment: 17 pages, uuencoded compressed postscrip
Iterative Interplay between Aharonov-Bohm Deficit Angle and Berry Phase
Geometric phases can be observed by interference as preferred scattering directions in the Aharonov-Bohm (AB) effect or as Berry phase shifts leading to precession on cyclic paths. Without curvature single-valuedness is lost in both case. It is shown how the deficit angle of the AB conic metric and the geometric precession cone vertex angle of the Berry phase can be adjusted to restore single-valuedness. The resulting interplay between both phases confirms the non--linear iterative system providing for generalized fine structure constants obtained in the preliminary work. Topological solitons of the scalar coupling field emerge as localized, non-dispersive and non-singular solutions of the (complex) sine-Gordon equation with a relation to the Thirring coupling constant and non-linear optics
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