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      Fractal boundary basins in spherically symmetric \(\phi^4\) theory

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          Abstract

          Results are presented from numerical simulations of the flat-space nonlinear Klein-Gordon equa- tion with an asymmetric double-well potential in spherical symmetry. Exit criteria are defined for the simulations that are used to help understand the boundaries of the basins of attraction for Gaussian "bubble" initial data. The first exit criteria, based on the immediate collapse or expan- sion of bubble radius, is used to observe the departure of the scalar field from a static intermediate attractor solution. The boundary separating these two behaviors in parameter space is smooth and demonstrates a time-scaling law with an exponent that depends on the asymmetry of the potential. The second exit criteria differentiates between the creation of an expanding true-vacuum bubble and dispersion of the field leaving the false vacuum; the boundary separating these basins of attraction is shown to demonstrate fractal behavior. The basins are defined by the number of bounces that the field undergoes before inducing a phase transition. A third, hybrid exit criteria is used to determine the location of the boundary to arbitrary precision and to characterize the threshold behavior. The possible effects this behavior might have on cosmological phase transitions are briefly discussed.

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          Most cited references 17

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              Fractal structure in the scalarλ(φ2−1)2theory

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                Author and article information

                Journal
                11 June 2010
                2011-06-13
                10.1103/PhysRevD.82.024038
                1006.2421

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                Custom metadata
                Phys.Rev.D82:024038,2010
                10 pages, 13 figures, 1 movie, resubmitted with additional paragraph. Matches published version
                gr-qc hep-ph hep-th

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