17
views
0
recommends
+1 Recommend
0 collections
0
shares
• Record: found
• Abstract: found
• Article: found
Is Open Access

# Fractal boundary basins in spherically symmetric $$\phi^4$$ theory

Preprint

Bookmark
There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

### 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.

### Most cited references17

• Record: found

### Universality and scaling in gravitational collapse of a massless scalar field.

(1993)
Bookmark
• Record: found

### Particlelike solutions of the Einstein-Yang-Mills equations.

(1988)
Bookmark
• Record: found

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

(1991)
Bookmark

### Author and article information

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