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Emergence of compact structures in a Klein-Gordon model.
Philip Rosenau1, Eugene Kashdan
1School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel. rosenau@post.tau.ac.il
Physical Review Letters
|April 7, 2010
Summary
Localized modes in the Klein-Gordon model can be made to have compact support by adding a specific potential. These particle-like modes are robust, shorten when moving, and interact upon contact.
Area of Science:
- Theoretical Physics
- Quantum Field Theory
Background:
- The Klein-Gordon (KG) model is Lorenz invariant with finite wave speed.
- Existing localized modes (solitons like Q balls and vortices) in the KG model lack compact support, extending indefinitely.
Purpose of the Study:
- To demonstrate that modifying the Klein-Gordon model's potential can create particle-like modes with strictly compact support.
- To investigate the properties and interactions of these novel, localized modes.
Main Methods:
- Appending a subquadratic term (b|phi|^(1+delta)) to the site potential of the Klein-Gordon equation.
- Analyzing the resulting particle-like modes for robustness, speed dependence, and interaction characteristics in 2D and 3D.
Main Results:
- The modified potential induces particle-like modes with strictly compact support.
- These modes exhibit robustness and shorten in their direction of motion.
- Interactions between modes occur only upon contact and range from nearly elastic to plastic.
Conclusions:
- The introduction of a specific subquadratic potential term fundamentally alters the nature of localized modes in the Klein-Gordon model.
- This modification allows for the creation of robust, finite-extent particle-like entities with controllable interaction properties.
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