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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

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Summary
This summary is machine-generated.

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.

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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.