Effect of Compactified Spatial Coordinate in Decay-Rate Phase Transition

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Abstract
The pahse transition from instanton-dominated quantum tunneling regime to sphaleron-dominated classical crossover regime is explored in (1+1)-dimensional scalar field theory when spatial coordinate is compactified. It is shown that the type of sphaleron transition is critically dependent on the circumference of the spatial coordinate. Based on our main result we conjecture the type of winding number phase transition in Mottola-Wipf model when spatial coordinate is compactified and discuss briefly its physical implications in baryon number violating process.

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