Mechanization of scalar field theory in 1+1 dimensions

Abstract

Abstract “Mechanization” is a procedure of replacing a scalar field in 1+1 dimensions with a piecewise linear function, i.e. a finite graph consisting of N joints (vertices) and straight segments (edges). As a result, the field theory is approximated by a sequence of algebraically tractable, general-purpose collective coordinate mechanical models. We observe the step-by-step emergence of dynamical objects and associated phenomena as N increases. “Mech-kinks” and “mech-oscillons”—mechanical analogs of kinks and oscillons (bions)—appear in the simplest models, while more intricate dynamical patterns, such as the bouncing phenomenon and bion pair-production, emerge gradually as decay states of high-N mech-oscillons.