The CWKB method of particle production in a periodic potential (Q1863130)

To understand time in all its forms and functions is really one of the most interesting as well as vital problems in nature. The method of complex time WKB (CWKB) approximation is very powerful, when used with appropriate caution. The authors have done here a good job of studying the problems of particle production in time-dependent periodic potentials within this approach. The question of particle production in the expanding universe has, of course, been of great significancc since long. The main historical milestones have been mentioned with particular emphasis on the principles around the CWKB approximation. Particle production in the large amplitude region is also discussed, which is followed by developing an analytic theory of parametric resonance particle generation in the fourth section. The standard form of equation with time-dependent potential \(V(t)\) with periodicity defined by \(V(t+T)=V(t)\) is used. In this paper, after listing their results briefly, the authors claim that the complex WBK approximation nicely reproduces all the essential aspects of particle production due to the inflation oscillation.