title: Defect production in nonlinear quench across a quantum critical point.
abstract: We show that the defect density n, for a slow nonlinear power-law quench with a rate tau(-1) and an exponent alpha>0, which takes the system through a critical point characterized by correlation length and dynamical critical exponents nu and z, scales as n approximately tau(-alphanud/(alphaznu+1)) [n approximately (alphag((alpha-1)/alpha)/tau)(nud/(znu+1))] if the quench takes the system across the critical point at time t=0 [t=t(0) not = 0], where g is a nonuniversal constant and d is the system dimension. These scaling laws constitute the first theoretical results for defect production in nonlinear quenches across quantum critical points and reproduce their well-known counterpart for a linear quench (alpha=1) as a special case. We supplement our results with numerical studies of well-known models and suggest experiments to test our theory.
authors.affiliation: Center for High Energy Physics, Indian Institute of Science, Bangalore, 560 012, India.
authors.forename: Diptiman
authors.initials: D
authors.lastname: Sen
authors.forename: K
authors.initials: K
authors.lastname: Sengupta
authors.forename: Shreyoshi
authors.initials: S
authors.lastname: Mondal