Perturbative, acausal effects in ultracold non-crossing atomic collisions

Abstract

Coupled second-order quantal wave equations are considered for a non-crossing atomic collision. They are reduced to exactly equivalent first-order equations. The semiclassical approximation transforms these equations into generalized projectile-target time-dependent interaction impact parameter equations. We show that in the suggested approach acausal, cybernetic effects are observed when terms propagate in the acausal (negative to positive time) direction. We summarize the results obtained and illustrate these effects in the quantal first Born approximation.

Semiclassical charge transfer in gravitational encounters

“…Thus the expressions (10) and (18) remain causal whereas expressions (9) and (12) amended as in (18) will result in acausality [10].…”

“…The square root singularity is removable by making the change of variable x 2 = R − 2m. Thus the expressions ( 10) and (18) remain causal whereas expressions ( 9) and ( 12) amended as in (18) will result in acausality [10].…”