📝 SummarXiv

Abstract

Instead of the conventional construction of symmetric and antisymmetric states by abruptly projecting with the symmetrizer or antisymmetrizer, this paper investigates rapid but continuous symmetrization via environment-induced decoherence. Density operators are transformed to a symmetric observable via a semigroup map obtained from an interacting Hamiltonian. Likewise, a completely positive dynamical map transforms a completely asymmetric state to either a symmetric or antisymmetric state. The theory is applied to analyze a collision between two identical particles having arbitrary spin and negligible spin interactions. We discuss extensions to larger domains via dynamical maps that are not completely positive.