Emergence of Symmetry in a System of Distinguishable but Identical Particles

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 perfectly asymmetric states to either symmetric or antisymmetric states. The theory is applied to analyse 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.