2014/12/10 by Scott Shermer, Shermer, Scott
Computer Science · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Information and Cryptography #Quantum many-body systems
paper · pdf · doi:10.48550/arxiv.1412.3185
openalex publication_date 2014/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Twisted classical solutions to the ℂPN-1 model play a key role in the analysis of such models on the spatially compactified cylinder \mathbbSL1 × ℝ1 and have recently been shown to be important for the resurgent structure of this quantum field theory. Instantons and non-self-dual solutions both fractionalize, and domain walls formed by such topological solutions can be associated with N-vacua having maximally repulsive energy eigenvalues. The purpose of this paper is to reinforce this view through the investigation of a number of parallels between the ℂPN-1 model and N-level quantum mechanical density matrices. Specifically, we demonstrate the existence of a time-evolution equation for the ℂPN-1 instanton projector analogous to the Liouville-von Neumann equation in the quantum mechanical formalism. The group theoretical analysis of density matrices and the ℂPN-1 model are also closely related. Finally, we explore the emergence of geometrical (Berry) phases in both systems and their interrelationship.