2019/06/17 by Sebastián Fortín, M. Gadella, Fortin, Sebastian +5
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1906.07226
openalex publication_date 2019/06/17 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
A fundamental aspect of the quantum-to-classical limit is the transition from\na non-commutative algebra of observables to commutative one. However, this\ntransition is not possible if we only consider unitary evolutions. One way to\ndescribe this transition is to consider the Gamow vectors, which introduce\nexponential decays in the evolution. In this paper, we give two mathematical\nmodels in which this transition happens in the infite time limit. In the first\none, we consider operators acting on the space of the Gamow vectors, which\nrepresent quantum resonances. In the second one, we use an algebraic formalism\nfrom scattering theory. We construct a non-commuting algebra which commutes in\nthe infinite time limit.\n