Continuous phase spaces and the time evolution of spins: star products and spin-weighted spherical harmonics. (10th January 2019)

• Record Type: Journal Article
• Authors: Koczor, Bálint; Zeier, Robert; Glaser, Steffen J
• Is Part Of: Journal of physics. Volume 52:Number 5(2019)
• Publication Date: 2019-01-10
• Subjects: phase-space methods -- spin systems -- time evolution -- star product -- spin-weighted spherical harmonics; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aaf302
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We study continuous phase spaces of single spins and develop a complete description of their time evolution. The time evolution is completely specified by so-called star products. We explicitly determine these star products for general spin numbers using a simplified approach which applies spin-weighted spherical harmonics. This approach naturally relates phase spaces of increasing spin number to their quantum-optical limit and allows for efficient approximations of the time evolution for large spin numbers. We also approximate phase-space representations of certain quantum states that are challenging to calculate for large spin numbers. All of these applications are explored in concrete examples and we outline extensions to coupled spin systems.