Some properties of Grassmannian coherent states and an entropic conjecture. (18th November 2015)

• Record Type: Journal Article
• Authors: Calixto, Manuel; Pérez-Romero, Emilio
• Is Part Of: Journal of physics. Volume 48:Number 49(2015)
• Publication Date: 2015-11-18
• Subjects: coherent states -- operator symbols -- fractional quantum Hall effect -- Husimi function; 03.65.Fd -- 02.40.Tt -- 73.43.-f; 81R30 -- 81R05 -- 32Q15; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8113/48/49/495304
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We analyze mathematical and physical properties of a previously introduced (Calixto and Pérez-Romero 2014 J. Phys. A: Math. Theor. 47 023027 ) family of U (4) coherent states (CS). They constitute a matrix version of standard spin U (2) CS when we add an extra (pseudospin) dichotomous degree of freedom: layer, sublattice, two-well, nucleon, etc. Applications to bilayer quantum Hall systems at fractions of filling factor are discussed, where Haldane's sphere picture is generalized to a Grassmannian picture. We also extend Wehrl's definition of entropy from Glauber to Grassmannian CS and state a conjecture on the entropy lower bound.