Some properties of Grassmannian coherent states and an entropic conjecture. (18th November 2015) - Calixto, Manuel; Pérez-Romero, Emilio
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.