2000/09/30 by Yu. M. Gufan, Al. V. Popov, G. Sartori +3 · 9 citations
Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Cold Atom Physics and Bose-Einstein Condensates #Degree (music) #Group (periodic table) #Invariant (physics) #Invariant theory #Isotropy #Pairing #Physics of Superconductivity and Magnetism #Space (punctuation) #Symmetry (geometry) #Symmetry group #cond-mat.supr-con #hep-th #math-ph #math.MP
paper · pdf · doi:10.1063/1.1345871
published in Journal of Mathematical Physics 42(4), 1533-1562 (American Institute of Physics) · 27 revtex pages, 2 figures, use of texdraw; minor changes in the bibliography and in Table III
arxiv created 2001/03/30 · openalex publication_date 2001/04/01 · arxiv updated 2011/08/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
A complete and rigorous determination of the possible ground states for D-wave pairing Bose condensates is presented, using a geometrical invariant theory approach to the problem. The order parameter is argued to be a vector, transforming according to a ten-dimensional real representation of the group G=O3⊗U1×〈T 〉. We determine the equalities and inequalities defining the orbit space of this linear group and its symmetry strata, which are in a one-to-one correspondence with the possible distinct phases of the system. We find 15 allowed phases (besides the unbroken one), with different symmetries, that we thoroughly determine. The group–subgroup relations between bordering phases are pointed out. The perturbative sixth degree corrections to the minimum of a fourth degree polynomial G-invariant free energy, calculated by Mermin, are also determined.