{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,7,31]],"date-time":"2023-07-31T04:28:04Z","timestamp":1690777684428},"reference-count":28,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Geom. Methods Mod. Phys."],"published-print":{"date-parts":[[2015,3]]},"abstract":"<jats:p> In this paper we present the induced representation of SO (2N) canonical transformation group and introduce [Formula: see text] coset variables. We give a derivation of the time-dependent Hartree\u2013Bogoliubov (TDHB) equation on the K\u00e4hler coset space [Formula: see text] from the Euler\u2013Lagrange equation of motion for the coset variables. The TDHB wave function represents the TD behavior of Bose condensate of fermion pairs. It is a good approximation for the ground state of the fermion system with a pairing interaction, producing the spontaneous Bose condensation. To describe the classical motion on the coset manifold, we start from the local equation of motion. This equation becomes a Riccati-type equation. After giving a simple two-level model and a solution for a coset variable, we can get successfully a general solution of time-dependent Riccati\u2013Hartree\u2013Bogoliubov equation for the coset variables. We obtain the Harish-Chandra decomposition for the SO (2N) matrix based on the nonlinear M\u00f6bius transformation together with the geodesic flow on the manifold. <\/jats:p>","DOI":"10.1142\/s0219887815500358","type":"journal-article","created":{"date-parts":[[2014,12,19]],"date-time":"2014-12-19T06:12:05Z","timestamp":1418969525000},"page":"1550035","source":"Crossref","is-referenced-by-count":2,"title":["$\\frac{{\\rm SO}(2N)}{U(N)}$ Riccati\u2013Hartree\u2013Bogoliubov equation based on the <font>SO<\/font>(2N) Lie algebra of the fermion operators"],"prefix":"10.1142","volume":"12","author":[{"given":"Seiya","family":"Nishiyama","sequence":"first","affiliation":[{"name":"Centro de F\u00edsica, Departamento de F\u00edsica, Universidade de Coimbra, P-3004-516 Coimbra, Portugal"}]},{"given":"Jo\u00e3o","family":"da Provid\u00eancia","sequence":"additional","affiliation":[{"name":"Centro de F\u00edsica, Departamento de F\u00edsica, Universidade de Coimbra, P-3004-516 Coimbra, Portugal"}]}],"member":"219","published-online":{"date-parts":[[2015,2,27]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/0370-2693(79)90964-X"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/S0550-3213(00)00666-0"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1070\/PU1959v002n02ABEH003122"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-61852-9"},{"key":"rf5","volume-title":"Quantum Theory of Finite Systems","author":"Blaizot J. 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