Topological Excitations in Quantum Condensates with Complex Order Parameters

2019 Fiscal Year Final Research Report

• Project/Area Number: 17K05554
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Condensed matter physics II
• Research Institution: Kindai University
• Principal Investigator: Nakahara Mikio 近畿大学, 理工学総合研究所, 研究員 (90189019)
• Co-Investigator(Kenkyū-buntansha): 高木 丈夫 福井大学, 学術研究院工学系部門, 教授 (00206723) ; 笠松 健一 近畿大学, 理工学部, 准教授 (70413763)
• Project Period (FY): 2017-04-01 – 2020-03-31
• Keywords: ボース凝縮 / 超流動ヘリウム3 / 量子渦 / スキルミオン / ホップ写像 / ユニタリーt-デザイン / アナログ重力 / 光格子

Outline of Final Research Achievements

Vortices in superfluid 3He-B under magnetic field were analyzed and phase diagram of various vortices were obtained as a function of pressure and magnetic field for example. Half-quantum vortices in 3He-A was analyze in the slab geometry. Link structure with arbitrary Hopf charge was obtained in the polar phase of F=1 BEC in a 3-d trap by manipulating the quadrupole field and uniform axial magnetic field as functions of time. The 3-d skyrmions in the cyclic and the biaxial nematic phases of F=2 BEC were analyzed. Analogue gravity associated with superfluid and Yang-Mills field was analyzed in a curved spacetime. It was shown that an average over unitary group manifold can be replaced by an average of a finite set of points in the unitary group (unitary t-design).

Free Research Field

数理系科学

Academic Significance and Societal Importance of the Research Achievements

本研究では，超流動3Heやスピン自由度を持つボース凝縮体など，複雑な秩序変数を持つ凝縮体におけるトポロジカル励起の研究や，組み合わせ論と量子情報の共通領域であるユニタリーt-デザインの研究など，物理学と数学の諸分野にまたがる研究を行った．ワークショップ等を通して，これらの分野の研究者の交流を深めた．また，多くの国際共同研究の成果を，インパクトファクターの高い雑誌に多数出版することにより，我が国および世界の学術的レベルの向上に寄与した．