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Yasuhiro2-Nov11-09
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2020年度量子力学3(遠隔講義)講義(初貝安弘),演習(吉田恒也),TA(若尾洋正,南島元)
量子力学における対称性の議論の基礎を学び,回転操作に関連する角運動量について詳しく議論する。その後,量子力学と群の関係の基礎についても学ぶ。
履修登録者は [遠隔講義へのLink]
筑波大学学内microsoft streamでの動画は [筑波大学microsoft stream]で「量子力学」を検索。

講義(初貝安弘)講義まとめ(学生の皆さん):PC でご覧下さい。iOSではスクロールしません。
第01回(2020−04-28):量子力学における対称性
第02回(2020−05-01):重要な対称性の具体例
第03回(2020−05-08):物理量の変換則
第04回(2020−05-12):ネーターの定理
第05回(2020−05-16):角運動量の代数と昇降演算子
第06回(2020−05-19):角運動量の量子化
第07回(2020−05-22):球面調和関数1
第08回(2020−05-29):球面調和関数2
第09回(2020−06-02):ゼーマン効果とスピン仮説
第10回(2020−06-06):パウリ行列と時間反転対称性
第11回(2020−06-09):一様磁場下の電子系(ランダウ準位)
第12回(2020−06-12):角運動量の合成1
第13回(2020−06-19):角運動量の合成2
第14回(2020−06-23):角運動量の合成3
第15回(2020−06-27):既約テンソル演算子
第16回(2020−06-30):対称操作のつくる群とその表現
第17回(2020−07-03):回転操作とオイラー角
第18回(2020−07-10):回転群の表現
第19回(2020−07-14):SU(2)とSO(3)
第20回(2020−07-21):回転行列と球面調和関数
第21回(2020−07-28):全体の復習+現代的な話題(ベリー接続)
(学生の皆さん,頑張りました!)
演習(吉田恒也)
第1回演習(2020−05-15): 演習問題0(基礎力確認)
第2回演習(2020−05-26): 演習問題1(量子力学における対称性)
第3回演習(2020−06-05): 演習問題2(角運動量の代数と量子化)
第4回演習(2020−06-16): 演習問題3(球面調和関数)
第5回演習(2020−06-26): 演習問題4(パウリ行列と時間反転対称性)
第6回演習(2020−07-07): 演習問題5(角運動量の合成1)
第7回演習(2020−07-17): 演習問題6(角運動量の合成2)
第8回演習(2020−07-24): 演習問題7(群の表現と量子力学)
第9回演習(2020−07-31): 演習問題8(回転群とその表現)
(皆さん演習も頑張りました。ご苦労様でした。)

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量子力学3-2020(筑波大学)遠隔講義
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Recent News
Poster : hatsugai on 2020-11-03 10:00:50 (298 reads)

Thouless' (adiabatic) pump in one-dimension is a typical topological phenomena characterized by the Chern number that correspondes to the quantized motion of the center of mass (COM). Although the COM is only well-defined with boudary (to set the origin of the coordinate), the COM experimentally observed is given by the bulk and the edge states do not contribute. Ultimate adiabaticity, that has never been achieved experimentaly, supports the quantization of the COM supplemented by the periodicity of the system with boundaries. This is the unique bulk-edge correspondence of the pump. We here propose a generic construction using a phase boundary line of the symmetry protect phase with two parameters works as a topological obstruction of the pump in extended parameter space. The construction is purely of manybody and the interaction can be one of the parameters. Have a look at "Interaction-induced topological charge pump" by Yoshihito Kuno and Yasuhiro Hatsugai, Phys. Rev. Research 2, 042024(R), (2020) (Open access)


Poster : hatsugai on 2020-10-28 10:28:43 (470 reads)

The Dirac cone is a typical singular energy dispersion in two dimensions that is a source of various non-trivial topological effects. When realized in real/synthetic materials, it is generically tilted and the equi-energy surface (curve) can be elliptic/hyperbolic (type I/II). The type III Dirac cone is a critical situation between the type I and II that potentially causes various non-trivial physics. As for realization of the type III Dirac cones, we are proposing a generic theoretical scheme without any fine tuning of material parameters . It may also help to synthesize in meta materials. The molecular orbital (MO) construction of the generic flat bands which we are also proposing plays a crutial role. Have a look at "Type-III Dirac Cones from Degenerate Directionally Flat Bands: Viewpoint from Molecular-Orbital Representation" by Tomonari Mizoguchi and Yasuhiro Hatsugai, J. Phys. Soc. Jpn. 89, 103704 (2020) Also arXiv:2007.14643. The paper has been selected as an Editors' choice of J. Phys. Soc. Jpn. (Sep. 2020). See also "News and comments" by Prof. N. Nagaosa.


Poster : hatsugai on 2020-10-01 16:07:56 (556 reads)

Motivated by a historical example, the Dirac Hamiltonian as a square-root of the Klein-Gordon Hamiltonian, its lattice analogue has been discussed recently. Zero energy states are shared by the parent and its descendant. The story is more than that. Not necessarily zero energy but its high energy part can also share topological characters. We hereby propose a “square-root higher order topological insulator (square-root HOTI)” when its squared parent is HOTI. Based on the simple observation that square of the decorated honeycomb lattice is given by a decoupled sum of the Kagome and honeycomb lattices, we have demonstrate that the “corner states” of the breezing Kagome lattice with boundaries share topological characters with its descendant as the decorated honeycomb lattice. Have a look at our recent paper just published online, "Square-root higher-order topological insulator on a decorated honeycomb lattice" by Tomonari Mizoguchi, Yoshihito Kuno, and Yasuhiro Hatsugai, Phys. Rev. A 102, 033527 (2020), also arXiv:2004.03235.


Poster : hatsugai on 2020-09-17 11:42:01 (372 reads)

As for a topological characterization of a full Liouvillian (including jump term) for the non hermitian fractional quantum Hall states, we are proposing a pseudospin Chern number associated with the Niu-Thouless-Wu type twists in the doubled Hilbert space. Numerical demonstration of the proposal is explicitely given and its validity is discussed. Have a look at "Fate of fractional quantum Hall states in open quantum systems: Characterization of correlated topological states for the full Liouvillian" by Tsuneya Yoshida, Koji Kudo, Hosho Katsura, and Yasuhiro Hatsugai, Phys. Rev. Research 2, 033428 (2020) (open access).


Poster : hatsugai on 2020-08-16 14:53:28 (606 reads)

Adiabatic deformation of gapped systems is a conceptual basis of topological phases. It implies that topological invariants of the bulk described by the Berry connection work as topological order parameters of the phase. This is independent of the well-established symmetry breaking scenario of the phase characterization. Adiabatic heuristic argument for the fractional quantum Hall states is one of the oldest such trials that states the "FRACTIONAL" state is deformed to the “INTEGER”. Although it is intuitive and physically quite natural, there exist several difficulties. How the states with different degeneracy are deformed each other adiabatically? We have clarified the questions and demonstrated this adiabatic deformation on a torus in the paper "Adiabatic heuristic principle on a torus and generalized Streda formula" by Koji Kudo and Yasuhiro Hatsugai , Phys. Rev. B 102, 125108 (2020) (also arXiv:2004.00859) What is deformed continuously is a gap not the states ! This is also sufficient for the topological stability of the Chern number (of the degenerate multiplet) as a topological order parameter. Have a look at.


    Search
    Bulk-edge correspondence
    [0] バルクとエッジ
    [1] Focus lecture
    [2] Original papers
    [3] Japanese Physical Society monthly issue Commentary (Only Japanese except abstract) [pdf]
    [4] "Band gap, dangling bond and spin : a physicist's viewpoint" [pdf]
    Topological phases
    [0]Historical project
    KAKEN-HI DB FY1992 : Topological effects in electronic/spin systems
    KAKEN-HI DB FY1994 : Topology & geometrical phases in condensed matter physics
    Some of my talk files
    [1] MIT, Boston (2003)
    [2] APS/JPS March Meeting (2004)
    [3] JPS Fall meeting, JAPAN (2004)
    [4] APS/JPS March meeting (2005)
    [5] JPS Fall meeting (2005):Entanglement
    [6] Superclean workshop, Nasu (2006)
    [7] MPIPKS, Dresden (2006)
    [8] KEK, Tsukuba (2007)
    [9] ETH, Zurich (2008)
    [10] ICREA, Sant Benet (2009)
    [11] JPS Meeting, Kumamoto (2009)
    [12]HMF19, Fukuoka (2010)
    [13] NTU, Singapore (2011)
    [14] ICTP, Trieste (2011)
    [15] Villa conf., Orland (2012)
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