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2009-11-16 8:50:48   by: hatsugai
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投稿者 : hatsugai 投稿日時: 2016-01-16 17:16:48 (69 ヒット)

Topological pump, proposal by Thouless and just recently realized experimeatally in Kyoto and Munich independently, is revisited from the bulk-edge correspondence (BEC). It's typically described by well known Harper equation as in QHE but the view point of BEC supplies quite different physical / mathematical structure. Pumped charge is carried by bulk but its quantization is guaranteed by the topological number defined by a singular motion of the center of mass caused by edge states. However this singular motion can not be observed in reality by a pumping of finite speed.The edge states are hidden! Counting the topological number by singularities of the spectral flow is a standard technique in the discussion of the Atiyah-Patodii-Singer index theorem. The same counting appears in the BEC in the pumping. It's a unexpected surprise. Have a look at arXiv:1601.03537


投稿者 : hatsugai 投稿日時: 2016-01-16 17:16:20 (397 ヒット)

Our paper is now online. Topology is not only for quantum world. Localised modes near the system boundaries also exist in a classical system that is predicted by bulk. This is the bulk-edge correspondence originally discussed in quantum systems such as quantum (spin) Hall states and graphene. Still this idea is valid in classical world. We discussed topological phenomena in mechanics for point particles connected with springs in a honeycomb shape. Also topological phase transitions associated with its tension is clearly demonstrated as a time evolution of the localized modes. [arXiv:1505.06679]


投稿者 : hatsugai 投稿日時: 2015-09-14 19:50:18 (701 ヒット)

We are organizing an international workshop on the bulk-edge correspondence / topological phases  Sep. 27-29 (2015) in Tokyo (Myogadani) supported by KAKENHI (JSPS research funding). Tentative program is ready and on the net.


    検索
    バルク・エッジ対応
    [0] バルクとエッジ
    [1] 集中講義
    [2] 原論文と解説
    [3] トポロジカル秩序とベリー接続:日本物理学会誌 「解説」 [JPS-HP] [pdf]
    [4] "Band gap, dangling bond and spin : a physicist's viewpoint" [pdf] [Web]
    トポロジカル相
    [0]昔の科研費
    科研費 1992年度:電子系スピン系におけるトポロジカル効果
    科研費 1994年度:物性論におけるトポロジーと幾何学的位相
    私の講演ファイルのいくつか
    [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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