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# Documents  Kotani, Motoko | enregistrements trouvés : 12

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## Interview at CIRM: Pavel Exner Exner, Pavel | CIRM H

Post-edited

Outreach;Mathematics Education and Popularization of Mathematics

Pavel Exner from the Academy of Sciences of the Czech Republic in Prague is president of the European Mathematical Society (2015-2018). He's currently also the scientific director at the Doppler Institute for Mathematical Physics and Applied Mathematics in Prague.

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## Emergent anyons in quantum Hall physics Rougerie, Nicolas | CIRM H

Post-edited

Research talks;Partial Differential Equations;Mathematical Physics

Anyons are by definition particles with quantum statistics different from those of bosons and fermions. They can occur only in low dimensions, 2D being the most relevant case for this talk. They have hitherto remained hypothetical, but there is good theoretical evidence that certain quasi-particles occuring in quantum Hall physics should behave as anyons.

I shall consider the case of tracer particles immersed in a so-called Laughlin liquid. I will argue that, under certain circumstances, these become anyons. This is made manifest by the emergence of a particular effective Hamiltonian for their motion. The latter is notoriously hard to solve even in simple cases, and well-controled simplifications are highly desirable. I will discuss a possible mean-field approximation, leading to a one-particle energy functional with self-consistent magnetic field.
Anyons are by definition particles with quantum statistics different from those of bosons and fermions. They can occur only in low dimensions, 2D being the most relevant case for this talk. They have hitherto remained hypothetical, but there is good theoretical evidence that certain quasi-particles occuring in quantum Hall physics should behave as anyons.

I shall consider the case of tracer particles immersed in a so-called Laughlin liquid. I ...

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## Operator algebras and mathematical physics.Proceedings of the 9th international conference on operator algebras and mathematical physicsSendai # August 1-12, 2016 Izumi, Masaki ; Kawahigashi, Yasuyuki ; Kotani, Motoko ; Matui, Hiroki ; Ozawa, Narutaka | Mathematical Society of Japan 2019

Congrès

- 218 p.
ISBN 978-4-86497-079-2

Advanced studies in pure mathematics , 0080

Localisation : Collection 1er étage

théorie des opérateurs # algèbre d'opérateurs # physique mathématique # opérateur vertex # théorie quantique des champs # hypergroupe # K-théorie # automorphisme # flip # groupe quantique # chaîne de spins

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## Probabilistic approach to geometry.Proceedings of the 1st international conferenceKyoto # July 28 - August 8, 2008 Kotani, Motoko ; Hino, Masanori ; Kumagai, Takashi | Mathematical Society of Japan 2010

Congrès

- 514 p.
ISBN 978-4-931469-58-7

Advanced studies in pure mathematics , 0057

Localisation : Collection 1er étage

probabilité # équation différentielle ordinaire # analyse globale # théorie des groupes # géométrie

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## Noncommutative geometry and physics 3:proceedings of the noncommutative geometry and physics 2008, on K-theory and D-branesShonan # february 18-22, 2008Proceedings of the RIMS thematic year 2010 on perspectives in deformation quantization and noncommutative geometryKyoto # april 1 - march 31, 2011 Dito, Giuseppe ; Kotani, Motoko ; Maeda, Yoshiaki ; Moriyoshi, Hitoshi ; Natsume, Toshikazu ; Watamura, Satoshi | World Scientific 2013

Congrès

- viii; 528 p.
ISBN 978-981-4425-00-1

Localisation : Colloque 1er étage (SHON)

théorie quantique # géométrie non-commutative # chaînes # K-théorie # géométrie différentielle appliquée à la physique # quantification

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## Noncommutativity and singularities:proceedings of French-Japanese symposiaBures-sur-Yvette # november 15-18 and november 20-23, 2006 Bourguignon, Jean-Pierre ; Kotani, Motoko ; Maeda, Yoshiaki ; Tose, Nobuyuki | Mathematical Society of Japan 2009

Congrès

- 363 p.
ISBN 978-4-931469-54-9

Advanced studies in pure mathematics , 0055

Localisation : Collection 1er étage

singularités # géométrie différentielle non-commutative

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## Spectral analysis in geometry and number theory:international conference on the occasion of Toshikazu Sunada's 60th birthdayNagoya # august 6-10, 2007 Kotani, Motoko ; Naito, Hisashi ; Tate, Tatsuya | American Mathematical Society 2009

Congrès

- xii; 342 p.
ISBN 978-0-8218-4269-0

Contemporary mathematics , 0484

Localisation : Collection 1er étage

géométrie spectrale # théorie des nombres # formule des traces # problème isospectrale # fonction zéta # ergodicité quantique # onde aléatoire # analyse géométrique discrète

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## Discrete geometric analysis :proceedings of the first JAMS symposium on ...#Dec. 12-20 Kotani, Motoko ; Shirai, Tomoyuki ; Sunada, Toshikazu | American Mathematical Society 2004

Congrès

- 258 p.
ISBN 978-0-8218-3351-3

Contemporary mathematics , 0347

Localisation : Collection 1er étage

géométrie différentielle # analyse mathématique # analyse géométrique # noyau de chaleur # marche aléatoire # limite de Poisson sur les groupes discrets # graphe

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## Twisted equivariant $\mathrm{K}$-theory and topological phases Kubota, Yosuke | CIRM H

Multi angle

Research talks;Mathematical Physics

The classification of topological phases in each Altland-Zirnbauer symmetry class is related to one of 2 complex or 8 real $\mathrm{K}$-theory by Kitaev. A more general framework, in which we deal with systems with an arbitrary symmetry of quantum mechanics specified by Wigner’s theorem, is introduced by Freed and Moore by using a generalization of twisted $\mathrm{K}$-theory. In this talk, we introduce the definition of twisted $\mathrm{K}$-theory in the sense of Freed-Moore for $C^*$-algebras, which gives a framework for the study of topological phases of non-periodic systems with a symmetry of quantum mechanics. Moreover, we introduce uses of basic tools in $\mathrm{K}$-theory of operator algebras such as inductions and the Green-Julg isomorphism for the study of topological phases. The classification of topological phases in each Altland-Zirnbauer symmetry class is related to one of 2 complex or 8 real $\mathrm{K}$-theory by Kitaev. A more general framework, in which we deal with systems with an arbitrary symmetry of quantum mechanics specified by Wigner’s theorem, is introduced by Freed and Moore by using a generalization of twisted $\mathrm{K}$-theory. In this talk, we introduce the definition of twisted \$\mathr...

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## Overdamping in gyroscopic systems composed of high-loss and lossless components Figotin, Alexander | CIRM H

Multi angle

Research talks;Partial Differential Equations;Mathematical Physics

Using a Lagrangian framework, we study overdamping phenomena in gyroscopic systems composed of two components, one of which is highly lossy and the other is lossless. The losses are accounted for by a Rayleigh dissipative function. We prove that selective overdamping is a generic phenomenon in Lagrangian systems with gyroscopic forces and give an analysis of the overdamping phenomena in such systems. Central to the analysis is the introduction of the notion of a dual Lagrangian system and this yields significant improvements on some results on modal dichotomy and overdamping. Using a Lagrangian framework, we study overdamping phenomena in gyroscopic systems composed of two components, one of which is highly lossy and the other is lossless. The losses are accounted for by a Rayleigh dissipative function. We prove that selective overdamping is a generic phenomenon in Lagrangian systems with gyroscopic forces and give an analysis of the overdamping phenomena in such systems. Central to the analysis is the introduction ...

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## Gysin maps and bulk-edge correspondence Matsuo, Shinichiroh | CIRM H

Multi angle

Research talks;Geometry;Mathematical Physics

We propose a yet another definition of KR-groups, which combines those of Atiyah and Karoubi and gives a simple proof of the Bott periodicity. Using the new definition, we can formulate the bulk-edge correspondence for free fermion systems as the functoriality of the Gysin map.
This is joint work with M. Furuta, S. Hayashi, M. Kotani, Y. Kubota, and K. Sato.

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## Topological nature of the Fu-Kane-Mele invariants De Nittis, Giuseppe | CIRM H

Multi angle

Research talks;Mathematical Physics

Condensed matter electronic systems endowed with odd time-reversal symmetry (TRS) (a.k.a. class AII topological insulators) show topologically protected phases which are described by an invariant known as Fu-Kane-Mele index. The construction of this in- variant, in its original form, is specific for electrons in a periodic background and is not immediately generalizable to other interesting physical models where different forms of TRS also play a role. By exploiting the fact that system with an odd TRS (in absence of disorder) can be classified by Quaternionic vector bundles, we introduce a Quaternionic topological invariant, called FKMM-invariant, which generalizes and explains the topological nature of the Fu-Kane-Mele index. We show that the FKMM-invariant is a universal characteristic class which can be defined for Quaternionic vector bundles in full generality, independently of the particular nature of the base space. Moreover, it suffices to discriminate among different topological phases of system with an odd TRS in low dimension. As a particular application we describe the complete classification over a big class of low dimensional involutive spheres and tori. We also compare our classification with recent results concerning the description of topological phases for two-dimensional adiabatically perturbed systems.
Joint work with: K. Gomi.
Condensed matter electronic systems endowed with odd time-reversal symmetry (TRS) (a.k.a. class AII topological insulators) show topologically protected phases which are described by an invariant known as Fu-Kane-Mele index. The construction of this in- variant, in its original form, is specific for electrons in a periodic background and is not immediately generalizable to other interesting physical models where different forms of TRS also play ...

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