m
• E

F Nous contacter

0

# Documents  Exner, Pavel | enregistrements trouvés : 9

O

P Q

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

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

Post-edited

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 ...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## 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.

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Mathematical results in quantum mechanicsQmath7 conference, prague, june 22-26, 1998 Dittrich Jaroslav ; Exner, Pavel ; Tater Milos | Birkhäuser Verlag 1999

Congrès

ISBN 978-0-8176-6097-0

Operator theory: advances and applications , 0108

Localisation : Collection 1er étage

Trace # chaos # equations de Schrödinger # formule de Trace # mecanique quantique

81-06

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Mathematical results in quantum mechanics :a conference on QMATH-8 ... held at the Universidad Nacional Autonoma de Mexico#Dec. 10-14 Weder, Ricardo ; Exner, Pavel ; Grebert, Bernoit | American Mathematical Society 2002

Congrès

- 350 p.
ISBN 978-0-8218-2900-4

Contemporary mathematics , 0307

Localisation : Collection 1er étage

mécanique quantique # mathématique de la physique # équation de Schrödinger # propriété spectrale # analyse spectrale # système quantique # algorithme de calcul quantique # théorie quantique des champs # scattering

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Analysis on graphs and its applications:selected papers based on the Isaac Newton Institute for Mathematical Sciences programme#Jan.8-June29 Exner, Pavel ; Keating, J.P. ; Kuchment, Peter ; Sunada, Toshikazu ; Teplyaev, Alexander | American Mathematical Society 2008

Congrès

- xiii, 705 p.
ISBN 978-0-8218-4471-7

Proceedings of symposia in pure mathematics , 0077

Localisation : Collection 1er étage

théorie des graphes # série Dirichlet # fonction zéta # fractals # EDP # théorie des opérateurs # analyse globale # variété # analyse combinatoire # contrôle des systèmes mécaniques # théorie quantique

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

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

Multi angle

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 ...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

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

Multi angle

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.

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

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

Multi angle

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 ...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

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

Multi angle

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...

#### Filtrer

##### Langue

Titres de périodiques et e-books électroniques (Depuis le CIRM)

Ressources Electroniques

Books & Print journals

Recherche avancée

0
Z