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# Documents  Kuchment, Peter | enregistrements trouvés : 17

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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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## 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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## Tomography, impedance imaging, and integral geometry :1993 AMS-SIAM summer seminar on the mathematics at Mount Holyoke College#June 7-18 Cheney, Margaret ; Kuchment, Peter ; Quinto, Eric Todd | American Mathematical Society 1994

Congrès

- 297 p.
ISBN 978-0-8218-0337-0

Lectures in applied mathematics , 0030

Localisation : Collection 1er étage

déficit Wilmore de surface convexe # géométrie intégrale # image d'impédance # méthode de propagation arrière en acoustique inverse # perturbation de Laplacien # problème inverse # tomographie diffuse de dimension 3 # tomographie à rayon X 3D # tomographie à émission de position # transformée de Radon horocyclique # équation différentielle

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## Waves in periodic and Random media :proceedings of AMS-IMS-SIAM joint summer research conference on ... held at Mount Holyoke College#June 22-28 Kuchment, Peter | American Mathematical Society 2003

Congrès

- 216 p.
ISBN 978-0-8218-3286-8

Contemporary mathematics , 0339

Localisation : Collection 1er étage

mouvement d'onde # photon # théorie spectrale d'opérateur différentiel périodique # localisation d'Anderson # théorie spectrale # opérateur aléatoire # cristal photonique # système mesoscopique

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## Spectral theory of Schrödinger operators :lecture notes from a workshop on ... held at Univercidad Nacional Autonoma de Mexico, IIMAS#Dec. 3-7 Kuchment, Peter | American Mathematical Society 2004

Congrès

- 249 p.
ISBN 978-0-8218-3297-4

Contemporary mathematics , 0340

Localisation : Collection 1er étage

opérateur de Schrödinger # opérateur différentiel # théorie spectrale # opérateur auto-adjoint # perturbation singulière # espace de Hilbert # propriété de recouvrement

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## Quantum graphs and their applications :proceedings of an AMS-IMS-SIAM joint summer research conference on quantum graphs and their applications#June 19-23 Berkolaiko, Gregory ; Carlson, Robert ; Fulling, Stephen A. ; Kuchment, Peter | American Mathematical Society 2006

Congrès

- 307 p.
ISBN 978-0-8218-3765-8

Contemporary mathematics , 0415

Localisation : Collection 1er étage

théorie quantique # combinatoires # graphe quantique # physique mathématique # équation différentielle # théorie spectrale # analyse global # fractales # localisation d'Anderson # réseau électrique # chaos quantique # physique mesoscopique # superconductivité # optique # modélisation des systèmes biologiques

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## 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

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## Spectral theory and geometric analysis.International conference in honor of Mikhail Shubin's 65th birthdayBoston # july 29 - august 2, 2009 Braverman, Maxim ; Friedlander, Leonid ; Kappeler, Thomas ; Kuchment, Peter ; Topalov, Peter ; Weitsman, Jonathan | American Mathematical Society 2011

Congrès

- vii; 213 p.
ISBN 978-0-8218-4948-4

Contemporary mathematics , 0535

Localisation : Collection 1er étage

analyse globale # EDP # problème spectral # opérateur intégral de Fourier # dérivées sur les surfaces de Riemann # équation de Ginzburg-Landau # trou noir

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## Tomography and inverse transport theory.International workshop on mathematical methods in emerging modalities of medical imagingBanff # october 25-30, 2009International workshop on inverse transport theory and tomographyBanff # may 16-21, 2010 Bal, Guillaume ; Finch, David ; Kuchment, Peter ; Schotland, John ; Stefanov, Plamen ; Uhlmann, Gunther | American Mathematical Society 2011

Congrès

- xii; 180 p.
ISBN 978-0-8218-5301-6

Contemporary mathematics , 0559

Localisation : Collection 1er étage

tomographie # problème inverse # théorie du transport

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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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## 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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## 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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## 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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## Floquet theory for partial differential equations Kuchment, Peter | Birkhäuser Verlag 1993

Ouvrage

ISBN 978-3-7643-2901-3

Operator theory: advances and applications , 0060

Localisation : Collection 1er étage

opérateur de Fredholm # théorie de Floquet # équation d'évaluation # équation différentielle aux dérivées partielles # équation elliptique # équation périodique

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## Voronezh winter mathematical schoolsDedicated to selim krein Kuchment, Peter ; Lin, Vladimir | American Mathematical Society 1998

Ouvrage

- 263 p.
ISBN 978-0-8218-0976-1

American mathematical society translations series 2 , 0184

Localisation : Collection 1er étage

EDP # analyse globale # courbe # ensemble de Mandelbrojt # espace de Banach # formule de trace # groupe de Heisenberg # géométrie complexe # géométrie riemannienne # plan # théorie d'opérateur # théorie des fonctions # théorème de Rham # torsion # transformation affine

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## Introduction to quantum graphs Berkolaiko, Gregory ; Kuchment, Peter | American Mathematical Society 2013

Ouvrage

- xiii; 270 p.
ISBN 978-0-8218-9211-4

Mathematical surveys and monographs , 0186

Localisation : Collection 1er étage

graphe quantique # spectre de graphe # problème aux limites

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## The Radon transform and medical imaging Kuchment, Peter | Society For Industrial And Applied Mathematics 2014

Ouvrage

- xvi; 240 p.
ISBN 978-1-611973-28-0

CBMS-NSF regional conference series in applied mathematics , 0085

Localisation : Collection 1er étage

tomographie # imagerie médicale # rayons X # inversion # stabilité # analyse de Fourier # opérateur linéaire # transformée de Radon

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