24–25 May 2012
Polygone Scientifique
Europe/Paris timezone

Session

Systemes integrables

1
24 May 2012, 14:00
Amphithéatre LPSC (Polygone Scientifique)

Amphithéatre LPSC

Polygone Scientifique

53, rue des Martyrs 38026 Grenoble Cedex

Conveners

Systemes integrables

  • Eric Ragoucy (LAPTh)

Systemes integrables

  • Eric Ragoucy (LAPTh)

Description

The notion of integrability is based on an essential property, namely the existence of an "adequate" number of conserved quantities in the system. This "adequate" number then allows for the full resolution of the model, i.e., to calculate exactly (without using approximations or perturbative techniques) all its physical quantities, such as energies, momenta, correlation functions, etc... Analytical and algebraic developments have grown in the 80s (starting with the study of spin chains) and there exists now a huge arsenal of mathematical tools to study such systems. Of course, not all systems are integrable, but, surprisingly enough, there are many integrable systems in physics, even if integrable techniques are not always used to solve them.

Integrable systems take place in many areas, in physics or in mathematics. In physics, they are involved in field theory and symmetries (especially in elementary particle physics, in string theories and in supersymmetric Yang-Mills theories), in statistical mechanics (for example in so-called ASEP models, for asymmetric exclusion principle), or condensed matter physics (e.g. in models used to describe nano-technology materials such as carbon nano-tubes). In mathematics, integrable systems are themselves the basis for the development of a particularly rich set of new mathematical structures (quantum groups, deformed algebras, Hopf and quasi-Hopf structures, etc...).

Presentation materials

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  1. Jean-Michel Maillet (ENS Lyon)
    24/05/2012, 14:00
    Systemes integrables
  2. Jean Avan (Université de Cergy)
    24/05/2012, 15:00
    Systemes integrables
    A major feature of quantum integrable systems is the quantum group structure encapsulated in the Yang Baxter equation RTT = TTR. The presence of boundaries to a quantum integrable system imposes to complement it by the boundary equation RKRK = KRKR. In parallel consistent deformations of the YB algebra have been defined, leading to so-called dynamical Yang Baxter equations. The work presented...
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  3. James Drummond (LAPTh & CERN)
    24/05/2012, 16:00
    Systemes integrables
    Nowadays, the notion of integrability is also used in string theories. The celebrated AdS / CFT correspondence conjecture between conformal field theories in four dimensions and string theory in a 11 dimensional space entered a predictive phase, following a tremendous breakthrough made in recent years. This conjecture predicts equivalence between operators in conformal field theories (eg N =...
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  4. Régis Melin (Institut Néel)
    24/05/2012, 16:30
    Systemes integrables
    The possibility of realizing in the future a source of spin-entangled pairs of electrons based on three-terminal normal metal-superconductor-normal metal structures has aroused considerable interest recently, both theoretical and experimental. The topic of available experiments is to measure either the current flowing in one of the normal electrodes in response to a voltage on the other...
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  5. Christoph Schenke (LPMMC)
    24/05/2012, 17:00
    Systemes integrables
    Recent experimental activities of boson trapping on a ring geometry open the way to explore this novel topology. We focus on a tight ring trap with strong transverse confinement leading to an effectively one-dimensional motion along its circumference. We consider a strongly interacting Bose gas on the ring subjected to a localized barrier potential which is suddenly set into motion. The...
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