Le cas classique le plus général est le poids de Jacobi w(x) = (1-x)^a(1+x)^b, -1 £ x £ 1; et les polynômes orthogonaux correspondants sont connus depuis longtemps, mais pas les polynômes skew-orthogonaux. Je décrirai une méthode élégante dûe à S. Ghosh de les construire. Violations of the fluctuation-dissipation theorem (FDT) out of equilibrium are well understood for mean field models, and can be used to define an effective temperature T_eff that shares many properties of the true thermodynamic temperature T. If and under what conditions an analogous T_eff exists in non-mean field systems is much less clear. A minimum requirement is that T_eff should be independent of the observable whose correlator and response are being considered.

We analyse in detail the observable-dependence of FDT violations in the coarsening dynamics of the Glauber-Ising chain at low temperature. The approach is based on a new method for solving the relevant hierarchy of dynamical equations for correlation and response functions, yielding explicit results even for e.g. domain wall observables and higher order spin products, as well as their nonlocal analogues. We find that long-wavelength observables give the simplest FDT plots: straight lines with a non-equilibrium slope 1/T_eff. Shorter wavelength observables give different, curved FDT plots, but with the same asymptotic slope because the latter is dominated by the long-wavelength contributions. A meaningful definition of an effective temperature is thus possible for large, non-equilibrated length scales. Recent simulations on 2d-Ising models at criticality suggest that this conclusion is rather generic. Lóbjectif est de donner une introduction à la biologie moléculaire, en montrant en particulier límportance des idées issues de la physique pour la compréhension du vivant.

King’s College, London

Dans la théorie des matrices aléatoires il est bien connu que pour les trois valeurs 1, 2 et 4 de b la fonction n! (n-m)! _a^b…_a^b _1 j<k n (x_j-x_k)^ _j=1^n w(x_j) (ou quaternionique) m×m pour le cas b = 2 (pour expression explicite du noyaux K_b(x,y) on a besoin de connaitre les polynômes orthogonaux (cas b = 2) ou skew-orthogonaux (cas b = 1 et 4) pour la fonction poids w(x).

Le cas classique le plus général est le poids de Jacobi w(x) = (1-x)^a(1+x)^b, -1 £ x £ 1; et les polynômes orthogonaux correspondants sont connus depuis longtemps, mais pas les polynômes skew-orthogonaux. Je décrirai une méthode élégante dûe à S. Ghosh de les construire. Violations of the fluctuation-dissipation theorem (FDT) out of equilibrium are well understood for mean field models, and can be used to define an effective temperature T_eff that shares many properties of the true thermodynamic temperature T. If and under what conditions an analogous T_eff exists in non-mean field systems is much less clear. A minimum requirement is that T_eff should be independent of the observable whose correlator and response are being considered.

We analyse in detail the observable-dependence of FDT violations in the coarsening dynamics of the Glauber-Ising chain at low temperature. The approach is based on a new method for solving the relevant hierarchy of dynamical equations for correlation and response functions, yielding explicit results even for e.g. domain wall observables and higher order spin products, as well as their nonlocal analogues. We find that long-wavelength observables give the simplest FDT plots: straight lines with a non-equilibrium slope 1/T_eff. Shorter wavelength observables give different, curved FDT plots, but with the same asymptotic slope because the latter is dominated by the long-wavelength contributions. A meaningful definition of an effective temperature is thus possible for large, non-equilibrated length scales. Recent simulations on 2d-Ising models at criticality suggest that this conclusion is rather generic. Lóbjectif est de donner une introduction à la biologie moléculaire, en montrant en particulier límportance des idées issues de la physique pour la compréhension du vivant.

King’s College, London