CMSP Section announces 3 seminars coming up

[Cond.Matt. & Stat.Mech.Section]

JOINT ICTP/SISSA STATISTICAL PHYSICS SEMINAR

 

Tuesday, 9 April  -   11:30 hrs.

 

Luigi Stasi Seminar Room -  ICTP Leonardo Building - 1st floor

 

Matteo MARSILI    (ICTP)



"Why do complex systems look critical"



Abstract



The study of complex systems is limited by the fact that only few variables are accessible for modeling and sampling, which are not necessarily the most relevant ones. In addition, empirical data typically under sample the space of possible states.

We study a class of complex systems, which are systems of many interacting degrees of freedom, which are known only in part, that optimize a given function. We show that the information that a sample contains on the behavior of the system is quantified by the entropy of the frequency with which different states occur. This allows us to characterize the properties of maximally informative samples:

In the under-sampling regime, the most informative frequency size distributions have power law behavior and Zipf's law emerges at the crossover between the under sampled regime and the regime where the sample contains enough statistics to make inference on the behavior of the system. These ideas are illustrated in some applications, showing that they can be used to identify relevant variables or to select most informative representations of data, e.g. in data clustering.

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SEMINAR on    Disorder and strong electron correlations



Thursday, 11 April -  11:30 a.m.



Luigi Stasi Seminar Room,  Leonardo Building - first floor



Giulio BIROLI    (Institut de Physique Théorique Saclay)



"Difference between ergodicity, level statistics and localization transitions on the Bethe lattice"



Abstract

 
Random Matrix Theory was initially developed to explain the eigen-energy distribution of heavy nuclei. It has become clear by now that its domain of application is much broader and extends to very different fields such as number theory and quantum chaos, just to cite a few. In particular, it has been conjectured—and proved or verified in some special cases—that quantum ergodic (or chaotic) systems are characterized by eigen-energies statistics in the same universality class of random matrices and by eigen-functions that are delocalized over the configuration space. On the contrary, non-ergodic quantum systems, such as integrable models, are expected to display a Poisson statistics of energy levels and localized wave-functions. Starting from Anderson’s pioneering papers, similar properties have also been studied for electrons hopping in a disordered environment. Remarkably, also in this case, similar features of the energy-level statistics have been found. All that has lead to the conjecture that delocalization in configuration space, ergodicity and level statistics are intertwined properties. 

In this talk we revisit the old problem of non-interacting electrons hopping on a Bethe lattice with on-site disorder. By using numerical simulations, the cavity method and mapping to directed polymers in random media we unveil the existence of an intermediate phase in which wave-functions are delocalized but the energy-level statistics is Poisson. This new phase, in which the system is non-ergodic but delocalized, may play an important role in several fields from random matrix theory to strongly interacting quantum disordered systems, in particular it could be related to the non-ergodic metallic phase conjectured to exist in the context of Many-Body Localization.

 

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JOINT ICTP/SISSA    APPLIED MATHEMATICS/STATISTICAL MECHANICS SEMINAR

 

Wednesday, 17 April   -   1:00 p.m.

 

SISSA, Santorio Building,    Room 4 (ground floor)



Vincenzo VITELLI    ( Instituut Lorentz, Leiden)



"Shocks in fragile matter"

 

Abstract


Non-linear sound is an extreme phenomenon typically observed in solids after violent explosions. But granular media are different. Right when they unjam, these fragile and disordered solids exhibit vanishing elastic moduli and sound speed, so that even tiny mechanical perturbations form supersonic shocks. Here, we perform simulations in which two-dimensional jammed granular packings are continuously compressed, and demonstrate that the resulting excitations are strongly nonlinear shocks, rather than linear waves. We capture the full dependence of the shock speed on pressure and compression speed by a surprisingly simple analytical model. We also treat shear shocks within a simplified viscoelastic model of nearly-isostatic random networks comprised of harmonic springs. In this case, anharmonicity does not originate locally from nonlinear interactions between particles, as in granular media; instead, it emerges from the global architecture of the network. As a result, the diverging width of the shear shocks bears a nonlinear signature of the diverging isostatic length associated with the loss of rigidity in these floppy networks.