The jamming paradigm: from computer science to field theory and beyond
Ada Altieri (LPTMS, Université Paris-Sud)
A recent challenging problem concerns the study of glassy systems at low temperature. We present a parallel derivation of an effective thermodynamic potential in two high-dimensional models: the negative perceptron and its generalization to sphere systems. They both define continuous constrained satisfaction problems with a critical jamming transition characterized by the same exponents. The disclosed method enables us to study the vibrational spectrum of soft modes and to deepen the diverging behavior of the stiffness coefficients. A pivotal feature emerging close to jamming is that the effective thermodynamic potential has a subleading logarithmic contribution, which turns out to be dominant in a suitable scaling limit.
A detailed analysis of higher-order corrections to the potential might also help in accounting for finite-dimensional systems and interpolating between different regimes.
Another interesting outcome concerns the extension of the jamming transition topic to generic Von Neumann problems, especially focusing on ecosystems in high dimension.
Réf: Ada Altieri, Silvio Franz & Giorgio Parisi, The jamming transition in high dimension: an analytical study of the TAP equations and the effective thermodynamic potential, J. Stat. Mech. (2016) 093301.
A story of disorder, interactions and a quantum fridge inside a microwave oven
Inés Rodríguez-Arias (LPTMS, Université Paris-Sud)
In my presentation I will show two models for dynamic nuclear polarization (DNP), an extremely promising technique that enhances the nuclear spin polarization in order to improve the nuclear magnetic resonance (NMR) signal-to-noise ratio.
We have found this technique to represent a good scenario to check the ergodicity properties of the eigenstates of the system in a standard DNP protocol. The structure of the eigenstates is indeed modified upon changing the strength of the dipolar interactions between electrons keeping a constant disorder. Firstly, I will present a spin model that shows a many-body localization (MBL) transition and that reproduces the so far unexplained results from the experiments. Secondly, I will compare this to an exactely solvable Anderson model, which undergoes an Anderson localization (AL) transition.
* Inés Rodríguez-Arias, Markus Müller, Alberto Rosso and Andrea De Luca, An exactly solvable model for Dynamic Nuclear polarization, preprint cond-mat arXiv:1703.05416.
* Andrea De Luca, Inés Rodríguez-Arias, Markus Müller and Alberto Rosso, Thermalization and many-body localization in systems under dynamic nuclear polarization, Phys. Rev. B 94, 014203 (2016).