Séminaire du LPTMS: Emmanuel Trizac et Christophe Texier


11:00 - 12:00

LPTMS-batiment 100, salle des conseils
15 Rue Georges Clemenceau, Orsay

Type d’évènement

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Shortcutting adiabaticity : how to change rapidly the state of a trapped gas ?

Emmanuel Trizac, LPTMS

Inspired from H-theorem requirements, a novel class of exact solutions to the quantum or classical Boltzmann equation is uncovered. These solutions, valid for arbitrary collision laws, hold for time-dependent confinement. We exploit them, in a reverse-engineering perspective, to work out a protocol that shortcuts any adiabatic transformation between two equilibrium states in an arbitrarily short time span, for an interacting system. Particle simulations corroborate the analytical predictions.


Topological phase transitions in multichannel disordered wires in the chiral  symmetry classes

Christophe Texier, LPTMS

We have considered the one-dimensional multichannel Dirac equation where the mass is a random NxN matrix with elements uncorrelated in space. In order to analyze the spectral properties of the model, we have introduced a matricial random process (Riccati matrix), related to the scattering matrix describing the reflection on the semi-infinite medium.
We have found that the stationary distribution of the Riccati matrix corresponds to a generalisation of the Laguerre ensemble of random matrices. The knowledge of this distribution has allowed us to derive explicit determinantal representations for the density of states (DoS), which is shown to present a power law behaviour at low energy.
Varying the mass over disorder ratio allows to drive N phase transitions where the DoS exponent vanishes and which are shown to be of topological nature as they correspond to the change of a topological quantum number (Witten index).
Reference :Aurélien Grabsch and Christophe Texier, Topological phase transitions and superuniversality in the 1D multichannel Dirac equation with random mass, preprint cond-mat arXiv:1506.05322

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