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Condensation with two constraints and disorder

Abstract : Motivated by the study of breathers in the disordered Discrete Non Linear Schr\"odinger equation, we study the uniform probability over the intersection of a simplex and an ellipsoid in $n$ dimensions, with quenched disorder in the definition of either the simplex or the ellipsoid. Unless the disorder is too strong, the phase diagram looks like the one without disorder, with a transition separating a fluid phase, where all variables have the same order of magnitude, and a condensed phase, where one variable is much larger than the others. We then show that the condensed phase exhibits "intermediate symmetry breaking": the site hosting the condensate is chosen neither uniformly at random, nor is it fixed by the disorder realization. In particular, the model mimicking the well-studied Discrete Non Linear Schr\"odinger model with frequency disorder shows a very weak symmetry breaking: all variables have a sizable probability to host the condensate (i.e. a breather in a DNLS setting), but its localization is still biased towards variables with a large linear frequency. Throughout the article, our heuristic arguments are complemented with direct Monte Carlo simulations.
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Contributor : Julien Barre <>
Submitted on : Wednesday, January 17, 2018 - 10:35:51 AM
Last modification on : Monday, February 10, 2020 - 2:25:37 PM



Julien Barre, Léo Mangeolle. Condensation with two constraints and disorder. Journal of Statistical Mechanics: Theory and Experiment, IOP Publishing, 2018, pp.043211. ⟨10.1088/1742-5468/aab67c⟩. ⟨hal-01686212⟩



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