M. Labousse^1,2,*, A. U. Oza³, S. Perrard^2,†, and J. W. M. Bush^4,‡

• ¹Institut Langevin, ESPCI Paristech, CNRS, UMR No. 7587, PSL Research University, Université Pierre and Marie Curie, 1 Rue Jussieu, 75005 Paris, France, EU
• ²Laboratoire Matière et Systèmes Complexes, Université Paris Diderot, Sorbonne Paris Cité, CNRS, UMR No. 7057, 10 Rue A. Domon and L. Duquet, 75013 Paris, France, EU
• ³Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
• ⁴Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA

• ^*Present address: Laboratoire Matériaux et Phénomènes Quantiques, Université Paris Diderot, Sorbonne Paris Cité, CNRS, UMR No. 7162, 10 Rue A. Domon and L. Duquet, 75013 Paris, France, EU.
• ^†Present address: Department of Physics and James Franck Institute, University of Chicago, Chicago, 929 E 57th St, IL 60637, USA.
• ^‡bush@math.mit.edu