Poisson Commuting Energies for a System of Infinitely Many Bosons

Autor:	Mendelson, Dana, Nahmod, Andrea R., Pavlović, Nataša, Rosenzweig, Matthew, Staffilani, Gigliola
Rok vydání:	2019
Předmět:	Mathematical Physics Mathematics - Analysis of PDEs
Druh dokumentu:	Working Paper
Popis:	We consider the cubic Gross-Pitaevskii (GP) hierarchy in one spatial dimension. We establish the existence of an infinite sequence of observables such that the corresponding trace functionals, which we call ``energies,'' commute with respect to the weak Lie-Poisson structure defined by the authors in arXiv:1908.03847. The Hamiltonian equation associated to the third energy functional is precisely the GP hierarchy. The equations of motion corresponding to the remaining energies generalize the well-known nonlinear Schr\"odinger hierarchy, the third element of which is the one-dimensional cubic nonlinear Schr\"odinger equation. This work provides substantial evidence for the GP hierarchy as a new integrable system. Comment: 97 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1910.06959 Zobrazit plný text záznamu View this record from Arxiv