Ruhl, Joanna — Lagrange bracket approach to quantum fluctuations in macroscopic parameters of NLS breathers

Joanna Ruhl
1Department of Physics, University of Massachusetts Boston, Boston, Massachusetts 02125, USA

In the focusing nonlinear Schrodinger equation, multisoliton ”breathers” may be created from a single mother soliton by quenching the strength of the nonlinear interaction. In ultracold-gas realizations, atop the mother soliton there are quantum fluctuations coming from its underlying quantum many-body nature, computable from the Bogoliubov theory. Post-quench, these fluctu- ations become the fluctuations in the macroscopic parameters of the daughters, which exist in a coherent macroscopic quantum state. We present a mean-field formalism that uses Lagrange brack- ets to compute, from given pre-quench fluctuations, the fluctuations of the macroscopic parameters of the daughter solitons, with results for both the 2-soliton and 3-soliton breathers.