Beyond-mean-field analysis of the Townes soliton and its breathing mode

By using the Bogoliubov perturbation theory we describe the self-bound ground state and excited breathing states of N N two-dimensional bosons with zero-range attractive interactions. Our results for the ground state energy B_N BN and size R_N RN improve previously known large- N N asymptotes and we better understand the crossover to the few-body regime. The breathing oscillations, absent at the mean-field level, result from the quantum-mechanical breaking of the mean-field scale symmetry. The breathing-mode frequency scales as Ω∝ |B_N|/√N Ω∝|BN|/N at large N N .