Two-dimensional dynamics with vortices and transverse breathing

Investigate the interplay among a linear parity-time-symmetric gain-loss gradient, vortices, and the transverse breathing mode in the two-dimensional extension of the interacting Gross–Pitaevskii equation in a harmonic trap.

Background

The paper analyzes one-dimensional Bose–Einstein-condensate dynamics in a harmonic trap with a linear imaginary gain-loss potential. In this setting, interactions couple gain-induced atom-number modulation to the condensate width and thereby shift the period of the center-of-mass Kohn oscillation.

The authors note that extending the system to two dimensions introduces additional degrees of freedom: the gain-loss gradient selects a preferred axis, while vortices and transverse breathing provide genuinely multidimensional dynamics. The interaction among these effects is explicitly left unresolved.