Exact dynamical response of an N - electron quantum dot subject to a time - dependent potential

We calculate analytically the exact dynamical response of a droplet of N interacting electrons in a quantum dot with an arbitrarily time-dependent parabolic confinement potential ω(t) and a perpendicular magnetic field. We find that, for certain frequency ranges, a sinusoidal perturbation acts like an attractive effective interaction between electrons. In the absence of a timeaveraged confinement potential, the N electrons can bind together to form a stable, free-standing droplet. PACS numbers: 73.61.-r, 03.65.Ge, 73.23.-b