Classical analog to the Airy wave packet

The solution of the Liouville equation for the ensemble of free particles is presented and the classical analog to the quantum accelerating Airy wave packet is constructed and discussed. Considering the motion of various classical packets – with an infinite and restricted distribution of velocities of particles – and also the motion of their fronts, we demonstrate in the simplest and most definite way why the packet can display a more sophisticated behaviour (even acceleration) as compared with a free individual particle that moves at a fixed velocity. A comparison of this classical solution with the quantum one in the Wigner representation of quantum mechanics, which provides the closest analogy, is also presented.

Self-accelerating matter waves

The free particle Schrödinger equation admits a nontrivial self-accelerating Airy wave packet solution. Recently, the Airy beams that freely accelerate in space was experimentally realized in photonics community. Here, we present self-accelerating waves for the Bose–Einstein condensate in a time-dependent harmonic oscillator potential. We show that parity and time reversal symmetries for self-accelerating waves are spontaneously broken.