Derivation of Effective Classical Hamiltonian for a Single Particle Bouncing on a 3d System of Oscillating Atomic Mirrors

Abstract

It has recently been established that particles bouncing resonantly on either an oscillating atomic mirror (1D case) or a properly arranged system of two oscillating mirrors (2D case) became a playground for discrete time crystal research. If these particles are bosonic and the strength of the interactions between them is properly chosen, they can be made to spontaneously break the discrete time translation symmetry of the Hamiltonian and form 1D or 2D discrete time crystals, respectively. Moreover, such a system is capable of realising analogues to various condensed matter phenomena in the time domain from Anderson localisation through topological time crystals, many-body localisation, Mott insulator phase to time lattices with exotic interactions. It should be noted here that while the procedure for obtaining a proper 1D effective classical Hamiltonian for the mentioned system is well developed, the only 2D case of a single particle bouncing between two orthogonal oscillating atomic mirrors is reducible into two independent 1D motions along the perpendicular axes. However, for an arbitrary angle the system is no longer separable and the problem becomes more complex except for specific angles. In this report, we tryied to generalize the approach to a 3D case by deriving an effective Hamiltonian for a single particle bouncing between three mutually orthogonal oscillating atomic mirrors.

Speaker

Churochkina Svetlana
Saratov State University
Россия

Discussion

Ask question