Classical periodic orbits from coherent states in mesoscopic quantum elliptic billiards

Jesus G. Riestra, Julio C. Gutierrez-Vega
Nonlinear Sciences, Chaotic Dynamics, Chaotic Dynamics (nlin.CD), Dynamical Systems (math.DS), Classical Physics (physics.class-ph), Quantum Physics (quant-ph)
2023-12-01 00:00:00
An analytical construction of a wave function with localization in classical periodic orbits in an elliptic billiard has been achieved by appropriately superposing nearly coherent states expressed as products of Mathieu functions. We analyze and discuss the rotational and librational regimes of motion in the elliptic billiard. Simplified line equations corresponding to the classical trajectories can be extracted from the quantum coherent state as an integral equation involving angular Mathieu functions. The phase factors appearing in the integrals are connected to classical initial positions and velocity components. We analyze the probability current density, the phase maps, and the vortex distributions of the coherent states for both rotational and librational motions. The coherent state may represent traveling and standing trajectories inside the elliptic billiard.
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