Related papers: Quantum states resembling classical periodic trajectories in mesoscopic elliptic billiards

Quantum states resembling classical periodic trajectories in mesoscopic elliptic billiards

URL: http://arxiv.org/abs/2312.00954v2
Date: Wed, 13 Mar 2024 13:02:53 GMT
Title: Quantum states resembling classical periodic trajectories in mesoscopic elliptic billiards
Authors: Jesus G. Riestra and Julio C. Gutierrez-Vega
Abstract summary: A quantum wave function with localization on classical periodic orbits in a mesoscopic elliptic billiard has been achieved. We analyze and discuss the rotational and librational regimes of motion in the elliptic billiard.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: A quantum wave function with localization on classical periodic orbits in a mesoscopic elliptic billiard has been achieved by appropriately superposing nearly degenerate eigenstates 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 state as an integral equation involving angular Mathieu functions. The phase factors appearing in the integrals are connected to the classical initial positions and velocity components. We analyze the probability current density, the phase maps, and the vortex distributions of the periodic orbit quantum states for both rotational and librational motions; furthermore, they may represent traveling and standing trajectories inside the elliptic billiard.

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