Caustics in a Near-Resonant Quantum Kicked Rotor

• URL: http://arxiv.org/abs/2507.15634v2
• Date: Fri, 22 Aug 2025 08:19:03 GMT
• Title: Caustics in a Near-Resonant Quantum Kicked Rotor
• Authors: Yi Cao, Shaowen Lan, Bin Sun, Jie Liu,
• Abstract summary: In this paper, we investigate the dynamics of the quantum kicked rotor in the near-resonant regime.<n>We analytically determine the locations of the caustic singularity and its recurring (or oscillating) period.<n>We also discuss the classical-quantum correspondence of the caustic singularity and find that chaos can disrupt the phase matching.
• Score: 9.121945883412755
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we investigate the dynamics of the quantum kicked rotor in the near-resonant regime and observe some interesting caustic structures in the distribution of wave amplitudes, such as recurring cusps, cusp oscillations, and even reticular cusps for high-order resonant cases. We derive the path integral expression for the quantum evolution of the wave functions and analytically determine the locations of the caustic singularity and its recurring (or oscillating) period. A scaling power law with an Arnold index of $1/4$, which relates the wave amplitude enhancement to the kicking strength and the resonant detuning parameter, has been derived and verified. We also discuss the classical-quantum correspondence of the caustic singularity and find that chaos can disrupt the phase matching, leading to the destruction of the caustic structure. Finally, possible experimental observations and some implications of these findings are discussed.

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