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Using complex analysis, we have investigated classical quasi-one-dimensionalatom-atom scattering under 2D harmonic confinement with two differentinteraction potential (Yukawa and Lennard-Jones) and found that theConfinement-Induced Resonance (CIR) that occurs in the quantum system seems tohave a classical analogy. We observed CIR in our classical results in the sensethat a clear minimum appeared in the transmission coefficient for the differentinteraction potentials. We also investigated the change in the value andposition of this minimum by varying the characteristic parameters of the systemincluding the angular momentum $L_z$ along the longitudinal axis. In thequantum case, it has already been shown that for the zero range Huangpotential, CIR occurs only for $L_z = 0$. Our results indicate that classicalCIR can also occur for $L_z \ne 0$ using finite range potentials. We haveendeavoured to provide extensive physical arguments to explain the observedresults and to support the proposed analogy between the classical and quantumregimes where applicable.

Confinement-induced resonance (CIR) in classical vs. quantum scattering under 2D harmonic confinement