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

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Abstract

Using complex analysis, we have investigated classical quasi-one-dimensional atom–atom scattering under 2D harmonic confinement with two different interaction potentials (Yukawa and Lennard-Jones) and found that the confinement-induced resonance (CIR) that occurs in the quantum system seems to have a classical analogue. We observed CIR in our classical results in the sense that a clear minimum appeared in the transmission coefficient for the different interaction potentials. We also investigated the changes in the value and position of this minimum by varying the characteristic parameters of the system including the angular momentum \(L_z\) along the longitudinal axis. In the quantum case, it has already been shown that for the zero range Huang potential, CIR occurs only for \(L_z = 0\). Our results indicate that classical CIR can also occur for \(L_z \ne 0\) using finite range potentials. We have endeavoured to provide extensive physical arguments to explain the observed results and to support the proposed analogy between the classical and quantum regimes where applicable.

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Notes

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    If the particle is not trapped, it will certainly be transmitted, \(T = 1\). However, if it is trapped with probability p, the probability of transmission will be \(T = 1- p \cdot p_r\), where \(p_t\) and \(p_r = 1 - p_t\) are the probability of transmission and reflection after trapping, respectively. Therefore, the more the probability of the particle being trapped, the higher will be the probability of it being reflected. CIR corresponds to the maximum probability of trapping manifesting itself in \(T- V_0\) graphs as \(T_\mathrm{min}\).

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Correspondence to Shahpoor Saeidian.

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Samadi, S., Farnudi, B. & Saeidian, S. Confinement-induced resonance (CIR) in classical vs. quantum scattering under 2D harmonic confinement. Eur. Phys. J. Plus 135, 28 (2020). https://doi.org/10.1140/epjp/s13360-019-00075-2

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