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Periodic oscillation of quantum diffusion in coupled one-dimensional systems

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Abstract

We analytically show that quantum diffusion in the coupled system composed of two identical chains exhibits a well-defined periodic oscillation in both transverse and longitudinal directions with a frequency determined by the interchain hopping strength, no matter whether the chains are periodic or non-periodic. We illustrate the result through numerical work on the coupled periodic chains and the quasiperiodic Aubry-Andre-Harper (AAH) chains with various modulations of onsite potentials supporting extended, critical, and localized states. We further numerically show that quantum diffusion in the coupled chains of different degrees of disorder W exhibits an exponential decay oscillation similar to the behavior of an underdamped harmonic oscillator, with a decay time inversely proportional to the square of W and a slight frequency change proportional to the square of W. Moreover, quantum diffusions in the coupled systems composed of two different chains are numerically studied, including periodic/disordered chains, periodic/AAH chains, and two different AAH chains, which exhibit the same behavior of under-damped periodic oscillation if the onsite potential difference between two chains is smaller than the interchain hoping strength. Existence of this universal periodic oscillation is a result of spectral splitting of the iso-spectra of two chains determined by interchain hopping, independent of system size, boundary condition, and intrachain onsite potentials. Because the oscillation frequency and spreading distance of wavepacket can be tuned separately by interchain hopping and intrachain potentials, the periodic oscillation of quantum diffusion in coupled chains is expected to find applications in control of quantum states and in designing nanoscale quantum devices.

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Authors and Affiliations

  1. Hunan Key Laboratory of Micro-Nano Energy Materials and Devices, School of Physics and Optoelectronics, Xiangtan University, Xiangtan, 411105, China

    JinYi Jiang, YanYan Lu, Chao Wang, Rémy Mosseri & JianXin Zhong

  2. Laboratoire de Physique Théorique de la Matière Condensée, Sorbonne Université, Centre National de la Recherche Scientifique, Paris, F-75005, France

    Rémy Mosseri

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  1. JinYi Jiang
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  2. YanYan Lu
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Correspondence to JianXin Zhong.

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This work was supported by the National Natural Science Foundation of China (Grant Nos. 11874316, and 11474244), the National Basic Research Program of China (Grant No. 2015CB921103), the Innovative Research Team in University (Grant No. IRT 17R91), and the International Visiting Faculty Program of Hunan Provincial Government, China.

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Jiang, J., Lu, Y., Wang, C. et al. Periodic oscillation of quantum diffusion in coupled one-dimensional systems. Sci. China Phys. Mech. Astron. 65, 247211 (2022). https://doi.org/10.1007/s11433-021-1822-9

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