Institute of Physics, University of Silesia, 40-007 Katowice, Poland.
J Phys Condens Matter. 2010 Jun 23;22(24):245301. doi: 10.1088/0953-8984/22/24/245301. Epub 2010 May 26.
We study currents in a quantum ring threaded by a magnetic flux which is varied in an arbitrary way from an initial constant value φ(1) at time t(1) to a final constant value φ(2) at time t(2). We analyze how the induced currents for t > t(2) can be controlled by the rate of flux variation [Formula: see text]. The dynamics of electrons in the ring is described using the Hubbard and the extended Hubbard models. In the Hubbard model with infinite on-site repulsion the current for t > t(2) is shown to be independent of the flux variation before t(2) and is fully determined by a solution of the initial equilibrium problem and by the value φ(2) of the flux. For intermediate values of the interaction strength the current displays regular or irregular time oscillations and the amplitude of oscillations is sensitive to the rate of the flux changing [Formula: see text]: slow changes of the flux result in small amplitudes of the current oscillations and vice versa. We demonstrate that the time dependence of the induced current bears information on electronic correlations. Our results have important implications for not only mesoscopic rings but also the designing of quantum motors built out of ring-shaped optical lattices.
我们研究了在一个被磁通量缠绕的量子环中的电流，该磁通量以任意方式从时间 t(1)的初始恒定值 φ(1)变化到时间 t(2)的最终恒定值 φ(2)。我们分析了在 t > t(2)时如何通过通量变化率[Formula: see text]来控制感应电流。环中电子的动力学使用 Hubbard 和扩展 Hubbard 模型来描述。在具有无限局域排斥的 Hubbard 模型中，对于 t > t(2)的电流被证明与 t(2)之前的通量变化无关，并且完全由初始平衡问题的解和通量的值 φ(2)决定。对于相互作用强度的中间值，电流显示出规则或不规则的时间振荡，并且振荡的幅度对通量变化率[Formula: see text]敏感：通量的缓慢变化导致电流振荡的幅度较小，反之亦然。我们证明了感应电流的时间依赖性承载了关于电子相关的信息。我们的结果不仅对介观环，而且对由环形光晶格构建的量子马达的设计都具有重要意义。
