低能级量子的双稳与混沌
Bistability and chaos at low-level of quanta
摘要：
我们在少量子水平上研究了非线性双稳和混沌现象。为此目的，我们考虑一个单模耗散振荡器与强克尔非线性耗散率驱动的单色力以及由一个训练的高斯脉冲。在态纯度和由主方程计算的Wigner函数的框架下，研究了振荡模中的量子效应和退相干。通过比较经典Poincaré截面上的Wigner函数和奇异吸引子的等值线图，我们证明了量子混沌机制。考虑到量子下限的双稳性，我们分析了系统出现双稳态的最小激发数是多少？我们还讨论了在几个量子范围内改变振荡激发数时振荡混沌区的形成。证明了高斯脉冲训练驱动下的振荡器的量子干涉现象，并建立了强非线性情况下混沌区的经典-量子对应边界.
英文摘要：
We study nonlinear phenomena of bistability and chaos at a level of few quanta. For this purpose we consider a single-mode dissipative oscillator with strong Kerr nonlinearity with respect to dissipation rate driven by a monochromatic force as well as by a train of Gaussian pulses. The quantum effects and decoherence in oscillatory mode are investigated on the framework of the purity of states and the Wigner functions calculated from the master equation. We demonstrate the quantum chaotic regime by means of a comparison between the contour plots of the Wigner functions and the strange attractors on the classical Poincaré section. Considering bistability at low-limit of quanta, we analyze what is the minimal level of excitation numbers at which the bistable regime of the system is displayed? We also discuss the formation of oscillatory chaotic regime by varying oscillatory excitation numbers at ranges of few quanta. We demonstrate quantum-interference phenomena that are assisted hysteresis-cycle behavior and quantum chaos for the oscillator driven by the train of Gaussian pulses as well as we establish the border of classical-quantum correspondence for chaotic regimes in the case of strong nonlinearities.
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