Magnus Expansion Approach to Parametric Oscillator Systems in a Thermal Bath
Magnus Expansion Approach to Parametric Oscillator Systems in a Thermal Bath
复制标题
热浴中参数振荡器系统的马格努斯展开方法
DOI：
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
L. Mathey
中科院分区：
文献类型：
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作者：
B. Zhu;T. Rexin;L. Mathey
摘要我们发展了一种周期驱动系统的Magnus形式，它在驱动项和驱动频率的倒数方面都提供了扩展，适用于孤立和耗散系统。我们推导出明确的公式与余弦依赖于时间的驱动项，高达四阶。我们将这些应用到耦合到热浴的经典参量振荡器的稳态，我们数值求解比较。除了在二阶动力学稳定，我们发现，更高的订单进一步renormalise的振荡器频率，并另外创建一个弱renormalised有效温度。重整化振荡器的频率是定量准确的参数不稳定性，我们确认数值。此外，一个截止依赖项的产生，这表明打破了系统的时间尺度的层次结构，作为不稳定性的前兆。最后，我们将这种形式主义的参数驱动链，作为一个例子，控制的分散体的多体系统。
Abstract We develop a Magnus formalism for periodically driven systems which provides an expansion both in the driving term and in the inverse driving frequency, applicable to isolated and dissipative systems. We derive explicit formulas for a driving term with a cosine dependence on time, up to fourth order. We apply these to the steady state of a classical parametric oscillator coupled to a thermal bath, which we solve numerically for comparison. Beyond dynamical stabilisation at second order, we find that the higher orders further renormalise the oscillator frequency, and additionally create a weakly renormalised effective temperature. The renormalised oscillator frequency is quantitatively accurate almost up to the parametric instability, as we confirm numerically. Additionally, a cut-off dependent term is generated, which indicates the break down of the hierarchy of time scales of the system, as a precursor to the instability. Finally, we apply this formalism to a parametrically driven chain, as an example for the control of the dispersion of a many-body system.
影响因子：
3.7
作者：
M. A. Sentef;A. F. Kemper;A. Georges;C. Kollath
通讯作者：
C. Kollath
影响因子：
64.8
作者：
Mankowsky, R.;Subedi, A.;Cavalleri, A.
通讯作者：
Cavalleri, A.
影响因子：
8.6
作者：
Denny, S. J.;Clark, S. R.;Jaksch, D.
通讯作者：
Jaksch, D.