屈曲纳米棒--一个两态系统及其动力学的系统加库模型
Buckled nano rod - a two state system and its dynamics using system plus reservoir model
摘要：
我们考虑一个受纵向压缩的悬挂弹性杆。压缩可以用来调整势能的横向位移从谐波到双阱区。当压缩应变增加到屈曲失稳时，基本振动模式的频率连续下降到零（第一屈曲失稳）。当调节杆两端之间的距离时，系统在不稳定性之外保持稳定，并产生横向运动的双阱势。势能曲线中的两个极小值描述了在特定应变下两种可能的屈曲状态。通过热涨落或量子隧穿，它可以从一个屈曲态过渡到另一个屈曲态。使用连续方法和过渡态理论（TST），可以计算从一种状态到另一种状态的转换速率。从一种状态变为另一种状态的鞍点是直棒配置。然而，在第二屈曲失稳时，该速率发散。在这一点上，直杆配置，这是一个鞍，直到那时，成为山顶和两个新的鞍产生。新的鞍形结构具有弯曲构型，并且当棒经历进一步的不稳定性时，它们保持稳定，并且根据鞍点附近的谐波近似计算的速率保持有限。在我们早期的文件经典率计算包括摩擦已进行[J.计算。Theor.纳米科学{ \bf 4}（2007）{ \it 1}]，通过假设杆的每一段都耦合到它自己的谐振子集合-我们的速率表达式通过第二屈曲不稳定性表现良好。在本文中，我们已经扩大了我们的方法来计算量子速率使用相同的系统加水库模型。我们发现摩擦降低了转化率。
英文摘要：
We consider a suspended elastic rod under longitudinal compression. The compression can be used to adjust potential energy for transverse displacements from harmonic to double well regime. As compressional strain is increased to the buckling instability, the frequency of fundamental vibrational mode drops continuously to zero (first buckling instability). As one tunes the separation between ends of a rod, the system remains stable beyond the instability and develops a double well potential for transverse motion. The two minima in potential energy curve describe two possible buckled states at a particular strain. From one buckled state it can go over to the other by thermal fluctuations or quantum tunnelling. Using a continuum approach and transition state theory (TST) one can calculate the rate of conversion from one state to other. Saddle point for the change from one state to other is the straight rod configuration. The rate, however, diverges at the second buckling instability. At this point, the straight rod configuration, which was a saddle till then, becomes hill top and two new saddles are generated. The new saddles have bent configurations and as rod goes through further instabilities, they remain stable and the rate calculated according to harmonic approximation around saddle point remains finite. In our earlier paper classical rate calculation including friction has been carried out [J. Comput. Theor. Nanosci. {\bf 4} (2007) {\it 1}], by assuming that each segment of the rod is coupled to its own collection of harmonic oscillators - our rate expression is well behaved through the second buckling instability. In this paper we have extended our method to calculate quantum rate using the same system plus reservoir model. We find that friction lowers the rate of conversion.
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