Buckled nano rod - a two state system and its dynamics

Abstract

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. The two minima in potential energy curve describe two possible buckled states at a particular strain. Using transition state theory (TST) we have calculated the rate of conversion from one state to other. If the strain $\epsilon$ is between $\epsilon_c$ and $4 \epsilon_c$, the saddle point is the straight rod. But for $\epsilon_c < 4 \epsilon_c$, the saddle is S-shaped. At $\epsilon_c = 4 \epsilon_c$ the simple TST rate diverges. We suggest methods to correct this divergence, both for classical and quantum calculations. We also find that zero point energy contributions can be quite large (as large as $10^9$) so that single mode calculations can lead to large errors in the rate.