Buckled nano rod - a two state system: quantum effects on its dynamics

TL;DR

This paper investigates the quantum effects on the dynamics of a buckled nano rod modeled as a two-state system, focusing on transition rates between buckled states and addressing divergence issues in classical rate calculations.

Contribution

It introduces a correction method for divergence in transition state theory rates and highlights the significance of zero point energy in quantum calculations for buckled nano rods.

Findings

Transition state theory rate diverges at a specific strain.

A correction method for quantum calculations is proposed.

Zero point energy significantly affects transition rates.

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. Using transition state theory (TST) we have calculated the rate of conversion from one state to other. If the strain $\epsilon = 4 \epsilon_c$ the simple TST rate diverges. We suggest a method to correct this divergence for quantum calculations. We also find that zero point energy contributions can be quite large so that single mode calculations can lead to large errors in the rate.