HomeCNU Journal of Higher Educationvol. 5 no. 1 (2011)

White Noise Path Integral Evaluation of the Characteristic Function of a Modified Wormlike Chain

Karl Patrick S. Casas | Jinky B. Bornales

 

Abstract:

The characteristic function of a wormlike chain is expressed as a Feynman path integral, obtained via the white noise functional approach. In order to describe the model statistically, the following physical assumptions are considered: (i) the wormlike chain curve is analogous to a trajectory of aquantum particle, and (ii) the total contour length L of the Wormlike chain is regarded as “time” t. The mathematical treatment is then facilitated by modifying its “Lagrangian”, given by Fixman and Kovac, wherein the resulting expression of the “Lagrangian” is just similar to the harmonic oscillator in an external electric field. Then, the cosine of the angle between the field vector and the tangent vector is approximated. In order to evaluate the characteristic function in one dimension only, we let this angle be linearly dependent on the contour distance of the chain. The characteristic function is then evaluated via white noise analysis. The result, with the field set to zero, is then compared to apropagator of a harmonic oscillator in an inverse potential.