Statistical Mechanics of Elastica on Plane as a Model of Supercoiled DNA-Origin of the MKdV hierarchy-

Abstract

In this article, I have investigated statistical mechanics of a non-stretched elastica in two dimensional space using path integral method. In the calculation, the MKdV hierarchy naturally appeared as the equations including the temperature fluctuation.I have classified the moduli of the closed elastica in heat bath and summed the Boltzmann weight with the thermalfluctuation over the moduli. Due to the bilinearity of the energy functional,I have obtained its exact partition function.By investigation of the system,I conjectured that an expectation value at a critical point of this system obeys the Painlevé equation of the first kind and its related equations extended by the KdV hierarchy.Furthermore I also commented onthe relation between the MKdV hierarchy and BRS transformationin this system.

AMS-Tex Use

Cited by in corpus (11)

• Hyperelliptic Solutions of KdV and KP equations: Reevaluation of Baker's Study on Hyperelliptic Sigma Functions
• Hyperelliptic Loop Solitons with Genus g: Investigations of a Quantized Elastica
• On Density of State of Quantized Willmore Surface-A Way to Quantized Extrinsic String in R^3
• Hyperelliptic Solutions of Modified Korteweg-de Vries Equation of Genus g: Essentials of Miura Transformation
• Statistical Mechanics of Non-stretching Elastica in Three Dimensional Space
• An algebro-geometric model for the shape of supercoiled DNA
• Closed Loop Solitons and Sigma Functions: Classical and Quantized Elasticas with Genera One and Two
• From Euler's elastica to the mKdV hierarchy, through the Faber polynomials
• Reality Conditions of Loop Solitons Genus g: Hyperelliptic am Functions
• Relations in a Loop Soliton as a Quantized Elastica
• On the Moduli of a quantized loop in P and KdV flows: Study of hyperelliptic curves as an extension of Euler's perspective of elastica I