On the Pseudo-Schr\"odinger Equation approximation of the Transfer-Integral operator for 1-dimensional DNA models
Abstract
The Transfer-Integral (TI) operator is a powerful method to investigate the statistical physics of 1-dimensional models, like those used to describe DNA denaturation. At the cost of a certain number of approximations, the TI equation can be reduced to a Pseudo-Schr\"odinger Equation (PSE), according to which the DNA sequence is equivalent to a point particle moving in a potential well. In this paper, I check the validity of the standard PSE approximation for two different 1-dimensional DNA models, and show that it fails to provide correct results for both of them. I then propose a generalized PSE, which works well for one of the two models. Finally, I discuss the particle description of DNA denaturation that is derived from this generalized PSE.
Keywords
Cite
@article{arxiv.1011.4431,
title = {On the Pseudo-Schr\"odinger Equation approximation of the Transfer-Integral operator for 1-dimensional DNA models},
author = {Marc Joyeux},
journal= {arXiv preprint arXiv:1011.4431},
year = {2011}
}
Comments
accepted in the Journal of Nonlinear Mathematical Physics