On the Pseudo-Schr\"odinger Equation approximation of the Transfer-Integral operator for 1-dimensional DNA models

TL;DR

This paper evaluates the accuracy of the Pseudo-Schrodinger Equation approximation for DNA models derived from the Transfer-Integral operator, finding limitations in the standard form and proposing a generalized version that improves results for certain models.

Contribution

The paper critically assesses the standard PSE approximation for DNA models and introduces a generalized PSE that enhances modeling accuracy for specific cases.

Findings

Standard PSE fails for both tested DNA models.

Generalized PSE improves results for one model.

Discussion of particle-based DNA denaturation model.

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.