ON THE PSEUDO-SCHRÖDINGER EQUATION APPROXIMATION OF THE TRANSFER-INTEGRAL OPERATOR FOR 1-DIMENSIONAL DNA MODELS

MARC JOYEUX
2011 Journal of Nonlinear Mathematical Physics  
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
more » ... imensional 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.
doi:10.1142/s1402925111001568 fatcat:k2gx3xvqere6rlfvnsgjxthz4e