The probability density for the area A enclosed by a polymer loop in crossed electric-magnetic fields is evaluated using the Hida-Streit formulation. In this approach, the many possible conformations of the polymer, x(v) and y(v), are represented by paths and are parametrized in terms Brownian motion. When the magnetic field is switched off, results agree with the works of Khandekar and Wiegel5

https://www.worldscientific.com/doi/pdf/10.1142/S2010194512007969

White noise path integral treatment of the probability distribution for the area enclosed by a polymer loop in crossed electric-magnetic fields

The statistical mechanical properties of plane polymer configurations which enclose a fixed area and are subject to an external electric field are investigated. For this purpose an exact expression for the generating functional is obtained and subsequently used to derive: (a) the distribution function for the enclosed area; (b) the mean square distance of a given repeating unit from the origin; (c) the entropic force on a repeating unit.

/pdf/plane-polymer-configurations-enclosing-a-fixed-area-in-an-4i3fqm2buw.pdf

Plane polymer configurations enclosing a fixed area in an electric field: Generating functional and statistical mechanical properties

This paper presents derivation of the probability distribution for the area enclosed by a polymer loop in a gel and under different external fields using white noise analysis. In this context, the polymer loop is represented by Brownian paths and its immersion in a gel constraints it to occupy a constant area[1]. The external fields considered are electric field, and crossed electric-magnetic fields.

http://iopscience.iop.org/article/10.1088/1757-899X/79/1/012012/pdf

On polymer loop in a gel under external fields: analytical approach using white noise analysis

The statistical mechanical properties of plane polymer loops enclosing a constant area are investigated, using a continuous model from the start. For this purpose an analytic expression for the generating functional is obtained, which in turn is used to derive (1) the distribution function for the enclosed area, (2) the average squared distance of a given repeating unit from the origin, and (3) the entropic force on a repeating unit.

/pdf/statistical-mechanical-properties-of-polymer-configurations-29qekh1ih0.pdf

D.C. Khandekar

Papers

Statistical Mechanical Properties of Polymer Configurations which Enclose a Constant Area