Abstract:
In this work we suggest the algorithm to solve the linear Fredholm integral equation of the second kind for the one-particle distribution function of simple liquid near the hard surface. The core and the right part of the equation are guessed using Percus-Yevick approximation defined on finite interval for spatial macroscopic liquid. We suggest an approach to solve the equation analytically for each interval where function is defined.
Keywords:supercooled liquid, ideal glass, partial distribution function, replicas, chaotic phase transition of the first kind, Fredholm equation of the second kind.