B Equilibrium Deformation of a Non-Linear Elastic Body

To calculate the integral, we divide the expression (A.l) into real and imaginary parts, taking into account that 

The imaginary part of (A.l) is equal to zero identically. The calculation of the real part determines the distribution function 

The mean square displacement for N steps can easily be calculated with the help of (A.2) 

As has been noted already the results are valid under the assumption of the independence of the separate steps and at large N. 

In an equilibrium state, the stress tensor is determined by the form and the volume of a deformed body. To determine the stress tensor of the deformed body at arbitrary (not small) deformation, we follow the method demonstrated by Landau and Lifshitz (1987b) for the calculation of the stress tensor for small deformation. 

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