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Fixed point of self-similar Lennard-Jones potentials in the glass transition

Jialin Wu
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Abstract

The existence of potential energy landscape in the glass transition has been theoretically proved using the recursive equation of reinforce-restraint of self-similar 8 orders of Lennard-Jones (L-J) potential fluctuations. The stability condition for fluctuation reinforce-restraint is just the Lindemann ratio that is exactly deduced as 0.1047in this paper. The origin and transfer of interface excitation comes of the balance between self-similar L-J potential fluctuation and geometric phase potential fluctuation, which also gives rise to a new attractive potential of -17/16ε_i, lower than the potential well energy -ε_i of i-th order of L-J potential, in the self-similar mean field of mean fields of different sizes. The delocalization energy of two-body is exactly the transfer energy of excited interface, and the delocalization path is along 8 orders of geodesics in topological analyses.

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Jialin Wu. 2007-01-09. Fixed point of self-similar Lennard-Jones potentials in the glass transition. https://arxiv.org/abs/math-ph/0701025

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