Condensed Matter


Basics of Deuteron-Cluster Dynamics by Langevin Equation

Authors: Akito Takahashi

This paper gives the follow-up study on the basics for our previous papers, Study on 4D/Tetrahedral Symmetric Condensate Condensation Motion by Non-Linear Langevin Equation, Symposium 998-Low Energy Nuclear Reactions Source Book, ACS, published on August 2008 from Oxford University Press. Pertaining to the quantum mechanics, the basics of new approach using the stochastic differential equation (Langevin equation) is written for quantifying dynamic motion of known molecules as D2+, D2 and D3+ as well as D-atom state. The role of the Platonic symmetry in these known molecules are discussed for deducing simple one-dimensional (Rdd dependent; here Rdd is distance between nearest d-d pair) Langevin equation and making quantum-mechanical ensemble averaging to obtain equation for expectation value. The methodology is applied for more complicated D-clusters as 4D/TSC and 6D/OSC which would keep the Platonic symmetry, by introducing the force fluctuation deviating from the ideal Platonic symmetry. Time-dependent TSC and OSC trapping potentials which take balance to getting back to the Platonic symmetry from the distorted states were defined and used for numerical solution of Langevin equation. Finally, time-dependent fusion rate formula for simultaneous 4D interaction was obtained based on the Fermi's golden rule and one-pion exchange potential of strong interaction. The 4D fusion is regarded to cause radiation-less excess heat and 4He ash in metal-deuterium systems under dynamic conditions

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Submission history

[v1] 14 Feb 2009

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