A simulated annealing based study of the effect of Gaussian perturbation in quartic oscillator and quadratic double well potentials

作者：Mukherjee Neetik^*

来源：Journal of Mathematical Chemistry, 2015, 53(1): 137-150.

DOI：10.1007/s10910-014-0415-0

• Unconstrained optimisation
• Simulated annealing
• Symmetric double well potential
• Gaussian perturbation
• Specific heat

Perturbation theory based model can be used to locate the quasi-degeneracy in an arbitrary double well potential. In this work, unconstrained optimisation has been done using Simulated Annealing to calculate the energy spectrum of double well potential. Using this calculation the author has studied the effect of a Gaussian perturbation on single and double well potential. A comparative study of quartic double well potential and Gaussian double well potential has also been done on the basis of chemical and statistical point of view. The efficiency of this method is notable. Numerical calculation shows that the proposed method can give extremely accurate results for symmetric double well potentials.
Repulsive Gaussian perturbation and attractive Quadratic Perturbation have been applied to a Quartic oscillator potential to compare the nature of double well. Both the perturbation leads to quasi degenerate potentials. Again, application of proper attractive Gaussian field removes normal quasi degeneracy but also generates accidental quasi degeneracy. Where lower state is an odd parity state and higher is an even parity state.

• 出版日期2015-1