Abstract
We analyse the phenomenon of quantum chaology in the polynomial classically regular multiple well model. The Time Dependent variational principle using generalised Gaussian trial wave function, which, in many-body theory, leads to the Time Dependent Hartree Fock approximation (TDHF), is used to study the system. The extended classical system with fluctuation variables non-linearly coupled to the average variables exhibit, with respect to the odd or even values of the adjustable order of non linearity $\bf m$$, energy dependent transitions between regular behaviour and semi quantum chaos monitored by Poincare sections, return map and phase portraits.
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