Abstract
We develop a field theoretical formalism for describing the non-linear dynamics of interacting nuclear, atomic and molecular species. Specifically, four simple types of reaction are considered all of which involve up to two reactants and two products. The equations of motion for space- and time-dependent quantum order parameter fields, describing the distribution of reactant and product species, are derived from Heisenberg's equation using appropriate second-quantised Hamiltonians. For simplicity, both internal degrees of freedom and heat bath modes are being neglected at this stage. We solve a number of cases exactly both in the space-independent and space-dependent régimes. The results obtained possess a variety of interesting properties which include solitonic behaviour and propagating waves of various types indicating the existence of a wealth of non-linear phenomena.
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