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Integrability in quantum theory has been defined in more than one ways.Recently, Braak suggested a new definition that a quantum system is integrableif the number of parameters required to specify the eigenstates and the numberdegrees of freedom (both discrete and continuous) are equal. It is argued thatthe dependence of uncertainty product of suitable operators on the atom-fieldinteraction strength is distinctly different for the integrable andnonintegrable cases. These studies indicate that uncertainty product is able toidentify nonintegrable atom-field systems in the context of the new definition.

Nonintegrability and quantum fluctuations in a quantum optical model