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Chaos in classical systems has been studied in plenty over many years.Although the search for chaos in quantum systems has been an area of prominentresearch over the last few decades, the detailed analysis of many inherentlychaotic quantum systems based on expectation values of dynamical variables hasnot been reported in the literature. In this paper, we extend the study ofdynamical behaviour using expectation values of variables to a $q$-deformedharmonic oscillator. The system is found to be periodic, quasi-periodic orchaotic depending on the values of the deformation parameter $q$ and thedeformed coherent amplitude $\alpha_{q}$, thus enabling us to explicitlyclassify the chaotic nature of the system on the basis of these parameters. Thechaotic properties of the system are clearly illustrated through recurrenceplots, power spectra, first-return-time distributions and Lyapunov exponents ofthe time series obtained for the expectation values of the dynamic variables.

the european physical journal. d, atomic, molecular and optical physics/the european physical journal. d, atomic, molecular, optical and plasma physics

Dynamics of observables in a $q$-deformed harmonic oscillator