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In this work we examine the effect of phase-space noncommutativity on sometypically quantum properties such as quantum beating, quantum information, anddecoherence. To exemplify these issues we consider the two-dimensionalnoncommutative quantum harmonic oscillator whose components behavior we monitorin time. This procedure allows us to determine how the noncommutativeparameters are related to the missing information quantified by the linearquantum entropy and by the mutual information between the relevant Hilbertspace coordinates. Particular questions concerning the thermodynamic limit ofsome relevant properties are also discussed in order to evidence the effects ofnoncommutativity. Finally, through an analogy with the Zeeman effect, weidentify how some aspects of the axial symmetry of the problem suggest thepossibility of decoupling the noncommutative quantum perturbations fromunperturbed commutative well-known solutions.

Probing phase-space noncommutativity through quantum beating, missing information and the thermodynamic limit