Decoherence of quantum Brownian motion in noncommutative space

The decoherence of a harmonic oscillator under two-dimensional quantum Brownian motion on a noncommutative plane is investigated. The interaction with the environment is considered by two separate models so-called coupled and uncoupled. The two-dimensional master equation and its noncommutative counterpart are derived for both employed models. The rate of the linear entropy (predictability sieve) is chosen as a criterion to investigate the purity in the presence of the space noncommutativity. Besides, a two-dimensional charged harmonic oscillator on a plane which is imposed by a perpendicular magnetic field is introduced as a realization of our model. Therefore, our approach provides a formalism to investigate the influence of the magnetic field on the decoherence of the pure states. We show that in the high magnetic field limit the rate of the decoherence will be decreased.

► Influence of noncommutative nature of space on decoherence is investigated.
► Our model is a two-dimensional quantum Brownian particle on a noncommutative space.
► We show that the rate of decoherence will be increased in noncommutative space.
► Constant magnetic field vertically imposed on a plane is introduced as physical realization.
► Via this model one can study magnetic field effects on decoherence of pure states.