Kinematical Brownian Motion of the Harmonic Oscillator in Non-Commutative Space

Tchoffo, Martin; Kuetche, J. C. Ngana; Fouokeng, Georges Collince; Afuoti, Ngwa Engelbert; Fai, Lukong Cornelius

doi:10.11648/j.ajmp.20140303.14

Cited by 3 publications

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“…Furthermore, Tchoffo et al in their investigation on kinematical Brownian motion of harmonic oscillator in NC space showed that the structure of Fokker Planck's equation is not modified (i.e. the factorization theorem is conserved in both commutative and NC space) [31]. More recently, Santos et al have introduced the Brownian motion of a particle in two-dimensional NC space using the standard NC algebra embodied by Weyl-Moyal formalism to find that, NCity induces a non-vanishing correlation between both coordinates at different times [32].…”

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Decoherence of quantum Brownian particle trapped in a penning potential in a non-commutative space

et al. 2019

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In this paper, the influence of non-commutativity on quantum systems interacting with the environment in the Penning trap potential is studied. The considered system is a Brownian particle expressed in non-commuting spatial coordinates coupled to a set of harmonic oscillators (environment). The equilibrium state of the total system has been evaluated using the fluctuation dissipation theorem. The effective parameters of the system are evaluated and compared with those of the system in commutative space. We found that non-commutativity effects give rise to an increase in decoherence in the system, and negative heat capacity confirms the presence of self-gravitation effects induced by non-commutativity. and plays an essential role in physics at the Planck's scale where quantum effects of the gravity might not be negligible [7]. Although NCity embodies a puzzle piece in high-energy scenario, great interest has also been addressed to its implications in condensed matter physics though the four fundamental interactions. Thus, the studies proved that there is a trace of NCity in the hydrogen atom [8][9][10], quantum Hall effect [11][12][13], Ahoronov-Bohm effect [14,15], graphene [16] and even in quantum information theory [17]. In the latter, several examples have been proposed and among them, we denote the phenomenon of decoherence. Quantum decoherence is considered to be a fundamental physical base for the transition from quantum to classical physics [18]. This phenomenon was first considered in 70ʼs and 80ʼs with the works of Zeh (1950) and Zureck (1991) on the emergence of classicality in the quantum framework [19,20]. Moreover, this phenomenon presents a profound implication in very high energy universe, where important applications correspond to supplying a mechanism in which the end of inflationary phase, enters smoothly to the radiation era [20][21][22][23][24]. Recently, Derakhshani suggests that, quantum decoherence concept can be sensibly applied to quantum gravity theories that posit classical time parameters or matter-clock variables at a fundamental level [25]. It will be therefore, very interesting to investigate this phenomenon of decoherence considering the space as NC. Whereas, it is important to mention that, before exploring the properties of particle in quantum physics, it is often necessary to trap the particle with a convenient potential. The harmonic potential and double well potential have already been used in several works in the study of the phenomenon of decoherence [26,27]. However, in this work, we trapped the Brownian particle in a Penning potential since its structure presents the advantage of combining the superposition of electric and magnetic field.Recently, with the new development in the physics of quantum open systems, Dragovich et al in 2005 investigated the influence of NCity on the occurrence of the so-called decoherence effect with external magnetic field, and they found that, decoherence can be highly affected when the external control (magnetic field) is constrained by the N...

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confidence: 99%