Decoherence of quantum Brownian motion in noncommutative space

Ghorashi, Sayed Ali Akbar; Harouni, M. Bagheri

doi:10.1016/j.physleta.2013.02.019

Cited by 14 publications

(22 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In these conditions, we fall on an effective Hamiltonian which has the same form as that found in the work of [26], but with the difference that our parameters contain NCity effects. So, (30) and (31) can be rewritten as follows:…”

Section: Effective Temperature and Effective Mass Of Brownian Particlmentioning

confidence: 99%

“…In the same idea, Dias and Prata in 2009 studied decoherence in NC Brownian particle using the exact master equation, they concluded that the NC to commutative (NC-C) transition takes places before the transition from classical mechanics to ordinary quantum mechanics, by comparing the decoherence time and the NC-C time transition [29]. Moreover, Ghoroshi et al in 2013 have looked forward to see the effects of NC space on decoherence by modifying the master equation of two-dimensional harmonic oscillators under the Brownian motion, and they found that the NC leads to an increase in the rate of decoherence [30]. 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.…”

mentioning

confidence: 99%

See 1 more Smart Citation

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

et al. 2019

View full text Add to dashboard Cite

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...

show abstract

Section: Effective Temperature and Effective Mass Of Brownian Particlmentioning

confidence: 99%

mentioning

confidence: 99%

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

et al. 2019

View full text Add to dashboard Cite

show abstract

“…In other words, the introduced Bopp shifts, (11) and (12), are a possible transformation that make a connection between the curvature and noncommutativity. It is worthwhile to notice that we have derived the exact Hamiltonian (4) without any limit on the magnitude of the curvature λ.…”

Section: Theoretical Frameworkmentioning

confidence: 99%

“…11 One of the best model which can demonstrate the physical results in an appropriate way is the harmonic oscillator. The harmonic oscillator has been studied 12,13 with various systems and conditions.…”

Section: Introductionmentioning

confidence: 99%

Equivalence of curvature and noncommutativity in a physical space: Harmonic oscillator on sphere

2014

View full text Add to dashboard Cite

We study the two-dimensional harmonic oscillator on a noncommutative plane. We show that by introducing appropriate Bopp shifts, one can obtain the Hamiltonian of a twodimensional harmonic oscillator on a sphere according to the Higgs model. By calculating the commutation relations, we show that this noncommutativity is strictly dependent on the curvature of the background space. In other words, we introduce a kind of duality between noncommutativity and curvature by introducing noncommutativity parameters as functions of curvature. Also, it is shown that the physical realization of such model is a charged harmonic oscillator in the presence of electromagnetic field.

show abstract

“…When solving the problem of ultraviolet divergences, Heisenberg and Schrödinger conjectured that space-time coordinates may be mutually non-commutative [7].This was the starting point of several researches on the development and the applications of non-commutative space in string theory, cosmology, and more recently quantum hall effect, spin-orbit interaction and in quantum dots [7][8][9][10]. The noncommutative analogue of the random variable, random walk, Gaussian, Levis, Ito, and Markovian processes seem to be the most investigated class of stochastic process in physics when studying probability theory and has been of great concern over the last twenty years [10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

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

Tchoffo¹,

Kuetche²,

Fouokeng³

et al. 2014

AJMP

View full text Add to dashboard Cite

In this work the Jacobi's second equality in the form of stochastic equation and the Wiener path integral approach are used to evaluate the probability density of harmonic oscillator in non-commutative space. Using the factorization theorem and the Mastubara formalism, the thermodynamic parameters are determined. The structure of Fokker-Planck equation remained the same even in a commutative and non-commutative space. Moreover, the noncommutative parameter is depicted for increasing value of the entropy.

show abstract

Decoherence of quantum Brownian motion in noncommutative space

Cited by 14 publications

References 33 publications

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

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

Equivalence of curvature and noncommutativity in a physical space: Harmonic oscillator on sphere

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

Contact Info

Product

Resources

About