Decoherence of a Damped Anisotropic Harmonic Oscillator under Magnetic Field Effects in a Two-Dimensional Noncommutative Phase-Space

Tcoffo, Martin; Deuto, Germain Yinde; Issofa, N.; Koumetio, Armel Azangue; Tchapda, L. S. Yonya; Tene, Alain Giresse

doi:10.4236/jamp.2020.812207

Cited by 5 publications

(6 citation statements)

References 49 publications

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“…We find that the temporal decay of coherence is fastest for a super Ohmic bath and slowest for a sub Ohmic bath, with an Ohmic bath exhibiting an intermediate rate of suppression of coherence. Again, the rate of decoherence is slower for higher values of the magnetic field, as has been pointed out in previous theoretical and experimental results [37][38][39][40]. These results can be later extended to non-commutative space in two dimensions and other anomalous types of couplings can be explored using similar formalism.…”

Section: Discussionsupporting

confidence: 78%

“…Using these and equations ( 28) and ( 29), one can derive the argument of the exponential factor in equation (38):…”

Section: Abrupt Cut-offmentioning

confidence: 99%

“…In the corresponding study linear entropy has been considered as the measure of the purity of the states in non-commutative space [37]. The density operator and the Wigner function for an an-harmonic oscillator were computed in a 2D non-commutative phase space and the effects of magnetic field on the decoherence rate were highlighted, using time-independent coefficients, featuring the Markovian heat bath dynamics [38][39][40]. Later, the master equation was derived for the momentum coupling scenario in the framework of non-Markovian dynamics [41].…”

Section: Introductionmentioning

confidence: 99%

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Decoherence and the ultraviolet cutoff: non-Markovian dissipative dynamics of a charged particle in a magnetic field

Bhattacharjee

Mandal

Sinha

2023

J. Phys. A: Math. Theor.

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We derive a non-Markovian master equation for a charged particle in a magnetic fieldcoupled to a bath and study decoherence by analyzing the temporal decay of the off-diagonalelements of the reduced density matrix in the position basis. The coherent oscillationscharacterised by the cyclotron frequency get suppressed as a result of decoherence due tocoupling with the environment. We consider an Ohmic bath with three distinct models forthe high-frequency cutoff for the spectral density of the bath and compare the three cases.As expected, the three cutoff models converge in the limit of the uppermost frequency ofthe bath tending to infinity. We notice a dramatic slowing down of loss of coherence in thelow-temperature limit dominated by zero point quantum fluctuations compared to the high-temperature classical limit dominated by thermal fluctuations. We also go beyond the Ohmicmodel and study super-Ohmic and sub-Ohmic baths with the spectral densities deviatingfrom a linear dependence on the frequency. Our results are testable in a state of the art coldatom laboratory.

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Section: Discussionsupporting

confidence: 78%

“…Using these and equations ( 28) and ( 29), one can derive the argument of the exponential factor in equation (38):…”

Section: Abrupt Cut-offmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Decoherence and the ultraviolet cutoff: non-Markovian dissipative dynamics of a charged particle in a magnetic field

Bhattacharjee

Mandal

Sinha

2023

J. Phys. A: Math. Theor.

View full text Add to dashboard Cite

show abstract

“…We find that the temporal decay of coherence is fastest for a super Ohmic bath and slowest for a sub Ohmic bath, with an Ohmic bath exhibiting an intermediate rate of suppression of coherence. Again, the rate of decoherence is slower for higher values of the magnetic field, as has been pointed out in previous theoretical and experimental results [34][35][36][37]. These results can be later extended to non-commutative space in two dimensions and other anomalous types of couplings can be explored using similar formalism and the outcomes can be further tested in suitable cold atom experiments [45,[49][50][51].…”

Section: Discussionsupporting

confidence: 66%

“…In the corresponding study linear entropy has been considered as the measure of the purity of the states in non-commutative space [34]. The density operator and the Wigner function for an an-harmonic oscillator were computed in a 2D non-commutative phase space and the effects of magnetic field on the decoherence rate were highlighted, using time-independent coefficients, featuring the Markovian heat bath dynamics [35][36][37]. Later, the master equation was derived for the momentum coupling scenario in the framework of non-Markovian dynamics [38].…”

Section: Introductionmentioning

confidence: 99%

Decoherence and the ultraviolet cutoff: non-Markovian dynamics of a charged particle in a magnetic field

Bhattacharjee¹,

Mandal²,

Sinha³

2023

Preprint

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We derive a non-Markovian master equation for a charged particle in a magnetic field coupled to a bath and study decoherence by analysing the temporal decay of the off-diagonal elements of the reduced density matrix in the position basis. The coherent oscillations characterised by the cyclotron frequency get suppressed as a result of decoherence due to coupling with the environment. We consider an Ohmic bath with three distinct models for the high-frequency cutoff for the spectral density of the bath and compare the three cases. As expected, the three cutoff models converge in the limit of the uppermost frequency of the bath tending to infinity. We notice a dramatic slowing down of loss of coherence in the low-temperature limit dominated by zero point quantum fluctuations compared to the hightemperature classical limit dominated by thermal fluctuations. We also go beyond the Ohmic model and study super-Ohmic and sub-Ohmic baths with the spectral densities deviating from a linear dependence on the frequency. Our results are testable in a state of the art cold atom laboratory.

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Effect of Non-Commutative Space on Quantum Correlations in Two Bilinearly Coupled Harmonic Oscillators Interacting with its Environment

et al. 2022

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Decoherence of a Damped Anisotropic Harmonic Oscillator under Magnetic Field Effects in a Two-Dimensional Noncommutative Phase-Space

Cited by 5 publications

References 49 publications

Decoherence and the ultraviolet cutoff: non-Markovian dissipative dynamics of a charged particle in a magnetic field

Decoherence and the ultraviolet cutoff: non-Markovian dissipative dynamics of a charged particle in a magnetic field

Decoherence and the ultraviolet cutoff: non-Markovian dynamics of a charged particle in a magnetic field

Effect of Non-Commutative Space on Quantum Correlations in Two Bilinearly Coupled Harmonic Oscillators Interacting with its Environment

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