Heat flow and noncommutative quantum mechanics in phase-space

Santos, Jonas F. G.

doi:10.1063/5.0010076

Cited by 14 publications

(5 citation statements)

References 85 publications

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“…It is worth to notice that these diffusion coefficients play an important role in the study of the dynamic of open quantum systems, since they are directly related to the preservation of crucial concepts such as uncertainty relation or non-negativity of the density matrix[50]. Solving equation(21), we obtain[32,55,56]:…”

mentioning

confidence: 99%

The dynamic of quantum entanglement of two dimensional harmonic oscillator in non-commutative space

Koumetio¹,

Germain²,

Tene³

et al. 2021

Phys. Scr.

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In the present paper, we study the influence of non-commutativity on entanglement in a system of two oscillators-modes in interaction with its environment. The considered system is a two-dimensional harmonic oscillator in non-commuting spatial coordinates coupled to its environment. The dynamics of the covariance matrix, the separability criteria for two Gaussian states in non-commutative space coordinates, and the logarithmic negativity are used to evaluate the quantum entanglement in the system, which is compared to the commutative space coordinates case. The result is applied for two initially entangled states, namely the squeezed vacuum and squeezed thermal states. It can be observed that the phenomenon of entanglement sudden death appears more early in the system for the case of squeezed vacuum state than in the case of squeezed thermal state. Thereafter, it is also observed that non-commutativity effects lead to an increasing of entanglement of initially entangled quantum states, and reduce the separability in the open quantum system. It turns out that a separable state in the usual commutative quantum mechanics might be entangled in non-commutative extension.

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mentioning

confidence: 99%

The dynamic of quantum entanglement of two dimensional harmonic oscillator in non-commutative space

Koumetio¹,

Germain²,

Tene³

et al. 2021

Phys. Scr.

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“…where σ aspt is the asymptotic covariance matrix reached when t → ∞ (complete thermalization). This formalism also provides an expression to obtain the internal energy of the system using the covariance matrix [49], given by U t = ω Tr [σ(t)] /4. We now pass to consider a PT -symmetric Hamiltonian following the concepts presented in section 2 to construct thermal states for the ancillas of the bath.…”

Section: Modeling a Thermal Reservoir Through Pt -Symmetric Hamiltoniansmentioning

confidence: 99%

Quantum thermodynamics aspects with a thermal reservoir based on PT -symmetric Hamiltonians

Santos¹,

Luiz²

2021

J. Phys. A: Math. Theor.

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We present results concerning aspects of quantum thermodynamics under the background of non-Hermitian quantum mechanics for the dynamics of a quantum harmonic oscillator. Since a better control over the parameters in quantum thermodynamics processes is desired, we use concepts from collisional model to introduce a simple prototype of thermal reservoir based on -symmetric Hamiltonians and study its effects under the thermalization process of a single harmonic oscillator prepared in a displaced thermal state. We verify that controlling the -symmetric features of the reservoir allows to reverse the heat flow between system and reservoir, as well as to preserve the coherence over a longer period of time and reduce the entropy production. Furthermore, we considered a modified quantum Otto cycle in which the standard hot thermal reservoir is replaced by the thermal reservoir based on -symmetric Hamiltonians. By defining an effective temperature depending on the -symmetric parameter, it is possible to interchange the quantum Otto cycle configuration from engine to refrigerator by varying the -symmetric parameter. Our results indicate that -symmetric effects could be useful to achieve an improvement in quantum thermodynamics protocols such as coherence protection and entropy production reduction.

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“…where σ aspt is the asymptotic covariance matrix reached when t → ∞ (complete thermalization). This formalism also provides an expression to obtain the internal energy of the system using the covariance matrix [45], given by U t = ωTr [σ(t)] /4. We now pass to consider a PT -symmetric Hamiltonian following the concepts presented in Sec.…”

Section: Modeling a Thermal Reservoir Through Pt -Symmetric Hamiltoniansmentioning

confidence: 99%

Quantum thermodynamics aspects with a thermal reservoir based on $\mathcal{PT}$-symmetric Hamiltonians

Santos,

Luiz

2021

Preprint

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Heat flow and noncommutative quantum mechanics in phase-space

Cited by 14 publications

References 85 publications

The dynamic of quantum entanglement of two dimensional harmonic oscillator in non-commutative space

The dynamic of quantum entanglement of two dimensional harmonic oscillator in non-commutative space

Quantum thermodynamics aspects with a thermal reservoir based on PT -symmetric Hamiltonians

Quantum thermodynamics aspects with a thermal reservoir based on $\mathcal{PT}$-symmetric Hamiltonians

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