Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:hep-th/0612020 · International Journal of Quantum Information

ENVIRONMENT-INDUCED DECOHERENCE IN NONCOMMUTATIVE QUANTUM MECHANICS

João Nuno Prata, Nuno Costa Dias

Published Feb 1, 2007• 2 citations
arXivHTMLPDF

Abstract

We address the question of the appearance of ordinary quantum mechanics in the context of noncommutative quantum mechanics. We review our derivation of the noncommutative extension of the Hu–Paz–Zhang master equation for a Brownian particle linearly coupled to a bath of harmonic oscillators. As a new contribution, we consider the particular case of an Ohmic regime.

DOI
10.1142/s021974990700275x

Related papers

Exact master equation for a noncommutative Brownian particle

Nuno Costa Dias, João Nuno Prata

We derive the Hu-Paz-Zhang master equation for a Brownian particle linearly coupled to a bath of harmonic oscillators on the plane with spatial noncommutativity. The results obtained are exact to all orders in the noncommutative parameter. As a by-product we derive some miscellaneous results such as the equilibrium Wigner distribution for the reservoir of noncommutative oscillators, the weak coupling limit of the master equation and a set of sufficient conditions for strict purity decrease of the Brownian particle. Finally, we consider a high-temperature Ohmic model and obtain an estimate for the time scale of the transition from noncommutative to ordinary quantum mechanics. This scale is considerably smaller than the decoherence scale.

•Jan 1, 2009•18 citations

Deformation quantization of noncommutative quantum mechanics and dissipation

Catarina Bastos, Orfeu Bertolami A, Nuno Costa Dias +1 more

We review the main features of the Weyl-Wigner formulation of noncommutative quantum mechanics. In particular, we present a ∗-product and a Moyal bracket suitable for this theory as well as the concept of noncommutative Wigner function. The properties of these quasi-distributions are discussed as well as their relation to the sets of ordinary Wigner functions and positive Liouville probability densities. Based on these notions we propose criteria for assessing whether a commutative regime has emerged in the realm of noncommutative quantum mechanics. To induce this noncommutative-commutative transition, we couple a particle to an external bath of oscillators. The master equation for the Brownian particle is deduced.

arXiv:hep-th/0612239•Journal of Physics Conference Series•May 1, 2007•4 citations

Alternative derivation of the Hu-Paz-Zhang master equation of quantum Brownian motion

J. J. Halliwell, T. Yu

Hu, Paz, and Zhang [B. L. Hu, J. P. Paz, and Y. Zhang, Phys. Rev. D 45, 2843 (1992)] have derived an exact master equation for quantum Brownian motion in a general environment via path integral techniques. Their master equation provides a very useful tool to study the decoherence of a quantum system due to the interaction with its environment. In this paper, we give an alternative and elementary derivation of the Hu-Paz-Zhang master equation, which involves tracing the evolution equation for the Wigner function. We also discuss the master equation in some special cases. \textcopyright{} 1996 The American Physical Society.

arXiv:quant-ph/9508004•Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields•Feb 15, 1996•150 citations

Demystifying decoherence and the master equation of quantum Brownian motion

John King Gamble, John F. Lindner

Quantum decoherence is a proposed mechanism for the emergence of classical physics from the quantum mechanics. It has been developed extensively in recent years, but is sufficiently technically complicated to discourage widespread understanding. In this paper we provide a gentle introduction to quantum decoherence. We introduce state operators and their density matrix representations to describe composite systems, such as an experiment and its environment. We illustrate how the loss of information about a subsystem can cause a quantum system to appear classical. We first analyze a discrete example of phase randomization, then a Bell state, and finally a continuous system. In the final case we provide an accessible derivation of a major early result of decoherence theory, the master equation of quantum Brownian motion. We conclude by applying the master equation to the decoherence of a simple harmonic oscillator, with results reminiscent of our earlier discrete examples.

American Journal of Physics•Feb 12, 2009•14 citations

Decoherence and disentanglement scenarios in non-Markovian quantum Brownian motion

Christian Hörhammer, H. Büttner

We study the non-Markovian decoherence and disentanglement dynamics of dissipative quantum systems with special emphasis on non-Gaussian continuous variable systems. The dynamics are described by the Hu–Paz–Zhang master equation of quantum Brownian motion. The time evolution of the decoherence function of a single-mode superposition is compared to the concurrence of a two-mode entangled state. It is verified that moderate non-Markovian influences slow down the decay of interference fringes and quantum correlations, while strong non-Markovian effects resulting from an out-of-resonance bath can even accelerate the loss of coherence, compared to predictions of Markovian approximations. Qualitatively different scenarios including exponential, Gaussian or algebraic decay of the decoherence function are analyzed. It is shown that partial revivals of coherence can occur in case of non-Lindblad-type dynamics.

Journal of Physics A Mathematical and Theoretical•Jun 11, 2008•9 citations

Non-Markovian decoherence and disentanglement scenarios in quantum Brownian motion

Christian Hörhammer, H. Buettner

We study the non-Markovian decoherence and disentanglement dynamics of dissipative quantum systems with special emphasis on non-Gaussian continuous variable systems. The dynamics are described by the Hu-Paz-Zhang master equation of quantum Brownian motion. The time evolution of the decoherence function of a single-mode superposition is compared to the concurrence of a two-mode entangled state. It is verified that moderate non-Markovian influences slow down the decay of interference fringes and quantum correlations, while strong non-Markovian effects resulting from an out-of-resonance bath can even accelerate the loss of coherence, compared to predictions of Markovian approximations. Qualitatively different scenarios including exponential, Gaussian or algebraic decay of the decoherence function are analyzed. It is shown that partial revivals of coherence can occur in case of non-Lindblad-type dynamics.

arXiv:0711.3138•Nov 20, 2007•0 citations
We address the question of the appearance of ordinary quantum mechanics in the context of noncommutative quantum mechanics. We review our derivation of the noncommutative extension of the Hu–Paz–Zhang master equation for a Brownian particle linearly coupled to a bath of harmonic oscillators. As a new contribution, we consider the particular case of an Ohmic regime.
We derive the Hu-Paz-Zhang master equation for a Brownian particle linearly coupled to a bath of harmonic oscillators on the plane with spatial noncommutativity. The results obtained are exact to all orders in the noncommutative parameter. As a by-product we derive some miscellaneous results such as the equilibrium Wigner distribution for the reservoir of noncommutative oscillators, the weak coupling limit of the master equation and a set of sufficient conditions for strict purity decrease of the Brownian particle. Finally, we consider a high-temperature Ohmic model and obtain an estimate for the time scale of the transition from noncommutative to ordinary quantum mechanics. This scale is considerably smaller than the decoherence scale.
We review the main features of the Weyl-Wigner formulation of noncommutative quantum mechanics. In particular, we present a ∗-product and a Moyal bracket suitable for this theory as well as the concept of noncommutative Wigner function. The properties of these quasi-distributions are discussed as well as their relation to the sets of ordinary Wigner functions and positive Liouville probability densities. Based on these notions we propose criteria for assessing whether a commutative regime has emerged in the realm of noncommutative quantum mechanics. To induce this noncommutative-commutative transition, we couple a particle to an external bath of oscillators. The master equation for the Brownian particle is deduced.
Hu, Paz, and Zhang [B. L. Hu, J. P. Paz, and Y. Zhang, Phys. Rev. D 45, 2843 (1992)] have derived an exact master equation for quantum Brownian motion in a general environment via path integral techniques. Their master equation provides a very useful tool to study the decoherence of a quantum system due to the interaction with its environment. In this paper, we give an alternative and elementary derivation of the Hu-Paz-Zhang master equation, which involves tracing the evolution equation for the Wigner function. We also discuss the master equation in some special cases. \textcopyright{} 1996 The American Physical Society.
Quantum decoherence is a proposed mechanism for the emergence of classical physics from the quantum mechanics. It has been developed extensively in recent years, but is sufficiently technically complicated to discourage widespread understanding. In this paper we provide a gentle introduction to quantum decoherence. We introduce state operators and their density matrix representations to describe composite systems, such as an experiment and its environment. We illustrate how the loss of information about a subsystem can cause a quantum system to appear classical. We first analyze a discrete example of phase randomization, then a Bell state, and finally a continuous system. In the final case we provide an accessible derivation of a major early result of decoherence theory, the master equation of quantum Brownian motion. We conclude by applying the master equation to the decoherence of a simple harmonic oscillator, with results reminiscent of our earlier discrete examples.
We study the non-Markovian decoherence and disentanglement dynamics of dissipative quantum systems with special emphasis on non-Gaussian continuous variable systems. The dynamics are described by the Hu–Paz–Zhang master equation of quantum Brownian motion. The time evolution of the decoherence function of a single-mode superposition is compared to the concurrence of a two-mode entangled state. It is verified that moderate non-Markovian influences slow down the decay of interference fringes and quantum correlations, while strong non-Markovian effects resulting from an out-of-resonance bath can even accelerate the loss of coherence, compared to predictions of Markovian approximations. Qualitatively different scenarios including exponential, Gaussian or algebraic decay of the decoherence function are analyzed. It is shown that partial revivals of coherence can occur in case of non-Lindblad-type dynamics.
We study the non-Markovian decoherence and disentanglement dynamics of dissipative quantum systems with special emphasis on non-Gaussian continuous variable systems. The dynamics are described by the Hu-Paz-Zhang master equation of quantum Brownian motion. The time evolution of the decoherence function of a single-mode superposition is compared to the concurrence of a two-mode entangled state. It is verified that moderate non-Markovian influences slow down the decay of interference fringes and quantum correlations, while strong non-Markovian effects resulting from an out-of-resonance bath can even accelerate the loss of coherence, compared to predictions of Markovian approximations. Qualitatively different scenarios including exponential, Gaussian or algebraic decay of the decoherence function are analyzed. It is shown that partial revivals of coherence can occur in case of non-Lindblad-type dynamics.