Exact solution of the Hu-Paz-Zhang master equation

Ford, G. W.; O’Connell, R. F.

doi:10.1103/physrevd.64.105020

Cited by 150 publications

(259 citation statements)

References 17 publications

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“…Two models were particularly important because they were rather close to reality, at least in specific circumstances. In one of them the environment is replaced by a collection of harmonic oscillators [3][4][5][6][7][8]. Another model represents decoherence as an accumulation of scattering phase shifts when particles from an external atmosphere collide with a macroscopic object [9].…”

Section: Some Questions About Decoherencementioning

confidence: 99%

Decoherence, irreversibility, and selection by decoherence of exclusive quantum states with definite probabilities

Omnès

2002

Phys. Rev. A

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The problem investigated in this paper is einselection, i. e. the selection of mutually exclusive quantum states with definite probabilities through decoherence. Its study is based on a theory of decoherence resulting from the projection method in the quantum theory of irreversible processes, which is general enough for giving reliable predictions. This approach leads to a definition (or redefinition) of the coupling with the environment involving only fluctuations. The range of application of perturbation calculus is then wide, resulting in a rather general master equation.Two distinct cases of decoherence are then found: (i) A "degenerate" case (already encountered with solvable models) where decoherence amounts essentially to approximate diagonalization; (ii) A general case where the einselected states are essentially classical. They are mixed states. Their density operators are proportional to microlocal projection operators (or "quasi projectors") which were previously introduced in the quantum expression of classical properties.It is found at various places that the main limitation in our understanding of decoherence is the lack of a systematic method for constructing collective observables.

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Section: Some Questions About Decoherencementioning

confidence: 99%

Decoherence, irreversibility, and selection by decoherence of exclusive quantum states with definite probabilities

Omnès

2002

Phys. Rev. A

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“…This master equation is typically solved numerically. In some cases, explicit solutions in closed form exist, e.g., for an initial Gaussian wave packet or a superposition of Gaussian wave packets [26]. In this paper we study the dynamics for initial Fock states of the harmonic oscillator and we use a perturbative approach that nonetheless allows to study non-Markovian features due to structured environments.…”

Section: Introductionmentioning

confidence: 99%

Environment-dependent dissipation in quantum Brownian motion

et al. 2009

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The dissipative dynamics of a quantum Brownian particle is studied for different types of environment. We derive analytic results for the time evolution of the mean energy of the system for Ohmic, sub-Ohmic and super-Ohmic environments, without performing the Markovian approximation. Our results allow to establish a direct link between the form of the environmental spectrum and the thermalization dynamics. This in turn leads to a natural explanation of the microscopic physical processes ruling the system time evolution both in the short-time non-Markovian region and in the long-time Markovian one. Our comparative study of thermalization for different environments sheds light on the physical contexts in which non-Markovian dissipation effects are dominant.

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“…The existence of an exact analytical solution of the Hu-PazZhang master equation [7,8] enables us to investigate the non-Markovian dynamics of the system. Since decoherence is a very rapid process the non-Markovian dy- * janika.paavola@utu.fi; www.openq.fi † sabrina.maniscalco@utu.fi; www.openq.fi namics often play a crucial role.…”

Section: Introductionmentioning

confidence: 99%

Decoherence control in different environments

Paavola

Maniscalco

2010

Phys. Rev. A

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We investigate two techniques for controlling decoherence, focusing on the crucial role played by the environmental spectrum. We show how environments with different spectra lead to very different dynamical behaviours. Our study clearly proves that such differences must be taken into account when designing decoherence control schemes. The two techniques we consider are reservoir engineering and quantum-Zeno control. We focus on a quantum harmonic oscillator initially prepared in a nonclassical state and derive analytically its non-Markovian dynamics in presence of different bosonic thermal environments. On the one hand we show how, by modifying the spectrum of the environment, it is possible to prolong or reduce the life of a Schrödinger cat state. On the other hand we study the effect of nonselective energy measurements on the degradation of quantumness of initial Fock states. In this latter case we see that the crossover between Zeno (QZE) and anti-Zeno (AZE) effects, discussed by Maniscalco et al. [Phys. Rev. Lett. 97, 130402 (2006)], is highly sensitive to the details of the spectrum. In particular, for certain types of spectra, even very small variations of the system frequency may cause a measurement-induced acceleration of decoherence rather than its inhibition.

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Exact solution of the Hu-Paz-Zhang master equation

Cited by 150 publications

References 17 publications

Decoherence, irreversibility, and selection by decoherence of exclusive quantum states with definite probabilities

Decoherence, irreversibility, and selection by decoherence of exclusive quantum states with definite probabilities

Environment-dependent dissipation in quantum Brownian motion

Decoherence control in different environments

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