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arXiv:quant-ph/0301039 · International Journal of Theoretical Physics

Master-Equations for the Study of Decoherence

B. Vacchini

Published Jul 1, 2005• 18 citations
arXivHTMLPDF
DOI
10.1007/s10773-005-7077-4

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We point out that the celebrated GRW master equation is invariant under translations, reflecting the homogeneity of space, thus providing a particular realization of a general class of translation-covariant Markovian master equations. Such master equations are typically used for the description of decoherence due to momentum transfers between the system and environment. Building on this analogy we show the exact relationship between the GRW master equation and decoherence master equations, further providing a collisional decoherence model formally equivalent to the GRW master equation. This allows for a direct comparison of order of magnitudes of relevant parameters. This formal analogy should not lead to confusion on the utterly different spirit of the two research fields, in particular it has to be stressed that the decoherence approach does not lead to a solution of the measurement problem. Building on this analogy however the feasibility of the extension of spontaneous localization models in order to avoid the infinite energy growth is discussed. Apart from a particular case considered in the paper, it appears that the amplification mechanism is generally spoiled by such modifications.
We present a remarkably simple derivation of an exact time-local master equation describing the dynamics of quantum states in harmonic traps subject to arbitrary fluctuating forces. The relation between our master equation and known master equations of irreversible harmonic oscillator dynamics are established. Motivated by recent experiments, we focus on decoherence and in particular on the precise decoherence dynamics of a superposition of wave packets. We determine the decaying purity resulting from the time evolution based on our master equation and study its connection to experimentally accessible observables. Finally, we discuss the heating of the system subjected to arbitrary Gaussian noise.