On the precise connection between the GRW master-equation and master-equations for the description of decoherence

Abstract

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 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.

9 pages, latex, no figures, to appear on J. Phys. A

References in corpus (15)

• Dynamical Reduction Models
• Collisional decoherence reexamined
• Why Decoherence has not Solved the Measurement Problem: A Response to P. W. Anderson
• Completely Positive Quantum Dissipation
• Martingale Models for Quantum State Reduction
• Quantum Master Equation of Particle in Gas Environment
• Master equation for a quantum particle in a gas
• Apparent wave function collapse caused by scattering
• A search for a border between classical and quantum worlds
• Test Particle in a Quantum Gas
• On the Energy Increase in Space-Collapse Models
• Translation-covariant Markovian master equation for a test particle in a quantum fluid
• On the quantum description of Einstein's Brownian motion
• Theory of decoherence due to scattering events and Lévy processes
• Master-equations for the study of decoherence

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