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Spacetime fluctuations and a stochastic Schrödinger-Newton equation. (English) Zbl 1379.81042

Summary: We propose a stochastic modification of the Schrödinger-Newton equation which takes into account the effect of extrinsic spacetime fluctuations. We use this equation to demonstrate gravitationally induced decoherence of two gaussian wave-packets, and obtain a decoherence criterion similar to those obtained in the earlier literature in the context of effects of gravity on the Schrödinger equation.

MSC:

81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
81V17 Gravitational interaction in quantum theory
35R60 PDEs with randomness, stochastic partial differential equations
81S22 Open systems, reduced dynamics, master equations, decoherence
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