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Open Quantum Systems Decoherence

Non-differentiable Bohmian trajectories

arXiv

Authors: Gebhard Gruebl, Markus Penz

Year

2010

Paper ID

10454

Status

Preprint

Abstract Read

~2 min

Abstract Words

110

Citations

N/A

Abstract

A solution ψ to Schrödinger's equation needs some degree of regularity in order to allow the construction of a Bohmian mechanics from the integral curves of the velocity field hbar Im left$bigtriangledown ψ/mψright$ . In the case of one specific non-differentiable weak solution Ψ we show how Bohmian trajectories can be obtained for Ψ from the trajectories of a sequence Ψ_n→ Ψ. For any real $t$ the sequence $Ψ_nleft( t,cdot right converges strongly.) The limiting trajectories no longer need to be differentiable. This suggests a way how Bohmian mechanics might work for arbitrary initial vectorsΨin the Hilbert space on which the Schrödinger evolution% Ψ\mapsto e^{-iht}Ψ$ acts.

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This paper contributes to the Open Quantum Systems & Decoherence research area in the Quantum Articles archive.
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A solution ψ to Schrödinger's equation needs some degree of regularity in order to allow the construction of a Bohmian mechanics from the integral curves of the velocity field...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1011.2852 [2] arXiv https://arxiv.org/abs/1011.2852 [3] Publisher https://arxiv.org/abs/1011.2852

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