Derivation of the local-mean stochastic quantum force

Roumen Tsekov*, Eyal Heifetz, Eliahu Cohen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

We regard the non-relativistic Schrödinger equation as an ensemble mean representation of the stochastic motion of a single particle in a vacuum, subject to an undefined stochastic quantum force. The local mean of the quantum force is found to be proportional to the third spatial derivative of the probability density function, while its associated pressure is proportional to the second spatial derivative. The latter arises from the single particle diluted gas pressure, and this observation allows to interpret the quantum Bohm potential as the energy required to put a particle in a bath of fluctuating vacuum at constant entropy and volume. The stochastic force expectation value is zero and is uncorrelated with the particle location, thus does not perform work on average. Nonetheless, it is anti-correlated with volume and this anti-correlation leads to an uncertainty relation. We analyze the dynamic Gaussian solution to the Schrödinger equation as a simple example for exploring the mean properties of this quantum force. We conclude with a few possible interpretations as to the origins of quantum stochasticity.

Original languageEnglish
Article number1750028
JournalFluctuation and Noise Letters
Volume16
Issue number3
DOIs
StatePublished - 1 Sep 2017

Funding

FundersFunder number
European Research CouncilAdG NLST
Horizon 2020 Framework Programme692146
European Commission291574

    Keywords

    • Madelung equations
    • Stochastic quantum mechanics
    • quantum potential

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