TY - JOUR

T1 - Derivation of the local-mean stochastic quantum force

AU - Tsekov, Roumen

AU - Heifetz, Eyal

AU - Cohen, Eliahu

N1 - Publisher Copyright:
© 2017 World Scientific Publishing Company.

PY - 2017/9/1

Y1 - 2017/9/1

N2 - 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.

AB - 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.

KW - Madelung equations

KW - Stochastic quantum mechanics

KW - quantum potential

UR - http://www.scopus.com/inward/record.url?scp=85027892265&partnerID=8YFLogxK

U2 - 10.1142/S0219477517500286

DO - 10.1142/S0219477517500286

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AN - SCOPUS:85027892265

SN - 0219-4775

VL - 16

JO - Fluctuation and Noise Letters

JF - Fluctuation and Noise Letters

IS - 3

M1 - 1750028

ER -