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 -