Time-dependent attractive thermal quantum force upon a Brownian free particle in the large friction regime

Details Time-dependent attractive thermal quantum force upon a Brownian free particle in the large friction regime Time-dependent attractive thermal quantum force upon a Brownian free particle in the large friction regime

2010-04-04

arxiv.org/abs/1004.0527v1

Physics

Condensed Matter

Statistical Mechanics

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Scientific paper

We quantize the Brownian motion undergone by a free particle in the absence of inertial force (the so-called large friction regime) as described by the diffusion equation early found out by Einstein in 1905. Accordingly, we are able to come up with a time-dependent attractive quantum force F(t) that acts upon the Brownian free particle as a result of quantum-mechanical thermal fluctuations of a heat bath consisting of a set of quantum harmonic oscillators having the same oscillation frequency /omega in thermodynamic equilibrium at temperature T. More specifically, at zero temperature we predict that the zero-point force is given by F^((T=0)) (t)=-[\omega/(1+2\omegat)^(3/2)] \sqrt(\gamma/2), where \gamma is the friction constant with dimensions of mass per time and /eta the Planck constant divided by 2\pi. For evolution times t~1/\omega, \omega~0^14 Hz, /gamma~10^(-10) kg/s, and /eta~10^(-34) m^2 kg/s, we find out F^((T=0)) ~10^(-8) N, which exhibits the same magnitude order as the Casimir electromagnetic quantum force, for instance. Thus, we reckon that novel quantum effects arising from our concept of time-dependent thermal quantum force F(t) may be borne out by some experimental set-up in nanotechnology.

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