2010/04/04 by A. O. Bolivar, Bolivar, A. O.
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Quantum Mechanics and Applications #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.1004.0527
Submitted.
arxiv created 2010/04/04 · openalex publication_date 2010/04/04 · arxiv updated 2010/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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)=-[ω/(1+2\omegat)^(3/2)] √(γ/2), where γis the friction constant with dimensions of mass per time and /eta the Planck constant divided by 2π. For evolution times t~1/ω, ω~014 Hz, /gamma~10^(-10) kg/s, and /eta~10^(-34) m2 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.