The Langevin Equation by W. T. Coffey, Yu. P. Kalmykov, J. T. Waldron

By W. T. Coffey, Yu. P. Kalmykov, J. T. Waldron

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14), we get kTt (AxT = 3^770 or RTt J(A*r=. 1 Brownian fluctuation of a very light mirror suspended upon a fine quartz fibre of torsion constant A. (a) Pressure 4 x 10 mm Hg. (b) Atmospheric pressure, (c) -4 Same system as curve b, except that the pressure is 10 mm Hg. The motion of the system is characterised by the angle through which the mirror has rotated from its position of equilibrium. One may expect that the system will perform Brownian motion of such magnitude that A

The reader familiar with these concepts may skip these sections if so desired. 5 Necessary Concepts of Statistical Mechanics The development [3] of statistical mechanics and the introduction of stochastic processes into physics began in the nineteenth century, when physicists were attempting to show that heat in a medium is due to the random motion of the constituent molecules. Excellent historical summaries are given by Jeans [23], in the first and second editions of Chapman and Cowling [24] and by Born [25].

Barnes and S. Silverman [26]; see detailed discussion in [1]). Chapter 1. Historical Background and Introductory Concepts 17 is the Avogadro number and R is the gas constant. 314 J K mol"1), all the other variables in Eq. 1) except N may be determined in a suitable experiment. Thus one may use Einstein's formula to estimate the Avogadro number N. 85 x 1023 mol -1 [5]. He also confirmed the relation between t, rj, and T predicted by the Einstein equation. He was awarded the Nobel prize for his work in 1926.

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