Erratum: Great moments in kinetic theory: 150 years of Maxwell's (other) equations (2017 Eur. J. Phys. 38 065103)

Abstract

In 1867, just two years after laying the foundations of electromagnetism, J. Clerk Maxwell presented a fundamental paper on kinetic gas theory, in which he described the evolution of the gas in terms of certain 'moments' of its velocity distribution function. This inspired Ludwig Boltzmann to formulate his famous kinetic equation, from which followed the H-theorem and the connection with entropy. On the occasion of the 150th anniversary of publication of Maxwellʼs paper, we review the Maxwell-Boltzmann formalism and discuss how its generality and adaptability enable it to play a key role in describing the behaviour of a variety of systems of current interest, in both gaseous and condensed matter, and in modern-day physics and technologies which Maxwell and Boltzmann could not possibly have foreseen. In particular, we illustrate the relevance and applicability of Maxwellʼs formalism to the dynamic field of plasma-wakefield acceleration.

Disorder-induced quantum-to-classical transition, or how the world becomes classical

“…That golden rule plays a major role also in decoherence theory [1]; and it continues to arouse a number of comments [26,27]. We remark that strict energy conservation, as expressed by the delta function of energy in (40), is obtained here without assuming longlived plane waves. The time-energy uncertainty relation invoked in textbooks [10] is unnecessary.…”

“…Omitting the p and t dependencies for a simpler notation, the expansion (36) of f W is recast as 2 Lorentz-type scattering term on the right-hand side, in which W p,p' d 3 p'/h 3 is the transition probability per unit time that a particle of momentum p gets scattered to momentum p'. Equations (40)(41) mean that, if the scatterers are distributed independently, the total scattering is proportional to the number N s of scatterers.…”

“…The time-energy uncertainty relation invoked in textbooks [10] is unnecessary. Even for a high scattering rate causing short-lived and energy-broadened states, expression (40)(41) of W p,p' is valid if used in (39) 3 . A similar conclusion had been reached in a different way in the case of a particle colliding inelastically [28].…”

“…The calculation of the right-hand side of (A.8), which involves the Fourier transform C ^U(q) of C U (s), is given elsewhere [16,31]. Equation (39)(40)…”