LETTERS TO THE EDITOR

ON THE APPLICATION OF THERMODYNAMICS TO ELECTRICAL FLUCTUATIONS*)

In the March 1954 issue of UFN there were published my article on the thermodynamics of electrical fluctuations and V. L. Ginzburg’s reply. The entire physical argument of that reply rests on the “scholastic” reasoning of M. L. Levin, refuted by a “real” example: a thin conductor \[compared with the thickness of the skin layer\] at a temperature of 0.1° K, for which the classical frequency region lies below \(10^{10}\). Making use of the known estimates of the number of collisions in metals, V. L. Ginzburg concludes that the dispersion of the conductivity \(\sigma\), and together with it that of the resistance \(R\), begins only at frequencies of the order of \(10^{12}\). However, as V. L. Ginzburg well knows \[see his review article in the November 1950 issue of *UFN*\], such a conclusion is groundless. At helium temperatures, even for metals, the skin-layer thickness \(\delta\) is less than the mean free path \(l\). Consequently, the conductor thickness \(a\) is also small in comparison with \(l\). Therefore one cannot in general speak of a conductivity \(\sigma\) that is the coefficient in Ohm’s law, which is valid only for \(l \ll \delta,\ l \ll a\).

Since the conductor thickness is small in comparison with the mean free path, electron-theory methods must be used to find the resistance \(R\). Without anticipating the results of such microscopic calculations, let us note, however, that—since at low radio frequencies \(\delta \gg l\), while at high frequencies \(\delta \ll l\)—there are no grounds for asserting in advance that the resistance \(R\) will be constant over the entire radio-frequency interval.

M. L. Levin

\[ * \qquad * \qquad * \]

In note 1, in my opinion, the erroneousness of the basic proposition contained in M. L. Levin’s article 2 was clarified. However, in his letter 3 M. L. Levin completely bypasses the questions discussed earlier 1, 2, makes new incorrect assertions, and at the same time, without any grounds whatever, declares that the “untenability” of my own conclusions is “well known” to me. All this makes it necessary to make several remarks.

1. The basic assertion contained in M. L. Levin’s article amounts to the claim that “in the quantum frequency region one cannot, even without taking the skin effect into account, regard the resistance as independent of frequency” 2. In 1 it was,

*) From the Editors. In publishing the letters of M. L. Levin and V. L. Ginzburg, the Editors consider the discussion on the application of thermodynamics to electrical fluctuations closed.