% Full name of corresponding author: Alexander Ya. Shul'man
% Full mail address: Institute of Radioengineering&Electronics of the RAS
%                    Moscow GSP-9, 101999 Russia
% email: ash@cplire.ru


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{\Large {\bf Contribution of One-Time Pair Correlation Function }}
{\Large {\bf to Kinetic Phenomena in Nonequilibrium Gas}}

{\em A.Ya. Shul'man}

Institute of Radioengineering and Electronics of the RAS

Moscow GSP-9, 101999 Russia. E-mail: ash@cplire.ru
\end{center}

The derivation of kinetic equation for one-particle distribution function $F(%
{\bf p},{\bf r},t)$ from BBGKY chain leads to the collision integral
expressed in terms of the two-particle correlation function. The latter is
in turn expressed by $F$ using Boltzmann's Sto\ss zahlansatz that implies
the neglect of initial one-time correlation function $g_2({\bf p}_1,{\bf p}%
_2,{\bf r},t)\,\,$ which is non-diagonal in the momentum space. In
non-equilibrium case, however, it has been established that pair collisions
generate the non-diagonal two-particle correlations that gives the essential
contribution to the current fluctuations of hot electrons [1,2]. Could these
correlations give also a contribution to the collision integral, i.e., to
kinetic properties of non-equilibrium electrons? The expression for electron
energy loss rate $P$ via phonons is re-derived in detail from this point of
view.

In fact, the formula for $P$ in terms of electron density-density
correlation function $\langle \rho \rho ^{+}\rangle _{{\bf k},\omega }$ was
obtained by Kogan [3] using Fermi Golden Rule. However, in order to come to
the well-known result for $P$ he applied fluctuation-dissipation theorem to
express $\langle \rho \rho ^{+}\rangle _{{\bf k},\omega }$ in terms of the
dielectric function of the electron gas. This step is equivalent to the
Sto\ss zahlansatz. We derive the expression for $P$ in terms of $\langle
\rho \rho ^{+}\rangle _{{\bf k},\omega }$ from quantum kinetic equation for
phonons interacting with non-equilibrium electron gas. The contribution of
the non-diagonal part of the nonequilibrium pair correlator to
phonon-electron collision integral and to $P$ is obtained and calculated
explicitly in the electron temperature approximation.

It is shown that these results may be obtained from non-linear kinetic
equation for fluctuating occupation numbers of one-particle states with
Langevin fluctuation force. Such an approach allows to formulate the simple
general conditions for two-particle correlator contribution might be
essential in kinetics. The derivation of this equation based on the
procedure of partial averaging over microscopic scale fluctuations similar
to the procedure using by H. Mori [4] to derive the classical generalized
Boltzmann equation for dense gases and liquids. However, in our case the
contribution obtained does not contain the extra powers of small parameters
of the kinetic theory.\thinspace

\thinspace

References

[1] {\sl S.V. Gantsevich, V.L. Gurevich, and R. Katilius}. FTT {\bf 11}, 308
(1969) [Sov. Phys. Sol. State {\bf 11}, 247 (1969)]

[2] {\sl A.Ya. Shul'man}. FTT {\bf 12}, 1181 (1970) [Sov. Phys. Sol. State 
{\bf 12}, 922 (1970)]

[3] {\sl Sh.M. Kogan}. FTT {\bf 4}, 2474 (1962) [Sov. Phys. Sol. State {\bf 4%
}, 1813 (1963)]

[4] {\sl H. Mori}. Prog. Theor. Phys. {\bf 49}, 1516 (1973)

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