[page 176, §1]

[176.1.1] A large variety of dynamic phenomena in condensed systems
can be described by a lattice gas model.
[176.1.2] Examples include transport in superionic solids,
phase separation in binary alloys, kinetics of spin models,
diffusion in metal-hydrogen systems or order-disorder phenomena
in chemisorbed monolayers at surfaces[1, 2, 3, 4].
[176.1.3] Moreover, the popular model of hopping transport on a percolating network
can be viewed as a special case.
[176.1.4] This is seen by considering a lattice gas with two species of particles,
A and B, for the case where the B-particles are frozen
into some random configuration.
[176.1.5] If, as usual, the A-particles are allowed to hop only into vacant lattice sites
then the problem is that of diffusion in a frozen disordered environment.
[176.1.6] Our interest in this problem stems from a case in which the B-particles
are not completely immobile, but very slow compared to the A-particles.
[176.1.7] The general objective in this paper will be
to calculate the transport coefficients for the A-particles.

[176.2.1] More specifically, we are motivated by the problem of calculating the
frequency dependent conductivity of

[176.3.1] Despite its conceptual simplicity the model contains many interesting features,
even if we neglect for the moment all interactions between particles,
except, of course, the hard core repulsion.
[page 177, §0]
[177.0.1] The hard core repulsion prevents double occupancy of lattice sites.
[177.0.2] In the limit

[177.1.1] Generally the system discussed above can be described
by a many particle master equation[1].
[177.1.2] This remains true even if interactions between particles are included.
[177.1.3] In the case of

[177.2.1] Let us first discuss the general framework of our approach.
[177.2.2] Instead of focussing on the case

[178.1.1] Finally the B-particles are allowed to move, i. e.

[178.2.1] The objective of this paper, as mentioned in the beginning, is the
calculation of the frequency dependent conductivity for the A-particles.
[178.2.2] In addition we wish to evaluate the correlation factor
for the selfâdiffusion constant in the d. c. limit.
[178.2.3] We assume here that the B-particles do not contribute to the conductivity.
[178.2.4] We will present results for the hexagonal and the fcc-lattice.
[178.2.5] The first because of its low coordination number
and its relevance for

[178.3.1] For the a.c. response we find a crossover between a low frequency regime
dominated by the effects of blocker motion, and at high frequency regime
in which the blockers, or equivalently vacancies, appear to form a frozen network.
[178.3.2] In addition we predict the appearance of novel features
in the real and imaginary part as a result of correlations.
[178.3.3] In the d. c. limit we calculate the correlation factor
for the self diffusion coefficient.
[178.3.4] It interpolates smoothly between the case