From the latter we obtain the internal energy and the Sommerfeld coefficient, . A straightforward calculation in the noninteracting RLM yields

where denotes the derivative of

(2.18) |

The result (2.17) for
has some interesting
implications. First, because
is connected to , it is apparent that the low-energy excitations
in the system
are controlled by spin degrees of freedom, a well-known feature of the Kondo
physics. However,
in our approach this result can be read off directly from
equ. (2.17). Second,
, i.e. we obtain the
correct scaling behavior
for
*directly* from the behavior of
. There is, however,
a nontrivial correction coming from the factor in parenthesis in
(2.17). Note that for
const. this
correction is one, but for the strongly -dependent
in Fig. 2.1 it is of the order of two. As we
will demonstrate later,
this difference is directly responsible for obtaining the correct Wilson ratio
in our approach.

From the mapping it is easy to calculate . Since the correlation function has to be evaluated within the RLM, one obtains for the imaginary part at

Again, this result provides direct access to an interpretation of the behavior of in terms of the physics of the resonant level model.