shot noise in mesoscopic conductors - Low Temperature Laboratory

Ya.M. Blanter, M. Bu( ttiker / Physics Reports 336 (2000) 1}166 131
We have thus presented a purely classical derivation of the Fano factor of a chaotic cavity (96).
This result was previously derived with the help of the scattering approach and RMT theory
(Section 2.6.5).
To what extent can the billiard with di!usive boundary scattering also describe cavities which
exhibit deterministic surface scattering? As we have stated above, if we consider an ensemble
member of a cavity with specular scattering at the surface, such scattering is deterministic and
noiseless. Thus, we can de"nitely not expect the model with a di!usive boundary layer to describe
an ensemble member. However, to the extent that we are interested in the description only of
ensemble-averaged quantities (which we are if we invoke a Boltzmann}Langevin equation) the
di!usive boundary layer model can also describe the ensemble-averaged behavior of cavities which
are purely deterministic. While in an individual cavity, a particle with an incident direction and
velocity generates a de"nite re#ected trajectory, we can, if we consider the ensemble-average,
associate with each incident trajectory, a re#ected trajectory of arbitrary direction. In the ensemble,
scattering can be considered probabilistic, and the di!usive boundary model can thus also be used
to describe cavities with completely deterministic scattering at the surface. This argument is correct,
if we can commute ensemble and statistical averages. To investigate this further, we present below
another discussion of the deterministic cavity.
6.7. Minimal correlation approach to shot noise in deterministic chaotic cavities
In cavities of su$ciently complicated shape, deterministic chaos appears due to specular
scattering at the surface. To provide a classical description of shot noise in this type of structures,
Ref. [99] designed an approach which it called a `minimal correlationa approach. It is not clear
whether it can be applied to a broad class of systems, and therefore, we decided to put it in this
section rather than to provide a separate section.
In a mesoscopic conductor, in the presence of elastic scattering only, the distribution function is
quite generally given by [110,111]
(r)
f (r)"
(r)
f , (249)
where (r) is the injectivity of contact n (the contribution to the local density of states (r) of contact
n.) For the ensemble-averaged distribution which we seek, we can replace the actual injectivities
and the actual local density of states by their ensemble average. For a cavity with classical contacts
(N