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shot noise in mesoscopic conductors - Low Temperature Laboratory

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98 Ya.M. Blanter, M. Bu( ttiker / Physics Reports 336 (2000) 1}166<br />

of the non-equilibrium distribution towards the <strong>in</strong>stantaneous equilibrium distribution function<br />

with the help of the Debye}Boltzmann-like equations<br />

d /dt"!( !f (t)) . (180)<br />

If the system is driven out of equilibrium, the <strong>in</strong>stantaneous distribution function is timedependent.<br />

Eq. (180) states that the non-equilibrium distribution tries to follow the <strong>in</strong>stantaneous<br />

distribution but can do that at best with a time lag determ<strong>in</strong>ed by . The time-dependent<br />

readjustment of the distribution is achieved with <strong>in</strong>elastic processes and is thus dissipative. To<br />

"nd the result<strong>in</strong>g <strong>noise</strong> we <strong>in</strong>vestigate the response of the current to a small oscillat<strong>in</strong>g phase<br />

()e superimposed on the dc phase. The current is I"!(e/)[(d /d) #(d /d) ].<br />

The Josephson relation, d/dt"!(2e/)

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