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{\large\bf Non--Fermi Liquid Signatures and Two-channel Kondo Impurities in
Diffusive Quantum Wires out of Equilibrium} \\

\bigskip
{\underline{Hans Kroha}}$^1$ and Fred Zawadowski$^2$\\

\bigskip
{\small{\em
\noindent $^{1}$ 
Institut f\"ur Theorie der Kondensierten Materie, Universit\"at Karlsruhe, 
Postfach 6980, 
76128 Karlsruhe, Germany

\noindent $^{2}$
Institute of Physics of the
Hungarian Academy of Sciences and Institute for
Solid State Physics, Technical University of Budapest,
                       H--1525 Budapest, Hungary }} \\

{\tt kroha@tkm.physik.uni-karlsruhe.de}
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\smallskip
\noindent
In recent experiments Pothier et al. measured
the nonequilibrium distribution function $f(E,U)$ in diffusive Cu [1]
and Au [2] quantum 
wires in the presence of a transport voltage $U$.
The experimentally observed scaling behavior, $f(E,U)=f(E/eU)$,
indicates the presence of a non--Fermi liquid interaction in the wire.

Using the auxiliary boson method (NCA), 
we calculate the nonequilibrium distribution function in a diffusive
wire in the presence of two-channel Kondo (2CK) impurities (two--level
systems). The NCA correctly decribes the non--Fermi liquid regime 
of these systems both in equilibrium [3,4] and in static nonequilibrium [5].
It is shown that the 
2CK effect reproduces the scaling form $f(E/eU)$ of the
distribution function in the regime $eU\gg T_K$, with $T_K$ the
Kondo temperature. The shape of $f(E/eU)$ is controlled by a
single parameter $r=\tau /\tau_D$, where $\tau$ and $\tau _D$
are the inelastic scattering time and the diffusion time through 
the wire, respectively. For varying wire lengths ($r\gg 1$) The 
2CK--induced, scaled distribution function agrees quantitatively with the
experimental results for all measured samples, $r$ being the only adjustable
parameter. 
This provides strong evidence for 2CK impurities to be present in Cu and Au 
quantum wires. Deviations from scaling at smaller bias voltages allow to
extract the Kondo temperature from the experimental data.
Additional experiments are proposed to further test the 2CK hypothesis.
\\[0.2cm]
\begin{itemize}
\item[[1]] H. Pothier, S. Gu\'eron, N. O. Birge, D. Esteve, and M. H. Devoret,
Phys. Rev. Lett. {\bf 79}, 3490 (1997).

\item[[2]]  H. Pothier, F. Pierre, N. O. Birge, D. Esteve, and M. H. Devoret,
in preparation (1999).

\item[[3]]  D. L. Cox and A. E. Ruckenstein, 
Phys. Rev. Lett. {\bf 71}, 1613 (1993).

\item[[4]]  J. Kroha, P. W\"olfle and T. A. Costi, Phys. Rev. Lett. 
{\bf 79}, 261 (1997);  J. Kroha and P. W\"olfle, Acta Phys. Pol. B,
{\bf 29}, 3781--3817 (1998). 

\item[[5]]  M. H. Hettler, J. Kroha, and S. Hershfield,
 Phys. Rev. Lett. {\bf 73}, 1967 (1994).
\end{itemize} 

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