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{\large\bf Plasmon and charge quantization in quantum 
 wires with two impurities} \\

\bigskip
{\underline{M. Grifoni}$^{1,2}$}, A. Braggio$^1$, M. Sassetti$^1$ and 
F. Napoli$^1$\\

\bigskip
{\small{\em
Dipartimento di fisica, Universit\`a di  Genova, 
 I-16146 Genova, Italy$^1$}} \\
{\small{\em
Institut f\"ur  Festk\"orperphysik, Universit\"at Karlsruhe, 
 D-76128 Karlsruhe, Germany$^2$}} \\

{\tt milena@tfp.uni-karlsruhe.de}
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\smallskip
\noindent
 A  main theme of correlated transport in mesoscopic systems is the   
Coulomb-blockade  of the dc-current
 through tiny tunnel junctions,  
%\cite{kulik,al86,in92}, 
 quantum wells
  or quantum dots 
 %\cite{beenakker,averin}
   when the bias voltage and the temperature are
smaller than the ``charging energy''  ${ E}_C=e^{2}/C$, where $e$
 is the elementary charge and 
$C$  is the  capacitance of the tunneling junction or of the  
 heterostructure. 
 In this case $C$ is a measurable quantity, which only depends on  geometric 
 parameters. 
%It was found to be of the order of $10^{-15}$F 
% and much smaller for metallic
%junctions \cite{in92}.
 Charging effects  also 
  dominate transport 
 %through small islands
%between two tunnel contacts (quantum dots), as well as transport 
 in quantum wires (QW)  with two impurities [1]. 
%\cite{kane92,Furusaki,SassettiDB}. 
 %In contrast to the single
 %tunneling junction case, and to the quantum dot case, the charging energy of
  In a  double barrier quantum wire (DBQW), however, ${C}$
  is not a simple macroscopic
 parameter but it   
   depends crucially on the character of the
 electron-electron  interaction. 
 %The case of 
 %  unscreened Coulomb interaction has been investigated in 
 % \cite{Maurey}. The
 %more realistic  finite range case has started to be
 %explored in \cite{Egger,Tobias}. 
 These theme will be pursued further here, where 
 we discuss the  {\em nonlinear DC transport}
 of one dimensional   interacting electrons in the
 sequential tunneling regime [2]. Starting from the microscopic 
 Luttinger liquid model, extended to include finite range interactions,
 the sequential tunneling rates are 
 %formally 
 evaluated.  
 As
expected,
  Coulomb blockade  phenomena occur. 
 %We shall find that a  consistent evaluation of charging effects  
 %in the presence of finite range interactions cannot be
 % restricted to an estimate  of the microscopic capacity,
 %but it must also include the evaluation of  the spectral density  
 %of the   bosonic modes. 
%Studies of the
 %DBQW microscopic capacitance will be provided, bridging between the 
 %zero range Luttinger liquid  case and the unscreened Wigner crystal
 %situation.  
 These QW phenomena, however, are 
{\em qualitatively} different from those
 found in metallic islands and in quantum dots. 
 % \cite{kane92,Furusaki,SassettiDB}. 
  First,  the
 current characteristics crucially depends on the
 {\em strength} of the electron-electron interaction as seen,
 e.g., in the conductance line-shape or in the slope of the Coulomb staircase.
 Second
 in a QW, where single particles excitations are absent,
 quantization effects  due to the confinement 
 manifest themeselves in a {\em discretized} spectral density of the bosonic
 charge-density excitation.
 %Another important characteristics which arises in confined quantum systems is
%the quantization of the energy levels or of other
% characteristic quantities in the direction of confinement.
% This is manifested, e.g., in the quantization of the energy levels of
% a quantum dot. In quantum wires, where only collective excitations
% exist, this results  
%s in 
% DBQW with  zero range interaction .
% In turn, is the spectral density    which
% explicitly determines 
% the current-voltage characteristics of such DBQW systems. 
 Thus, the {\em fine structure}
 of the current characteristics, 
  which shows up at  low enough temperatures, is a signature
 of the  
 discreteness of the (interaction-dependent) plasmon spectrum. 
 This fine structure is qualitatively different from the one
 arising from the discreteness of
the electrons levels in small area quantum dots.\\ 

\bigskip
\noindent
[1] C.~L.\ Kane and M.~P.~A.\ Fisher, 
    Phys.\ Rev.\ B {\bf 46}, 15233 (1992); 
    A.\ Furusaki and N.\ Nagaosa, Phys.\ Rev.\ B {\bf 47}, 3287 (1993);
    M.\ Sassetti, F.\ Napoli and U.\ Weiss, 
Phys.\ Rev.\ B {\bf 52}, 11213 (1995);\\
\noindent
[2] A.\ Braggio, M.\ Grifoni, M.\ Sassetti and F.\ Napoli, in preparation.
 

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