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Coulomb Interaction and Transport in Tunnel Junctions and Quantum Dots
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In the first part of the paper the AC conductance of a quasi-one-dimensional tunnel junction involving a potential barrier is calculated in linear response. Its frequency dependence is used to define a dynamical capacitance. The influence of phase breaking electron-phonon interactions is investigated. It is argued that Coulomb interaction is of minor importance at higher frequencies and that dynamic and static capacitances are the same. The argument provides a high-frequency limit for turnstile operation. In the second part, the quantum mechanical properties of few interacting electron confined within a quasi-one-dimensional system of finite length with Coulomb interactions are investigated by numerical diagonalization. The limitations of the description in terms of a capacitance are discussed. For sufficiently low density the electrons become localized, forming a Wigner molecule. The energetically lowest excitations are identified as vibrational and tunneling modes, both being collective modes involving all the electron.
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