No abstract

No abstract

We derive an analytic, albeit approximate, expression for the ground state energy of N Coulomb interacting anyons with fractional statistics ν, 0 ≤ |ν| ≤ 1, confined in a two-dimensional well (with characteristic frequency ω 0 ) and subjected to an external magnetic field (with cyclotron frequency ω c ). We apply a variational principle combined with a regularization procedure which consists of fitting a cut-off parameter to existing exact analytical results in the noninteracting case, and to numerical calculations for electrons in quantum dots in the interacting case. The resulting expression depends upon parameters of the system |ν|, N, ω 0 , r 0 , a B and ω c , where r 0 represents a characteristic unit length and a B the Bohr radius. Validity of the result is critically assessed by comparison with exact, approximate, and numerical results from the literature.

We present a useful numerical method of investigating the electron conduction through a region where the obstacles are placed in a quasi-one-dimensional system. Using this method, we have studied the interference e6'ects of electron waves scattered by obstacles such as impurities. Electron conduction through slits in a quantum wire has also been investigated, and it has been found that the conductance is heavily modulated by the interference among the incident wave and electron waves scattered by the edges and potential barriers.