Stability of the shell structure in 2D quantum dots

We study the effects of external impurities on the shell structure in semiconductor quantum dots by using a fast response-function method for solving the Kohn-Sham equations. We perform statistics of the addition energies up to 20 interacting electrons. The results show that the shell structure is generally preserved even if effects of high disorder are clear. The Coulomb interaction and the variation in ground-state spins have a strong effect on the addition-energy distributions, which in the noninteracting single-electron picture correspond to level statistics showing mixtures of Poisson and Wigner forms.Comment: 7 pages, 8 figures, submitted to Phys. Rev.

Dynamics of compressible edge and bosonization

We work out the dynamics of the compressible edge of the quantum Hall system based on the electrostatic model of Chklovskii et al.. We introduce a generalized version of Wen's hydrodynamic quantization approach to the dynamics of sharp edge and rederive Aleiner and Glazman's earlier result of multiple density modes. Bosonic operators of density excitations are used to construct fermions at the interface of the compressible and incompressible region. We also analyze the dynamics starting with the second-quantized Hamiltonian in the lowest Landau level and work out the time development of density operators. Contrary to the hydrodynamic results, the density modes are strongly coupled. We argue that the coupling suppresses the propagation of all acoustic modes, and that the excitations with large wavevectors are subject to decay due to coupling to the dissipative acoustic modes.A possible correction to the tunneling density of states is discussed.Comment: 7 pages, Revtex, 1 figur

Berry's phase with quantized field driving: effects of inter-subsystem coupling

The effect of inter-subsystem couplings on the Berry phase of a composite system as well as that of its subsystem is investigated in this paper. We analyze two coupled spin-$\frac 1 2$ particles with one driven by a quantized field as an example, the pure state geometric phase of the composite system as well as the mixed state geometric phase for the subsystem is calculated and discussed.Comment: 4 pages, 1 figur

Improved transfer matrix method without numerical instability

A new improved transfer matrix method (TMM) is presented. It is shown that the method not only overcomes the numerical instability found in the original TMM, but also greatly improves the scalability of computation. The new improved TMM has no extra cost of computing time as the length of homogeneous scattering region becomes large. The comparison between the scattering matrix method(SMM) and our new TMM is given. It clearly shows that our new method is much faster than SMM.Comment: 5 pages,3 figure

Bloch electron in a magnetic field and the Ising model

The spectral determinant det(H-\epsilon I) of the Azbel-Hofstadter Hamiltonian H is related to Onsager's partition function of the 2D Ising model for any value of magnetic flux \Phi=2\pi P/Q through an elementary cell, where P and Q are coprime integers. The band edges of H correspond to the critical temperature of the Ising model; the spectral determinant at these (and other points defined in a certain similar way) is independent of P. A connection of the mean of Lyapunov exponents to the asymptotic (large Q) bandwidth is indicated.Comment: 4 pages, 1 figure, REVTE

The flux phase problem on the ring

We give a simple proof to derive the optimal flux which minimizes the ground state energy in one dimensional Hubbard model, provided the number of particles is even.Comment: 8 pages, to appear in J. Phys. A: Math. Ge

A single defect approximation for localized states on random lattices

Geometrical disorder is present in many physical situations giving rise to eigenvalue problems. The simplest case of diffusion on a random lattice with fluctuating site connectivities is studied analytically and by exact numerical diagonalizations. Localization of eigenmodes is shown to be induced by geometrical defects, that is sites with abnormally low or large connectivities. We expose a ``single defect approximation'' (SDA) scheme founded on this mechanism that provides an accurate quantitative description of both extended and localized regions of the spectrum. We then present a systematic diagrammatic expansion allowing to use SDA for finite-dimensional problems, e.g. to determine the localized harmonic modes of amorphous media.Comment: final version as published, 6 pages, 1 ps-figur

Analysis of the Strong Coupling Limit of the Richardson Hamiltonian using the Dyson Mapping

The Richardson Hamiltonian describes superconducting correlations in a metallic nanograin. We do a perturbative analysis of this and related Hamiltonians, around the strong pairing limit, without having to invoke Bethe Ansatz solvability. Rather we make use of a boson expansion method known as the Dyson mapping. Thus we uncover a selection rule that facilitates both time-independent and time-dependent perturbation expansions. In principle the model we analise is realised in a very small metalic grain of a very regular shape. The results we obtain point to subtleties sometimes neglected when thinking of the superconducting state as a Bose-Einstein condensate. An appendix contains a general presentation of time-independent perturbation theory for operators with degenerate spectra, with recursive formulas for corrections of arbitrarily high orders.Comment: New final version accepted for publication in PRB. 17 two-column pages, no figure

On confined fractional charges: a simple model

We address the question whether features known from quantum chromodynamics (QCD) can possibly also show up in solid-state physics. It is shown that spinless fermions of charge $e$ on a checkerboard lattice with nearest-neighbor repulsion provide for a simple model of confined fractional charges. After defining a proper vacuum the system supports excitations with charges $\pm e/2$ attached to the ends of strings. There is a constant confining force acting between the fractional charges. It results from a reduction of vacuum fluctuations and a polarization of the vacuum in the vicinity of the connecting strings.Comment: 5 pages, 3 figure

Comment on "Boson-fermion model beyond the mean-field approximation"

In a recent paper [A.S.Alexandrov, J.Phys.:Condens.Matter 8, 6923 (1996); cond-mat/9603111], it has been suggested that there is no Cooper pairing in boson-fermion models of superconductivity. We show that this conjecture is based on an inconsistent approximation that violates an exact identity. Quite generally, the divergence of the fermion t-matrix (the Thouless criterion) is accompanied by the condensation of a boson mode.Comment: LaTeX, 5 pages, 2style files included, 4 embedded EPS figures, submitted to J.Phys.:Condens.Matte