1,079 research outputs found
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- 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 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
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
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