1,013 research outputs found
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
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
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
Duality Relation among Periodic Potential Problems in the Lowest Landau Level
Using a momentum representation of a magnetic von Neumann lattice, we study a
two-dimensional electron in a uniform magnetic field and obtain one-particle
spectra of various periodic short-range potential problems in the lowest Landau
level.We find that the energy spectra satisfy a duality relation between a
period of the potential and a magnetic length. The energy spectra consist of
the Hofstadter-type bands and flat bands. We also study the connection between
a periodic short-range potential problem and a tight-binding model.Comment: 6 pages, 3 figures, final version to appear in PR
Weak disorder expansion for localization lengths of quasi-1D systems
A perturbative formula for the lowest Lyapunov exponent of an Anderson model on a strip is presented. It is expressed in terms of an energy-dependent doubly stochastic matrix, the size of which is proportional to the strip width. This matrix and the resulting perturbative expression for the Lyapunov exponent are evaluated numerically. Dependence on energy, strip width and disorder strength are thoroughly compared with the results obtained by the standard transfer matrix method. Good agreement is found for all energies in the band of the free operator and this even for quite large values of the disorder strength
Longitudinal Force on a Moving Potential
We show a formal result of the longitudinal force acting on a moving
potential. The potential can be velocity-dependent, which appears in various
interesting physical systems, such as electrons in the presence of a magnetic
flux-line, or phonons scattering off a moving vortex. By using the phase-shift
analysis, we are able to show the equivalence between the adiabatic
perturbation theory and the kinetic theory for the longitudinal force in the
dilute gas limit.Comment: RevTeX, 4 pages, revised tex
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
Scattering of Phonons by a Vortex in a Superfluid
Recent work gives a transverse force on an isolated moving vortex which is
independent of the normal fluid velocity, but it is widely believed that the
asymmetry of phonon scattering by a vortex leads to a transverse force
dependent on the relative motion of the normal component and the vortex. We
show that a widely accepted derivation of the transverse force is in error, and
that a careful evaluation leads to a much smaller transverse force. We argue
that a different approach is needed to get the correct expression.
\pacs{67.40.Vs,67.57.Fg,47.37.+q,47.32.Cc}Comment: 4 page
Vortex mass in a superfluid at low frequencies
An inertial mass of a vortex can be calculated by driving it round in a
circle with a steadily revolving pinning potential. We show that in the low
frequency limit this gives precisely the same formula that was used by Baym and
Chandler, but find that the result is not unique and depends on the force field
used to cause the acceleration. We apply this method to the Gross-Pitaevskii
model, and derive a simple formula for the vortex mass. We study both the long
range and short range properties of the solution. We agree with earlier results
that the non-zero compressibility leads to a divergent mass. From the
short-range behavior of the solution we find that the mass is sensitive to the
form of the pinning potential, and diverges logarithmically when the radius of
this potential tends to zero.Comment: 4 page
Quadrupole correlations and inertial properties of rotating nuclei
The contribution of quantum shape fluctuations to inertial properties of
rotating nuclei has been analyzed for QQ-nuclear interaction using the random
phase approximation (RPA). The different recipes to treat the cranking mean
field plus RPA problem are considered. The effects of the dN=2 quadrupole
matrix elements and the role of the volume conservation condition are
discussed.Comment: 14 pages, 7 figures, To be published in J. Phys. G: Nucl. Phy
- …