132 research outputs found
Integer quantum Hall effect and Hofstadter's butterfly spectra in three-dimensional metals in external periodic modulations
We propose that Hofstadter's butterfly accompanied by quantum Hall effect
that is similar to those predicted to occur in 3D tight-binding systems by
Koshino {\it et al.} [Phys. Rev. Lett. {\bf 86}, 1062 (2001)] can be realized
in an entirely different system -- 3D metals applied with weak external
periodic modulations (e.g., acoustic waves). Namely, an effect of two periodic
potentials interferes with Landau's quantization due to an applied magnetic
field \Vec{B}, resulting generally in fractal energy gaps as a function of
the tilting angle of \Vec{B}, for which the accompanying quantized Hall
tensors are computed. The phenomenon arises from the fact that, while the
present system has a different physical origin for the butterfly from the 3D
tight-binding systems, the mathematical forms are remarkably equivalent.Comment: 4 pages, 2 figure
Duality and integer quantum Hall effect in isotropic 3D crystals
We show here a series of energy gaps as in Hofstadter's butterfly, which have
been shown to exist by Koshino et al [Phys. Rev. Lett. 86, 1062 (2001)] for
anisotropic three-dimensional (3D) periodic systems in magnetic fields
\Vec{B}, also arise in the isotropic case unless \Vec{B} points in
high-symmetry directions. Accompanying integer quantum Hall conductivities
can, surprisingly, take values
even for a fixed direction of \Vec{B}
unlike in the anisotropic case. We can intuitively explain the high-magnetic
field spectra and the 3D QHE in terms of quantum mechanical hopping by
introducing a ``duality'', which connects the 3D system in a strong \Vec{B}
with another problem in a weak magnetic field .Comment: 7 pages, 6 figure
Phase Diagram for the Hofstadter butterfly and integer quantum Hall effect in three dimensions
We give a perspective on the Hofstadter butterfly (fractal energy spectrum in
magnetic fields), which we have shown to arise specifically in
three-dimensional(3D) systems in our previous work. (i) We first obtain the
`phase diagram' on a parameter space of the transfer energies and the magnetic
field for the appearance of Hofstadter's butterfly spectrum in anisotropic
crystals in 3D. (ii) We show that the orientation of the external magnetic
field can be arbitrary to have the 3D butterfly. (iii) We show that the
butterfly is beyond the semiclassical description. (iv) The required magnetic
field for a representative organic metal is estimated to be modest (
T) if we adopt higher Landau levels for the butterfly. (v) We give a simpler
way of deriving the topological invariants that represent the quantum Hall
numbers (i.e., two Hall conductivity in 3D, , in
units of ).Comment: 8 pages, 8 figures, eps versions of the figures will be sent on
request to [email protected]
Conductance of tubular nanowires with disorder
We calculate the conductance of tubular-shaped nanowires having many
potential scatterers at random positions. Our approach is based on the
scattering matrix formalism and our results analyzed within the scaling theory
of disordered conductors. When increasing the energy the conductance for a big
enough number of impurities in the tube manifests a systematic evolution from
the localized to the metallic regimes. Nevertheless, a conspicuous drop in
conductance is predicted whenever a new transverse channel is open. Comparison
with the semiclassical calculation leading to purely ohmic behavior is made.Comment: 8 pages, 5 figure
Graph products of spheres, associative graded algebras and Hilbert series
Given a finite, simple, vertex-weighted graph, we construct a graded
associative (non-commutative) algebra, whose generators correspond to vertices
and whose ideal of relations has generators that are graded commutators
corresponding to edges. We show that the Hilbert series of this algebra is the
inverse of the clique polynomial of the graph. Using this result it easy to
recognize if the ideal is inert, from which strong results on the algebra
follow. Non-commutative Grobner bases play an important role in our proof.
There is an interesting application to toric topology. This algebra arises
naturally from a partial product of spheres, which is a special case of a
generalized moment-angle complex. We apply our result to the loop-space
homology of this space.Comment: 19 pages, v3: elaborated on connections to related work, added more
citations, to appear in Mathematische Zeitschrif
Integer quantum Hall effect for hard-core bosons and a failure of bosonic Chern-Simons mean-field theories for electrons at half-filled Landau level
Field-theoretical methods have been shown to be useful in constructing simple
effective theories for two-dimensional (2D) systems. These effective theories
are usually studied by perturbing around a mean-field approximation, so the
question whether such an approximation is meaningful arises immediately. We
here study 2D interacting electrons in a half-filled Landau level mapped onto
interacting hard-core bosons in a magnetic field. We argue that an interacting
hard-core boson system in a uniform external field such that there is one flux
quantum per particle (unit filling) exhibits an integer quantum Hall effect. As
a consequence, the mean-field approximation for mapping electrons at
half-filling to a boson system at integer filling fails.Comment: 13 pages latex with revtex. To be published in Phys. Rev.
Finite Size and Current Effects on IV Characteristics of Josephson Junction Arrays
The effects of finite size and of finite current on the current-voltage
characteristics of Josephson junction arrays is studied both theoretically and
by numerical simulations. The cross-over from non-linear to linear behavior at
low temperature is shown to be a finite size effect and the non-linear behavior
at higher temperature, , is shown to be a finite current effect.
These are argued to result from competition between the three length scales
characterizing the system. The importance of boundary effects is discussed and
it is shown that these may dominate the behavior in small arrays.Comment: 5 pages, figures included, to appear in PR
Early Stages of Homopolymer Collapse
Interest in the protein folding problem has motivated a wide range of
theoretical and experimental studies of the kinetics of the collapse of
flexible homopolymers. In this Paper a phenomenological model is proposed for
the kinetics of the early stages of homopolymer collapse following a quench
from temperatures above to below the theta temperature. In the first stage,
nascent droplets of the dense phase are formed, with little effect on the
configurations of the bridges that join them. The droplets then grow by
accreting monomers from the bridges, thus causing the bridges to stretch.
During these two stages the overall dimensions of the chain decrease only
weakly. Further growth of the droplets is accomplished by the shortening of the
bridges, which causes the shrinking of the overall dimensions of the chain. The
characteristic times of the three stages respectively scale as the zeroth, 1/5
and 6/5 power of the the degree of polymerization of the chain.Comment: 11 pages, 3 figure
Higher Order Effects in the Dielectric Constant of Percolative Metal-Insulator Systems above the Critical Point
The dielectric constant of a conductor-insulator mixture shows a pronounced
maximum above the critical volume concentration. Further experimental evidence
is presented as well as a theoretical consideration based on a phenomenological
equation. Explicit expressions are given for the position of the maximum in
terms of scaling parameters and the (complex) conductances of the conductor and
insulator. In order to fit some of the data, a volume fraction dependent
expression for the conductivity of the more highly conductive component is
introduced.Comment: 4 pages, Latex, 4 postscript (*.epsi) files submitted to Phys Rev.
Fluctuation Relations for Diffusion Processes
The paper presents a unified approach to different fluctuation relations for
classical nonequilibrium dynamics described by diffusion processes. Such
relations compare the statistics of fluctuations of the entropy production or
work in the original process to the similar statistics in the time-reversed
process. The origin of a variety of fluctuation relations is traced to the use
of different time reversals. It is also shown how the application of the
presented approach to the tangent process describing the joint evolution of
infinitesimally close trajectories of the original process leads to a
multiplicative extension of the fluctuation relations.Comment: 38 page
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