3,150 research outputs found
Arithmetic-Progression-Weighted Subsequence Sums
Let be an abelian group, let be a sequence of terms
not all contained in a coset of a proper subgroup of
, and let be a sequence of consecutive integers. Let
which is a particular kind of weighted restricted sumset. We show that , that if , and also
characterize all sequences of length with . This
result then allows us to characterize when a linear equation
where are
given, has a solution modulo with all
distinct modulo . As a second simple corollary, we also show that there are
maximal length minimal zero-sum sequences over a rank 2 finite abelian group
(where and ) having
distinct terms, for any . Indeed, apart from
a few simple restrictions, any pattern of multiplicities is realizable for such
a maximal length minimal zero-sum sequence
Coulomb drag between one-dimensional conductors
We have analyzed Coulomb drag between currents of interacting electrons in
two parallel one-dimensional conductors of finite length attached to
external reservoirs. For strong coupling, the relative fluctuations of electron
density in the conductors acquire energy gap . At energies larger than
, where
is the impurity scattering rate, and for , where is the
fluctuation velocity, the gap leads to an ``ideal'' drag with almost equal
currents in the conductors. At low energies the drag is suppressed by coherent
instanton tunneling, and the zero-temperature transconductance vanishes,
indicating the Fermi liquid behavior.Comment: 5 twocolumn pages in RevTex, added 1 eps-Figure and calculation of
trans-resistanc
Strong-coupling branching of FQHL edges
We have developed a theory of quasiparticle backscattering in a system of
point contacts formed between single-mode edges of several Fractional Quantum
Hall Liquids (FQHLs) with in general different filling factors and one
common single-mode edge of another FQHL. In the strong-tunneling limit,
the model of quasiparticle backscattering is obtained by the duality
transformation of the electron tunneling model. The new physics introduced by
the multi-point-contact geometry of the system is coherent splitting of
backscattered quasiparticles at the point contacts in the course of propagation
along the common edge . The ``branching ratios'' characterizing the
splitting determine the charge and exchange statistics of the edge
quasiparticles that can be different from those of Laughlin's quasiparticles in
the bulk of FQHLs. Accounting for the edge statistics is essential for the
system of more than one point contact and requires the proper description of
the flux attachement to tunneling electrons.Comment: 12 pages, 2 figure
Fractional charge in transport through a 1D correlated insulator of finite length
Transport through a one channel wire of length confined between two leads
is examined when the 1D electron system has an energy gap : induced by the interaction in charge mode (: charge velocity in the
wire). In spinless case the transformation of the leads electrons into the
charge density wave solitons of fractional charge entails a non-trivial low
energy crossover from the Fermi liquid behavior below the crossover energy to the insulator one with the
fractional charge in current vs. voltage, conductance vs. temperature, and in
shot noise. Similar behavior is predicted for the Mott insulator of filling
factor .Comment: 5 twocolumn pages in RevTex, no figure
Quantum-Hall activation gaps in graphene
We have measured the quantum-Hall activation gaps in graphene at filling
factors and for magnetic fields up to 32 T and temperatures
from 4 K to 300 K. The gap can be described by thermal excitation to
broadened Landau levels with a width of 400 K. In contrast, the gap measured at
is strongly temperature and field dependent and approaches the expected
value for sharp Landau levels for fields T and temperatures
K. We explain this surprising behavior by a narrowing of the lowest Landau
level.Comment: 4 pages, 4 figures, updated version after review, accepted for PR
Scaling of the quantum-Hall plateau-plateau transition in graphene
The temperature dependence of the magneto-conductivity in graphene shows that
the widths of the longitudinal conductivity peaks, for the N=1 Landau level of
electrons and holes, display a power-law behavior following with a scaling exponent . Similarly the
maximum derivative of the quantum Hall plateau transitions
scales as with a scaling exponent
for both the first and second electron and hole Landau
level. These results confirm the universality of a critical scaling exponent.
In the zeroth Landau level, however, the width and derivative are essentially
temperature independent, which we explain by a temperature independent
intrinsic length that obscures the expected universal scaling behavior of the
zeroth Landau level
Threshold features in transport through a 1D constriction
Suppression of electron current through a 1D channel of length
connecting two Fermi liquid reservoirs is studied taking into account the
Umklapp electron-electron interaction induced by a periodic potential. This
interaction causes Hubbard gaps for . In the perturbative
regime where ( charge velocity), and for small deviations
of the electron density from its commensurate values
can diverge with some exponent as voltage or temperature decreases above
, while it goes to zero below . This results
in a nonmonotonous behavior of the conductance.Comment: Final variant published in PRL, 79, 1714; minor correction
Gap opening in the zeroth Landau level of graphene
We have measured a strong increase of the low-temperature resistivity
and a zero-value plateau in the Hall conductivity at
the charge neutrality point in graphene subjected to high magnetic fields up to
30 T. We explain our results by a simple model involving a field dependent
splitting of the lowest Landau level of the order of a few Kelvin, as extracted
from activated transport measurements. The model reproduces both the increase
in and the anomalous plateau in in terms of
coexisting electrons and holes in the same spin-split zero-energy Landau level.Comment: 4 pages, 3 figure
- …