100 research outputs found
Antidot tunneling between Quantum Hall liquids with different filling factors
We consider tunneling through two point contacts between two edges of Quantum
Hall liquids of different filling factors with
. Properties of the antidot formed between the point
contacts in the strong-tunneling limit are shown to be very different from the
case, and include vanishing average total current in the two
contacts and quasiparticles of charge . For , quasiparticle tunneling
leads to non-trivial -state dynamics of effective flux through the antidot
which restores the regular ``electron'' periodicity of the current in flux
despite the fractional charge and statistics of quasiparticles.Comment: 5 two-column pages, 2 figure
DRILL 3.1
Distance learning can offer a solution to a long-standing challenge of undergraduate education: how to assign an appropriate amount of work to each student, and how to assess this work efficiently. In this paper I describe the Depository of Repetitive Internet-based probLems and Lessons (DRILL), an online system for providing education and assessment for precalculus, which can substitute for routine problems given in homework and as exam questions. Its special features include: adaptive testing, on-the-fly question generation, instant assessment, context-sensitive help, question balancing, and two-dimensional test design
Mach-Zehnder interferometer in the Fractional Quantum Hall regime
We consider tunneling between two edges of Quantum Hall liquids (QHL) of
filling factors , with , through
two point contacts forming Mach-Zehnder interferometer. Quasi-particle
description of the interferometer is derived explicitly through the instanton
duality transformation of the initial electron model. For , tunneling of quasiparticles of charge leads to non-trivial
-state dynamics of effective flux through the interferometer, which restores
the regular ``electron'' periodicity of the current in flux. The exact solution
available for equal propagation times between the contacts along the two edges
demonstrates that the interference pattern in the tunneling current depends on
voltage and temperature only through a common amplitude.Comment: five two-column pages in RevTex4, 1 eps figur
Mimeomatroids
A mimeomatroid is a matroid union of a matroid with itself. We develop several properties of mimeomatroids, including a generalization of Rado\u27s theorem, and prove a weakened version of a matroid conjecture by Rota[2]
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
Geometry of Jump Systems
A jump system is a set of lattice points satisfying a certain two-step axiom. We present a variety of results concerning the geometry of these objects, including a characterization of two-dimensional jump systems, necessary (though not sufficient) properties of higher-dimensional jump systems, and a characterization of constant-sum jump systems
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