3,904 research outputs found
Hyperbolic Supersymmetric Quantum Hall Effect
Developing a non-compact version of the SUSY Hopf map, we formulate the
quantum Hall effect on a super-hyperboloid. Based on group
theoretical methods, we first analyze the one-particle Landau problem, and
successively explore the many-body problem where Laughlin wavefunction,
hard-core pseudo-potential Hamiltonian and topological excitations are derived.
It is also shown that the fuzzy super-hyperboloid emerges in the lowest Landau
level.Comment: 14 pages, two columns, no figures, published version, typos correcte
Unification of Laughlin and Moore-Read States in SUSY Quantum Hall Effect
Based on the recently proposed SUSY quantum Hall effect, we show that
Laughlin and Moore-Read states are related by a hidden SUSY transformation.
Regarding the SUSY Laughlin wavefunction as a master wavefunction, Laughlin and
Moore-Read states appear as two extreme limits of component wavefunctions.
Realizations of topological excitations on Laughlin and Moore-Read states are
also discussed in the SUSY formalism. We develop a streographically projected
formulation of the SUSY quantum Hall effect. With appropriate interpretation of
Grassmann odd coordinates, we illustrate striking analogies between SUSY
quantum Hall effect and superfluidity.Comment: 5 pages, 1 figure, typos fixe
Quantum Hall Liquid on a Noncommutative Superplane
Supersymmetric quantum Hall liquids are constructed on a noncommutative
superplane.
We explore a supersymmetric formalism of the Landau problem. In the lowest
Landau level, there appear spin-less bosonic states and spin-1/2 down fermionic
states, which exhibit a super-chiral property. It is shown the Laughlin
wavefunction and topological excitations have their superpartners. Similarities
between supersymmetric quantum Hall systems and bilayer quantum Hall systems
are discussed.Comment: 11 pages, 3 figures, 1 table, minor corrections, published in
Phys.Rev.
Non-Commutative Geometry in Higher Dimensional Quantum Hall Effect as A-Class Topological Insulator
We clarify relations between the higher dimensional quantum Hall effect and
A-class topological insulator. In particular, we elucidate physical
implications of the higher dimensional non-commutative geometry in the context
of A-class topological insulator. This presentation is based on
arXiv:1403.5066.Comment: 5 pages, 1 table; contribution to the proceedings of the Workshop on
Noncommutative Field Theory and Gravity, Corfu, Greece, September 8-15, 2013,
Fortschritte der Physik 201
Analytic continuations of Fourier and Stieltjes transforms and generalized moments of probability measures
We consider analytic continuations of Fourier transforms and Stieltjes
transforms. This enables us to define what we call complex moments for some
class of probability measures which do not have moments in the usual sense.
There are two ways to generalize moments accordingly to Fourier and Stieltjes
transforms; however these two turn out to coincide. As applications, we give
short proofs of the convergence of probability measures to Cauchy distributions
with respect to tensor, free, Boolean and monotone convolutions.Comment: 13 pages; to appear in Journal of Theoretical Probabilit
Hopf Maps, Lowest Landau Level, and Fuzzy Spheres
This paper is a review of monopoles, lowest Landau level, fuzzy spheres, and
their mutual relations. The Hopf maps of division algebras provide a prototype
relation between monopoles and fuzzy spheres. Generalization of complex numbers
to Clifford algebra is exactly analogous to generalization of fuzzy two-spheres
to higher dimensional fuzzy spheres. Higher dimensional fuzzy spheres have an
interesting hierarchical structure made of "compounds" of lower dimensional
spheres. We give a physical interpretation for such particular structure of
fuzzy spheres by utilizing Landau models in generic even dimensions. With
Grassmann algebra, we also introduce a graded version of the Hopf map, and
discuss its relation to fuzzy supersphere in context of supersymmetric Landau
model.Comment: v2: note and references added; v3: references adde
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