5,984 research outputs found
Quantum Hall Effect and Noncommutative Geometry
We study magnetic Schrodinger operators with random or almost periodic
electric potentials on the hyperbolic plane, motivated by the quantum Hall
effect in which the hyperbolic geometry provides an effective Hamiltonian. In
addition we add some refinements to earlier results. We derive an analogue of
the Connes-Kubo formula for the Hall conductance via the quantum adiabatic
theorem, identifying it as a geometric invariant associated to an algebra of
observables that turns out to be a crossed product algebra. We modify the
Fredholm modules defined in [CHMM] in order to prove the integrality of the
Hall conductance in this case.Comment: 18 pages, paper rewritte
Quantum Hall Effect on the Hyperbolic Plane in the presence of disorder
We study both the continuous model and the discrete model of the integer
quantum Hall effect on the hyperbolic plane in the presence of disorder,
extending the results of an earlier paper [CHMM]. Here we model impurities,
that is we consider the effect of a random or almost periodic potential as
opposed to just periodic potentials. The Hall conductance is identified as a
geometric invariant associated to an algebra of observables, which has plateaus
at gaps in extended states of the Hamiltonian. We use the Fredholm modules
defined in [CHMM] to prove the integrality of the Hall conductance in this
case. We also prove that there are always only a finite number of gaps in
extended states of any random discrete Hamiltonian. [CHMM] A. Carey, K.
Hannabuss, V. Mathai and P. McCann, Quantum Hall Effect on the Hyperbolic
Plane, Communications in Mathematical Physics, 190 vol. 3, (1998) 629-673.Comment: LaTeX2e, 17 page
Quantum Hall Effect on the Hyperbolic Plane
In this paper, we study both the continuous model and the discrete model of
the Quantum Hall Effect (QHE) on the hyperbolic plane. The Hall conductivity is
identified as a geometric invariant associated to an imprimitivity algebra of
observables. We define a twisted analogue of the Kasparov map, which enables us
to use the pairing between -theory and cyclic cohomology theory, to identify
this geometric invariant with a topological index, thereby proving the
integrality of the Hall conductivity in this case.Comment: AMS-LaTeX, 28 page
Twisted K-theory and K-theory of bundle gerbes
In this note we introduce the notion of bundle gerbe K-theory and investigate
the relation to twisted K-theory. We provide some examples. Possible
applications of bundle gerbe K-theory to the classification of D-brane charges
in non-trivial backgrounds are discussed.Comment: 29 pages, corrected typos, added references, included new section on
twisted Chern character in non-torsion cas
The Kinematics of HH 34 from HST Images with a Nine-year Time Baseline
We study archival HST [S II] 6716+30 and Hα images of the HH 34 outflow, taken in 1998.71 and in 2007.83. The ~9 yr time baseline and the high angular resolution of these observations allow us to carry out a detailed proper-motion study. We determine the proper motions of the substructure of the HH 34S bow shock (from the [S II] and Hα frames) and of the aligned knots within ~30'' from the outflow source (only from the [S II] frames). We find that the present-day motions of the knots along the HH 34 jet are approximately ballistic, and that these motions directly imply the formation of a major mass concentration in ~900 yr, at a position similar to the one of the present-day HH 34S bow shock. In other words, we find that the knots along the HH 34 jet will merge to form a more massive structure, possibly resembling HH 34S
Riding a Spiral Wave: Numerical Simulation of Spiral Waves in a Co-Moving Frame of Reference
We describe an approach to numerical simulation of spiral waves dynamics of
large spatial extent, using small computational grids.Comment: 15 pages, 14 figures, as accepted by Phys Rev E 2010/03/2
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