100 research outputs found
Constant magnetic field and 2d non-commutative inverted oscillator
We consider a two-dimensional non-commutative inverted oscillator in the
presence of a constant magnetic field, coupled to the system in a
``symplectic'' and ``Poisson'' way. We show that it has a discrete energy
spectrum for some value of the magnetic field.Comment: 7 pages, LaTeX file, no figures, PACS number: 03.65.-
A Matrix Model for \nu_{k_1k_2}=\frac{k_1+k_2}{k_1 k_2} Fractional Quantum Hall States
We propose a matrix model to describe a class of fractional quantum Hall
(FQH) states for a system of (N_1+N_2) electrons with filling factor more
general than in the Laughlin case. Our model, which is developed for FQH states
with filling factor of the form \nu_{k_1k_2}=\frac{k_1+k_2}{k_1k_2} (k_1 and
k_2 odd integers), has a U(N_1)\times U(N_2) gauge invariance, assumes that FQH
fluids are composed of coupled branches of the Laughlin type, and uses ideas
borrowed from hierarchy scenarios. Interactions are carried, amongst others, by
fields in the bi-fundamentals of the gauge group. They simultaneously play the
role of a regulator, exactly as does the Polychronakos field. We build the
vacuum configurations for FQH states with filling factors given by the series
\nu_{p_1p_2}=\frac{p_2}{p_1p_2-1}, p_1 and p_2 integers. Electrons are
interpreted as a condensate of fractional D0-branes and the usual degeneracy of
the fundamental state is shown to be lifted by the non-commutative geometry
behaviour of the plane. The formalism is illustrated for the state at
\nu={2/5}.Comment: 40 pages, 1 figure, clarifications and references adde
A Quantum Hall Fluid of Vortices
In this note we demonstrate that vortices in a non-relativistic Chern-Simons
theory form a quantum Hall fluid. We show that the vortex dynamics is
controlled by the matrix mechanics previously proposed by Polychronakos as a
description of the quantum Hall droplet. As the number of vortices becomes
large, they fill the plane and a hydrodynamic treatment becomes possible,
resulting in the non-commutative theory of Susskind. Key to the story is the
recent D-brane realisation of vortices and their moduli spaces.Comment: 10 pages. v2(3): (More) References adde
Jain States in a Matrix Theory of the Quantum Hall Effect
The U(N) Maxwell-Chern-Simons matrix gauge theory is proposed as an extension
of Susskind's noncommutative approach. The theory describes D0-branes,
nonrelativistic particles with matrix coordinates and gauge symmetry, that
realize a matrix generalization of the quantum Hall effect. Matrix ground
states obtained by suitable projections of higher Landau levels are found to be
in one-to-one correspondence with the expected Laughlin and Jain hierarchical
states. The Jain composite-fermion construction follows by gauge invariance via
the Gauss law constraint. In the limit of commuting, ``normal'' matrices the
theory reduces to eigenvalue coordinates that describe realistic electrons with
Calogero interaction. The Maxwell-Chern-Simons matrix theory improves earlier
noncommutative approaches and could provide another effective theory of the
fractional Hall effect.Comment: 35 pages, 3 figure
About the self-dual Chern-Simons system and Toda field theories on the noncommutative plane
The relation of the noncommutative self-dual Chern-Simons (NCSDCS) system to
the noncommutative generalizations of Toda and of affine Toda field theories is
investigated more deeply. This paper continues the programme initiated in , where it was presented how it is possible to define Toda
field theories through second order differential equation systems starting from
the NCSDCS system. Here we show that using the connection of the NCSDCS to the
noncommutative chiral model, exact solutions of the Toda field theories can be
also constructed by means of the noncommutative extension of the uniton method
proposed in by Ki-Myeong Lee. Particularly some
specific solutions of the nc Liouville model are explicit constructed.Comment: 24 page
NC Effective Gauge Model for Multilayer FQH States
We develop an effective field model for describing FQH states with rational
filling factors that are not of Laughlin type. These kinds of systems, which
concern single layer hierarchical states and multilayer ones, were observed
experimentally; but have not yet a satisfactory non commutative effective field
description like in the case of Susskind model. Using brane analysis and
fiber bundle techniques, we first classify such states in terms of
representations characterized, amongst others, by the filling factor of the
layers; but also by proper subgroups of the underlying gauge symmetry.
Multilayer states in the lowest Landau level are interpreted in terms of
systems of branes; but hierarchical ones are realized as Fiber bundles on
which we construct explicitly. In this picture, Jain and Haldane series
are recovered as special cases and have a remarkable interpretation in terms of
Fiber bundles with specific intersection matrices. We also derive the general
NC commutative effective field and matrix models for FQH states, extending
Susskind theory, and give the general expression of the rational filling
factors as well as their non abelian gauge symmetries.Comment: 54 pages 11 figures, LaTe
Superconformal mechanics
We survey the salient features and problems of conformal and superconformal
mechanics and portray some of its developments over the past decade. Both
classical and quantum issues of single- and multiparticle systems are covered.Comment: 1+68 pages, invited review for Journal of Physics A; v2: revised text
extended by 4 pages and 11 references, published versio
Noncommutative Fluids
We review the connection between noncommutative gauge theory, matrix models
and fluid mechanical systems. The noncommutative Chern-Simons description of
the quantum Hall effect and bosonization of collective fermion states are used
as specific examples.Comment: To appear in "Seminaire Poincare X", Institut Henri Poincare, Paris;
references adde
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