2,677 research outputs found
Adiabatic Cooling with Non-Abelian Anyons
We show in this Letter that the ground state degeneracy associated with the
presence of non-Abelian anyons can be probed by using an adiabatic cooling
process based on the non-Abelian entropy. In particular, we show that when the
number of such anyons is increased adiabatically at sufficiently low
temperatures, the non-Abelian liquid undergoes cooling, whereas heating occurs
in the Abelian case. Estimates are provided for the cooling power produced by
the non-Abelian anyon refrigerator, and its implementation in non-Abelian
fractional quantum Hall liquids is discussed
The Quantum Group Structure of 2D Gravity and Minimal Models II: The Genus-Zero Chiral Bootstrap
The F and B matrices associated with Virasoro null vectors are derived in
closed form by making use of the operator-approach suggested by the Liouville
theory, where the quantum-group symmetry is explicit. It is found that the
entries of the fusing and braiding matrices are not simply equal to
quantum-group symbols, but involve additional coupling constants whose
derivation is one aim of the present work. Our explicit formulae are new, to
our knowledge, in spite of the numerous studies of this problem. The
relationship between the quantum-group-invariant (of IRF type) and
quantum-group-covariant (of vertex type) chiral operator-algebras is fully
clarified, and connected with the transition to the shadow world for
quantum-group symbols. The corresponding 3-j-symbol dressing is shown to reduce
to the simpler transformation of Babelon and one of the author (J.-L. G.) in a
suitable infinite limit defined by analytic continuation. The above two types
of operators are found to coincide when applied to states with Liouville
momenta going to in a suitable way. The introduction of
quantum-group-covariant operators in the three dimensional picture gives a
generalisation of the quantum-group version of discrete three-dimensional
gravity that includes tetrahedra associated with 3-j symbols and universal
R-matrix elements. Altogether the present work gives the concrete realization
of Moore and Seiberg's scheme that describes the chiral operator-algebra of
two-dimensional gravity and minimal models.Comment: 56 pages, 22 figures. Technical problem only, due to the use of an
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Operator Coproduct-Realization of Quantum Group Transformations in Two Dimensional Gravity, I.
A simple connection between the universal matrix of (for
spins \demi and ) and the required form of the co-product action of the
Hilbert space generators of the quantum group symmetry is put forward. This
gives an explicit operator realization of the co-product action on the
covariant operators. It allows us to derive the quantum group covariance of the
fusion and braiding matrices, although it is of a new type: the generators
depend upon worldsheet variables, and obey a new central extension of
realized by (what we call) fixed point commutation relations. This
is explained by showing that the link between the algebra of field
transformations and that of the co-product generators is much weaker than
previously thought. The central charges of our extended algebra,
which includes the Liouville zero-mode momentum in a nontrivial way are related
to Virasoro-descendants of unity. We also show how our approach can be used to
derive the Hopf algebra structure of the extended quantum-group symmetry
U_q(sl(2))\odot U_{\qhat}(sl(2)) related to the presence of both of the
screening charges of 2D gravity.Comment: 33 pages, latex, no figure
Quantum Group Structure and Local Fields in the Algebraic Approach to 2D Gravity
This review contains a summary of work by J.-L. Gervais and the author on the
operator approach to 2d gravity. Special emphasis is placed on the construction
of local observables -the Liouville exponentials and the Liouville field itself
- and the underlying algebra of chiral vertex operators. The double quantum
group structure arising from the presence of two screening charges is discussed
and the generalized algebra and field operators are derived. In the last part,
we show that our construction gives rise to a natural definition of a quantum
tau function, which is a noncommutative version of the classical
group-theoretic representation of the Liouville fields by Leznov and Saveliev.Comment: 38 pages, LaTex file. Proceedings of the Vth International Conference
on Mathematical Physics, Strings and Quantum gravity, Alushta, Ukraine 199
Resistively Detected NMR in Quantum Hall States: Investigation of the anomalous lineshape near
A study of the resistively detected nuclear magnetic resonance (RDNMR)
lineshape in the vicinity of was performed on a high-mobility 2D
electron gas formed in GaAs/AlGaAs. In higher Landau levels, application of an
RF field at the nuclear magnetic resonance frequency coincides with an observed
minimum in the longitudinal resistance, as predicted by the simple hyperfine
interaction picture. Near however, an anomalous dispersive lineshape is
observed where a resistance peak follows the usual minimum. In an effort to
understand the origin of this anomalous peak we have studied the resonance
under various RF and sample conditions. Interestingly, we show that the
lineshape can be completely inverted by simply applying a DC current. We
interpret this as evidence that the minima and maxima in the lineshape
originate from two distinct mechanisms.Comment: 5 pages, 3 figures, EP2DS 17, to be published in Physica
Strong-Coupling Effects in "Dirty" Superfluid
The contribution of the strong-coupling effects to the free energy of the
"dirty" superfluid is estimated using a simple model. It is shown that
the strong-coupling effects are less susceptible to the quasiparticle
scattering events in comparison to the weak-coupling counterpart. This supports
the conclusion about stabilization of the -phase in aerogel environment at
pressures where the -phase takes over in bulk superfluid , in
accordance with recent experimental observations in zero magnetic field.Comment: 10 pages, LaTeX file. This is a revised version of the paper with
some additional comments and references, and corrected typos. Submitted to
Journal of Physics: Condensed Matte
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