13,294 research outputs found
Charge and Statistics of Quantum Hall Quasi-Particles. A numerical study of mean values and fluctuations
We present Monte Carlo studies of charge expectation values and charge
fluctuations for quasi-particles in the quantum Hall system. We have studied
the Laughlin wave functions for quasi-hole and quasi-electron, and also Jain's
definition of the quasi-electron wave function. The considered systems consist
of from 50 to 200 electrons, and the filling fraction is 1/3. For all
quasi-particles our calculations reproduce well the expected values of charge;
-1/3 times the electron charge for the quasi-hole, and 1/3 for the
quasi-electron. Regarding fluctuations in the charge, our results for the
quasi-hole and Jain quasi-electron are consistent with the expected value zero
in the bulk of the system, but for the Laughlin quasi-electron we find small,
but significant, deviations from zero throughout the whole electron droplet. We
also present Berry phase calculations of charge and statistics parameter for
the Jain quasi-electron, calculations which supplement earlier studies for the
Laughlin quasi-particles. We find that the statistics parameter is more well
behaved for the Jain quasi-electron than it is for the Laughlin quasi-electron.Comment: 39 pages, 27 figure
Hyperbolic Unfoldings of Minimal Hypersurfaces
We study the intrinsic geometry of area minimizing (and also of almost
minimizing) hypersurfaces from a new point of view by relating this subject to
quasiconformal geometry. For any such hypersurface we define and construct a
so-called S-structure which reveals some unexpected geometric and analytic
properties of the hypersurface and its singularity set. In this paper, this is
used to prove the existence of hyperbolic unfoldings: canonical conformal
deformations of the regular part of these hypersurfaces into complete Gromov
hyperbolic spaces of bounded geometry with Gromov boundary homeomorphic to the
singular set
Universal microstructure and mechanical stability of jammed packings
Jammed packings' mechanical properties depend sensitively on their detailed
local structure. Here we provide a complete characterization of the pair
correlation close to contact and of the force distribution of jammed
frictionless spheres. In particular we discover a set of new scaling relations
that connect the behavior of particles bearing small forces and those bearing
no force but that are almost in contact. By performing systematic
investigations for spatial dimensions d=3-10, in a wide density range and using
different preparation protocols, we show that these scalings are indeed
universal. We therefore establish clear milestones for the emergence of a
complete microscopic theory of jamming. This description is also crucial for
high-precision force experiments in granular systems.Comment: 11 pages, 7 figure
Bifurcation sets arising from non-integer base expansions
Given a positive integer and , let be the set
of having a unique -expansion: there exists a unique
sequence with each such that
Denote by the set of corresponding sequences of all points in
.
It is well-known that the function is a Devil's
staircase, where denotes the topological entropy of . In this paper we {give several characterizations of} the bifurcation set
Note that is contained in the set of bases
such that . By using a transversality technique
we also calculate the Hausdorff dimension of the difference . Interestingly this quantity is always strictly
between and . When the Hausdorff dimension of is ,
where is the unique root in of the equation
.Comment: 28 pages, 1 figures and 1 table. To appear in J. Fractal Geometr
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