6,000 research outputs found
Rotating black hole orbit functionals in the frequency domain
In many astrophysical problems, it is important to understand the behavior of
functions that come from rotating (Kerr) black hole orbits. It can be
particularly useful to work with the frequency domain representation of those
functions, in order to bring out their harmonic dependence upon the fundamental
orbital frequencies of Kerr black holes. Although, as has recently been shown
by W. Schmidt, such a frequency domain representation must exist, the coupled
nature of a black hole orbit's and motions makes it difficult to
construct such a representation in practice. Combining Schmidt's description
with a clever choice of timelike coordinate suggested by Y. Mino, we have
developed a simple procedure that sidesteps this difficulty. One first Fourier
expands all quantities using Mino's time coordinate . In particular,
the observer's time is decomposed with . The frequency domain
description is then built from the -Fourier expansion and the
expansion of . We have found this procedure to be quite simple to implement,
and to be applicable to a wide class of functionals. We test the procedure
using a simple test function, and then apply it in a particularly interesting
case, the Weyl curvature scalar used in black hole perturbation
theory.Comment: 16 pages, 2 figures. Submitted to Phys Rev D. New version gives a
vastly improved algorithm due to Drasco for computing the Fourier transforms.
Drasco has been added as an author. Also fixed some references and
exterminated a small herd of typos; final published versio
Minimal excitation states for heat transport in driven quantum Hall systems
We investigate minimal excitation states for heat transport into a fractional
quantum Hall system driven out of equilibrium by means of time-periodic voltage
pulses. A quantum point contact allows for tunneling of fractional
quasi-particles between opposite edge states, thus acting as a beam splitter in
the framework of the electron quantum optics. Excitations are then studied
through heat and mixed noise generated by the random partitioning at the
barrier. It is shown that levitons, the single-particle excitations of a filled
Fermi sea recently observed in experiments, represent the cleanest states for
heat transport, since excess heat and mixed shot noise both vanish only when
Lorentzian voltage pulses carrying integer electric charge are applied to the
conductor. This happens in the integer quantum Hall regime and for Laughlin
fractional states as well, with no influence of fractional physics on the
conditions for clean energy pulses. In addition, we demonstrate the robustness
of such excitations to the overlap of Lorentzian wavepackets. Even though mixed
and heat noise have nonlinear dependence on the voltage bias, and despite the
non-integer power-law behavior arising from the fractional quantum Hall
physics, an arbitrary superposition of levitons always generates minimal
excitation states.Comment: 15 pages, 7 figure
Interference, Coulomb blockade, and the identification of non-abelian quantum Hall states
We examine the relation between different electronic transport phenomena in a
Fabry-Perot interferometer in the fractional quantum Hall regime. In
particular, we study the way these phenomena reflect the statistics of quantum
Hall quasi-particles. For two series of states we examine, one abelian and one
non-abelian, we show that the information that may be obtained from
measurements of the lowest order interference pattern in an open Fabry-Perot
interferometer is identical to the one that may be obtained from the
temperature dependence of Coulomb blockade peaks in a closed interferometer. We
argue that despite the similarity between the experimental signatures of the
two series of states, interference and Coulomb blockade measurements are likely
to be able to distinguish between abelian and non-abelian states, due to the
sensitivity of the abelian states to local perturbations, to which the
non-abelian states are insensitive.Comment: 10 pages. Published versio
Chiral topological spin liquids with projected entangled pair states
Topological chiral phases are ubiquitous in the physics of the Fractional
Quantum Hall Effect. Non-chiral topological spin liquids are also well known.
Here, using the framework of projected entangled pair states (PEPS), we
construct a family of chiral spin liquids on the square lattice which are
generalized spin-1/2 Resonating Valence Bond (RVB) states obtained from
deformed local tensors with symmetry. On a cylinder, we construct
four topological sectors with even or odd number of spinons on the boundary and
even or odd number of () fluxes penetrating the cylinder which,
we argue, remain orthogonal in the limit of infinite perimeter. The analysis of
the transfer matrix provides evidence of short-range (long-range) triplet
(singlet) correlations as for the critical (non-chiral) RVB state. The
Entanglement Spectrum exhibits chiral edge modes, which we confront to
predictions of Conformal Field Theory, and the corresponding Entanglement
Hamiltonian is shown to be long ranged.Comment: 7 pages, 6 figures, Final version (small changes
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