1,643 research outputs found
Inversion of Toeplitz operators, Levinson equations, and Gohberg-Krein factorization—A simple and unified approach for the rational case
AbstractThe problem of the inversion of the Toeplitz operator TΦ, associated with the operator-valued function Φ defined on the unit circle, is known to involve the associated Levinson system of equations and the Gohberg-Krein factorization of Φ. A simplified and self-contained approach, making clear the connections between these three problems, is presented in the case where Φ is matrix-valued and rational. The key idea consists in looking at the Levinson system of equations associated with Φ−1(z−1), rather than that associated with Φ(z). As a consequence, a new invertibility criterion for Toeplitz operators with rational matrix-valued symbols is derived
An electronic Mach-Zehnder interferometer in the Fractional Quantum Hall effect
We compute the interference pattern of a Mach-Zehnder interferometer
operating in the fractional quantum Hall effect. Our theoretical proposal is
inspired by a remarkable experiment on edge states in the Integer Quantum Hall
effect (IQHE). The Luttinger liquid model is solved via two independent
methods: refermionization at nu=1/2 and the Bethe Ansatz solution available for
Laughlin fractions. The current differs strongly from that of single electrons
in the strong backscattering regime. The Fano factor is periodic in the flux,
and it exhibits a sharp transition from sub-Poissonian (charge e/2) to
Poissonian (charge e) in the neighborhood of destructive interferences
Euclidean versus hyperbolic congestion in idealized versus experimental networks
This paper proposes a mathematical justification of the phenomenon of extreme
congestion at a very limited number of nodes in very large networks. It is
argued that this phenomenon occurs as a combination of the negative curvature
property of the network together with minimum length routing. More
specifically, it is shown that, in a large n-dimensional hyperbolic ball B of
radius R viewed as a roughly similar model of a Gromov hyperbolic network, the
proportion of traffic paths transiting through a small ball near the center is
independent of the radius R whereas, in a Euclidean ball, the same proportion
scales as 1/R^{n-1}. This discrepancy persists for the traffic load, which at
the center of the hyperbolic ball scales as the square of the volume, whereas
the same traffic load scales as the volume to the power (n+1)/n in the
Euclidean ball. This provides a theoretical justification of the experimental
exponent discrepancy observed by Narayan and Saniee between traffic loads in
Gromov-hyperbolic networks from the Rocketfuel data base and synthetic
Euclidean lattice networks. It is further conjectured that for networks that do
not enjoy the obvious symmetry of hyperbolic and Euclidean balls, the point of
maximum traffic is near the center of mass of the network.Comment: 23 pages, 4 figure
Quantum phase transition of dynamical resistance in a mesoscopic capacitor
We study theoretically dynamic response of a mesoscopic capacitor, which
consists of a quantum dot connected to an electron reservoir via a point
contact and capacitively coupled to a gate voltage. A quantum Hall edge state
with a filling factor nu is realized in a strong magnetic field applied
perpendicular to the two-dimensional electron gas. We discuss a noise-driven
quantum phase transition of the transport property of the edge state by taking
into account an ohmic bath connected to the gate voltage. Without the noise,
the charge relaxation for nu>1/2 is universally quantized at R_q=h/(2e^2),
while for nu<1/2, the system undergoes the Kosterlitz-Thouless transtion, which
drastically changes the nature of the dynamical resistance. The phase
transition is facilitated by the noisy gate voltage, and we see that it can
occur even for an integer quantum Hall edge at nu=1. When the dissipation by
the noise is sufficiently small, the quantized value of R_q is shifted by the
bath impedance.Comment: 5 pages, 2 figures, proceeding of the 19th International Conference
on the Application of High Magnetic Fields in Semiconductor Physics and
Nanotechnology (HMF-19
Robustness of energy landscape control for spin networks under decoherence
Quantum spin networks form a generic system to describe a range of quantum
devices for quantum information processing and sensing applications.
Understanding how to control them is essential to achieve devices with
practical functionalities. Energy landscape shaping is a novel control paradigm
to achieve selective transfer of excitations in a spin network with
surprisingly strong robustness towards uncertainties in the Hamiltonians. Here
we study the effect of decoherence, specifically generic pure dephasing, on the
robustness of these controllers. Results indicate that while the effectiveness
of the controllers is reduced by decoherence, certain controllers remain
sufficiently effective, indicating potential to find highly effective
controllers without exact knowledge of the decoherence processes.Comment: 6 pages, 6 figure
The Large Scale Curvature of Networks
Understanding key structural properties of large scale networks are crucial
for analyzing and optimizing their performance, and improving their reliability
and security. Here we show that these networks possess a previously unnoticed
feature, global curvature, which we argue has a major impact on core
congestion: the load at the core of a network with N nodes scales as N^2 as
compared to N^1.5 for a flat network. We substantiate this claim through
analysis of a collection of real data networks across the globe as measured and
documented by previous researchers.Comment: 4 pages, 5 figure
Observation of coherent backscattering of light by cold atoms
Coherent backscattering (CBS) of light waves by a random medium is a
signature of interference effects in multiple scattering. This effect has been
studied in many systems ranging from white paint to biological tissues.
Recently, we have observed CBS from a sample of laser-cooled atoms, a
scattering medium with interesting new properties. In this paper we discuss
various effects, which have to be taken into account for a quantitative study
of coherent backscattering of light by cold atoms.Comment: 25 pages LaTex2e, 17 figures, submitted to J. Opt. B: Quant. Semicl.
Op
Nearest-neighbor distribution for singular billiards
The exact computation of the nearest-neighbor spacing distribution P(s) is
performed for a rectangular billiard with point-like scatterer inside for
periodic and Dirichlet boundary conditions and it is demonstrated that for
large s this function decreases exponentially. Together with the results of
[Bogomolny et al., Phys. Rev. E 63, 036206 (2001)] it proves that spectral
statistics of such systems is of intermediate type characterized by level
repulsion at small distances and exponential fall-off of the nearest-neighbor
distribution at large distances. The calculation of the n-th nearest-neighbor
spacing distribution and its asymptotics is performed as well for any boundary
conditions.Comment: 38 pages, 10 figure
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