42,282 research outputs found
Charge Fractionalization on Quantum Hall Edges
We discuss the propagation and fractionalization of localized charges on the
edges of quantum Hall bars of variable widths, where interactions between the
edges give rise to Luttinger liquid behavior with a non-trivial interaction
parameter g. We focus in particular on the separation of an initial charge
pulse into a sharply defined front charge and a broader tail. The front pulse
describes an adiabatically dressed electron which carries a non-integer charge,
which is \sqrt{g} times the electron charge. We discuss how the presence of
this fractional charge can, in principle, be detected through measurements of
the noise in the current created by tunneling of electrons into the system. The
results are illustrated by numerical simulations of a simplified model of the
Hall bar.Comment: 15 page
Log-correlated Gaussian fields: an overview
We survey the properties of the log-correlated Gaussian field (LGF), which is
a centered Gaussian random distribution (generalized function) on , defined up to a global additive constant. Its law is determined by the
covariance formula
which holds for mean-zero test functions . The LGF belongs to
the larger family of fractional Gaussian fields obtained by applying fractional
powers of the Laplacian to a white noise on . It takes the
form . By comparison, the Gaussian free field (GFF)
takes the form in any dimension. The LGFs with coincide with the 2D GFF and its restriction to a line. These objects
arise in the study of conformal field theory and SLE, random surfaces, random
matrices, Liouville quantum gravity, and (when ) finance. Higher
dimensional LGFs appear in models of turbulence and early-universe cosmology.
LGFs are closely related to cascade models and Gaussian branching random walks.
We review LGF approximation schemes, restriction properties, Markov properties,
conformal symmetries, and multiplicative chaos applications.Comment: 24 pages, 2 figure
Truncated Levy statistics for transport in disordered semiconductors
Probabilistic interpretation of transition from the dispersive transport
regime to the quasi-Gaussian one in disordered semiconductors is given in terms
of truncated Levy distributions. Corresponding transport equations with
fractional order derivatives are derived. We discuss physical causes leading to
truncated waiting time distributions in the process and describe influence of
truncation on carrier packet form, transient current curves and frequency
dependence of conductivity. Theoretical results are in a good agreement with
experimental facts.Comment: 6 pages, 4 figures, presented in "Nonlinear Science and Complexity -
2010" (Turkey, Ankara
SU(2) and SU(1,1) Approaches to Phase Operators and Temporally Stable Phase States: Applications to Mutually Unbiased Bases and Discrete Fourier Transforms
We propose a group-theoretical approach to the generalized oscillator algebra
Ak recently investigated in J. Phys. A: Math. Theor. 43 (2010) 115303. The case
k > or 0 corresponds to the noncompact group SU(1,1) (as for the harmonic
oscillator and the Poeschl-Teller systems) while the case k < 0 is described by
the compact group SU(2) (as for the Morse system). We construct the phase
operators and the corresponding temporally stable phase eigenstates for Ak in
this group-theoretical context. The SU(2) case is exploited for deriving
families of mutually unbiased bases used in quantum information. Along this
vein, we examine some characteristics of a quadratic discrete Fourier transform
in connection with generalized quadratic Gauss sums and generalized Hadamard
matrices
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