161 research outputs found
Hierarchical Structure of Azbel-Hofstader Problem: Strings and loose ends of Bethe Ansatz
We present numerical evidence that solutions of the Bethe Ansatz equations
for a Bloch particle in an incommensurate magnetic field (Azbel-Hofstadter or
AH model), consist of complexes-"strings". String solutions are well-known from
integrable field theories. They become asymptotically exact in the
thermodynamic limit. The string solutions for the AH model are exact in the
incommensurate limit, where the flux through the unit cell is an irrational
number in units of the elementary flux quantum.
We introduce the notion of the integral spectral flow and conjecture a
hierarchical tree for the problem. The hierarchical tree describes the topology
of the singular continuous spectrum of the problem. We show that the string
content of a state is determined uniquely by the rate of the spectral flow
(Hall conductance) along the tree. We identify the Hall conductances with the
set of Takahashi-Suzuki numbers (the set of dimensions of the irreducible
representations of with definite parity).
In this paper we consider the approximation of noninteracting strings. It
provides the gap distribution function, the mean scaling dimension for the
bandwidths and gives a very good approximation for some wave functions which
even captures their multifractal properties. However, it misses the
multifractal character of the spectrum.Comment: revtex, 30 pages, 6 Figs, 8 postscript files are enclosed, important
references are adde
Quantized bulk fermions in the Randall-Sundrum brane model
The lowest order quantum corrections to the effective action arising from
quantized massive fermion fields in the Randall-Sundrum background spacetime
are computed. The boundary conditions and their relation with gauge invariance
are examined in detail. The possibility of Wilson loop symmetry breaking in
brane models is also analysed. The self-consistency requirements, previously
considered in the case of a quantized bulk scalar field, are extended to
include the contribution from massive fermions. It is shown that in this case
it is possible to stabilize the radius of the extra dimensions but it is not
possible to simultaneously solve the hierarchy problem, unless the brane
tensions are dramatically fine tuned, supporting previous claims.Comment: 25 pages, 1 figure, RevTe
Complementarity of information sent via different bases
We discuss quantitatively the complementarity of information transmitted by a
quantum system prepared in a basis state in one out of several different
mutually unbiased bases (MUBs). We obtain upper bounds on the information
available to a receiver who has no knowledge of which MUB was chosen by the
sender. These upper bounds imply a complementarity of information encoded via
different MUBs and ultimately ensure the security in quantum key distribution
protocols.Comment: 9 pages, references adde
Theory of Two-Dimensional Quantum Heisenberg Antiferromagnets with a Nearly Critical Ground State
We present the general theory of clean, two-dimensional, quantum Heisenberg
antiferromagnets which are close to the zero-temperature quantum transition
between ground states with and without long-range N\'{e}el order. For
N\'{e}el-ordered states, `nearly-critical' means that the ground state
spin-stiffness, , satisfies , where is the
nearest-neighbor exchange constant, while `nearly-critical' quantum-disordered
ground states have a energy-gap, , towards excitations with spin-1,
which satisfies . Under these circumstances, we show that the
wavevector/frequency-dependent uniform and staggered spin susceptibilities, and
the specific heat, are completely universal functions of just three
thermodynamic parameters. Explicit results for the universal scaling functions
are obtained by a expansion on the quantum non-linear sigma model,
and by Monte Carlo simulations. These calculations lead to a variety of
testable predictions for neutron scattering, NMR, and magnetization
measurements. Our results are in good agreement with a number of numerical
simulations and experiments on undoped and lightly-doped .Comment: 81 pages, REVTEX 3.0, smaller updated version, YCTP-xxx
Search for charginos in e+e- interactions at sqrt(s) = 189 GeV
An update of the searches for charginos and gravitinos is presented, based on
a data sample corresponding to the 158 pb^{-1} recorded by the DELPHI detector
in 1998, at a centre-of-mass energy of 189 GeV. No evidence for a signal was
found. The lower mass limits are 4-5 GeV/c^2 higher than those obtained at a
centre-of-mass energy of 183 GeV. The (\mu,M_2) MSSM domain excluded by
combining the chargino searches with neutralino searches at the Z resonance
implies a limit on the mass of the lightest neutralino which, for a heavy
sneutrino, is constrained to be above 31.0 GeV/c^2 for tan(beta) \geq 1.Comment: 22 pages, 8 figure
Hadronization properties of b quarks compared to light quarks in e+e- -> q qbar from 183 to 200 GeV
The DELPHI detector at LEP has collected 54 pb^{-1} of data at a
centre-of-mass energy around 183 GeV during 1997, 158 pb^{-1} around 189 GeV
during 1998, and 187 pb^{-1} between 192 and 200 GeV during 1999. These data
were used to measure the average charged particle multiplicity in e+e- -> b
bbar events, _{bb}, and the difference delta_{bl} between _{bb} and the
multiplicity, _{ll}, in generic light quark (u,d,s) events: delta_{bl}(183
GeV) = 4.55 +/- 1.31 (stat) +/- 0.73 (syst) delta_{bl}(189 GeV) = 4.43 +/- 0.85
(stat) +/- 0.61 (syst) delta_{bl}(200 GeV) = 3.39 +/- 0.89 (stat) +/- 1.01
(syst). This result is consistent with QCD predictions, while it is
inconsistent with calculations assuming that the multiplicity accompanying the
decay of a heavy quark is independent of the mass of the quark itself.Comment: 13 pages, 2 figure
Measurement of the beam-helicity asymmetry in photoproduction of π0η pairs on carbon, aluminum, and lead
The beam-helicity asymmetry was measured, for the first time, in photoproduction of
π0η pairs on carbon, aluminum, and lead, with the A2 experimental setup at MAMI. The results are compared to an earlier measurement on a free proton and to the corresponding theoretical calculations. The Mainz model is used to predict the beam-helicity asymmetry for the nuclear targets. The present results indicate that the photoproduction mechanism for π0η pairs on nuclei is similar to photoproduction on a free nucleon. This process is dominated by the D33 partial wave with the ηΔ(1232) intermediate state
A muon-track reconstruction exploiting stochastic losses for large-scale Cherenkov detectors
IceCube is a cubic-kilometer Cherenkov telescope operating at the South Pole. The main goal of IceCube is the detection of astrophysical neutrinos and the identification of their sources. High-energy muon neutrinos are observed via the secondary muons produced in charge current interactions with nuclei in the ice. Currently, the best performing muon track directional reconstruction is based on a maximum likelihood method using the arrival time distribution of Cherenkov photons registered by the experiment\u27s photomultipliers. A known systematic shortcoming of the prevailing method is to assume a continuous energy loss along the muon track. However at energies >1 TeV the light yield from muons is dominated by stochastic showers. This paper discusses a generalized ansatz where the expected arrival time distribution is parametrized by a stochastic muon energy loss pattern. This more realistic parametrization of the loss profile leads to an improvement of the muon angular resolution of up to 20% for through-going tracks and up to a factor 2 for starting tracks over existing algorithms. Additionally, the procedure to estimate the directional reconstruction uncertainty has been improved to be more robust against numerical errors
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