3,700 research outputs found
Exact Multifractal Spectra for Arbitrary Laplacian Random Walks
Iterated conformal mappings are used to obtain exact multifractal spectra of
the harmonic measure for arbitrary Laplacian random walks in two dimensions.
Separate spectra are found to describe scaling of the growth measure in time,
of the measure near the growth tip, and of the measure away from the growth
tip. The spectra away from the tip coincide with those of conformally invariant
equilibrium systems with arbitrary central charge , with related
to the particular walk chosen, while the scaling in time and near the tip
cannot be obtained from the equilibrium properties.Comment: 4 pages, 3 figures; references added, minor correction
Community Detection as an Inference Problem
We express community detection as an inference problem of determining the
most likely arrangement of communities. We then apply belief propagation and
mean-field theory to this problem, and show that this leads to fast, accurate
algorithms for community detection.Comment: 4 pages, 2 figure
QED corrections to isospin-related decay rates of charged and neutral B mesons
We estimate the isospin-violating QED radiative corrections to the
charged-to-neutral ratios of the decay rates for B^+ and B^0 in non-leptonic B
meson decays. In particular, these corrections are potentially important for
precision measurement of the charged-to-neutral production ratio of B meson in
e^+e^- annihilation. We calculate explicitly the QED corrections to the ratios
of two different types of decay rates \Gamma(B^+ \to J/\psi K^+)/\Gamma(B^0 \to
J/\psi K^0) and \Gamma(B^+ \to D^+_S \bar{D^0})/\Gamma(B^0 \to D^+_S D^-)
taking into account the form factors of the mesons based on the vector meson
dominance model, and compare them with the results obtained for the point-like
mesons.Comment: 7 pages, 9 eps figure
Automorphic Equivalence within Gapped Phases of Quantum Lattice Systems
Gapped ground states of quantum spin systems have been referred to in the
physics literature as being `in the same phase' if there exists a family of
Hamiltonians H(s), with finite range interactions depending continuously on , such that for each , H(s) has a non-vanishing gap above its
ground state and with the two initial states being the ground states of H(0)
and H(1), respectively. In this work, we give precise conditions under which
any two gapped ground states of a given quantum spin system that 'belong to the
same phase' are automorphically equivalent and show that this equivalence can
be implemented as a flow generated by an -dependent interaction which decays
faster than any power law (in fact, almost exponentially). The flow is
constructed using Hastings' 'quasi-adiabatic evolution' technique, of which we
give a proof extended to infinite-dimensional Hilbert spaces. In addition, we
derive a general result about the locality properties of the effect of
perturbations of the dynamics for quantum systems with a quasi-local structure
and prove that the flow, which we call the {\em spectral flow}, connecting the
gapped ground states in the same phase, satisfies a Lieb-Robinson bound. As a
result, we obtain that, in the thermodynamic limit, the spectral flow converges
to a co-cycle of automorphisms of the algebra of quasi-local observables of the
infinite spin system. This proves that the ground state phase structure is
preserved along the curve of models .Comment: Updated acknowledgments and new email address of S
Uniformity of V minus Near Infrared Color Evolution of Type Ia Supernovae, and Implications for Host Galaxy Extinction Determination
From an analysis of SNe 1972E, 1980N, 1981B, 1981D, 1983R, 1998bu, 1999cl,
and 1999cp we find that the intrinsic V-K colors of Type Ia SNe with
multi-color light curve shape (MLCS) parameter -0.4 < Delta < +0.2 suggest a
uniform color curve. V-K colors become bluer linearly with time from roughly
one week before B-band maximum until one week after maximum, after which they
redden linearly until four weeks after maximum. V-H colors exhibit very similar
color evolution. V-J colors exhibit slightly more complex evolution, with
greater scatter. The existence of V minus near infrared color relations allows
the construction of near infrared light curve templates that are an improvement
on those of Elias et al. (1985).
We provide optical BVRI and infrared JHK photometry of the Type Ia supernovae
1999aa, 1999cl, and 1999cp. SN 1999aa is an overluminous "slow decliner" (with
Delta = -0.47 mag). SN 1999cp is a moderately bright SN unreddened in its host.
SN 1999cl is extremely reddened in its host. The V minus near infrared colors
of SN 1999cl yield A_V = 2.01 +/- 0.11 mag. This leads to a distance for its
host galaxy (M 88) in agreement with other distance measurements for members of
the Virgo cluster.Comment: 57 pages, 13 postscript figures, to appear in the August 20, 2000,
issue of the Astrophysical Journal. Contains updated references and a number
of minor corrections dealt with when page proofs were correcte
Physical consequences of PNP and the DMRG-annealing conjecture
Computational complexity theory contains a corpus of theorems and conjectures
regarding the time a Turing machine will need to solve certain types of
problems as a function of the input size. Nature {\em need not} be a Turing
machine and, thus, these theorems do not apply directly to it. But {\em
classical simulations} of physical processes are programs running on Turing
machines and, as such, are subject to them. In this work, computational
complexity theory is applied to classical simulations of systems performing an
adiabatic quantum computation (AQC), based on an annealed extension of the
density matrix renormalization group (DMRG). We conjecture that the
computational time required for those classical simulations is controlled
solely by the {\em maximal entanglement} found during the process. Thus, lower
bounds on the growth of entanglement with the system size can be provided. In
some cases, quantum phase transitions can be predicted to take place in certain
inhomogeneous systems. Concretely, physical conclusions are drawn from the
assumption that the complexity classes {\bf P} and {\bf NP} differ. As a
by-product, an alternative measure of entanglement is proposed which, via
Chebyshev's inequality, allows to establish strict bounds on the required
computational time.Comment: Accepted for publication in JSTA
Interference of Spontaneous Emission of Light from two Solid-State Atomic Ensembles
We report an interference experiment of spontaneous emission of light from
two distant solid-state ensembles of atoms that are coherently excited by a
short laser pulse. The ensembles are Erbium ions doped into two LiNbO3 crystals
with channel waveguides, which are placed in the two arms of a Mach-Zehnder
interferometer. The light that is spontaneously emitted after the excitation
pulse shows first-order interference. By a strong collective enhancement of the
emission, the atoms behave as ideal two-level quantum systems and no which-path
information is left in the atomic ensembles after emission of a photon. This
results in a high fringe visibility of 95%, which implies that the observed
spontaneous emission is highly coherent
- …