30,667 research outputs found
String breaking and lines of constant physics in the SU(2) Higgs model
We present results for the ground state and first excited state static
potentials in the confinement "phase" of the SU(2) Higgs model. String breaking
and the crossing of the energy levels are clearly visible. We address the
question of the cut-off effects in our results and observe a remarkable scaling
of the static potentials.Comment: LATTICE99(Higgs), 3 pages, 4 figure
Conformal Bootstrap in the Regge Limit
We analytically solve the conformal bootstrap equations in the Regge limit
for large N conformal field theories. For theories with a parametrically large
gap, the amplitude is dominated by spin-2 exchanges and we show how the
crossing equations naturally lead to the construction of AdS exchange Witten
diagrams. We also show how this is encoded in the anomalous dimensions of
double-trace operators of large spin and large twist. We use the chaos bound to
prove that the anomalous dimensions are negative. Extending these results to
correlators containing two scalars and two conserved currents, we show how to
reproduce the CEMZ constraint that the three-point function between two
currents and one stress tensor only contains the structure given by
Einstein-Maxwell theory in AdS, up to small corrections. Finally, we consider
the case where operators of unbounded spin contribute to the Regge amplitude,
whose net effect is captured by summing the leading Regge trajectory. We
compute the resulting anomalous dimensions and corrections to OPE coefficients
in the crossed channel and use the chaos bound to show that both are negative.Comment: 40 pages, 1 figure; V2: Small corrections and clarification
Approximate Two-Party Privacy-Preserving String Matching with Linear Complexity
Consider two parties who want to compare their strings, e.g., genomes, but do
not want to reveal them to each other. We present a system for
privacy-preserving matching of strings, which differs from existing systems by
providing a deterministic approximation instead of an exact distance. It is
efficient (linear complexity), non-interactive and does not involve a third
party which makes it particularly suitable for cloud computing. We extend our
protocol, such that it mitigates iterated differential attacks proposed by
Goodrich. Further an implementation of the system is evaluated and compared
against current privacy-preserving string matching algorithms.Comment: 6 pages, 4 figure
The streaming -mismatch problem
We consider the streaming complexity of a fundamental task in approximate
pattern matching: the -mismatch problem. It asks to compute Hamming
distances between a pattern of length and all length- substrings of a
text for which the Hamming distance does not exceed a given threshold . In
our problem formulation, we report not only the Hamming distance but also, on
demand, the full \emph{mismatch information}, that is the list of mismatched
pairs of symbols and their indices. The twin challenges of streaming pattern
matching derive from the need both to achieve small working space and also to
guarantee that every arriving input symbol is processed quickly.
We present a streaming algorithm for the -mismatch problem which uses
bits of space and spends \ourcomplexity time on
each symbol of the input stream, which consists of the pattern followed by the
text. The running time almost matches the classic offline solution and the
space usage is within a logarithmic factor of optimal.
Our new algorithm therefore effectively resolves and also extends an open
problem first posed in FOCS'09. En route to this solution, we also give a
deterministic -bit encoding of all
the alignments with Hamming distance at most of a length- pattern within
a text of length . This secondary result provides an optimal solution to
a natural communication complexity problem which may be of independent
interest.Comment: 27 page
String Matching and 1d Lattice Gases
We calculate the probability distributions for the number of occurrences
of a given letter word in a random string of letters. Analytical
expressions for the distribution are known for the asymptotic regimes (i) (Gaussian) and such that is finite
(Compound Poisson). However, it is known that these distributions do now work
well in the intermediate regime . We show that the
problem of calculating the string matching probability can be cast into a
determining the configurational partition function of a 1d lattice gas with
interacting particles so that the matching probability becomes the
grand-partition sum of the lattice gas, with the number of particles
corresponding to the number of matches. We perform a virial expansion of the
effective equation of state and obtain the probability distribution. Our result
reproduces the behavior of the distribution in all regimes. We are also able to
show analytically how the limiting distributions arise. Our analysis builds on
the fact that the effective interactions between the particles consist of a
relatively strong core of size , the word length, followed by a weak,
exponentially decaying tail. We find that the asymptotic regimes correspond to
the case where the tail of the interactions can be neglected, while in the
intermediate regime they need to be kept in the analysis. Our results are
readily generalized to the case where the random strings are generated by more
complicated stochastic processes such as a non-uniform letter probability
distribution or Markov chains. We show that in these cases the tails of the
effective interactions can be made even more dominant rendering thus the
asymptotic approximations less accurate in such a regime.Comment: 44 pages and 8 figures. Major revision of previous version. The
lattice gas analogy has been worked out in full, including virial expansion
and equation of state. This constitutes the main part of the paper now.
Connections with existing work is made and references should be up to date
now. To be submitted for publicatio
Seeds of large-scale anisotropy in string cosmology
Pre-big bang cosmology predicts tiny first-order dilaton and metric
perturbations at very large scales. Here we discuss the possibility that other
-- more copiously generated -- perturbations may act, at second order, as
scalar seeds of large-scale structure and CMB anisotropies. We study, in
particular, the cases of electromagnetic and axionic seeds. We compute the
stochastic fluctuations of their energy-momentum tensor and determine the
resulting contributions to the multipole expansion of the temperature
anisotropy. In the axion case it is possible to obtain a flat or slightly
tilted blue spectrum that fits present data consistently, both for massless and
for massive (but very light) axions.Comment: 27 pages, LATEX, one figure included using eps
String patterns in the doped Hubbard model
Understanding strongly correlated quantum many-body states is one of the most
difficult challenges in modern physics. For example, there remain fundamental
open questions on the phase diagram of the Hubbard model, which describes
strongly correlated electrons in solids. In this work we realize the Hubbard
Hamiltonian and search for specific patterns within the individual images of
many realizations of strongly correlated ultracold fermions in an optical
lattice. Upon doping a cold-atom antiferromagnet we find consistency with
geometric strings, entities that may explain the relationship between hole
motion and spin order, in both pattern-based and conventional observables. Our
results demonstrate the potential for pattern recognition to provide key
insights into cold-atom quantum many-body systems.Comment: 8+28 pages, 5+10 figure
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