819 research outputs found
Two-Sided Derivatives for Regular Expressions and for Hairpin Expressions
The aim of this paper is to design the polynomial construction of a finite
recognizer for hairpin completions of regular languages. This is achieved by
considering completions as new expression operators and by applying derivation
techniques to the associated extended expressions called hairpin expressions.
More precisely, we extend partial derivation of regular expressions to
two-sided partial derivation of hairpin expressions and we show how to deduce a
recognizer for a hairpin expression from its two-sided derived term automaton,
providing an alternative proof of the fact that hairpin completions of regular
languages are linear context-free.Comment: 28 page
Heavy Quark Thermalization in Classical Lattice Gauge Theory: Lessons for Strongly-Coupled QCD
Thermalization of a heavy quark near rest is controlled by the correlator of
two electric fields along a temporal Wilson line. We address this correlator
within real-time, classical lattice Yang-Mills theory, and elaborate on the
analogies that exist with the dynamics of hot QCD. In the weak-coupling limit,
it can be shown analytically that the dynamics on the two sides are closely
related to each other. For intermediate couplings, we carry out
non-perturbative simulations within the classical theory, showing that the
leading term in the weak-coupling expansion significantly underestimates the
heavy quark thermalization rate. Our analytic and numerical results also yield
a general understanding concerning the overall shape of the spectral function
corresponding to the electric field correlator, which may be helpful in
subsequent efforts to reconstruct it from Euclidean lattice Monte Carlo
simulations.Comment: 22 pages. v2: a reference and clarifications added; published versio
Hard thermal loops and the entropy of supersymmetric Yang-Mills theories
We apply the previously proposed scheme of approximately self-consistent
hard-thermal-loop resummations in the entropy of high-temperature QCD to N=4
supersymmetric Yang-Mills (SYM) theories and compare with a (uniquely
determined) R[4,4] Pad\'e approximant that interpolates accurately between the
known perturbative result and the next-to-leading order strong-coupling result
obtained from AdS/CFT correspondence. We find good agreement up to couplings
where the entropy has dropped to about 85% of the Stefan-Boltzmann value. This
is precisely the regime which in purely gluonic QCD corresponds to temperatures
above 2.5 times the deconfinement temperature and for which this method of
hard-thermal-loop resummation has given similar good agreement with lattice QCD
results. This suggests that in this regime the entropy of both QCD and N=4 SYM
is dominated by effectively weakly coupled hard-thermal-loop quasiparticle
degrees of freedom. In N=4 SYM, strong-coupling contributions to the
thermodynamic potential take over when the entropy drops below 85% of the
Stefan-Boltzmann value.Comment: 14 pages, 2 figures, JHEP3. v2: revised and expanded, with unchanged
HTL results but corrected NLO strong-coupling result from AdS/CFT (which is
incorrectly reproduced in almost all previous papers comparing weak and
strong coupling results of N=4 SYM) and novel (unique) Pade approximant
interpolating between weak and strong coupling result
Quantum-fluctuation-induced repelling interaction of quantum string between walls
Quantum string, which was brought into discussion recently as a model for the
stripe phase in doped cuprates, is simulated by means of the
density-matrix-renormalization-group method. String collides with adjacent
neighbors, as it wonders, owing to quantum zero-point fluctuations. The energy
cost due to the collisions is our main concern. Embedding a quantum string
between rigid walls with separation d, we found that for sufficiently large d,
collision-induced energy cost obeys the formula \sim exp (- A d^alpha) with
alpha=0.808(1), and string's mean fluctuation width grows logarithmically \sim
log d. Those results are not understood in terms of conventional picture that
the string is `disordered,' and only the short-wave-length fluctuations
contribute to collisions. Rather, our results support a recent proposal that
owing to collisions, short-wave-length fluctuations are suppressed, but
instead, long-wave-length fluctuations become significant. This mechanism would
be responsible for stabilizing the stripe phase
Detecting a stochastic background of gravitational radiation: Signal processing strategies and sensitivities
We analyze the signal processing required for the optimal detection of a
stochastic background of gravitational radiation using laser interferometric
detectors. Starting with basic assumptions about the statistical properties of
a stochastic gravity-wave background, we derive expressions for the optimal
filter function and signal-to-noise ratio for the cross-correlation of the
outputs of two gravity-wave detectors. Sensitivity levels required for
detection are then calculated. Issues related to: (i) calculating the
signal-to-noise ratio for arbitrarily large stochastic backgrounds, (ii)
performing the data analysis in the presence of nonstationary detector noise,
(iii) combining data from multiple detector pairs to increase the sensitivity
of a stochastic background search, (iv) correlating the outputs of 4 or more
detectors, and (v) allowing for the possibility of correlated noise in the
outputs of two detectors are discussed. We briefly describe a computer
simulation which mimics the generation and detection of a simulated stochastic
gravity-wave signal in the presence of simulated detector noise. Numerous
graphs and tables of numerical data for the five major interferometers
(LIGO-WA, LIGO-LA, VIRGO, GEO-600, and TAMA-300) are also given. The treatment
given in this paper should be accessible to both theorists involved in data
analysis and experimentalists involved in detector design and data acquisition.Comment: 81 pages, 30 postscript figures, REVTE
Thermodynamics of AdS/QCD
We study finite temperature properties of four dimensional QCD-like gauge
theories in the gauge theory/gravity duality picture. The gravity dual contains
two deformed 5d AdS metrics, with and without a black hole, and a dilaton. We
study the thermodynamics of the 4d boundary theory and constrain the two
metrics so that they correspond to a high and a low temperature phase separated
by a first order phase transition. The equation of state has the standard form
for the pressure of a strongly coupled fluid modified by a vacuum energy, a bag
constant. We determine the parameters of the deformation by using QCD results
for and the hadron spectrum. With these parameters, we show that the
phase transition in the 4d boundary theory and the 5d bulk Hawking-Page
transition agree. We probe the dynamics of the two phases by computing the
quark-antiquark free energy in them and confirm that the transition corresponds
to confinement-deconfinement transition.Comment: 1+19 pages, 6 figures, references added, section 3 improve
Baryonic Response of Dense Holographic QCD
The response function of a homogeneous and dense hadronic system to a
time-dependent (baryon) vector potential is discussed for holographic dense QCD
(D4/D8 embedding) both in the confined and deconfined phases. Confined
holographic QCD is an uncompressible and static baryonic insulator at large N_c
and large \lambda, with a gapped vector spectrum and a massless pion.
Deconfined holographic QCD is a diffusive conductor with restored chiral
symmetry and a gapped transverse baryonic current. Similarly, dense D3/D7 is
diffusive for any non-zero temperature at large N_c and large \lambda. At zero
temperature dense D3/D7 exhibits a baryonic longitudinal visco-elastic mode
with a first sound speed \lambda/\sqrt{3} and a small width due to a shear
viscosity to baryon ratio \eta/n_B=\hbar/4. This mode is turned diffusive by
arbitrarily small temperatures, a hallmark of holography.Comment: V2: 47 pages, 7 figures, references added, typos correcte
Deep inelastic scattering off a N=4 SYM plasma at strong coupling
By using the AdS/CFT correspondence we study the deep inelastic scattering of
an R-current off a N=4 supersymmetric Yang-Mills (SYM) plasma at finite
temperature and strong coupling. Within the supergravity approximation valid
when the number of colors is large, we compute the structure functions by
solving Maxwell equations in the space-time geometry of the AdS_5 black
three-brane. We find a rather sharp transition between a low energy regime
where the scattering is weak and quasi-elastic, and a high-energy regime where
the current is completely absorbed. The critical energy for this transition
determines the plasma saturation momentum in terms of its temperature T and the
Bjorken x variable: Q_s=T/x. These results suggest a partonic picture for the
plasma where all the partons have transverse momenta below the saturation
momentum and occupation numbers of order one.Comment: Version accepted for publication in JHEP: more references added; some
technical points were displaced from Sect. 4 to the new Appendix
Quantum-fluctuation-induced collisions and subsequent excitation gap of an elastic string between walls
An elastic string embedded between rigid walls is simulated by means of the
density-matrix renormalization group. The string collides against the walls
owing to the quantum-mechanical zero-point fluctuations. Such ``quantum
entropic'' interaction has come under thorough theoretical investigation in the
context of the stripe phase observed experimentally in doped cuprates. We found
that the excitation gap opens in the form of exponential singularity DeltaE ~
exp(-Ad^sigma) (d: wall spacing) with the exponent sigma =0.6(3), which is
substantially smaller than the meanfield value sigma=2. That is, the excitation
gap is much larger than that anticipated from meanfield, suggesting that the
string is subjected to robust pinning potential due to the quantum collisions.
This feature supports Zaanen's ``order out of disorder'' mechanism which would
be responsible to the stabilization of the stripe phase
- …