74,072 research outputs found
One-loop diagrams in the Random Euclidean Matching Problem
The matching problem is a notorious combinatorial optimization problem that
has attracted for many years the attention of the statistical physics
community. Here we analyze the Euclidean version of the problem, i.e. the
optimal matching problem between points randomly distributed on a
-dimensional Euclidean space, where the cost to minimize depends on the
points' pairwise distances. Using Mayer's cluster expansion we write a formal
expression for the replicated action that is suitable for a saddle point
computation. We give the diagrammatic rules for each term of the expansion, and
we analyze in detail the one-loop diagrams. A characteristic feature of the
theory, when diagrams are perturbatively computed around the mean field part of
the action, is the vanishing of the mass at zero momentum. In the non-Euclidean
case of uncorrelated costs instead, we predict and numerically verify an
anomalous scaling for the sub-sub-leading correction to the asymptotic average
cost.Comment: 17 pages, 7 figure
Entanglement and chaos in warped conformal field theories
Various aspects of warped conformal field theories (WCFTs) are studied
including entanglement entropy on excited states, the Renyi entropy after a
local quench, and out-of-time-order four-point functions. Assuming a large
central charge and dominance of the vacuum block in the conformal block
expansion, (i) we calculate the single-interval entanglement entropy on an
excited state, matching previous finite temperature results by changing the
ensemble; and (ii) we show that WCFTs are maximally chaotic, a result that is
compatible with the existence of black holes in the holographic duals. Finally,
we relax the aforementioned assumptions and study the time evolution of the
Renyi entropy after a local quench. We find that the change in the Renyi
entropy is topological, vanishing at early and late times, and nonvanishing in
between only for charged states in spectrally-flowed WCFTs.Comment: 31 pages; v2: corrected typos, matches published versio
Critical Ising Model in Varying Dimension by Conformal Bootstrap
The single-correlator conformal bootstrap is solved numerically for several
values of dimension 4>d>2 using the available SDPB and Extremal Functional
methods. Critical exponents and other conformal data of low-lying states are
obtained over the entire range of dimensions with up to four-decimal precision
and then compared with several existing results. The conformal dimensions of
leading-twist fields are also determined up to high spin, and their
d-dependence shows how the conformal states rearrange themselves around d=2.2
for matching the Virasoro conformal blocks in the d=2 limit. The decoupling of
states at the Ising point is studied for 3>d>2 and the vanishing of one
structure constant at d=3 is found to persist till d=2 where it corresponds to
a Virasoro null-vector condition.Comment: 43 pages, 15 figures, 7 tables, numerical data and Mathematica files
are available upon request; v2: epsilon-expansion data adde
Finite-size effects on multibody neutrino exchange
The effect of multibody massless neutrino exchanges between neutrons inside a
finite-size neutron star is studied. We use an effective Lagrangian, which
incorporates the effect of the neutrons on the neutrinos. Following Schwinger,
it is shown that the total interaction energy density is computed by comparing
the zero point energy of the neutrino sea with and without the star. It has
already been shown that in an infinite-size star the total energy due to
neutrino exchange vanishes exactly. The opposite claim that massless neutrino
exchange would produce a huge energy is due to an improper summation of an
infrared-divergent quantity. The same vanishing of the total energy has been
proved exactly in the case of a finite star in a one-dimensional toy model.
Here we study the three-dimensional case. We first consider the effect of a
sharp star border, assumed to be a plane. We find that there is a non-
vanishing of the zero point energy density difference between the inside and
the outside due to the refraction index at the border and the consequent
non-penetrating waves. An analytical and numerical calculation for the case of
a spherical star with a sharp border confirms that the preceding border effect
is the dominant one. The total result is shown to be infrared-safe, thus
confirming that there is no need to assume a neutrino mass. The ultraviolet
cut-offs, which correspond in some sense to the matching of the effective
theory with the exact one, are discussed. Finally the energy due to long
distance neutrino exchange is of the order of , i.e. negligible with respect to the neutron mass density.Comment: Latex file (Revtex), 34 pages, 8 postscripted figure
Hydrogen-like Spectrum of Spontaneously Created Brane Universes with deSitter Ground State
Unification of Randall-Sundrum and Regge-Teitelboim brane cosmologies gives
birth to a serendipitous Higgs-deSitter interplay. A localized
Dvali-Gabadadze-Porrati scalar field, governed by a particular (analytically
derived) double-well quartic potential, becomes a mandatory ingredient for
supporting a deSitter brane universe. When upgraded to a general Higgs
potential, the brane surface tension gets quantized, resembling a Hydrogen atom
spectrum, with deSitter universe serving as the ground state. This reflects the
local/global structure of the Euclidean manifold: From finite energy density
no-boundary initial conditions, via a novel acceleration divide filter, to
exact matching conditions at the exclusive nucleation point. Imaginary time
periodicity comes as a bonus, with the associated Hawking temperature vanishing
at the continuum limit. Upon spontaneous creation, while a finite number of
levels describe universes dominated by a residual dark energy combined with
damped matter oscillations, an infinite tower of excited levels undergo a Big
Crunch.Comment: 5 PRL style pages, 4 figure
Ultracold Bosons with 3-Body Attractive Interactions in an Optical Lattice
We study the effect of an optical lattice (OL) on the ground-state properties
of one-dimensional ultracold bosons with three-body attraction and two-body
repulsion, which are described by a cubic-quintic Gross-Pitaevskii equation
with a periodic potential. Without the OL and with a vanishing two-body
interaction term, soliton solutions of the Townes type are possible only at a
critical value of the three-body interaction strength, at which an infinite
degeneracy of the ground-state occurs; a repulsive two-body interaction makes
such localized solutions unstable. We show that the OL opens a stability window
around the critical point when the strength of the periodic potential is above
a critical threshold. We also consider the effect of an external parabolic
trap, studying how the stability of the solitons depends on matching between
minima of the periodic potential and the minimum of the parabolic trap.Comment: Special issue of European Physical Journal B on the conference
"Theory of Quantum Gases and Quantum Coherence" held in Grenoble, 200
Homological mirror symmetry for toric orbifolds of toric del Pezzo surfaces
We formulate a conjecture which describes the Fukaya category of an exact
Lefschetz fibration defined by a Laurent polynomial in two variables in terms
of a pair consisting of a consistent dimer model and a perfect matching on it.
We prove this conjecture in some cases, and obtain homological mirror symmetry
for quotient stacks of toric del Pezzo surfaces by finite subgroups of the
torus as a corollary.Comment: 23 pages, 40 figures; v2:completely rewritten; v3:Incorporated
suggestions by the refere
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