Haut PDF Fixing the quantum three-point function

Fixing the quantum three-point function

Fixing the quantum three-point function

result is given by the inhomogeneous three-point vertex, after fixing the inhomogeneities. We find that the integrands match, which is already a strong evidence that the corre- spondence with the string theory persists at one loop. Moreover, we reveal through this comparison the reason for the asymmetric form of the gauge theory structure constant, while the string theory result is completely symmetric with respect to permutations of the three operators. To complete the result one should also compare the integration contours. This is a subtle issue which is still lacking complete understanding, both in the gauge and in the string theory. At the present stage the contours of integration are chosen case by case by taking into account the analytic properties of the solution.
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Conformal blocks for the four-point function in conformal quantum mechanics

Conformal blocks for the four-point function in conformal quantum mechanics

are not invariant [R vacuum jn ¼ 0i]. Nevertheless results obey the conformal constraints. For the two- and three-point functions an AdS 2 bulk dual can be identified [ 1 ]. We have not accomplished that for the four-point function. But the simplicity of the block structure—just one block is needed to reproduce the four- point function—gives the hope that a dual model in the AdS 2 bulk can be found. It is interesting to observe that the AdS 2 bulk propagator is given by a hypergeometric function, just as G 4 and its conformal block are.
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Clustering and the Three-Point Function

Clustering and the Three-Point Function

In this paper, we address one simple but intriguing example of such phenomena in the context of the AdS/CFT correspondence; namely the emergence of the classical string world- sheet from the three-point functions in the planar N = 4 super Yang-Mills theory (SYM). On the one hand, a non-perturbative framework to compute the three-point functions of N = 4 SYM, called the hexagon vertex, was put forward recently in [ 1 ]. It describes the three-point functions in terms of the dynamics of “magnons”, which are the elementary fields constituting the gauge-invariant operator. On the other hand, the AdS/CFT implies that the very same object in the strong coupling limit admits a totally different description in terms of the classical string worldsheet and that the three-point function is given by its area [ 2 – 5 ]. However, apart from some partial results given in [ 1 ], it is still not clear whether and how these two descriptions are consistent with each other.
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The VIMOS Public Extragalactic Redshift Survey (VIPERS). Exploring the dependence of the three-point correlation function on stellar mass and luminosity at $0.5 < z < 1.1$

The VIMOS Public Extragalactic Redshift Survey (VIPERS). Exploring the dependence of the three-point correlation function on stellar mass and luminosity at $0.5 < z < 1.1$

Acknowledgments We acknowledge the crucial contribution of the ESO staff for the management of service observations. In particular, we are deeply grateful to M. Hilker for his constant help and support of this programme. Italian participation in VIPERS has been funded by INAF through PRIN 2008 and 2010 programmes. LG and BRG acknowledge support of the European Research Council through the Darklight ERC Advanced Research Grant (# 291521). OLF acknowledges support of the European Research Council through the EARLY ERC Advanced Research Grant (# 268107). AP, KM, and JK have been supported by the National Science Centre (grants UMO-2012/07/B/ST9/04425 and UMO- 2013/09/D/ST9/04030), the Polish-Swiss Astro Project (co- financed by a grant from Switzerland, through the Swiss Contribution to the enlarged European Union). KM was sup- ported by the Strategic Young Researcher Overseas Visits Program for Accelerating Brain Circulation No. R2405. RT acknowledges financial support from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement n. 202686. MM, EB, FM, and LM acknowledge the support from grants ASI-INAF I/023/12/0 and PRIN MIUR 2010-2011. LM also ac- knowledges financial support from PRIN INAF 2012. Research conducted within the scope of the HECOLS International Associated Laboratory, supported in part by the Polish NCN grant DEC-2013/08/M/ST9/00664. We thank Hong Guo for kindly providing the data of their paper for comparison.
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Anomalous dimensions of monopole operators in three-dimensional quantum electrodynamics

Anomalous dimensions of monopole operators in three-dimensional quantum electrodynamics

The partition function on S 2 × R can be evaluated perturbatively in 1=Nf as follows. To leading order in N f one can ignore the fluctuations of the gauge field and perform a Gaussian integral over the fermionic fields. The results obtained by this procedure agree with those of Ref. [24]. The next order term in the large-N f expansion comes from performing a functional integral over the fluctuations of the gauge field. This integral is also Gaussian, because the higher-order terms in the effective action for the gauge field fluctuations are suppressed by positive powers of 1=Nf . The evaluation of this Gaussian integral is the main focus of this paper. Similar but significantly simpler computations were performed in Ref. [33], where the contribution to the S 2 ground-state energy coming from a scalar fluctuation was computed in a similar setup, and in Ref. [25], where an integral over gauge field fluctuations on S 3 was computed in the absence of any monopoles.
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Hexagonal lattices with three-point interactions

Hexagonal lattices with three-point interactions

is its deformed length. The ε 2 scaling factor is the right one to obtain a finite nonzero limit energy (without rescaling). Then there is a two-point, Lennard-Jones type contribution of the form R k ε (ϕ ε ) = ε 2 r (ε −1 |ϕ ε (b k )|), (3) where r : R + → ¯ R + is a Lennard-Jones type potential, i.e., a continuous function such that r (0) = +∞, r is decreasing on [0, 1], r(1) = 0, r is nondecreasing on [1, +∞[, and r(`) → c when ` → +∞ for some constant c ≥ 0. The sum of these two terms forms an energy for each bond that is minimum at the natural length ε. This energy is infinitely repulsive when the deformed length of a bond goes to 0 and tends to +∞ when the deformed length of a bond goes to +∞. While the former behavior is desirable from the atomistic modeling point of view, the latter one is more debatable, because interatomic forces should tend to 0 when the interatomic distance tends to +∞. It is mostly there for coercivity reasons. We refer to [4] for work in which such coercivity assumptions are not made.
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Point-spread function retrieval for fluorescence microscopy

Point-spread function retrieval for fluorescence microscopy

2.2. Proposed theoretical PSF model Before we formulate the model for the PSF, it is important to review the assumptions that will be used in the following section. We will primarily assume that the light used for illu- minating the specimen is either circularly polarized or phase randomized. Secondly, from the experiments conducted in the context of our current application, we conclude that vecto- rial diffraction models offer limited improvement in accuracy than scalar diffraction models (especially for CLSM). This is true even when the difference between the refractive indices of the objective lens and immersion medium is large; like in the case of imaging from air objective lens into specimen em- bedded in oil or glycerol [6]. We thus justify our usage of scalar models to calculate the PSF as they are computation- ally less expensive (one integral each for illumination and de- tection PSF) to calculate than the vectorial models (three in- tegrals for each of the illumination and detection PSF). The model used here is an extension of P. A. Stokseth’s [1] work on deriving the Optical Transfer Function (OTF) for a de- focused system from the corresponding pupil function. For a microscope with a circular aperture, it is straight forward to show the equivalence between Stokseth’s, and Gibson and Lanni’s scalar model (see [6]).
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Critical phenomena near the antiferromagnetic quantum critical point of heavy fermions

Critical phenomena near the antiferromagnetic quantum critical point of heavy fermions

共Received 18 January 2000; revised manuscript received 27 April 2000兲 We present a paper of the critical phenomena around the quantum critical point in heavy-fermion systems. In the framework of the S ⫽1/2 Kondo lattice model, we introduce an extended decoupling scheme of the Kondo interaction, which allows one to treat the spin fluctuations and the Kondo effect on an equal footing. The calculations, developed in a self-consistent one-loop approximation, lead to the formation of a damped collective mode with a dynamic exponent z ⫽2 in the case of an antiferromagnetic instability. The system displays a quantum-classical crossover at finite temperature depending on how the energy of the mode, on the scale of the magnetic correlation length, compares to k B T. The low-temperature behavior, in the different regimes separated by the crossover temperatures, is then discussed for both two- and three-dimensional systems.
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Thermal Enhancement of Interference Effects in Quantum Point Contacts

Thermal Enhancement of Interference Effects in Quantum Point Contacts

Adel Abbout, Gabriel Lemari´e, and Jean-Louis Pichard Service de Physique de l’ ´ Etat Condens´e (CNRS URA 2464), IRAMIS/SPEC, CEA Saclay, 91191 Gif-sur-Yvette, France We study an electron interferometer formed with a quantum point contact and a scanning probe tip in a two-dimensional electron gas. The images giving the conductance as a function of the tip position exhibit fringes spaced by half the Fermi wavelength. For a contact opened at the edges of a quantized conductance plateau, the fringes are enhanced as the temperature T increases and can persist beyond the thermal length l T . This unusual effect is explained assuming a simplified
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A three-parameter magnitude phase function for asteroids

A three-parameter magnitude phase function for asteroids

ACCEPTED MANUSCRIPT the function values at the fixed angles and, occasionally, the first derivatives of the functions at the ends of the entire angular interpolation range as the free parameters (or unknowns). As a result, the number of free parameters is large but manageable. The optimization method includes ingredients from simulated annealing methods (e.g., Press et al. 1992; also compare to MCMC or Markov-Chain Monte-Carlo methods, Gilks et al. 1996). The optimization of the basis-function values proceeds from a chosen starting point via a Monte Carlo method that proposes random moves based on Gaussian proposal prob- ability densities, but gives rise to a move only if the proposed new point in the parameter space results in improved fits to all the observational data. The data are grouped according to differing phase-curve shapes to allow for wide applicability of the new basis functions. In optimizing the basis functions, the data are properly weighted by the asteroid groups and number of members within each group.
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Eulerian triangulations: two-point function and hull perimeter statistics

Eulerian triangulations: two-point function and hull perimeter statistics

choices are more natural than others and, in particular, lead to some Y k with a direct combinatorial interpretation. As a natural extension of our result, we note that an expression for the slice generating function of planar Eulerian triangulations was given in [8] which incorporates more parame- ters by assigning different weights to the vertices of each (gray, black or white) color. Again this expression is the result of some educated guess and no constructive derivation was provided. It is easy to incorporate such color-dependent vertex weights in our approach. This then leads to three copies of the generating functions Φ and Ω, determined by three independent closed systems, each depending on the three vertex weights at hand. Unfortu- nately, although there is no fundamental obstacle in using our method to solve these systems, expressions become rather involved and we were not able to recover the expression of [8].
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POINT-SPREAD FUNCTION MODEL FOR FLUORESCENCE MACROSCOPY IMAGING

POINT-SPREAD FUNCTION MODEL FOR FLUORESCENCE MACROSCOPY IMAGING

In this paper, we model the point-spread function (PSF) of a fluo- rescence MACROscope with a field aberration. The MACROscope is an imaging arrangement that is designed to directly study small and large specimen preparations without physically sectioning them. However, due to the different optical components of the MACRO- scope, it cannot achieve the condition of lateral spatial invariance for all magnifications. For example, under low zoom settings, this field aberration becomes prominent, the PSF varies in the lateral field, and is proportional to the distance from the center of the field. On the other hand, for larger zooms, these aberrations become gradually ab- sent. A computational approach to correct this aberration often relies on an accurate knowledge of the PSF. The PSF can be defined either theoretically using a scalar diffraction model or empirically by ac- quiring a three-dimensional image of a fluorescent bead that approx- imates a point source. The experimental PSF is difficult to obtain and can change with slight deviations from the physical conditions. In this paper, we model the PSF using the scalar diffraction approach, and the pupil function is modeled by chopping it. By comparing our modeled PSF with an experimentally obtained PSF, we validate our hypothesis that the spatial variance is caused by two limiting optical apertures brought together on different conjugate planes.
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Breakdown of the integer and fractional quantum Hall states in a quantum point contact

Breakdown of the integer and fractional quantum Hall states in a quantum point contact

We measure I c as a function of magnetic field within each plateau and of gate voltage at fixed magnetic field. In each case we sweep I dc between ±100 nA, alternating directions, while stepping B or VG after each sweep. For each value of B or V G we calculate |I c | as described above; the spread in |I c | at each point is predominantly the result of hysteresis in the I dc sweep direction. We observe two different types of hysteresis, each of which seems to occur inconsistently. One is similar to that observed in previous experiments, 6,14,21 illustrated in Fig. 4(a). This type of hysteresis may be explained by the electron heating model of breakdown; 22 however, as discussed below, the electron heating model cannot explain our results in the fractional quantum Hall regime. We also observe a strange type of hysteresis illustrated in Fig. 4(b). In some cases, both types of hysteresis occur simultaneously. For all measurements, the I dc sweep rate is 0.7 nA/s. We have tested the dependence on sweep rate at filling factors 2 and 5, sweeping I dc with fixed B and V G , and find no significant differences for slower sweep rates down to ~1 × 10 -3 nA/s.
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Nonconvex optimization for 3D point source localization using a rotating point spread function

Nonconvex optimization for 3D point source localization using a rotating point spread function

for the Poisson noise model assumed here. In order to verify this, we study the case of low photon number in this subsection. In Figure 13 , we see the observed image with three different photon numbers per source, namely 500, 1000, and 2000. For the case of 500 photons per source, the image is very dim, and we can barely distinguish the rotating PSF signal from the background noise, so we do not consider this case any further. For the case of 1000 photons being emitted by each point source, the corresponding image follows a Poisson distribution with a mean of 1000 photons. We take each image to contain 15 point sources. As before, we first randomly generated 20 images, which were used for training parameters. Then we tested 50 different observed images by using the trained parameter values. We got 90.53% for the recall rate and 78.32% for the precision rate in the KL-NC algorithm, but only 81.33% and 64.24%, respectively, for the two rates in the ` 2 -NC algorithm. For evaluation of the flux
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Estimating the galaxy two-point correlation function using a split random catalog

Estimating the galaxy two-point correlation function using a split random catalog

number of pairs with these small separations is much smaller, the computation time is not a similar issue as for large separations. The results of our analysis will have an impact also on the computationally more demanding task of covariance matrix esti- mation. However, since in that case the exact computational cost is determined by the balance of data catalogs and random cata- logs, which does not need to be the same as for the individual two-point correlation estimate, we postpone a quantitative anal- ysis to a future, dedicated study. The same kind of methods can be applied to higher-order statistics (three-point and four-point correlation functions) to speed up their estimation ( Slepian & Eisenstein 2015 ).
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Dynamic spin-correlation function near the antiferromagnetic quantum phase transition of heavy fermions

Dynamic spin-correlation function near the antiferromagnetic quantum phase transition of heavy fermions

In this paper, we develop a systematic approach to the Kondo-lattice model for S 51/2(N52) in which the Kondo- like and the spin degrees of freedom are treated on an equal footing. The presented approach shows some similarities with earlier works. 11,15 But while Refs. 11 and 15 essentially describe the phase diagram of the Kondo lattice at a mean- field level, we focus on the effects of spin fluctuations in the magnetically disordered phase hence bringing the spin- fluctuation and the Kondo-effect theories together. The saddle-point results and the Gaussian fluctuations in the charge channel are consistent with the standard 1/N theories. In addition, the Gaussian fluctuations in the spin channel restore the spin-fluctuation effects that were missing in the 1/N expansion. The general expression of the dynamical spin susceptibility that we derive reproduces some of the features postulated in the phenomenological models. It presents a two-component behavior: a quasielastic component superim- posed on an inelastic peak with renormalized values of the relaxation rates, susceptibilities and v max . In a very striking
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Stable reduction of three point covers

Stable reduction of three point covers

Let X be a smooth projective curve over C. A celebrated theorem of Belyi states that X can be defined over a number field K if and only if there exists a rational function f on X with exactly three critical values, see [3], [13]. If such a function f exists, we can normalize it in such a way that the critical values are 0, 1 and ∞. After this normalization, we may view f as a finite cover f : X → P 1 which is ´ etale over P 1 − {0, 1, ∞}. We call f a three point cover. Another common name for f is Belyi map. The monodromy group of f is defined as the Galois group of the Galois closure of f .
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Kaplow, Louis: Competition Policy and Price Fixing

Kaplow, Louis: Competition Policy and Price Fixing

All this shows that there is a gap between the economic and legal approaches to collusion. The economic approach highlights nor communication nor agreement to analyze the collusion. It is dynamic and strategic interdependence induces actors to seek a non-cooperative equilibrium in their favor. The legal approach is more ambiguous. Seeking traces of an agreement or exchange to prove the existence of collusion, it is cantilevered. On the one hand, this research is unnecessary and wrong in situations where there exist favorable conditions for collusion. On the other hand, this search for a favorable non-cooperative equilibrium can be made very difficult in situations where the conditions that favor collusion are not present. In the absence of hard evidence, it can be very difficult to prove that a given behavior can be explained only by a concerted practice. For example, after the Second World War, the two major producers ICI and Solvay of a variety of soda for the glass had shared the international market according to an explicit agreement (known as Page 1000 assigning continental Europe to Solvay and UK to ICI). At the request of the European Commission in 1972, this agreement was broken. Nevertheless, the market allocation between these two producers remained unchanged. Despite the fact that ICI provided in part from Solvay, the Belgian company has always refused to become an operator on the UK market, despite the price increases that could incite it. The Commission saw in the maintaining of the market’s distribution an evidence of the persistence of an implicit functioning of the Agreement Page 1000, even though every company justified its behavior by the fear of competitor’s retaliation if it were to enter the market. It is necessary to keep in mind that if Article 101 of the Treaty prohibits any form of collusion that hinders competition, it does not remove to economic agents the right to adapt themselves intelligently to the existing and anticipated conduct of their rivals (see Encaoua and Guesnerie, 2006, p. 70).
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The Structural Dynamics of Engineered beta-Lactamases Vary Broadly on Three Timescales yet Sustain Native Function

The Structural Dynamics of Engineered beta-Lactamases Vary Broadly on Three Timescales yet Sustain Native Function

ard deviation suggests motions occurring on a slower timescale. Those slower motions were confirmed and char- acterized (Figs S1 and S2). S 2 in those regions generally could not be characterized by NMR due to overlapping/ broad peaks, further demonstrating the value of the simulations. Dynamics on the intermediate (ns- µs) timescale. To investigate the intermediate timescale of motions, we extracted the Cα root mean square fluctuation (RMSF) from the molecular dynamics simulations (Fig. S2 and Table S6). As observed for fast motions, the core of each β-lactamase was rigid, while the surface loops were more flexible (Fig.  3 ). TEM-1 and the chimeras showed significantly more ns-µs dynamic residues than PSE-4, in agreement with the higher sequence similarity of the chimeras to TEM-1. The substitution of up to 19 amino acids in TEM-1 did not markedly alter ns-µs dynamics.
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Ubiquity of quantum zero point fluctuations in dislocations glide

Ubiquity of quantum zero point fluctuations in dislocations glide

I. INTRODUCTION The implication of quantum mechanics in plasticity of crys- tals has long been a matter of theoretical investigations. The main efforts were concentrated on accounting for interactions between phonons and dislocations [ 1 – 3 ] because they are the key physical ingredients in the process of conversion of plastic work into heat during deformation [ 4 , 5 ] as well as in the process of thermal activation of dislocation glide [ 1 , 6 ]. Modern simulation tools [ 7 , 8 ] have allowed us recently to sup- plement the theory and shed new light on the low-temperature deformation tests. Employing atomic scale simulations based on the embedded atom method (EAM) [ 9 , 10 ] it was found that along the dislocation glide the zero-point energy (ZPE), which in the harmonic approximation is merely the sum of phonon frequencies times half ¯h, varies with an amplitude of same order as the dislocation Peierls barrier but with an opposite sign. The variation of the ZPE was found to yield a significant Peierls stress reduction for the screw dislocation in body-centered-cubic (bcc) Fe [ 7 ]. This result showed how quantum fluctuations could be involved in the plasticity of certain metals even though they are constituted of atoms with some relatively heavy masses in comparison with conventional quantum crystals [ 11 ] as solid He or H 2 . A recent experimental
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