Single-valued hyperlogarithms, correlation functions and closed string amplitudes

Previous research has revealed the uniqueness-facilitation effect in the multiple object tracking (MOT) task: simple distinct identities and surface features of moving targets could facilitate attentional tracking. By adapting compound stimuli, the present study investigated whether the global or local properties played the main role in the uniqueness-facilitation effect in the MOT task. The uniqueness of local properties, of global properties or of both local and global properties were considered. Observers’ tracking performance in alternative conditions were compared with that in the homogeneous condition wherein all stimuli have identical local and global properties. Results from two experiments suggest that the global properties played the key role in facilitating tracking. The distinctiveness of local properties can also facilitate tracking with global properties being homogeneous. However, when the stimuli’s global properties are distinct from each other—whether the local properties being unique or not—observers’ tracking performance can achieve the same level as that in the unitary-uniqueness condition wherein the moving objects were distinct unitary letters. These results revealed a global superiority effect in the MOT task. Finally, the facilitation effects of the global and local properties might depend on the stimulus sparsity. When the compound stimuli had fewer local elements, the uniqueness facilitation effect on tracking decreased.

We show that the single trace heterotic N-point tree-level gauge amplitude ANHET can be obtained from the corresponding type I amplitude ANI by the single-valued (sv) projection: ANHET=sv(ANI). This projection maps multiple zeta values to single-valued multiple zeta values. The latter represent a subclass of multiple zeta values originating from single-valued multiple polylogarithms at unity. Similar relations between open and closed string amplitudes or amplitudes of different string vacua can be established. As a consequence the α′-expansion of a closed string amplitude is dictated by that of the corresponding open string amplitude. The combination of single-valued projections, Kawai–Lewellen–Tye relations and Mellin correspondence reveal a unity of all tree-level open and closed superstring amplitudes together with the maximally supersymmetric Yang–Mills and supergravity theories.

Chapter 9 Asymptotic Behavior of MP2 Correlation Energies for Closed-Shell Atoms

Logarithmic conformal field theories have a vast range of applications, from critical percolation to systems with quenched disorder. In this paper we thoroughly examine the structure of these theories based on their symmetry properties. Our analysis is model-independent and holds for any spacetime dimension. Our results include a determination of the general form of correlation functions and conformal block decompositions, clearing the path for future bootstrap applications. Several examples are discussed in detail, including logarithmic generalized free fields, holographic models, self-avoiding random walks and critical percolation.

Main disadvantage of a multicarrier communication system is high peak to average power ratio (PAPR) of the transmitted signal. The high PAPR causes the performance degradation due to nonlinear distortion in the high power amplifier (HPA). PAPR value is closely depends on transmitted power and correlation properties of the user’s spreading code. High peak and low average value of the transmitted power increases the PAPR. On the other side high auto correlation function (ACF) value and low cross correlation function (CCF) value of the spreading code also increases the PAPR. But to eliminate the multiple access interference (MAI) in receiver end, ACF should be peak and CCF should be posses zero for all time shifts. So, there is a conflicting nature of PAPR and bit error rate (BER). That’s why an exhaustive effort has been made in this paper for proper distribution of transmitted power within an acceptable range of peak transmitted power and evaluates the new spreading codes using Genetic Algorithms (GA). In general, to obtain optimum PAPR reduction using GA, total searching time to find out the proper amplitude and phase parameters must be accomplished. Simulation results show that PAPR and BER performance using this proposed technique is better than conventional network.

We derive model-independent, universal upper bounds on the operator product expansion coefficients in unitary 4-dimensional conformal field theories. The method uses the conformal block decomposition and the crossing symmetry constraint of the 4-point function. In particular, the operator product expansion coefficient of three identical dimension $d$ scalar primaries is found to be bounded by $\ensuremath{\simeq}10(d\ensuremath{-}1)$ for $1<d<1.7$. This puts strong limits on unparticle self-interaction cross sections at the LHC.

In this paper we study the relationships between local and global properties in networks of dynamical systems by focusing on two global properties, synchronization and peak-to-peak dynamics, and on two local properties, coherence of the components of the network and coupling strength. The analysis is restricted to networks of low-dimensional chaotic oscillators, i.e. oscillators which have peak-to-peak dynamics when they work in isolation. The results are obtained through simulation, first by considering pairs of coupled Lorenz, Rössler and Chua systems, and then by studying the behavior of spatially extended tritrophic food chains described by the Rosenzweig–MacArthur model. The conclusion is that synchronization and peak-to-peak dynamics are different aspects of the same collective behavior, which is easily obtained by enhancing local coupling and coherence. The importance of these findings is briefly discussed within the context of ecological modeling.

The existence or not of Landau poles is one of the oldest open questions in non-asymptotic quantum field theories. We investigate the Landau pole issue in two condensed matter systems whose long-wavelength physics is described by appropriate quantum field theories: the critical quantum magnet and Dirac fermions in graphene with long-range Coulomb interactions. The critical quantum magnet provides a classic example of a quantum phase transition, and it is well described by the $\phi^4$ theory. We find that the irrelevant but symmetry-allowed couplings, such as the $\phi^6$ potential, can significantly change the fate of the Landau pole in the $\phi^4$ theory. We obtain the coupled beta functions of a $\phi^4 + \phi^6$ potential at both small and large orders. Already from the 1-loop calculation, the Landau pole is replaced by an ultraviolet fixed point. A Lipatov analysis at large orders reveals that the inclusion of a $\phi^6$ term also has important repercussions for the high-order expansion of the beta functions. We also investigate the role of the Landau pole in 2+1 dimensional Dirac fermions with Coulomb interactions, e.g., graphene. Both the weak-coupling perturbation theory up to 2 loops and a low-order large-N calculation show the absence of a Landau pole. Furthermore, we calculate the asymptotic expansion coefficients of the beta function. We find that the asymptotic coefficient is bounded by that of a $\phi^4$ theory, so graphene is free from Landau poles if the $\phi^4$ theory does not manifest a Landau pole. We briefly discuss possible experiments that could potentially probe the existence of a Landau pole in these systems. Studying Landau poles in suitable condensed matter systems is of considerable fundamental importance since the relevant Landau pole energy scales in particle physics, whether it is quantum electrodynamics or Higgs physics, are completely unattainable.

Temporal evolution characteristics and prediction methods of spatial correlation function shape of rough soil surfaces

Single-active-electron potentials are computed for selected molecules, and molecular wave functions with the correct asymptotic behavior are produced. Asymptotic expansion coefficients are extracted from the wave functions and used to compute alignment-dependent ionization yields from molecular tunneling theory. The predictions of molecular tunneling theory are benchmarked by ab initio calculations based on the solution of the time-dependent Schrödinger equation within the single-active-electron approximation.

This study compared adults (Homo sapiens), young children (Homo sapiens), and adult tamarins (Saguinus oedipus) while they discriminated global and local properties of stimuli. Subjects were trained to discriminate a circle made of circle elements from a square made of square elements and were tested with circles made of squares and squares made of circles. Adult humans showed a global bias in testing that was unaffected by the density of the elements in the stimuli. Children showed a global bias with dense displays but discriminated by both local and global properties with sparse displays. Adult tamarins' biases matched those of the children. The striking similarity between the perceptual processing of adult monkeys and humans diagnosed with autism and the difference between this and normatively developing human perception is discussed.

We consider the non-equilibrium dynamics after a sudden quench of the magnetic field in the transverse field Ising chain starting from excited states of the pre-quench Hamiltonian. We prove that stationary values of local correlation functions can be described by the generalized Gibbs ensemble. Then we study the full time evolution of the transverse magnetization by means of stationary phase methods. The equal-time two-point longitudinal correlation function is analytically derived for a particular class of excited states for quenches within the ferromagnetic phase, and studied numerically in general. The full time dependence of the entanglement entropy of a block of spins is also obtained analytically for the same class of states and for arbitrary quenches.

Within the Ultra-relativistic Quantum Molecular Dynamics model (UrQMD) coupled with nucleon coalescence model and Mini-Spanning-Tree model, the yields of light nuclei have been stimulated in Au + Au collisions over an energy range of sNN=2.0∼7.7GeV and the momentum correlation functions of light nuclei pairs have been calculated by both the Lednický-Lyuboshitz and the Correlation After Burner methods. We compare the yields of light nuclei and their momentum correlation functions at midrapidity in this energy region with experimental data. It is found that there are differences between the results of the two models, and the coalescence method seems less valid at low collision energy. Furthermore, both the peak values of proton-proton correlation functions and the transition point of elliptic flows from out-of-plane to in-plane emission show a turning point around 3-4 GeV, which suggests that there is a relation between momentum correlation function and collective flow of particles.

The typical method for obtaining a power spectrum from values of the correlation function is through the FFT (fast Fourier transform). A novel approach to improving the FFT spectrum when it is corrupted by noise is presented. The method minimises a relative entropy functional involving spectral densities and requires knowledge only of the variance of the noise that is corrupting the FFT spectrum.

An explicit Wigner formulation of Minkowski particle states for noninertial observers is unknown. Here, we derive a general prescription to compute the characteristic function for Minkowski-Fock states in accelerated frames. For the special case of single-particle and two-particle states, this method enables one to derive mean values of particle numbers and correlation function in the momentum space, and the way they are affected by the acceleration of the observer. We show an indistinguishability between Minkowski single-particle and two-particle states in terms of Rindler particle distribution that can be regarded as a way for the observer to detect any acceleration of the frame. We find that for two-particle states the observer is also able to detect acceleration by measuring the correlation between Rindler particles with different momenta.