γγ→tcˉ+ctˉ\gamma\gamma \to t\bar{c}+c\bar{t} in a supersymmetric theory with an explicit R-parity violation

We studied the process $\gamma\gamma \to t\bar{c}+c\bar{t}$ in a $R_{p}$ violating supersymmetric Model with the effects from both B- and L-violating interactions. The calculation shows that it is possible to detect a $R_{p}$ violating signal at the Next Linear Collider. Information about the B-violating interaction in this model could be obtained under very clean background, if we take the present upper bounds for the parameters in the supersymmetric $\rlap/ R_{p}$ interactions. Even if we can not detect a signal of $\rlap/R_{p}$ in the experiment, we may get more stringent constraints on the heavy-flavor $\rlap/R_{p}$ couplings.Comment: 16 pages, 6 figure

Asymptotic stability of the sine-Gordon kinks under perturbations in weighted Sobolev norms

We study the asymptotic stability of the sine-Gordon kinks under small perturbations in weighted Sobolev norms. Our main tool is the B\"acklund transform which reduces the study of the asymptotic stability of the kinks to the study of the asymptotic decay of solutions near zero. Our results consist of two parts. First, we present a different proof of the local asymptotic stability result in arXiv:2009.04260. In its proof, we apply a result obtained by the inverse scattering method on the local decay of the solutions with sufficiently small and localized initial data. Moreover, we prove an $L^\infty$-type asymptotic stability result which is similar to that in arXiv:2106.09605; the main difference is that we remove the assumptions on the spatial symmetry of the perturbations. In its proof, we apply a result obtained by the method of testing by wave packets on the pointwise decay of the solutions with small and localized data.Comment: 54 page

Sequential Neural Barriers for Scalable Dynamic Obstacle Avoidance

There are two major challenges for scaling up robot navigation around dynamic obstacles: the complex interaction dynamics of the obstacles can be hard to model analytically, and the complexity of planning and control grows exponentially in the number of obstacles. Data-driven and learning-based methods are thus particularly valuable in this context. However, data-driven methods are sensitive to distribution drift, making it hard to train and generalize learned models across different obstacle densities. We propose a novel method for compositional learning of Sequential Neural Control Barrier models (SNCBFs) to achieve scalability. Our approach exploits an important observation: the spatial interaction patterns of multiple dynamic obstacles can be decomposed and predicted through temporal sequences of states for each obstacle. Through decomposition, we can generalize control policies trained only with a small number of obstacles, to environments where the obstacle density can be 100x higher. We demonstrate the benefits of the proposed methods in improving dynamic collision avoidance in comparison with existing methods including potential fields, end-to-end reinforcement learning, and model-predictive control. We also perform hardware experiments and show the practical effectiveness of the approach in the supplementary video.Comment: To be published in IROS 202

Gravitational Fluctuations as an Alternative to Inflation

The ability to reproduce the observed matter power spectrum $P(k)$ to high accuracy is often considered as a triumph of inflation. In this work, we explore an alternative explanation for the power spectrum based on nonperturbative quantum field-theoretical methods applied to Einstein's gravity, instead of ones based on inflation models. In particular the power spectral index, which governs the slope on the $P(k)$ graph, can be related to critical scaling exponents derived from the Wilson renormalization group analysis. We find that the derived value fits favorably with the Sloan Digital Sky Survey telescope data. We then make use of the transfer functions, based only on the Boltzmann equations which describe states out of equilibrium, and Einstein's General Relativity, to extrapolate the power spectrum to the Cosmic Microwave Background (CMB) regime. We observe that the results fit rather well with current data. Our approach contrasts with the conventional explanation which uses inflation to generate the scale invariant Harrison-Zel'dovich spectrum on CMB scales, and uses the transfer function to extrapolate it to galaxy regime. The results we present here only assume quantum field theory and Einstein's Gravity, and hence provide a competing explanation of the power spectrum, without relying on the assumptions usually associated with inflationary models. At the end, we also outline several testable predictions in this picture that deviate from the conventional picture of inflation, and which hopefully will become verifiable in the near future with increasingly accurate measurements.Comment: 33 pages, 6 figures. One figure added following the July 2018 release of new Planck data. Typos fixed, more references added. Paper now conforms to the published versio

Gravitational Fluctuations as an Alternative to Inflation II. CMB Angular Power Spectrum

Power spectra always play an important role in the theory of inflation. In particular, the ability to reproduce the galaxy matter power spectrum and the CMB temperature angular power spectrum coefficients to high accuracy is often considered a triumph of inflation. In our previous work, we presented an alternative explanation for the matter power spectrum based on nonperturbative quantum field-theoretical methods applied to Einstein's gravity, instead of inflation models based on scalar fields. In this work, we review the basic concepts and provide further in-depth investigations. We first update the analysis with more recent data sets and error analysis, and then extend our predictions to the CMB angular spectrum coefficients, which we did not consider previously. Then we investigate further the potential freedoms and uncertainties associated with the fundamental parameters that are part of this picture, and show how recent cosmological data provides significant constraints on these quantities. Overall, we find good general consistency between theory and data, even potentially favoring the gravitationally-motivated picture at the largest scales. We summarize our results by outlining how this picture can be tested in the near future with increasingly accurate astrophysical measurements.Comment: 43 pages, 8 figures (typos fixed, references added

Dyson's Equations for Quantum Gravity in the Hartree-Fock Approximation

Unlike scalar and gauge field theories in four dimensions, gravity is not perturbatively renormalizable and as a result perturbation theory is badly divergent. Often the method of choice for investigating nonperturbative effects has been the lattice formulation, and in the case of gravity the Regge-Wheeler lattice path integral lends itself well for that purpose. Nevertheless, lattice methods ultimately rely on extensive numerical calculations, leaving a desire for alternate calculations that can be done analytically. In this work we outline the Hartree-Fock approximation to quantum gravity, along lines which are analogous to what is done for scalar fields and gauge theories. The starting point is Dyson's equations, a closed set of integral equations which relate various physical amplitudes involving graviton propagators, vertex functions and proper self-energies. Such equations are in general difficult to solve, and as a result not very useful in practice, but nevertheless provide a basis for subsequent approximations. This is where the Hartree-Fock approximation comes in, whereby lowest order diagrams get partially dressed by the use of fully interacting Green's function and self-energies, which then lead to a set of self-consistent integral equations. Specifically, for quantum gravity one finds a nontrivial ultraviolet fixed point in Newton's constant G for spacetime dimensions greater than two, and nontrivial scaling dimensions between d=2 and d=4, above which one obtains Gaussian exponents. In addition, the Hartree-Fock approximation gives an explicit analytic expression for the renormalization group running of Newton's constant, suggesting gravitational antiscreening with Newton's G slowly increasing on cosmological scales.Comment: 71 pages, 21 figures. More typos fixed, references adde

Tuning of one-dimensional plasmons by Ag-Doping in Ag-√3-ordered atomic wires

We generated arrays of silver wires with a height of 1 atom and an average width of 11 atoms on the Si(557) surface via self-assembly with local √3 x √3 order, and investigated the 1D plasmon formation in them using a combination of high-resolution electron loss spectroscopy with low-energy electron diffraction. After a series of thermal desorption experiments followed by adding small concentrations of Ag, pure Ag-√3 ordered arrays of nanowires, separated by (113) facets, are intrinsically semi metallic or semiconducting, i.e., the metallicity of the Ag wires seems to be caused by excess atoms added to the (locally) perfectly ordered √3 x √3 layer. The proof has been carried out by post-adsorption of Ag atoms in the range between 0.004 to 0.03 monolayers and the quantitative determination of the frequency dependence of the 1D plasmon due to this excess Ag concentration. As expected for a doping mechanism, there is no minimum excess concentration. The lack of temperature dependence is not compatible with the formation of an adatom gas in the second layer, but suggests extrinsic doping by adatoms bound at the stepped (113) facets. Although strong deviations from a nearly free electron gas are expected in 1D, the Ag concentration dependence of the 1D plasmonic losses is fully compatible with the √ne dependence predicted by this model. Adsorption of traces of residual gas can have a qualitatively similar doping effect.Niedersächsisches Ministerium für Wissenschaft und Kultur/Contacts in NanosystemsDF