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关键词： Quantum anomaly   Dimensional transmutation   Contact interactions   Tan's contact  

摘要： A system of two-species, one-dimensional fermions, with an attractive two-body interaction of the derivative-delta type, features a scale anomaly. In contrast to the well-known two-dimensional case with contact interactions, and its one-dimensional cousin with three-body interactions (studied recently by some of us and others), the present case displays dimensional transmutation featuring a power-law rather than a logarithmic behavior. We use both the Schrodinger equation and quantum field theory to study bound and scattering states, showing consistency between both approaches. We show that the expressions for the reflection (R) and the transmission (T) coefficients of the renormalized, anomalous derivative-delta potential are identical to those of the regular delta potential. The second-order virial coefficient is calculated analytically using the Beth-Uhlenbeck formula, and we make comments about the proper epsilon(B) -> 0 (where epsilon(B) is the bound-state energy) limit. We show the impact of the quantum anomaly (which appears as the binding energy of the two-body problem, or equivalently as Tan's contact) on the equation of state and on other universal relations. Our emphasis throughout is on the conceptual and structural aspects of this problem. (C) 2021 Elsevier Inc. All rights reserved.

关键词： Lattice dynamics  

摘要： The Quantum Self-Consistent Ab-Initio Lattice Dynamics package (QSCAILD) is a python library that computes temperature-dependent effective 2nd and 3rd order interatomic force constants in crystals, including anharmonic effects. QSCAILD's approach is based on the quantum statistics of a harmonic model. The program requires the forces acting on displaced atoms of a solid as an input, which can be obtained from an external code based on density functional theory, or any other calculator. This article describes QSCAILD's implementation, clarifies its connections to other methods, and illustrates its use in the case of the SrTiO3 cubic perovskite structure. Program summary Program Title: QSCAILD CPC Library link to program files: https://***/10.17632/y4c922fwtf.1 Licensing provisions: GNU General Public License version 3.0 Programming language: Python External routines/libraries: MPI, NumPy, SciPy, spglib, phonopy, sklearn Nature of problem: Calculation of effective interatomic force constants at finite temperature Solution method: Regression analysis of forces from density functional theory coupled with a harmonic model of the quantum canonical ensemble, performed in an iterative way to achieve self-consistency of the phonon spectrum (C) 2021 Elsevier B.V. All rights reserved.

关键词： Parabolic p-Laplacian system   Time-discretization   Discrete Morse flow method   Approximation   Regularity  

摘要： A regularity for a parabolic p-Laplacian system (p > 2) is studied by the use of the discrete Morse flow method which is known as one of the ways to approximate a solution to parabolic partial differential equations. Our approximate solution is constructed from the sequence of minimizers of variational functionals whose Euler-Lagrange equations are the time discretized p-Laplacian system. The aim of this paper is to establish that the regularity estimates for the approximate solution hold uniformly on two approximation parameters and show strong convergence of the approximate solution.

摘要： Lipid-peptide interactions are involved in many essential processes of living organisms, such as cell fusion or transport processes and are therefore, in the center of research interest. One efficient technique to analyze such interactions is the electron paramagnetic resonance (EPR) spectroscopy, in particular the double electron electron resonance (DEER) and pulsed electron double resonance (PELDOR) experiments, which allow to determine intramolecular distances within peptides and to investigate the orientation of peptides incorporated into membranes. One requirement to use this analytical technique is the labeling of the peptides with molecules that bear a paramagnetic center such as a nitroxide radical. Thereby, the peptides can be labeled either by direct incorporation of the spin label into the peptide backbone during the peptide synthesis or by side-directed spin labeling (SDSL). To improve the accuracy of distance and orientation-selection measurements by EPR spectroscopy the aim of this work was to design and synthesize a new spin label with enhanced rigidity for direct incorporation into peptides. The design of the new and rigid spin label was based on the approach to stabilize the peptide conformation by direct incorporation of the spin label. In the course of this work, a new spin label that is capable to induce B-turn conformations by geometrical preorganization was designed and its synthesis tested. In addition to that, one goal was the investigation of more complex protein systems using the the semi-rigid 4-(3,3,5,5-tetra-methyl-2,6-dioxo-4-oxylpiperazin-1-yl)-l-phenylglycine (TOPP) spin label, which requires a reliable and general method for incorporation of this spin label into large peptide systems. One established method to construct large peptide systems is the native chemical ligation (NCL). This method enables the synthesis of large peptide systems from two or more peptide fragments and allows the incorporation of modified peptide fragments. Th

关键词： Atomic and molecular physics   Condensed-matter physics   Quantum simulation  

摘要： Particles subject to confinement experience an attractive potential that increases without bound as they separate. A prominent example is colour confinement in particle physics, in which baryons and mesons are produced by quark confinement. Confinement can also occur in low-energy quantum many-body systems when elementary excitations are confined into bound quasiparticles. Here we report the observation of magnetic domain-wall confinement in interacting spin chains with a trapped-ion quantum simulator. By measuring how correlations spread, we show that confinement can suppress information propagation and thermalization in such many-body systems. We quantitatively determine the excitation energy of domain-wall bound states from the non-equilibrium quench dynamics. We also study the number of domain-wall excitations created for different quench parameters, in a regime that is difficult to model with classical computers. This work demonstrates the capability of quantum simulators for investigating high-energy physics phenomena, such as quark collision and string breaking. Long-range Ising interactions present in one-dimensional spin chains can induce a confining potential between pairs of domain walls, slowing down the thermalization of the system. This has now been observed in a trapped-ion quantum simulator.

摘要： We present asymptotically sharp inequalities, containing a 2nd term, for the Dirichlet and Neumann eigenvalues of the Laplacian on a domain, which are complementary to the familiar Berezin-Li-Yau and Kroger inequalities in the limit as the eigenvalues tend to infinity. We accomplish this in the framework of the Riesz mean R-1(z) of the eigenvalues by applying the averaged variational principle with families of test functions that have been corrected for boundary behaviour.

关键词： quantum thermodynamics   schwarzschild black-hole   space time  

摘要： We study space-time back-reaction configuration in the interior of a Schwarzschild Black-Hole (B-H) using Relativistic Quantum Geometry described in (Ridao and Bellini 2015 Astrophys. Space Sci. 357 94) and (Ridao and Bellini 2015 Phys. Lett. B 751 565). We found discrete energy levels for a scalar field from a polynomial condition for Heun Confluent functions expanded around the Schwarzschild radius. From the solutions it is obtained that the uncertainty principle is valid for each energy level of space-time, in the form: E-n r(sh,n) = /2. Temperature, entropy and the B-H mass are dependent on the number of states in the B-H, such that the Bekenstein-Hawking (BH) results are obtained in a limit case.

关键词： Matrix completion   Graph theory   Laplacian matrix   Total variation   Singular value decomposition  

摘要： We propose two graph matrix completion algorithms called GMCM-DL and GMCR-DL, by employing a new definition of Graph Total Variation for matrices based on the directed Laplacian Matrix. We show that these algorithms outperform their peers in terms of RMSEs for both cases of uniform and row observations.

关键词： Sublevel set estimate   Hessian   Laplace operator   Brownian motion   Champagne domain   Potential theory  

摘要： Carbery proved that if u : Rn. R is a positive, strictly convex function satisfying detD2u = 1, then we have the estimate x. Rn : u(x) = s n sn/2 and this is optimal. We give a short proof that also implies other results. Our main result is an estimate for the sublevel set of functions u : [0, 1]2. R satisfying 1 = u = c for some universal constant c: for any a > 0, we have x. [0, 1]2 : | u(x)| = e c v e + ea- 1 2 [0,1]2 |. u| |u| a dx. For `typical' functions, we expect the integral to be finite fora < 1. While Carbery-ChristWright have shown that no sublevel set estimates independently of u exist, this result shows that for `typical' functions satisfying u 1, we expect the sublevel set to be e1/2-. We do not know whether this is sharp or whether similar statements are true in higher dimensions.

关键词： Graph convolutional networks   Manifold learning   p-Laplacian   Semi-supervised classification  

摘要： The graph convolutional networks (GCN) generalizes convolution neural networks into the graph with an arbitrary topology structure. Since the geodesic function in the null space of the graph Laplacian matrix is constant, graph Laplacian fails to preserve the local topology structure information between samples properly. GCN thus cannot learn better representative sample features by the convolution operation of the graph Laplacian based structure information and input sample information. To address this issue, this paper exploits the manifold structure information of data by the graph p-Laplacian matrix and proposes the graph p-Laplacian convolutional networks (GpLCN). As the graph p-Laplacian matrix is a generalization of the graph Laplacian matrix, GpLCN can extract more abundant sample features and improves the classification performance utilizing graph p-Laplacian to preserve the rich intrinsic data manifold structure information. Moreover, after simplifying and deducing the formula of the one-order spectral graph p-Laplacian convolution, we introduce a new layer-wise propagation rule based on the one-order approximation. Extensive experiment results on the Citeseer, Cora and Pubmed database demonstrate that our GpLCN outperforms GCN. (C) 2021 Elsevier Inc. All rights reserved.