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Brooks’ Theorem in Graph Streams: A Single-Pass Semi-Streaming Algorithm for Δ-Coloring

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arXiv 2022年

作者： Assadi, Sepehr Kumar, Pankaj Mittal, Parth Department of Computer Science Rutgers University United States Cheriton School of Computer Science University of Waterloo Canada Department of Applied Mathematics Faculty of Mathematics and Physics Charles University Prague Czech Republic

Every graph with maximum degree Δ can be colored with (Δ + 1) colors using a simple greedy algorithm. Remarkably, recent work has shown that one can find such a coloring even in the semi-streaming model: there exists a randomized algorithm that with high probability finds a (Δ + 1)-coloring of the input graph in only O(n · polylog n) space assuming a single pass over the edges of the graph in any arbitrary order. But, in reality, one almost never needs (Δ + 1) colors to properly color a graph. Indeed, the celebrated Brooks’ theorem states that every (connected) graph beside cliques and odd cycles can be colored with Δ colors. Can we find a Δ-coloring in the semi-streaming model as well? We settle this key question in the affirmative by designing a randomized semi-streaming algorithm that given any graph, with high probability, either correctly declares that the graph is not Δ-colorable or outputs a Δ-coloring of the graph. The proof of this result starts with a detour. We first (provably) identify the extent to which the previous approaches for streaming coloring fail for Δ-coloring: for instance, all these prior approaches can handle streams with repeated edges and they can run in O(n2) time, whereas © 2022, CC BY.

关键词： Coloring

Perfect quantum protractors

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arXiv 2023年

作者： Piotrak, Michal Kopciuch, Marek Fard, Arash Dezhang Smolis, Magdalena Pustelny, Szymon Korzekwa, Kamil Department of Physics Imperial College London LondonSW7 2AZ United Kingdom Department of Physics and Astronomy University College London LondonWC1E 6BT United Kingdom Doctoral School of Exact and Natural Sciences Jagiellonian University Faculty of Physics Astronomy and Applied Computer Sciences Kraków30-348 Poland Faculty of Physics Astronomy and Applied Computer Science Jagiellonian University Kraków30-348 Poland

In this paper we introduce and investigate the concept of a perfect quantum protractor, a pure quantum state |ψ〉 ∈ H that generates three different orthogonal bases of H under rotations around each of the three perpendicular axes. Such states can be understood as pure states of maximal uncertainty with regards to the three components of the angular momentum operator, as we prove that they maximise various entropic and variance-based measures of such uncertainty. We argue that perfect quantum protractors can only exist for systems with a well-defined total angular momentum j, and we prove that they do not exist for j ∈ {1/2, 2, 5/2}, but they do exist for j ∈ {1, 3/2, 3} (with numerical evidence for their existence when j = 7/2). We also explain that perfect quantum protractors form an optimal resource for a metrological task of estimating the angle of rotation around (or the strength of magnetic field along) one of the three perpendicular axes, when the axis is not a priori known. Finally, we demonstrate this metrological utility by performing an experiment with warm atomic vapours of rubidium-87, where we prepare a perfect quantum protractor for a spin-1 system, let it precess around x, y or z axis, and then employ it to optimally estimate the rotation angle. © 2023, CC BY.

关键词： Angular momentum

Quantum chaos and level dynamics

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arXiv 2023年

作者： Zakrzewski, Jakub Institute of Theoretical Physics Faculty of Physics Astronomy and Applied Computer Science Jagiellonian University Lojasiewicza 11 Kraków30-348 Poland Mark Kac Complex Systems Research Center Jagiellonian University Kraków30-348 Poland

We review application of level dynamics to spectra of quantally chaotic systems. We show that statistical mechanics approach gives us predictions about level statistics intermediate between integrable and chaotic dynamics. Then we discuss in detail different statistical measures involving level dynamics such as level avoided-crossing distributions, slope and curvature of level distributions showing both the postulate of unversality and its limitations. We mention shortly the experimental confirmations of these theories. We concentrate in some detail on measures imported from quantum information approach such as the fidelity susceptibility and more generally geometric tensor matrix elements. The possible open problems are suggested. © 2023, CC BY.

关键词： Dynamics

Quantum correction to a new Wilson line-based action for Gluodynamics

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arXiv 2023年

作者： Kakkad, Hiren Kotko, Piotr Stasto, Anna Faculty of Physics and Applied Computer Science AGH University of Krakow al. A. Mickiewicza 30 Krakow30-059 Poland Physics Department The Pennsylvania State University 104 Davey Lab University ParkPA16802 United States

We discuss a new classical action that enables efficient computation of the gluonic tree amplitudes but does not contain any triple point vertices. This new formulation is obtained via a canonical transformation of the light-cone Yang-Mills action, with the field transformations based on Wilson line functionals. In addition to MHV vertices, the action contains also NkMHV vertices, where 1 ≤ k ≤ n − 4, and n is the number of external legs. We computed tree-level amplitudes up to 8 gluons and found agreement with standard results. The classical action is however not sufficient to obtain rational parts of amplitudes, in particular the finite amplitudes with all same helicity gluons. In order to systematically develop quantum corrections to this new action, we derive the one-loop effective action, in such a way there are no quantum contributions missing at one loop. Copyright © 2023, The Authors. All rights reserved.

关键词： Trees (mathematics)

Generic Hardware Realization of K Nearest Neighbors on FPGA

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Generic Hardware Realization of K Nearest Neighbors on FPGA

2022 International Conference on Microelectronics, ICM 2022

作者： Yacoub, Mohammed H. Ismail, Samar M. Said, Lobna A. Madian, Ahmed H. Radwan, Ahmed G. Giza Egypt School of Engineering and Computer Science Egypt National Centre for Radiation Research and Technology Radiation Engineering Department Cairo11787 Egypt Cairo University Faculty of Engineering Engineering Mathematics and Physics Department Giza12613 Egypt Nile University School of Engineering and Applied Sciences Giza Egypt

ISBN: (纸本)9781665493246

K Nearest Neighbors (KNN) algorithm is a straight-forward yet powerful Machine Learning (ML) tool widely used in classification, clustering, and regression applications. In this work, KNN is applied, with three distance metrics, to classify different datasets, experimentally testing each distance metric effect on the classification performance. A static K is applied for the whole dataset optimally chosen based on a 5-fold cross-validation. A reconfigurable hardware realization on field programmable gate array (FPGA) of each distance metric applying selection sort algorithm is proposed. The FPGA realization reaches a throughput up to 4.44 Gbit/sec while only occupying 1% of the Genesys 2 Kintex-7 board area. The algorithm managed to classify all the tested datasets with above 90% accuracy. © 2022 IEEE.

关键词： Machine learning

Interplay between extended s-wave symmetry of the gap and spin-orbit coupling in the low electron concentration regime of quasi-two-dimensional superconductors

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Physical Review B 2022年第18期106卷 184508-184508页

作者： M. Zegrodnik P. Wójcik Academic Centre for Materials and Nanotechnology AGH University of Science and Technology Aleja Mickiewicza 30 30-059 Krakow Poland AGH University of Science and Technology Faculty of Physics and Applied Computer Science al. A. Mickiewicza 30 30-059 Krakow Poland

We analyze the real-space paired state with the k-dependent superconducting gap in the presence of Rashba-type spin-orbit coupling and external magnetic field. We show that the extended s-wave pairing symmetry is the most probable scenario to appear in the low electron concentration regime. According to our study, the van Hove singularity induced by the spin-orbit coupling may lead to a significant enhancement of the superconducting gap, critical temperature, and critical magnetic field. Moreover, the combined effect of the spin-orbit coupling and the external magnetic field results in a nonzero total momentum of the Cooper pairs, which is a characteristic feature of the so-called helical state. In such a situation, due to the C4 symmetry breaking, a small d-wave and p-wave contributions to the pairing appear, which significantly change the character of the helical state. The obtained results are discussed in the context of the experimental data related with the unconventional superconducting features of the transition metal oxide interfaces as well as the recently reported supercurrent diode effect.

关键词： FFLO Spin-orbit coupling Superconducting order parameter Superconductivity Superconductors 2-dimensional systems Two-dimensional electron system Unconventional superconductors Lattice models in condensed matter

Bulk-boundary correspondence from hyperinvariant tensor networks

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Physical Review D 2025年第2期111卷 026006-026006页

作者： Rafał Bistroń Mykhailo Hontarenko Karol Życzkowski Institute of Theoretical Physics Faculty of Physics Astronomy and Applied Computer Science Jagiellonian University ul. Łojasiewicza 11 30-348 Kraków Poland Doctoral School of Exact and Natural Sciences Jagiellonian University ul. Łojasiewicza 11 30-348 Kraków Poland Center for Theoretical Physics (CFT) Polish Academy of Sciences Al. Lotników 32/46 02-668 Warszawa Poland

We introduce a tensor network designed to faithfully simulate the AdS/CFT correspondence, akin to the multiscale entanglement renormalization ansatz (MERA), following hyperinvariant tensor network. The proposed construction integrates bulk indices within the network architecture to uphold the key features of the HAPPY code, including complementary recovery. This framework accurately reproduces the boundary conformal field theory’s (CFT) two- and three-point correlation functions, while considering the image of any bulk operator. Furthermore, we provide an explicit methodology for calculating the correlation functions in an efficient manner. Our findings highlight the physical aspects of the relation between bulk and boundary within the tensor network models, contributing to the understanding and simulation of holographic principles in quantum information.

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Numerical model of harmonic Hall voltage detection for spintronic devices

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Physical Review B 2022年第2期106卷 024403-024403页

作者： Sławomir Ziętek Jakub Mojsiejuk Krzysztof Grochot Stanisław Łazarski Witold Skowroński Tomasz Stobiecki Institute of Electronics AGH University of Science and Technology Aleja Adama Mickiewicza 30 30-059 Kraków Poland Faculty of Physics and Applied Computer Science AGH University of Science and Technology Aleja Adama Mickiewicza 30 30-059 Kraków Poland

We present a numerical macrospin model for harmonic voltage detection in multilayer spintronic devices. The core of the computational backend is based on the Landau-Lifshitz-Gilbert-Slonczewski equation, which combines high performance and satisfactory agreement with the experimental results in large-scale applications. We compare the simulations with the experimental findings in a Ta/CoFeB bilayer system for angular- and magnetic-field-dependent resistance measurements, electrically detected magnetization dynamics, and harmonic Hall voltage detection. Using simulated scans of the selected system parameters such as the polar angle θ, magnetization saturation (μ0Ms), or uniaxial magnetic anisotropy (Ku), we show the resultant changes in the harmonic Hall voltage, demonstrating the dominating influence of the μ0Ms on the first and second harmonics. In the spin-diode ferromagnetic resonance method, the (μ0Ms, Ku) parameter space may be optimized numerically to obtain a set of viable curves that fit the experimental data.

关键词： Magnetotransport Spin dynamics Spintronics

Electric dipole spin resonance in a single- and two-electron quantum dot defined in two-dimensional electron gas at the SrTiO3/LaAlO3 interface

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Physical Review B 2024年第15期109卷 155306-155306页

作者： B. Szafran M. Zegrodnik M. P. Nowak R. Citro P. Wójcik AGH University of Krakow Faculty of Physics and Applied Computer Science Al. Mickiewicza 30 30-059 Krakow Poland AGH University of Krakow Academic Centre for Materials and Nanotechnology Al. Mickiewicza 30 30-059 Krakow Poland Department of Physics E. R. Caianiello University of Salerno and CNR-SPIN Via Giovanni Paolo II 132 Fisciano (Sa) Italy

We investigate the energy spectrum of a single- and two-electron quantum dot (QD) embedded in two-dimensional electron gas at the interface between SrTiO3 and LaAlO3, in the presence of the external magnetic field. For this purpose, the three-band model of 3d electrons defined on the square lattice of Ti ions was utilized. We demonstrate that, for the weak parabolic confinement potential, the low-energy spectrum is sufficiently well described by the effective Hamiltonian reduced to the one dxy orbital with the spin-orbit interaction originating from the coupling to the dxz and dyz bands. This is not the case for stronger confinement where contribution of the states related to the dxz/yz orbital is relevant. Based on the time-dependent calculations, we discuss in detail the manipulation of the electron spin in a QD by external AC voltages, in the context of the electric dipole spin resonance. The allowed and forbidden transitions are discussed in detail with respect to the parity selection rule. Our calculations show that, for a single-electron QD, the spin flip in the ground state has the character of a Rabi resonance, while for two electrons, the singlet-triplet transition is forbidden by the parity symmetry. For the two-electron QD, we demonstrate that the spin-flip transition can still be accomplished via a second-order, two-photon process that has a two-state Rabi character for low AC field amplitude. The violation of the parity symmetry on the spin-flip transitions is also analyzed.

关键词： Spin dynamics Spin-orbit coupling Quantum dots Transition metal oxides Two-dimensional electron gas