46,604 research outputs found

    MAS: A versatile Landau-fluid eigenvalue code for plasma stability analysis in general geometry

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    We have developed a new global eigenvalue code, Multiscale Analysis for plasma Stabilities (MAS), for studying plasma problems with wave toroidal mode number n and frequency omega in a broad range of interest in general tokamak geometry, based on a five-field Landau-fluid description of thermal plasmas. Beyond keeping the necessary plasma fluid response, we further retain the important kinetic effects including diamagnetic drift, ion finite Larmor radius, finite parallel electric field, ion and electron Landau resonances in a self-consistent and non-perturbative manner without sacrificing the attractive efficiency in computation. The physical capabilities of the code are evaluated and examined in the aspects of both theory and simulation. In theory, the comprehensive Landau-fluid model implemented in MAS can be reduced to the well-known ideal MHD model, electrostatic ion-fluid model, and drift-kinetic model in various limits, which clearly delineates the physics validity regime. In simulation, MAS has been well benchmarked with theory and other gyrokinetic and kinetic-MHD hybrid codes in a manner of adopting the unified physical and numerical framework, which covers the kinetic Alfven wave, ion sound wave, low-n kink, high-n ion temperature gradient mode and kinetic ballooning mode. Moreover, MAS is successfully applied to model the Alfven eigenmode (AE) activities in DIII-D discharge #159243, which faithfully captures the frequency sweeping of RSAE, the tunneling damping of TAE, as well as the polarization characteristics of KBAE and BAAE being consistent with former gyrokinetic theory and simulation. With respect to the key progress contributed to the community, MAS has the advantage of combining rich physics ingredients, realistic global geometry and high computation efficiency together for plasma stability analysis in linear regime.Comment: 40 pages, 21 figure

    Rank-based linkage I: triplet comparisons and oriented simplicial complexes

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    Rank-based linkage is a new tool for summarizing a collection SS of objects according to their relationships. These objects are not mapped to vectors, and ``similarity'' between objects need be neither numerical nor symmetrical. All an object needs to do is rank nearby objects by similarity to itself, using a Comparator which is transitive, but need not be consistent with any metric on the whole set. Call this a ranking system on SS. Rank-based linkage is applied to the KK-nearest neighbor digraph derived from a ranking system. Computations occur on a 2-dimensional abstract oriented simplicial complex whose faces are among the points, edges, and triangles of the line graph of the undirected KK-nearest neighbor graph on SS. In SK2|S| K^2 steps it builds an edge-weighted linkage graph (S,L,σ)(S, \mathcal{L}, \sigma) where σ({x,y})\sigma(\{x, y\}) is called the in-sway between objects xx and yy. Take Lt\mathcal{L}_t to be the links whose in-sway is at least tt, and partition SS into components of the graph (S,Lt)(S, \mathcal{L}_t), for varying tt. Rank-based linkage is a functor from a category of out-ordered digraphs to a category of partitioned sets, with the practical consequence that augmenting the set of objects in a rank-respectful way gives a fresh clustering which does not ``rip apart`` the previous one. The same holds for single linkage clustering in the metric space context, but not for typical optimization-based methods. Open combinatorial problems are presented in the last section.Comment: 37 pages, 12 figure

    Entanglement in the full state vector of boson sampling

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    The full state vector of boson sampling is generated by passing S single photons through beam splitters of M modes. The initial Fock state is expressed withgeneralized coherent states, and an exact application of the unitary evolution becomes possible. Due to the favorable polynomial scaling in M , we can investigate Renyi entanglement entropies for moderate particle and huge mode numbers. We find (almost) Renyi index independent symmetric Page curves with maximum entropy at equal partition. Furthermore, the maximum entropy as a function of mode index saturates as a function of M in the collision-free subspace case. The asymptotic value of the entropy increases linearly with S. Furthermore, we show that the build-up of the entanglement leads to a cusp at subsystem size equal to S in the asymmetric entanglement curve. The maximum entanglement is reached surprisingly early before the mode population is distributed over the whole system

    Quantum Mechanics Lecture Notes. Selected Chapters

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    These are extended lecture notes of the quantum mechanics course which I am teaching in the Weizmann Institute of Science graduate physics program. They cover the topics listed below. The first four chapter are posted here. Their content is detailed on the next page. The other chapters are planned to be added in the coming months. 1. Motion in External Electromagnetic Field. Gauge Fields in Quantum Mechanics. 2. Quantum Mechanics of Electromagnetic Field 3. Photon-Matter Interactions 4. Quantization of the Schr\"odinger Field (The Second Quantization) 5. Open Systems. Density Matrix 6. Adiabatic Theory. The Berry Phase. The Born-Oppenheimer Approximation 7. Mean Field Approaches for Many Body Systems -- Fermions and Boson

    A hybrid quantum algorithm to detect conical intersections

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    Conical intersections are topologically protected crossings between the potential energy surfaces of a molecular Hamiltonian, known to play an important role in chemical processes such as photoisomerization and non-radiative relaxation. They are characterized by a non-zero Berry phase, which is a topological invariant defined on a closed path in atomic coordinate space, taking the value π\pi when the path encircles the intersection manifold. In this work, we show that for real molecular Hamiltonians, the Berry phase can be obtained by tracing a local optimum of a variational ansatz along the chosen path and estimating the overlap between the initial and final state with a control-free Hadamard test. Moreover, by discretizing the path into NN points, we can use NN single Newton-Raphson steps to update our state non-variationally. Finally, since the Berry phase can only take two discrete values (0 or π\pi), our procedure succeeds even for a cumulative error bounded by a constant; this allows us to bound the total sampling cost and to readily verify the success of the procedure. We demonstrate numerically the application of our algorithm on small toy models of the formaldimine molecule (\ce{H2C=NH}).Comment: 15 + 10 pages, 4 figure

    Barren plateaus in quantum tensor network optimization

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    We analyze the barren plateau phenomenon in the variational optimization of quantum circuits inspired by matrix product states (qMPS), tree tensor networks (qTTN), and the multiscale entanglement renormalization ansatz (qMERA). We consider as the cost function the expectation value of a Hamiltonian that is a sum of local terms. For randomly chosen variational parameters we show that the variance of the cost function gradient decreases exponentially with the distance of a Hamiltonian term from the canonical centre in the quantum tensor network. Therefore, as a function of qubit count, for qMPS most gradient variances decrease exponentially and for qTTN as well as qMERA they decrease polynomially. We also show that the calculation of these gradients is exponentially more efficient on a classical computer than on a quantum computer

    Soliton Gas: Theory, Numerics and Experiments

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    The concept of soliton gas was introduced in 1971 by V. Zakharov as an infinite collection of weakly interacting solitons in the framework of Korteweg-de Vries (KdV) equation. In this theoretical construction of a diluted soliton gas, solitons with random parameters are almost non-overlapping. More recently, the concept has been extended to dense gases in which solitons strongly and continuously interact. The notion of soliton gas is inherently associated with integrable wave systems described by nonlinear partial differential equations like the KdV equation or the one-dimensional nonlinear Schr\"odinger equation that can be solved using the inverse scattering transform. Over the last few years, the field of soliton gases has received a rapidly growing interest from both the theoretical and experimental points of view. In particular, it has been realized that the soliton gas dynamics underlies some fundamental nonlinear wave phenomena such as spontaneous modulation instability and the formation of rogue waves. The recently discovered deep connections of soliton gas theory with generalized hydrodynamics have broadened the field and opened new fundamental questions related to the soliton gas statistics and thermodynamics. We review the main recent theoretical and experimental results in the field of soliton gas. The key conceptual tools of the field, such as the inverse scattering transform, the thermodynamic limit of finite-gap potentials and the Generalized Gibbs Ensembles are introduced and various open questions and future challenges are discussed.Comment: 35 pages, 8 figure

    Variations on the Goroff-Sagnotti operator

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    The effect of modifying General Relativity with the addition of some higher dimensional operators, generalizations of the Goroff-Sagnotti operator, is discussed. We determine in particular, the general solution of the classical equations of motion, assuming it to be spherically symmetric, not necessarily static. Even in the non-spherically symmetric case, we present a necessary condition for an algebraically generic spacetime to solve the corresponding equations of motion. Some examples of an application of said condition are explicitly worked out.Comment: 12 page

    Full trajectory optimizing operator inference for reduced-order modeling using differentiable programming

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    Accurate and inexpensive Reduced Order Models (ROMs) for forecasting turbulent flows can facilitate rapid design iterations and thus prove critical for predictive control in engineering problems. Galerkin projection based Reduced Order Models (GP-ROMs), derived by projecting the Navier-Stokes equations on a truncated Proper Orthogonal Decomposition (POD) basis, are popular because of their low computational costs and theoretical foundations. However, the accuracy of traditional GP-ROMs degrades over long time prediction horizons. To address this issue, we extend the recently proposed Neural Galerkin Projection (NeuralGP) data driven framework to compressibility-dominated transonic flow, considering a prototypical problem of a buffeting NACA0012 airfoil governed by the full Navier-Stokes equations. The algorithm maintains the form of the ROM-ODE obtained from the Galerkin projection; however coefficients are learned directly from the data using gradient descent facilitated by differentiable programming. This blends the strengths of the physics driven GP-ROM and purely data driven neural network-based techniques, resulting in a computationally cheaper model that is easier to interpret. We show that the NeuralGP method minimizes a more rigorous full trajectory error norm compared to a linearized error definition optimized by the calibration procedure. We also find that while both procedures stabilize the ROM by displacing the eigenvalues of the linear dynamics matrix of the ROM-ODE to the complex left half-plane, the NeuralGP algorithm adds more dissipation to the trailing POD modes resulting in its better long-term performance. The results presented highlight the superior accuracy of the NeuralGP technique compared to the traditional calibrated GP-ROM method

    Qluster: An easy-to-implement generic workflow for robust clustering of health data

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    The exploration of heath data by clustering algorithms allows to better describe the populations of interest by seeking the sub-profiles that compose it. This therefore reinforces medical knowledge, whether it is about a disease or a targeted population in real life. Nevertheless, contrary to the so-called conventional biostatistical methods where numerous guidelines exist, the standardization of data science approaches in clinical research remains a little discussed subject. This results in a significant variability in the execution of data science projects, whether in terms of algorithms used, reliability and credibility of the designed approach. Taking the path of parsimonious and judicious choice of both algorithms and implementations at each stage, this article proposes Qluster, a practical workflow for performing clustering tasks. Indeed, this workflow makes a compromise between (1) genericity of applications (e.g. usable on small or big data, on continuous, categorical or mixed variables, on database of high-dimensionality or not), (2) ease of implementation (need for few packages, few algorithms, few parameters, ...), and (3) robustness (e.g. use of proven algorithms and robust packages, evaluation of the stability of clusters, management of noise and multicollinearity). This workflow can be easily automated and/or routinely applied on a wide range of clustering projects. It can be useful both for data scientists with little experience in the field to make data clustering easier and more robust, and for more experienced data scientists who are looking for a straightforward and reliable solution to routinely perform preliminary data mining. A synthesis of the literature on data clustering as well as the scientific rationale supporting the proposed workflow is also provided. Finally, a detailed application of the workflow on a concrete use case is provided, along with a practical discussion for data scientists. An implementation on the Dataiku platform is available upon request to the authors
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