46,604 research outputs found
MAS: A versatile Landau-fluid eigenvalue code for plasma stability analysis in general geometry
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
Rank-based linkage is a new tool for summarizing a collection 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 . Rank-based linkage is applied
to the -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
-nearest neighbor graph on . In steps it builds an
edge-weighted linkage graph where
is called the in-sway between objects and . Take to be
the links whose in-sway is at least , and partition into components of
the graph , for varying . 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
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
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
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 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
points, we can use single Newton-Raphson steps to update our state
non-variationally. Finally, since the Berry phase can only take two discrete
values (0 or ), 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
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
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
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
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
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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