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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Two transitions in complex eigenvalue statistics: Hermiticity and integrability breaking

Open quantum systems have complex energy eigenvalues which are expected to follow non-Hermitian random matrix statistics, when chaotic, or two-dimensional (2d) Poisson statistics, when integrable. We investigate the spectral properties of a many-body quantum spin chain, i.e., the Hermitian Heisenberg model with imaginary disorder. Its rich complex eigenvalue statistics is found to separately break both Hermiticity and integrability at different scales of the disorder strength. With no disorder, the system is integrable and Hermitian, with spectral statistics corresponding to the 1d Poisson point process. At very small disorder, we find a transition from 1d Poisson statistics to an effective D -dimensional Poisson point process, showing Hermiticity breaking. At intermediate disorder, we find integrability breaking, as inferred from the statistics matching that of non-Hermitian complex symmetric random matrices in class AI † . For large disorder, as the spins align, we recover the expected integrability (now in the non-Hermitian setup), indicated by 2d Poisson statistics. These conclusions are based on fitting the spin-chain data of numerically generated nearest- and next-to-nearest-neighbor spacing distributions to an effective 2d Coulomb gas description at inverse temperature β . We confirm that such an effective description of random matrices also applies in classes AI † and AII † up to next-to-nearest-neighbor spacings. Published by the American Physical Society 2025

Akemann, Gernot (ORCID:0000000217104258)↗
DOE OSTI2011

Stability of nonlinear Vlasov-Poisson equilibria through spectral deformation and Fourier-Hermite expansion

We study the stability of spatially periodic, nonlinear Vlasov-Poisson equilibria as an eigenproblem in a Fourier-Hermite basis (in the space and velocity variables, respectively) of finite dimension, N. When the advection term in the Vlasov equation is dominant, the convergence with N of the eigenvalues is rather slow, limiting the applicability of the method. We use the method of spectral deformation introduced by Crawford and Hislop [Ann. Phys. (NY) 189, 265 (1989)] to selectively damp the continuum of neutral modes associated with the advection term, thus accelerating convergence. We validate and benchmark the performance of our method by reproducing the kinetic dispersion relation results for linear (spatially homogeneous) equilibria. Finally, we study the stability of a periodic Bernstein-Greene-Kruskal mode with multiple phase-space vortices, compare our results with numerical simulations of the Vlasov-Poisson system, and show that the initial unstable equilibrium may evolve to different asymptotic states depending on the way it was perturbed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Compact feature-aware Hermite-style high-order surface reconstruction

High-order surface reconstruction is now a commonly used technique for mesh generation and adaptation, geometric and physical modeling, and high-order numerical methods for solving partial differential equations (PDEs). However, surface reconstruction from a relatively coarse mesh remained a challenging problem, especially for surfaces with sharp features. Here in this paper, we introduce a new method to address this challenge by improving the previous state of the art, including continuous moving frames (CMF) and weighted averaging of local fittings (WALF) (Eng Comput 28 (2012)), in two aspects. First, we significantly improve the robustness of reconstruction from coarse meshes using a Hermite-style least squares approximation to incorporate normals of the surface and tangents of the feature curves. Second, we ensure both G 0 continuity and high-order accuracy of the reconstruction near sharp features by generating parametric surface elements with an iterative feature-aware parameterization. We present the theoretical framework of our method and compare it against point-based methods in terms of accuracy and stability. We demonstrate the use of the proposed technique in generating high-order meshes for finite element methods, and show that it enables nearly identical solutions as using the meshes generated from exact geometry, while allowing additional flexibility.

42 ENGINEERING↗
DOE OSTI2014

Hermite WENO limiting for multi-moment finite-volume methods using the ADER-DT time discretization for 1-D systems of conservation laws

New Hermite Weighted Essentially Non-Oscillatory (HWENO) interpolants are developed and investigated within the Multi-Moment Finite-Volume (MMFV) formulation using the ADER-DT time discretization. Whereas traditional WENO methods interpolate pointwise, function-based WENO methods explicitly form a non-oscillatory, high-order polynomial over the cell in question. This study chooses a function-based approach and details how fast convergence to optimal weights for smooth flow is ensured. Methods of sixth-, eighth-, and tenth-order accuracy are developed. We compare these against traditional single-moment WENO methods of fifth-, seventh-, ninth-, and eleventh-order accuracy to compare against more familiar methods from literature. The new HWENO methods improve upon existing HWENO methods (1) by giving a better resolution of unreinforced contact discontinuities and (2) by only needing a single HWENO polynomial to update both the cell mean value and cell mean derivative. Test cases to validate and assess these methods include 1-D linear transport, the 1-D inviscid Burger's equation, and the 1-D inviscid Euler equations. Smooth and non-smooth flows are used for evaluation. These HWENO methods performed better than comparable literature-standard WENO methods for all regimes of discontinuity and smoothness in all tests herein. They exhibit improved optimal accuracy due to the use of derivatives, and they collapse to solutions similar to typical WENO methods when limiting is required. The study concludes that the new HWENO methods are robust and effective when used in the ADER-DT MMFV framework. Finally, these results are intended to demonstrate capability rather than exhaust all possible implementations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Hermite polynomials and quasi-classical asymptotics

We study an unorthodox variant of the Berezin-Toeplitz type of quantization scheme, on a reproducing kernel Hilbert space generated by the real Hermite polynomials and work out the associated quasi-classical asymptotics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Efficient modeling of photonic crystals with local Hermite polynomials

Developing compact algorithms for accurate electrodynamic calculations with minimal computational cost is an active area of research given the increasing complexity in the design of electromagnetic composite structures such as photonic crystals, metamaterials, optical interconnects, and on-chip routing. We show that electric and magnetic (EM) fields can be calculated using scalar Hermite interpolation polynomials as the numerical basis functions without having to invoke edge-based vector finite elements to suppress spurious solutions or to satisfy boundary conditions. This approach offers several fundamental advantages as evidenced through band structure solutions for periodic systems and through waveguide analysis. Compared with reciprocal space (plane wave expansion) methods for periodic systems, advantages are shown in computational costs, the ability to capture spatial complexity in the dielectric distributions, the demonstration of numerical convergence with scaling, and variational eigenfunctions free of numerical artifacts that arise from mixed-order real space basis sets or the inherent aberrations from transforming reciprocal space solutions of finite expansions. The photonic band structure of a simple crystal is used as a benchmark comparison and the ability to capture the effects of spatially complex dielectric distributions is treated using a complex pattern with highly irregular features that would stress spatial transform limits. This general method is applicable to a broad class of physical systems, e.g., to semiconducting lasers which require simultaneous modeling of transitions in quantum wells or dots together with EM cavity calculations, to modeling plasmonic structures in the presence of EM field emissions, and to on-chip propagation within monolithic integrated circuits.

36 MATERIALS SCIENCE↗
DOE OSTI2018

Hermite Methods for the Scalar Wave Equation

Arbitrary order dissipative and conservative Hermite methods for the scalar wave equation are presented here. Both methods use $(m+1)^d$ degrees of freedom per node for the displacement in $d$ dimensions; the dissipative and conservative methods achieve orders of accuracy $(2m-1)$ and $2m$, respectively. Stability and error analyses as well as implementation strategies for accelerators are also given.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

A third-order implicit discontinuous Galerkin method based on a Hermite WENO reconstruction for time-accurate solution of the compressible Navier-Stokes equations

Here, a space and time third-order discontinuous Galerkin method based on a Hermite weighted essentially non-oscillatory reconstruction is presented for the unsteady compressible Euler and Navier–Stokes equations. At each time step, a lower-upper symmetric Gauss–Seidel preconditioned generalized minimal residual solver is used to solve the systems of linear equations arising from an explicit first stage, single diagonal coefficient, diagonally implicit Runge–Kutta time integration scheme. The performance of the developed method is assessed through a variety of unsteady flow problems. Numerical results indicate that this method is able to deliver the designed third-order accuracy of convergence in both space and time, while requiring remarkably less storage than the standard third-order discontinous Galerkin methods, and less computing time than the lower-order discontinous Galerkin methods to achieve the same level of temporal accuracy for computing unsteady flow problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Arbitrarily High-Order-Accurate, Hermite WENO Limited, Boundary-Averaged Multi-Moment Constrained Finite-Volume (BA-MCV) Schemes for 1-D Transport

This study introduces the Boundary Averaged Multi-moment Constrained finite-Volume (BA- MCV) scheme for 1-D transport with Hermite Weighted Essentially Non-Oscillatory (HWENO) limiting using the ADER Differential Transform (ADER-DT) time discretization. The BA- MCV scheme evolves a cell average using a Finite-Volume (FV) scheme, and it adds further constraints as point wise derivatives of the state at cell boundaries, which are evolved in strong form using PDE derivatives. The resulting scheme maintains a Maximum Stable CFL (MSCFL) value of one no matter how high-order the scheme is. Also, parallel communication requirements are very low and will be described. h-refinement experiments demonstrate proper convergence order, and p-refinement experiments demonstrate expected exponential convergence. The over- all ADER-DT + BA-MCV + HWENO scheme is a scalable and larger time step alternative to Galerkin methods for multi-moment fluid simulation in climate and weather applications.

Norman, Matthew↗
DOE OSTI2022

Curving the space by non-Hermiticity

Quantum systems are often classified into Hermitian and non-Hermitian ones. Extraordinary non-Hermitian phenomena, ranging from the non-Hermitian skin effect to the supersensitivity to boundary conditions, have been widely explored. Whereas these intriguing phenomena have been considered peculiar to non-Hermitian systems, we show that they can be naturally explained by a duality between non-Hermitian models in flat spaces and their counterparts, which could be Hermitian, in curved spaces. For instance, prototypical one-dimensional (1D) chains with uniform chiral tunnelings are equivalent to their duals in two-dimensional (2D) hyperbolic spaces with or without magnetic fields, and non-uniform tunnelings could further tailor local curvatures. Such a duality unfolds deep geometric roots of non-Hermitian phenomena, delivers an unprecedented routine connecting Hermitian and non-Hermitian physics, and gives rise to a theoretical perspective reformulating our understandings of curvatures and distance. In practice, it provides experimentalists with a powerful two-fold application, using non-Hermiticity to engineer curvatures or implementing synthetic curved spaces to explore non-Hermitian quantum physics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

Laguerre–Gauss and Hermite–Gauss soft X-ray states generated using diffractive optics

Light’s capacity to carry angular momentum is integral to our knowledge of physics and ability to probe matter. In addition to spin, photons can occupy free-space orbital angular momentum eigenstates. Visible light orbital angular momentum is used in quantum information experiments, super-resolution microscopy, optical tweezers and angular momentum transfer to atoms in optical lattices. Soft X-ray orbital angular momentum applications, slowed by the lack of suitable optics and the rarity of coherent X-ray sources, could enable the direct alteration of atomic states through orbital angular momentum exchange, and methods to study the electronic properties of quantum materials. We have made soft X-ray diffractive optics that generate single Laguerre–Gauss modes, observed carrying up to 30$\hbar$ angular momentum per photon, or their superpositions. We also present Hermite–Gauss diffractive optics and a soft X-ray orbital angular momentum analyser. Finally, these tools could enable both the manipulation and finer characterization of topologically complex electronic matter, such as magnetic skyrmions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2013

New families of superintegrable systems from Hermite and Laguerre exceptional orthogonal polynomials

In recent years, many exceptional orthogonal polynomials (EOP) were introduced and used to construct new families of 1D exactly solvable quantum potentials, some of which are shape invariant. In this paper, we construct from Hermite and Laguerre EOP and their related quantum systems new 2D superintegrable Hamiltonians with higher-order integrals of motion and the polynomial algebras generated by their integrals of motion. We obtain the finite-dimensional unitary representations of the polynomial algebras and the corresponding energy spectrum. We also point out a new type of degeneracies of the energy levels of these systems that is associated with holes in sequences of EOP.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Small-displacement measurements using high-order Hermite-Gauss modes

We present a scheme for small-displacement measurements using high-order Hermite-Gauss modes and balanced homodyne detection. We demonstrate its use with experimental results of displacement measurements using fundamental transverse mode TEM{sub 00} and first order transverse mode TEM{sub 10} as signal modes. The results show a factor of 1.41 improvement in measurement precision with the TEM{sub 10} mode compared with that with the TEM{sub 00} mode. This scheme has potential applications in precision metrology, atomic force microscopy, and optical imaging.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Enhanced relativistic self-focusing of Hermite-cosh-Gaussian laser beam in plasma under density transition

Enhanced and early relativistic self-focusing of Hermite-cosh-Gaussian (HChG) beam in the plasmas under density transition has been investigated theoretically using Wentzel-Kramers-Brillouin and paraxial ray approximation for mode indices m=0, 1, and 2. The variation of beam width parameter with normalized propagation distance for m=0, 1, and 2 is reported, and it is observed that strong self-focusing occurs as the HChG beam propagates deeper inside the nonlinear medium as spot size shrinks due to highly dense plasmas and the results are presented graphically. A comparative study between self-focusing of HChG beam in the presence and absence of plasmas density transition is reported. The dependency of beam width parameter on the normalized propagation distance for different values of decentered parameter “b” has also been presented graphically. For m=0 and 1, strong self-focusing is reported for b=1.8, and for m=2 and b=1.8, beam gets diffracted. The results obtained indicate the dependency of the self-focusing of the HChG beam on the selected values of decentered parameter. Moreover, proper selection of decentered parameter results strong self-focusing of HChG beam. Stronger self-focusing of laser beam is observed due to the presence of plasma density transition which might be very useful in the applications like the generation of inertial fusion energy driven by lasers, laser driven accelerators, etc.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2015

Self-focusing of Hermite-Gaussian laser beam with relativistic nonlinearity

This paper presents an investigation of self-focusing of Hermite-Gaussian laser beams in plasma considering relativistic nonlinearity. The differential equations for beam width parameters are obtained using the usual Wentzel–Kramers–Brillouin and paraxial approximations. The nonlinearity in the dielectric constant is assumed to be aroused mainly due to the relativistic mass correction of electron. To highlight the nature of focusing, graphical results of the behavior of beam-width parameters with the dimensionless distance of propagation is presented. The numerical computation is completed by using Taylor series method. The present work is helpful to understand issues related to the beam propagation in laser plasma interaction experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Quantum dynamics of electronic transitions with Gauss-Hermite wave packets

A new methodology based on the superposition of time-dependent Gauss-Hermite wave packets is developed to describe the wave function of a system in which several interacting electronic states are coupled to a bath of harmonic oscillators. The equations of motion for the wave function parameters are obtained by employing the Dirac-Frenkel time-dependent variational principle. The methodology is applied to study the quantum dynamical behaviour of model systems with two interacting electronic states characterized by a relatively large reorganization energy and a range of energy biases. The favourable scaling properties make it a promising tool for the study of the dynamics of chemico-physical processes in molecular systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Effects of artificial collisions, filtering, and nonlocal closure approaches on Hermite-based Vlasov–Poisson simulations

Kinetic simulations of collisionless plasmas are computationally challenging due to phase-space mixing and filamentation, resulting in fine-scale velocity structures. This study compares three methods developed to reduce artifacts related to limited velocity resolution in Hermite-based Vlasov–Poisson simulations: artificial collisions, filtering, and nonlocal closure approaches. We evaluate each method's performance in approximating the linear kinetic response function and suppressing recurrence in linear and nonlinear regimes. Numerical simulations of Landau damping demonstrate that artificial collisions, particularly higher orders of the Lenard-Bernstein collisional operator, most effectively recover the correct damping rate across a range of wavenumbers. Moreover, Hou-Li filtering and nonlocal closures underdamp high wavenumber modes in linear simulations, and the Lenard-Bernstein collisional operator overdamps low wavenumber modes in both linear and nonlinear simulations. This study demonstrates that hypercollisions offer a robust approach to kinetic simulations, accurately capturing collisionless dynamics with limited velocity resolution.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Generation of Hermite–Gaussian modes of high-power femtosecond laser radiation using binary-phase diffractive optical elements

We present the results of experiments on generation of Hermite–Gaussian modes up to the third order inclusive using binary-phase diffractive optical elements (DOEs) illuminated by subterawatt femtosecond laser pulses. We perform a compariosn of the mode formation using DOEs designed by the kinoform method and the fractional coding technique, when the DOEs are illuminated by both femtosecond radiation and cw laser radiation at close wavelengths. (laser beams)

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗