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All sourcesNASA NTRSDOE OSTI
NASA NTRS2018

An Overview of Methods for Deriving the Radiative Transfer Theory from the Maxwell Equations. II: Approach Based on the Dyson and Bethe-Salpeter Equations

In this paper, the vector radiative transfer equation is derived by means of the vector integral Foldy equations describing the electromagnetic scattering by a group of particles. By assuming that in a discrete random medium the positions of the particles are statistically independent and by applying the Twersky approximation to the order-of-scattering expansion of the total field, we derive the Dyson equation for the coherent field and the ladder approximated Bethe–Salpeter equation for the dyadic correlation function. Then, under the far-field assumption for sparsely distributed particles, the Dyson equation is reduced to the Foldy integral equation for the coherent field, while the iterated solution of the Bethe–Salpeter equation ultimately yields the vector radiative transfer equation.

Electromagnetic scattering↗
DOE OSTI2025

Efficient Hamiltonian encoding algorithms for extracting quantum control mechanism as interfering pathway amplitudes in the Dyson series

Hamiltonian encoding is a methodology for revealing the mechanism behind the dynamics governing controlled quantum systems. In this paper, following Mitra and Rabitz \cite{abhra_1}, we define mechanism via pathways of eigenstates that describe the evolution of the system, where each pathway is associated with a complex-valued amplitude corresponding to a term in the Dyson series. The evolution of the system is determined by the constructive and destructive interference of these pathway amplitudes. Pathways with similar attributes can be grouped together into pathway classes. The amplitudes of pathway classes are computed by modulating the Hamiltonian matrix elements and decoding the subsequent evolution of the system rather than by direct computation of the individual terms in the Dyson series. The original implementation of Hamiltonian encoding was computationally intensive and became prohibitively expensive in large quantum systems. This paper presents two new encoding algorithms that calculate the amplitudes of pathway classes by using techniques from graph theory and algebraic topology to exploit patterns in the set of allowed transitions, greatly reducing the number of matrix elements that need to be modulated. These new algorithms provide an exponential decrease in both computation time and memory utilization with respect to the Hilbert space dimension of the system. To demonstrate the use of these techniques, they are applied to two illustrative state-to-state transition problems.

Abrams, Erez [Princeton University, Massachusetts ↗
NASA NTRS2008

Long-Wave Infrared Dyson Spectrometer

Preliminary results are presented for an ultra compact long-wave infrared slit spectrometer based on the dyson concentric design. The dyson spectrometer has been integrated in a dewar environment with a quantum well infrared photodetecor (QWIP), concave electron beam fabricated diffraction grating and ultra precision slit. The entire system is cooled to cryogenic temperatures to maximize signal to noise ratio performance, hence eliminating thermal signal from transmissive elements and internal stray light. All of this is done while maintaining QWIP thermal control. A general description is given of the spectrometer, alignment technique and predicated performance. The spectrometer has been designed for optimal performance with respect to smile and keystone distortion. A spectral calibration is performed with NIST traceable targets. A 2-point non-uniformity correction is performed with a precision blackbody source to provide radiometric accuracy. Preliminary laboratory results show excellent agreement with modeled noise equivalent delta temperature and detector linearity over a broad temperature range.

imaging↗
DOE OSTI2025

A Practical Framework for Simulating Time-Resolved Spectroscopy Based on a Real-Time Dyson Expansion

Time-resolved spectroscopy is a powerful tool for probing electron dynamics in molecules and solids, revealing transient phenomena on subfemtosecond time scales. The interpretation of experimental results is often enhanced by parallel numerical studies, which can provide insight and validation for experimental hypotheses. However, developing a theoretical framework for simulating time-resolved spectra remains a significant challenge. The most suitable approach involves the many-body nonequilibrium Green's function formalism, which accounts for crucial dynamical many-body correlations during time evolution. While these dynamical correlations are essential for observing emergent behavior in time-resolved spectra, they also render the formalism prohibitively expensive for large-scale simulations. Substantial effort has been devoted to reducing this computational cost─through approximations and numerical techniques─while preserving the key dynamical correlations. The ultimate goal is to enable first-principles simulations of time-dependent systems ranging from small molecules to large, periodic, multidimensional solids. Here, in this perspective, we outline key challenges in developing practical simulations for time-resolved spectroscopy, with a particular focus on Green's function methodologies. We highlight a recent advancement toward a scalable framework: the real-time Dyson expansion (RT-DE) [Phys. Rev. Lett. 2024, 133, 226902]. We introduce the theoretical foundation of RT-DE and discuss strategies for improving scalability, which have already enabled simulations of system sizes beyond the reach of previous fully dynamical approaches. We conclude with an outlook on future directions for extending RT-DE to first-principles studies of dynamically correlated, nonequilibrium systems.

Reeves, Cian C. [Univ. of California, Santa Barbar↗
DOE OSTI2024

BPZ equations for higher degenerate fields and nonperturbative Dyson-Schwinger equations

In the two-dimensional Liouville conformal field theory, correlation functions involving a degenerate field satisfy partial differential equations due to the decoupling of the null descendant field. On the other hand, the instanton partition function of a four-dimensional N = 2 supersymmetric theory in the Ω -background at a special point of the parameter space also satisfies a partial differential equation resulting from the constraints of the gauge field configurations. This partial differential equation can be proved using the nonperturbative Dyson-Schwinger equations. We show for the next-to-simplest case that the partial differential equations obtained from two different perspectives can be identified, thereby confirming an assertion of the Bogomol’nyi-Prasad-Sommerfield/conformal field theory correspondence. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
NASA NTRS1985

Remote sensing of earth terrain

Progress on the investigation of the anisotropy of the terrain media, such as vegetation canopy and sea ice, and the study of the fluctuation-dissipation theorem in conjunction with the application of strong fluctuation theory for passive remote sensing of snowpacks is reported. The Feynman diagrammatic technique is used to derive the Dyson equation for the mean field and the Bethe-Salpeter equation for the correlation or the covariance of the field for electromagnetic wave propagation and scattering in an anisotropic random medium. With the random permittivity expressed in a general form, the bilocal and the nonlinear approximations are employed to solve the Dyson equation and the ladder approximation to the Bethe-Salpeter equation. The mean dyadic Green's function for a two layer anisotropic random medium with arbitrary three dimensional correlation function was investigated with the zeroth-order solutions to the Dyson equation under the four characteristic waves associated with the coherent vector fields propagating in an anisotropic random medium layer, which are the ordinary and extraordinary waves with upward and downward propagating vectors.

Kong, J. A.↗
NASA NTRS1985

Electromagnetic wave scattering in a two-layer anisotropic random medium

For electromagnetic wave propagation and scattering in an anisotropic random medium, the Dyson equation for the mean field and the Bethe-Salpeter equation for the correlation or the covariance of the field were derived. With the random permittivity expressed in a general anisotropic form, the bilocal and the nonlinear approximations are employed to solve the Dyson equation, and the ladder approximation to solve the Bethe-Salpeter equation. The mean dyadic Green's function for a two-layer anisotropic random medium with arbitrary three-dimensional correlation functions has been investigated with the zeroth-order solutions to the Dyson equation under the nonlinear approximation. The effective propagation constants are calculated for the four characteristic waves associated with the coherent vector fields, propagating in an anisotropic random-medium layer, which are the ordinary and extraordinary waves with upward- and downward-propagating vectors.

Lee, J. K.↗
DOE OSTI2024

Thermal quasiparticle theory

The widely used thermal Hartree–Fock (HF) theory is generalized to include the effect of electron correlation while maintaining its quasi-independent-particle framework. An electron-correlated internal energy (or grand potential) is postulated in consultation with the second-order finite-temperature many-body perturbation theory (MBPT), which then dictates the corresponding thermal orbital (quasiparticle) energies in such a way that all fundamental thermodynamic relations are obeyed. The associated density matrix is of a one-electron type, whose diagonal elements take the form of the Fermi–Dirac distribution functions, when the grand potential is minimized. The formulas for the entropy and chemical potential are unchanged from those of Fermi–Dirac or thermal HF theory. The theory thus stipulates a finite-temperature extension of the second-order Dyson self-energy of one-particle many-body Green’s function theory and can be viewed as a second-order, diagonal, frequency-independent, thermal inverse Dyson equation. At low temperatures, the theory approaches finite-temperature MBPT of the same order, but it may outperform the latter at intermediate temperatures by including additional electron-correlation effects through orbital energies. Here, a physical meaning of these thermal orbital energies is proposed (encompassing that of thermal HF orbital energies, which has been elusive) as a finite-temperature version of Janak’s theorem.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS2011

HyTES: Thermal Imaging Spectrometer Development

The Jet Propulsion Laboratory has developed the Hyperspectral Thermal Emission Spectrometer (HyTES). It is an airborne pushbroom imaging spectrometer based on the Dyson optical configuration. First low altitude test flights are scheduled for later this year. HyTES uses a compact 7.5-12 micrometer m hyperspectral grating spectrometer in combination with a Quantum Well Infrared Photodetector (QWIP) and grating based spectrometer. The Dyson design allows for a very compact and optically fast system (F/1.6). Cooling requirements are minimized due to the single monolithic prism-like grating design. The configuration has the potential to be the optimal science-grade imaging spectroscopy solution for high altitude, lighter-than-air (HAA, LTA) vehicles and unmanned aerial vehicles (UAV) due to its small form factor and relatively low power requirements. The QWIP sensor allows for optimum spatial and spectral uniformity and provides adequate responsivity which allows for near 100mK noise equivalent temperature difference (NEDT) operation across the LWIR passband. The QWIP's repeatability and uniformity will be helpful for data integrity since currently an onboard calibrator is not planned. A calibration will be done before and after eight hour flights to gage any inconsistencies. This has been demonstrated with lab testing. Further test results show adequate NEDT, linearity as well as applicable earth science emissivity target results (Silicates, water) measured in direct sunlight.

remote sensing↗
NASA NTRS2011

The Hyperspectral Thermal Emission Spectrometer (HyTES): Preliminary Results

The Hyperspectral Thermal Emission Spectrometer (HyTES) is being developed as part of the risk reduction activities associated with the Hyperspectral Infrared Imager (HyspIRI). HyspIRI is one of the Tier 2 Decadal Survey Missions. HyTES will provide information on how to place the filters on the HyspIRI Thermal Infrared Instrument (TIR) as well as provide antecedent science data. The pushbroom design has 512 spatial pixels over a 50-degree field of view and 256 spectral channels between 7.5 micrometers to 12 micrometers. HyTES includes many key enabling state-of-the-art technologies including a high performance convex diffraction grating, a quantum well infrared photodetector (QWIP) focal plane array, and a compact Dyson-inspired optical design. The Dyson optical design allows for a very compact and optically fast system (F/1.6). It also minimizes cooling requirements due to the fact it has a single monolithic prism-like grating design which allows baffling for stray light suppression. The monolithic configuration eases mechanical tolerancing requirements which are a concern since the complete optical assembly is operated at cryogenic temperatures ((is) approximately 100K). The QWIP allows for optimum spatial and spectral uniformity and provides adequate responsivity or D-star to allow 200mK noise equivalent temperature difference (NEDT) operation across the LWIR passband. Assembly of the system is nearly complete. After completion, alignment results will be presented which show low keystone and smile distortion. This is required to minimize spatial-spectral mixing between adjacent spectral channels and spatial positions. Predictions show the system will have adequate signal to noise for laboratory calibration targets.

Moon Mineralogical Mapper (M3).↗
NASA NTRS2009

Thermal Infrared Spectral Imager for Airborne Science Applications

An airborne thermal hyperspectral imager is under development which utilizes the compact Dyson optical configuration and quantum well infrared photo detector (QWIP) focal plane array. The Dyson configuration uses a single monolithic prism-like grating design which allows for a high throughput instrument (F/1.6) with minimal ghosting, stray-light and large swath width. The configuration has the potential to be the optimal imaging spectroscopy solution for lighter-than-air (LTA) vehicles and unmanned aerial vehicles (UAV) due to its small form factor and relatively low power requirements. The planned instrument specifications are discussed as well as design trade-offs. Calibration testing results (noise equivalent temperature difference, spectral linearity and spectral bandwidth) and laboratory emissivity plots from samples are shown using an operational testbed unit which has similar specifications as the final airborne system. Field testing of the testbed unit was performed to acquire plots of apparent emissivity for various known standard minerals (such as quartz). A comparison is made using data from the ASTER spectral library.

QWIP↗
NASA NTRS2005

Stirling Analysis Comparison of Commercial Versus High-Order Methods

Recently, three-dimensional Stirling engine simulations have been accomplished utilizing commercial Computational Fluid Dynamics software. The validations reported can be somewhat inconclusive due to the lack of precise time accurate experimental results from engines, export control/proprietary concerns, and the lack of variation in the methods utilized. The last issue may be addressed by solving the same flow problem with alternate methods. In this work, a comprehensive examination of the methods utilized in the commercial codes is compared with more recently developed high-order methods. Specifically, Lele's compact scheme and Dyson's Ultra Hi-Fi method will be compared with the SIMPLE and PISO methods currently employed in CFD-ACE, FLUENT, CFX, and STAR-CD (all commercial codes which can in theory solve a three-dimensional Stirling model with sliding interfaces and their moving grids limit the effective time accuracy). We will initially look at one-dimensional flows since the current standard practice is to design and optimize Stirling engines with empirically corrected friction and heat transfer coefficients in an overall one-dimensional model. This comparison provides an idea of the range in which commercial CFD software for modeling Stirling engines may be expected to provide accurate results. In addition, this work provides a framework for improving current one-dimensional analysis codes.

Dyson, Rodger W.↗
NASA NTRS2007

Stirling Analysis Comparison of Commercial vs. High-Order Methods

Recently, three-dimensional Stirling engine simulations have been accomplished utilizing commercial Computational Fluid Dynamics software. The validations reported can be somewhat inconclusive due to the lack of precise time accurate experimental results from engines, export control/ proprietary concerns, and the lack of variation in the methods utilized. The last issue may be addressed by solving the same flow problem with alternate methods. In this work, a comprehensive examination of the methods utilized in the commercial codes is compared with more recently developed high-order methods. Specifically, Lele's Compact scheme and Dyson s Ultra Hi-Fi method will be compared with the SIMPLE and PISO methods currently employed in CFD-ACE, FLUENT, CFX, and STAR-CD (all commercial codes which can in theory solve a three-dimensional Stirling model although sliding interfaces and their moving grids limit the effective time accuracy). We will initially look at one-dimensional flows since the current standard practice is to design and optimize Stirling engines with empirically corrected friction and heat transfer coefficients in an overall one-dimensional model. This comparison provides an idea of the range in which commercial CFD software for modeling Stirling engines may be expected to provide accurate results. In addition, this work provides a framework for improving current one-dimensional analysis codes.

Dyson, Rodger W.↗
NASA NTRS2009

Compact Infrared Spectrometers

Concentric spectrometer forms are advantageous for constructing a variety of systems spanning the entire visible to infrared range. Spectrometer examples are given, including broadband or high resolution forms. Some issues associated with the Dyson catadioptric type are also discussed.

imaging spectroscopy↗
DOE OSTI2024

Perturbative unorientable JT gravity and matrix models

We consider an orthogonal polynomial formulation of the double scaling limit of multicritical matrix models in the β = 1 Dyson-Wigner class. They capture the physics of 2D quantum gravity coupled to minimal matter on unorientable surfaces, otherwise called unoriented minimal strings. We derive a formula for the density of states valid to all orders in perturbation theory. We show how to define an interpolation between the multicritical models and that a certain interpolation among an infinite number of them provides an alternative definition of unoriented JT gravity. We discuss the strengths and weaknesses of our formulation.

1/N Expansion↗
DOE OSTI2024

Open-closed string duality, branes, and topological recursion

We consider matrix models exhibiting open-closed string duality in two-dimensional string theories with various amounts of supersymmetry. In particular, a relationship between matrix models in the β = 2 Wigner-Dyson class and models in the (1 + 2Γ, 2) Altland-Zirnbauer class relates the perturbative solutions of the two systems’ string equations. Point-like operator insertions in the closed string theory are mapped to the topological expansion of the free energy in the open string theory. We compute correlation functions of macroscopic loop operators and FZZT branes in a general topological gravity background. The relationship between the topological recursion of moduli space volumes and branes is discussed by analyzing the Virasoro conditions in the matrix models.

2D Gravity↗