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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 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 OSTI2023

Soft gravitons in the BFSS matrix model

BFSS proposed that asymptotically flat M-theory is dual to a large N limit of the matrix quantum mechanics describing N nonrelativistic D0-branes. Recent insights on the soft symmetries of any quantum theory of gravity in asymptotically flat space are applied to the BFSS matrix model. It is shown that soft gravitons are realized by submatrices whose rank is held fixed in the large N M-theory limit, rather than the usual linear scaling with N for hard gravitons. The soft expansion is identified with the large N expansion and the soft theorem becomes a universal formula for the quantum mechanical scattering of such submatrix excitations. This formula is shown to be the Ward identity of large type IIA U(1) RR asymptotic gauge symmetry in the matrix model, whose asymptotic boundaries are at future and past timelike infinity.

1/N Expansion↗
DOE OSTI2016

Chaos in matrix models and black hole evaporation

Is the evaporation of a black hole described by a unitary theory? In order to shed light on this question—especially aspects of this question such as a black hole’s negative specific heat—we consider the real-time dynamics of a solitonic object in matrix quantum mechanics, which can be interpreted as a black hole (black zero-brane) via holography. We point out that the chaotic nature of the system combined with the flat directions of its potential naturally leads to the emission of D0-branes from the black brane, which is suppressed in the large N limit. Simple arguments show that the black zero-brane, like the Schwarzschild black hole, has negative specific heat, in the sense that the temperature goes up when it evaporates by emitting D0-branes. While the largest Lyapunov exponent grows during the evaporation, the Kolmogorov-Sinai entropy decreases. These are consequences of the generic properties of matrix models and gauge theory. Based on these results, we give a possible geometric interpretation of the eigenvalue distribution of matrices in terms of gravity. Applying the same argument in the M-theory parameter region, we provide a scenario to derive the Hawking radiation of massless particles from the Schwarzschild black hole. In conclusion, we suggest that by adding a fraction of the quantum effects to the classical theory, we can obtain a matrix model whose classical time evolution mimics the entire life of the black brane, from its formation to the evaporation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Convergence in High Probability of the Quantum Diffusion in a Random Band Matrix Model

We consider Hermitian random band matrices H in d⩾1 dimensions. The matrix elements H{sub xy}, indexed by x,y∈Λ⊂ℤ{sup d}, are independent, uniformly distributed random variable if |x−y| is less than the band width W, and zero otherwise. We update the previous results of the converge of quantum diffusion in a random band matrix model from convergence of the expectation to convergence in high probability. The result is uniformly in the size |Λ| of the matrix.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Fuzzy spheres in stringy matrix models: quantifying chaos in a mixed phase space

We consider a truncation of the BMN matrix model to a configuration of two fuzzy spheres, described by two coupled non-linear oscillators dependent on the mass parameter μ. The classical phase diagram of the system generically (μ ≠ 0) contains three equilibrium points: two centers and a center-saddle; as μ → 0 the system exhibits a pitchfork bifurcation. We demonstrate that the system is exactly integrable in quadratures for μ = 0, while for very large values of μ, it approaches another integrable point characterized by two harmonic oscillators. The classical phase space is mixed, containing both integrable islands and chaotic regions, as evidenced by the classical Lyapunov spectrum. At the quantum level, we explore indicators of early and late time chaos. The eigenvalue spacing is best described by a Brody distribution, which interpolates between Poisson and Wigner distributions; it dovetails, at the quantum level, the classical results and reemphasizes the notion that the quantum system is mixed. We also study the spectral form factor and the quantum Lyapunov exponent, as defined by out-of-time-ordered correlators. These two indicators of quantum chaos exhibit weak correlations with the Brody distribution. We speculate that the behavior of the system as μ → 0 dominates the spectral form factor and the quantum Lyapunov exponent, making these indicators of quantum chaos less effective in the context of a mixed phase space.

AdS-CFT correspondence↗
DOE OSTI2024

Nonperturbative random matrix model of N = 2 JT supergravity

It is shown how to nonperturbatively define a random matrix model that captures key physics of N = 2 Jackiw-Teitelboim supergravity, going well beyond the perturbative topological expansion defined recently by Turiaci and Witten. A decomposition into an infinite family of certain multicritical models is derived, leading to the definition of a nonlinear ordinary differential equation from which the physics may be computed. Bogomol’nyi-Prasad-Sommerfield (BPS) states are naturally described by the model. The nonperturbative completions of the spectral densities for non-BPS multiplets are readily extracted. Published by the American Physical Society 2024

Johnson, Clifford V. (ORCID:0000000189645830)↗
DOE OSTI2018

More on the new large D limit of matrix models

In this paper, we extend the recent analysis of the new large D limit of matrix models to the cases where the action contains arbitrary multi-trace interaction terms as well as to arbitrary correlation functions. We discuss both the cases of complex and Hermitian matrices, with U(N){sup 2}×O(D) and U(N)×O(D) symmetries respectively. In the latter case, the new large D limit is consistent for planar diagrams; at higher genera, it crucially requires the tracelessness condition. For similar reasons, the large N limit of tensor models with reduced symmetries is typically inconsistent already at leading order without the tracelessness condition. We also further discuss some interesting properties of purely bosonic models pointed out recently and explain that the standard argument predicting a non-trivial IR behavior in fermionic models à la SYK does not work for bosonic models. Finally, we explain that the new large D scaling is consistent with linearly realized supersymmetry.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Finite-temperature phase diagram of the Berenstein-Maldacena-Nastase matrix model on the lattice

We investigate the thermal phase structure of the Berenstein-Maldacena-Nastase matrix model using nonperturbative lattice Monte Carlo calculations. Our main analyses span 3 orders of magnitude in the coupling, involving systems with sizes up to 𝑁𝜏 =24 lattice sites and SU⁡(𝑁) gauge groups with 8 ≤𝑁 ≤16. In addition, we carry out extended checks of discretization artifacts for 𝑁𝜏 ≤128 and gauge group SU(4). We find results for the deconfinement temperature that interpolate between the perturbative prediction at weak coupling and the large-𝑁 dual supergravity calculation at strong coupling. While we confirm that the phase transition is first order for strong coupling, it appears to be continuous for weaker couplings.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Density-Matrix Model for Photon-Driven Transport in Quantum Cascade Lasers

In this report we develop a time-dependent density-matrix model to study photon-assisted (PA) electron transport in quantum cascade lasers. The Markovian equation of motion for the density matrix in the presence of an optical field is solved for an arbitrary field amplitude. Level-broadening terms emerge from microscopic Hamiltonians and supplant the need for empirical parameters that are often employed in related approaches. We show that, in quantum cascade lasers with diagonal design, photon resonances have a pronounced impact on electron dynamics around and above the lasing threshold, an effect that stems from the large spatial separation between the upper and lower lasing states. With the inclusion of PA tunneling, the calculated current density and output power are in good agreement with experiment.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Higher rank ABJM Wilson loops from matrix models

We compute the vacuum expectation values of 1/6 supersymmetric Wilson loops in higher dimensional representations of the gauge group in ABJM theory. We then present results for the m-symmetric and m-antisymmetric representations by exploiting standard matrix model techniques. At leading order, in the saddle point approximation, our expressions reproduce holographic results from both D6 and D2 branes corresponding to the antisymmetric and symmetric representations, respectively. We also compute 1/N corrections to the leading saddle point results.

1/N Expansion↗
DOE OSTI2024

Random matrix model of the Virasoro minimal string

The model of two dimensional quantum gravity defining the Virasoro minimal string, presented recently by Collier, Eberhardt, Mühlmann, and Rodriguez, was also shown to be perturbatively (in topology) equivalent to a random matrix model. An alternative definition is presented here, in terms of double-scaled orthogonal polynomials, thereby allowing direct access to nonperturbative physics. Already at leading order, the defining string equation’s properties yield valuable information about the nonperturbative fate of the model, confirming that the case ( c = 25 , c ^ = 1 ) (central charges of spacelike and timelike Liouville sectors) is special, by virtue of sharing certain key features of the N = 1 supersymmetric JT gravity string equation. Solutions of the full string equation are constructed using a special limit, and the (Cardy) spectral density is completed to all genus and beyond. The distributions of the underlying discrete spectra are readily accessible too, as is the spectral form factor. Some examples of these are exhibited. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2023

Even spheres as joint spectra of matrix models

The Clifford spectrum is a form of joint spectrum for noncommuting matrices. This theory has been applied in photonics, condensed matter and string theory. In applications, the Clifford spectrum can be efficiently approximated using numerical methods, but this only is possible in low dimensional example. In this paper we examine the higher-dimensional spheres that can arise from theoretical examples. We also describe a constructive method to generate five real symmetric almost commuting matrices that have a K-theoretical obstruction to being close to commuting matrices. For this, we look to matrix models of topological electric circuits.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

2D dilaton-gravity, deformations of the minimal string, and matrix models

A large class of two-dimensional dilaton-gravity theories in asymptotically AdS2 spacetimes are holographically dual to a matrix integral, interpreted as an ensemble average over Hamiltonians. Viewing these theories as Jackiw–Teitelboim gravity with a gas of defects, we extend this duality to a broader class of dilaton potentials compared to previous work by including conical defects with small deficit angles. In order to do this we show that these theories are equal to the large p limit of a natural deformation of the (2, p) minimal string theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Flow and transport in three-dimensional discrete fracture matrix models using mimetic finite difference on a conforming multi-dimensional mesh

Here, we present a comprehensive workflow to simulate single-phase flow and transport in fractured porous media using the discrete fracture matrix approach. The workflow has three primary parts: (1) a method for conforming mesh generation of and around a three-dimensional fracture network, (2) the discretization of the governing equations using a second-order mimetic finite difference method, and (3) implementation of numerical methods for high-performance computing environments. A method to create a conforming Delaunay tetrahedralization of the volume surrounding the fracture network, where the triangular cells of the fracture mesh are faces in the volume mesh, that addresses pathological cases which commonly arise and degrade mesh quality is also provided. Our open-source subsurface simulator uses a hierarchy of process kernels (one kernel per physical process) that allows for both strong and weak coupling of the fracture and matrix domains. We provide verification tests based on analytic solutions for flow and transport, as well as numerical convergence. We also provide multiple expositions of the method in complex fracture networks. In the first example, we demonstrate that the method is robust by considering two scenarios where the fracture network acts as a barrier to flow, as the primary pathway, or offers the same resistance as the surrounding matrix. In the second test, flow and transport through a three-dimensional stochastically generated network containing 257 fractures is presented.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A Mixed Fracture-Matrix Model for Evaluating Well Orientation and Completion Options for the Utah FORGE Site

Orientation and completion for well pairs that have been subjected to multi-zonal stimulation play a critical role in the long-term performance of an Enhanced Geothermal Reservoir. Here we present the development of a methodology to rapidly and efficiently numerically simulate mixed fracture-matrix flow systems for evaluation of well design and completion options. An example evaluation based on a small fracture network representative of FORGE Well 16(A and B)-78(32) follows a discussion of the theory and model validation.

58 GEOSCIENCES↗
DOE OSTI2021

A Mixed Fracture-Matrix Model for Evaluating Well Orientation and Completion Options for the Utah FORGE Site

Orientation and completion for well pairs that have been subjected to multi-zonal stimulation play a critical role in the long-term performance of an Enhanced Geothermal Reservoir. Here we present the development of a methodology to rapidly and efficiently numerically simulate mixed fracture-matrix flow systems for evaluation of well design and completion options. An example evaluation based on a small fracture network representative of FORGE Well 16(A and B)-78(32) follows a discussion of the theory and model validation.

15 GEOTHERMAL ENERGY↗