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All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

Accurate prediction of diradical chemistry from a single-reference density-matrix method: Model application to the bicyclobutane to gauche-1,3-butadiene isomerization

Multireference correlation in diradical molecules can be captured by a single-reference 2-electron reduced-density-matrix (2-RDM) calculation with only single and double excitations in the 2-RDM parametrization. The 2-RDM parametrization is determined by N-representability conditions that are non-perturbative in their treatment of the electron correlation. Conventional single-reference wave function methods cannot describe the entanglement within diradical molecules without employing triple- and potentially even higher-order excitations of the mean-field determinant. In the isomerization of bicyclobutane to gauche-1,3-butadiene the parametric 2-RDM (p2-RDM) method predicts that the diradical disrotatory transition state is 58.9 kcal/mol above bicyclobutane. This barrier is in agreement with previous multireference calculations as well as recent Monte Carlo and higher-order coupled cluster calculations. The p2-RDM method predicts the Nth natural-orbital occupation number of the transition state to be 0.635, revealing its diradical character. The optimized geometry from the p2-RDM method differs in important details from the complete-active-space self-consistent-field geometry used in many previous studies including the Monte Carlo calculation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Krylov complexity in mixed phase space

We investigate the Krylov complexity of thermofield double states in systems with mixed phase space, uncovering a direct correlation with the Brody distribution, which interpolates between Poisson and Wigner statistics. Our analysis spans two-dimensional random matrix models featuring (I) GOE-Poisson and (II) GUE-Poisson transitions and extends to higher-dimensional cases, including a stringy matrix model (GOE-Poisson) and the mass-deformed SYK model (GUE-Poisson). Krylov complexity consistently emerges as a reliable marker of quantum chaos, displaying a characteristic peak in the chaotic regime that gradually diminishes as the Brody parameter approaches zero, signaling a shift toward integrability. These results establish Krylov complexity as a powerful diagnostic of quantum chaos and highlight its interplay with eigenvalue statistics in mixed phase systems.

chaos & nonlinear dynamics↗
DOE OSTI2022

Replica symmetry breaking for the integrable two-site Sachdev–Ye–Kitaev model

We analyze a two-body non-Hermitian two-site Sachdev–Ye–Kitaev (SYK) model with the couplings of one site complex conjugated to the other site. This model, with no explicit coupling between the sites, shows an infinite number of second-order phase transitions, which is a consequence of the factorization of the partition function into a product over Matsubara frequencies. We calculate the quenched free energy in two different ways: first in terms of the single-particle energies and second by solving the Schwinger–Dyson equations of the two-site model. The first calculation can be done entirely in terms of a one-site model. The conjugate replica enters due to non-analyticities when Matsubara frequencies enter the spectral support of the coupling matrix. The second calculation is based on the replica trick of the two-site partition function. Both methods give the same result. The free-fermion partition function can also be rephrased as a matrix model for the coupling matrix. Up to minor details, this model is the random matrix model that describes the chiral phase transition of QCD, and the order parameter of the two-body model corresponds to the chiral condensate of QCD. Comparing to the corresponding four-body model, we are able to determine which features of the free energy are due to the chaotic nature of the four-body model. The high-temperature phase of both models is entropy dominated, and in both cases, the free energy is determined by the spectral density. The chaotic four-body SYK model has a low-temperature phase whose free energy is almost temperature-independent, signaling an effective gap of the theory even though the actual spectrum does not exhibit a gap. On the other hand, the low-temperature free energy of the two-body SYK model is not flat; in fact, it oscillates to arbitrarily low temperature. This indicates a less desirable feature that the entropy of the two-body model is not always positive in the low-temperature phase, which most likely is a consequence of the non-hermiticity.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Sub-leading structures in superconformal indices: subdominant saddles and logarithmic contributions

We systematically study various sub-leading structures in the superconformal index of N = 4 supersymmetric Yang-Mills theory with SU(N) gauge group. We concentrate in the superconformal index description as a matrix model of elliptic gamma functions and in the Bethe-Ansatz presentation. Our saddle-point approximation goes beyond the Cardy-like limit and we uncover various saddles governed by a matrix model corresponding to SU(N) Chern-Simons theory. The dominant saddle, however, leads to perfect agreement with the Bethe-Ansatz approach. We also determine the logarithmic correction to the superconformal index to be log N, finding precise agreement between the saddle-point and Bethe-Ansatz approaches in their respective approximations. We generalize the two approaches to cover a large class of 4d N = 1 superconformal theories. We find that also in this case both approximations agree all the way down to a universal contribution of the form log N. The universality of this last result constitutes a robust signature of this ultraviolet description of asymptotically AdS 5 black holes and could be tested by low-energy IIB supergravity.

1/N expansion↗
DOE OSTI2024

Three point amplitudes in matrix theory

We compute the three graviton amplitude in the Banks-Fischler-Shenker-Susskind matrix model for M-theory. Even though the three point amplitude is determined by super Poincare invariance in eleven dimensional M-theory, it requires a non-trivial computation in the matrix model. We consider a configuration where all three gravitons carry non-zero longitudinal momentum. To simplify the problem, we compactify one additional dimension and relate the amplitude to a supersymmetric index computation. Here, we find agreement with the expected answer even at finite values of N.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Dynamics of disordered mechanical systems with large connectivity, free probability theory, and quasi-Hermitian random matrices

Disordered mechanical systems with high connectivity represent a limit opposite to the more familiar case of disordered crystals. Individual ions in a crystal are subjected essentially to nearest-neighbor interactions. In contrast, the systems studied in this paper have all their degrees of freedom coupled to each other. Thus, the problem of linearized small oscillations of such systems involves two full positive-definite and non-commuting matrices, as opposed to the sparse matrices associated with disordered crystals. Consequently, the familiar methods for determining the averaged vibrational spectra of disordered crystals, introduced many years ago by Dyson and Schmidt, are inapplicable for highly connected disordered systems. In this paper we apply random matrix theory (RMT) to calculate the averaged vibrational spectra of such systems, in the limit of infinitely large system size. At the heart of our analysis lies a calculation of the average spectrum of the product of two positive definite random matrices by means of free probability theory techniques. We also show that this problem is intimately related with quasi-hermitian random matrix theory (QHRMT), which means that the ‘hamiltonian’ matrix is hermitian with respect to a non-trivial metric. This extends ordinary hermitian matrices, for which the metric is simply the unit matrix. The analytical results we obtain for the spectrum agree well with our numerical results. The latter also exhibit oscillations at the high-frequency band edge, which fit well the Airy kernel pattern. We also compute inverse participation ratios of the corresponding amplitude eigenvectors and demonstrate that they are all extended, in contrast with conventional disordered crystals. Finally, we compute the thermodynamic properties of the system from its spectrum of vibrations. In addition to matrix model analysis, we also study the vibrational spectra of various multi-segmented disordered pendula, as concrete realizations of highly connected mechanical systems. A universal feature of the density of vibration modes, common to both pendula and the matrix model, is that it tends to a non-zero constant at vanishing frequency.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Free Fermions and the Classical Compact Groups

There is a close connection between the ground state of non-interacting fermions in a box with classical (absorbing, reflecting, and periodic) boundary conditions and the eigenvalue statistics of the classical compact groups. The associated determinantal point processes can be extended in two natural directions: (i) we consider the full family of admissible quantum boundary conditions (i.e., self-adjoint extensions) for the Laplacian on a bounded interval, and the corresponding projection correlation kernels; (ii) we construct the grand canonical extensions at finite temperature of the projection kernels, interpolating from Poisson to random matrix eigenvalue statistics. The scaling limits in the bulk and at the edges are studied in a unified framework, and the question of universality is addressed. Whether the finite temperature determinantal processes correspond to the eigenvalue statistics of some matrix models is, a priori, not obvious. We complete the picture by constructing a finite temperature extension of the Haar measure on the classical compact groups. The eigenvalue statistics of the resulting grand canonical matrix models (of random size) corresponds exactly to the grand canonical measure of free fermions with classical boundary conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Spontaneous CP violation and horizontal symmetry in the MSSM: toward lepton flavor naturalness

We study the contributions of supersymmetric models with a U(1) horizontal symmetry and only spontaneous CP breaking to various lepton flavor observables, such as μ → eγ and the electron electric dipole moment. We show that both a horizontal symmetry and a lack of explicit CP violation can alleviate the existing bounds from such observables. The undetermined \( \mathcal{O} \) (1) coefficients in such mass matrix models muddle the interpretation of the bounds from various flavor observables. To overcome this, we define a new fine-tuning measure for different observables in such setups. This allows us to study how naturally the observed IR flavor observables can emerge from a given mass matrix model. We use our flavor-naturalness measure in study of our supersymmetric models and quantify the degree of fine tuning required by the bounds from various lepton flavor observables at each mass scale of sleptons, neutralinos, and charginos.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Scaling similarities and quasinormal modes of D0 black hole solutions

We study the gravity solution dual to the D0 brane quantum mechanics, or BFSS matrix model, in the ’t Hooft limit. The classical physics described by this gravity solution is invariant under a scaling transformation, which changes the action with a specific critical exponent, sometimes called the hyperscaling violating exponent. We present an argument for this critical exponent from the matrix model side, which leads to an explanation for the peculiar temperature dependence of the entropy in this theory, S ∝ T 9/5 . We also present a similar argument for all other Dp-brane geometries. We then compute the black hole quasinormal modes. This involves perturbing the finite temperature geometry. These perturbations can be easily obtained by a mathematical trick where we view the solution as the dimensional reduction of an Ad S2+9/5 × S 8 geometry.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

To gauge or not to gauge?

The D0 brane, or BFSS, matrix model is a quantum mechanical theory with an interesting gravity dual. We consider a variant of this model where we treat the SU(N) symmetry as a global symmetry, rather than as a gauge symmetry. This variant contains new non-singlet states. We consider the impact of these new states on its gravity dual. We argue that the gravity dual is essentially the same as the one for the original matrix model. The non-singlet states have higher energy at strong coupling and are therefore dynamically suppressed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

An Unsteady State Gas Transport Model in Matrix Laboratory (MATLAB) for PWR Gas Management

Reactor Coolant System (RCS) hydrogen gas management can be a challenge at Pressurized Water Reactors (PWRs) during shutdown, startup, and steady state operation. Poor hydrogen control can result in higher general corrosion rates for RCS components and increases in critical path time for shutdown or startup. Also, performance indicator penalties may be accrued by entry into Electric Power Research Institute (EPRI) Action Level conditions or by accrual of Chemistry Effectiveness Index (CEI) penalties established by the Institute of Nuclear Power Operations (INPO). Furthermore, poor hydrogen control may increase industrial safety risk due to the creation of an explosive environment. Part of the hydrogen management difficulty arises from the interaction of several phenomena that require complex simulations to fully understand. While hydrogen gas transport models have been developed, the application of these models is limited by the computational intensity required to accurately model the dynamism inherent in plant shutdown or startup. Subsequently, a gas transport model is developed in a suitable computational program to meet these needs and provide input to an optimized RCS hydrogen management strategy for all operational modes. The gas transport model is used to model RCS hydrogen behavior for an example PWR during an End of Cycle (EOC) Forced Outage (FO) startup, a refueling outage (RFO) shutdown, and during nominal steady state operation. The computational software selected is Matrix Laboratory (MATLAB{sup R})

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2018

An extracellular matrix (ECM) model at high malignant colorectal tumor increases chondroitin sulfate chains to promote epithelial-mesenchymal transition and chemoresistance acquisition

Highlights: • Effect of ECM dynamics in tumor progression on EMT and chemoresistance were assessed. • 5-FU increased EMT genes and ABCB1 expression via TGF-β signaling. • High malignant tumor ECM promoted EMT and ABCB1 expression via TGF-β signaling. • High malignant tumor ECM possessed chondroitin sulfate chains at high level. • Increased chondroitin sulfate promoted EMT genes and ABCB1 expression. Chemoresistance is one of the major barriers for tumor chemotherapy. It is clinically known that chemoresistance increases during tumor progression. Additionally, the extracellular matrix (ECM) is also remodeled during tumor progression. However, it remains unclear how ECM remodeling contributes to chemoresistance acquisition. Recently, it has been reported that epithelial-mesenchymal transition (EMT) contributes to chemoresistance acquisition. Here, how ECM remodeling contributes to 5-fluorouracil (5-FU) resistance acquisition was investigated from the viewpoints of EMT using in vitro ECM models mimicking native ECM in colorectal tumor tissue at three different malignant levels. 5-FU partially induced EMT and increased ABCB1 in colorectal HT-29 cells via TGF-β signaling (an invasive tumor cell model). When HT-29 cells were cultured on an ECM model (high malignant matrices) mimicking native ECM in highly malignant tumor tissues, the cells facilitated TGF-β-induced EMT and increased ABCB1 upregulation compared with that of other ECM models mimicking the low malignant level and normal tissues. High malignant matrices contained more chondroitin sulfate (CS) chains than those of other ECM models. Finally, CS chain-reduced high malignant matrices could not facilitate ABCB1 upregulation and TGF-β-induced EMT. These results demonstrated that ECM remodeling during tumor progression increased CS chains to facilitate EMT and ABCB1 upregulation, contributing to chemoresistance acquisition.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Fishnet four-point integrals: integrable representations and thermodynamic limits

In this work, we consider four-point integrals arising in the planar limit of the conformal “fishnet” theory in four dimensions. They define a two-parameter family of higher-loop Feynman integrals, which extend the series of ladder integrals and were argued, based on integrability and analyticity, to admit matrix-model-like integral and determinantal representations. In this paper, we prove the equivalence of all these representations using exact summation and integration techniques. We then analyze the large-order behaviour, corresponding to the thermodynamic limit of a large fishnet graph. The saddle-point equations are found to match known two-cut singular equations arising in matrix models, enabling us to obtain a concise parametric expression for the free-energy density in terms of complete elliptic integrals. Interestingly, the latter depends non-trivially on the fishnet aspect ratio and differs from a scaling formula due to Zamolodchikov for large periodic fishnets, suggesting a strong sensitivity to the boundary conditions. We also find an intriguing connection between the saddle-point equation and the equation describing the Frolov-Tseytlin spinning string in AdS 3 × S 1 , in a generalized scaling combining the thermodynamic and short-distance limits.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Topics in String Theory, Quantum Field Theory And Quantum Gravity

This is the final technical report for DOE Award No. DE-SC0021528 - Topics in string theory, quantum field theory and quantum gravity. The goals of the research program were in three areas - understanding quantum gravity and the internal description of quantum systems using the gauge/gravity correspondence, aspects of entanglement in eld theory, gravity and string theory, and the characterization of the behavior of strongly interacting quantum eld theories. The primary results were on the microscopic understanding of the ER=EPR correspondence as a string duality, and on a matrix model description of the addition of end of the world branes and propagating matter to two dimensional Jackiw-Teitelboim gravity. The former led to the completion of the work shortly after the end of the reporting period and continuing work investigating the properties of the associated stringy black hole microstates. The latter led to the work, which also appeared shortly after the end of the reporting period, and a continuing project to nd a matrix model formulation of the eigenstate thermalization hypothesis and JT gravity with propagating matter.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Model for Characterization and Optimization of Spectrally Selective Structures to Reduce the Operating Temperature and Improve the Energy Yield of Photovoltaic Modules

Many existing commercially manufactured photovoltaic modules include a cover layer of glass, commonly coated with a single layer antireflection coating (ARC) to reduce reflection losses. As many common photovoltaic cells, including c-Si, CdTe, and CIGS, decrease in efficiency with increasing temperature, a more effective coating would increase reflection of sub-bandgap light while still acting as an antireflection coating for higher energy photons. The sub-bandgap reflection would reduce parasitic sub-bandgap absorption and therefore reduce operating temperature. This reduction under realistic outdoor conditions would lead to an increase in annual energy yield of a photovoltaic module beyond what is achieved by a single layer ARC. However, calculating the actual increase in energy yield provided by this approach is difficult without using time-consuming simulation. Here, we present a time-independent matrix model which can quickly determine the percentage change in annual energy yield of a module with a spectrally selective mirror by comparison to a baseline module with no mirror. The energy benefit is decomposed into a thermal component from temperature reduction and an optical component from increased transmission of light above the bandgap and therefore increased current generation. Time-independent matrix model calculations are based on real irradiance conditions that vary with geographic location and module tilt angle. The absolute predicted values of energy yield improvement from the model are within 0.1% of those obtained from combined ray-tracing and time-dependent finite-element simulations and compute 1000x faster. Uncertainty in the model result is primarily due to effects of wind speed on module temperature. Optimization of the model result produces a 13-layer and a 20-layer mirror, which increase annual module energy yield by up to 4.0% compared to a module without the mirror, varying depending on the module location and tilt angle. Finally, we analyze how spectrally selective mirrors affect the loss pathways of the photovoltaic module.

14 SOLAR ENERGY↗
DOE OSTI2022

Molecular polariton electroabsorption

Abstract We investigate electroabsorption (EA) in organic semiconductor microcavities to understand whether strong light-matter coupling non-trivially alters their nonlinear optical [ $${\chi }^{(3)}\left(\omega,{{{{\mathrm{0,0}}}}}\right)$$ χ ( 3 ) ω , 0, 0 ] response. Focusing on strongly-absorbing squaraine (SQ) molecules dispersed in a wide-gap host matrix, we find that classical transfer matrix modeling accurately captures the EA response of low concentration SQ microcavities with a vacuum Rabi splitting of $$\hslash \Omega \approx 200$$ ℏ Ω ≈ 200 meV, but fails for high concentration cavities with $$\hslash \Omega \approx 420$$ ℏ Ω ≈ 420 meV. Rather than new physics in the ultrastrong coupling regime, however, we attribute the discrepancy at high SQ concentration to a nearly dark H-aggregate state below the SQ exciton transition, which goes undetected in the optical constant dispersion on which the transfer matrix model is based, but nonetheless interacts with and enhances the EA response of the lower polariton mode. These results indicate that strong coupling can be used to manipulate EA (and presumably other optical nonlinearities) from organic microcavities by controlling the energy of polariton modes relative to other states in the system, but it does not alter the intrinsic optical nonlinearity of the organic semiconductor inside the cavity.

42 ENGINEERING↗
DOE OSTI2025

Mind the crosscap: $τ$-scaling in non-orientable gravity and time-reversal-invariant systems

Spectral statistics of quantum chaotic systems are governed by random matrix universality. In many cases of interest, time-reversal symmetry selects the Gaussian Orthogonal Ensemble (GOE) as the relevant universality class. In holographic CFTs, this is mirrored by the presence of non-orientable geometries in the dual gravitational path integral. In this work, we analyze general properties of these matrix models and their gravitational counterparts. First, we develop a formalism to express the universal level statistics in the canonical ensemble for arbitrary spectral curves, leading to a topological expansion with finite radius of convergence in the late-time $τ$-scaling limit. Then, we focus on topological gravity and study topological recursion on the moduli space of non-orientable surfaces. We find that the Weil-Petersson volumes display non-analytic behaviour multiplying polynomials in the boundary lengths. The volumes give rise to wormholes with late-time divergences, in contrast with the orientable case, which is finite. We identify systematic cancellations among WP volumes implied by the consistency and finiteness of the $τ$-scaling limit. In particular, the cancellation of late-time divergences requires a nontrivial genus resummation. Working in the gravitational microcanonical ensemble, we derive and resum all orders of the topological expansion matching the GOE matrix model in the high-energy regime.

Chaotic Dynamics (nlin.CD)↗
DOE OSTI2015

Comparative study of 0° X-cut and Y + 36°-cut lithium niobate high-voltage sensing

A comparison study between Y + 36° and 0° X-cut lithium niobate (LiNbO{sub 3}) was performed to evaluate the influence of crystal cut on the acoustic propagation to realize a piezoelectric high-voltage sensor. The acoustic time-of-flight for each crystal cut was measured when applying direct current (DC), alternating current (AC), and pulsed voltages. Results show that the voltage-induced shift in the acoustic wave propagation time scaled quadratically with voltage for DC and AC voltages applied to X-cut crystals. For the Y + 36° crystal, the voltage-induced shift scales linearly with DC voltages and quadratically with AC voltages. When applying 5 μs voltage pulses to both crystals, the voltage-induced shift scaled linearly with voltage. For the Y + 36° cut, the voltage-induced shift from applying DC voltages ranged from 10 to 54 ps and 35 to 778 ps for AC voltages at 640 V over the frequency range of 100 Hz–100 kHz. Using the same conditions as the Y + 36° cut, the 0° X-cut crystal sensed a shift of 10–273 ps for DC voltages and 189–813 ps for AC voltage application. For 5 μs voltage pulses, the 0° X-cut crystal sensed a voltage induced shift of 0.250–2 ns and the Y + 36°-cut crystal sensed a time shift of 0.115–1.6 ns. This suggests a frequency sensitive response to voltage where the influence of the crystal cut was not a significant contributor under DC, AC, or pulsed voltage conditions. The measured DC data were compared to a 1-D impedance matrix model where the predicted incremental length changed as a function of voltage. When the voltage source error was eliminated through physical modeling from the uncertainty budget, the combined uncertainty of the sensor (within a 95% confidence interval) decreased to 0.0033% using a Y + 36°-cut crystal and 0.0032% using an X-cut crystal for all the voltage conditions used in this experiment.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗