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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Quantum chaos, integrability, and late times in the Krylov basis

Quantum chaotic systems are conjectured to display a spectrum whose fine-grained features (gaps and correlations) are well described by random matrix theory (RMT). We propose and develop a complementary version of this conjecture: quantum chaotic systems display a Lanczos spectrum whose local means and covariances are well described by RMT. To support this proposal, we first demonstrate its validity in examples of chaotic and integrable systems. We then show that for Haar-random initial states in RMTs the mean and covariance of the Lanczos spectrum suffice to produce the full long-time behavior of general survival probabilities including the spectral form factor, as well as the spread complexity. In addition, for initial states with continuous overlap with energy eigenstates, we analytically find the long-time averages of the probabilities of Krylov basis elements in terms of the mean Lanczos spectrum. This analysis suggests a notion of eigenstate complexity, the statistics of which differentiate integrable systems and classes of quantum chaos. Lastly, we clarify the relation between spread complexity and the universality classes of RMT by exploring various values of the Dyson index and Poisson distributed spectra.

Combinatorics↗
DOE OSTI2020

Slow scrambling and hidden integrability in a random rotor model

In this work, we analyze the out-of-time-order correlation functions of a solvable model of a large number $\textit{N}$ of $\textit{M}$-component quantum rotors coupled by Gaussian-distributed random, infinite-range exchange interactions. We focus on the growth of commutators of operators at a temperature $\textit{T}$ above the zero temperature quantum critical point separating the spin-glass and paramagnetic phases. In the large $\textit{N, M}$ limit, the squared commutators of the rotor fields do not display any exponential growth of commutators, in spite of the absence of any sharp quasiparticlelike excitations in the disorder-averaged theory. We show that in this limit, the problem is integrable and points out interesting connections to random-matrix theory. At leading order in 1/$\textit{M}$, there are no modifications to the critical behavior but an irrelevant term in the fixed-point action leads to a small exponential growth of the squared commutator. We also introduce and comment on a generalized model involving $\textit{p}$-pair rotor interactions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Dissociative Recombination of Cold HeH + Ions

The HeH + cation is the simplest molecular prototype of the indirect dissociative recombination (DR) process that proceeds through electron capture into Rydberg states of the corresponding neutral molecule. This Letter develops the first application of our recently developed energy-dependent frame transformation theory to the indirect DR processes. The theoretical model is based on the multichannel quantum-defect theory with the vibrational basis states computed using exterior complex scaling of the nuclear Hamiltonian. The ab initio electronic R-matrix theory is adopted to compute quantum defects as functions of the collision energy and of the internuclear distance. The resulting DR rates are convolved over the beam energy distributions relevant to a recent experiment at the Cryogenic Storage Ring, giving good agreement between the experiment and the theory.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Eigenstate thermalization in ( 2 + 1 )-dimensional SU(2) lattice gauge theory

We present preliminary numerical evidence for the hypothesis that the Hamiltonian SU(2) gauge theory discretized on a lattice obeys the eigenstate thermalization hypothesis (ETH). To do so we study three approximations: (a) a linear plaquette chain in a reduced Hilbert space limiting the electric field basis to j = 0 , 1 2 , (b) a two-dimensional honeycomb lattice with periodic or closed boundary condition and the same Hilbert space constraint, and (c) a chain of only three plaquettes but such a sufficiently large electric field Hilbert space ( j ≤ 7 2 ) that convergence of all energy eigenvalues in the analyzed energy window is observed. While an unconstrained Hilbert space is required to reach the continuum limit of SU(2) gauge theory, numerical resource constraints do not permit us to realize this requirement for all values of the coupling constant and large lattices. In each of the three studied cases we check first for random matrix theory (RMT) behavior in the eigenenergy spectrum and then analyze the diagonal as well as the off-diagonal matrix elements between energy eigenstates for a few operators. Within current uncertainties all results for (a), (b) and (c) agree with ETH predictions. Furthermore, we find the off-diagonal matrix elements of the electric energy operator exhibit RMT behavior in frequency windows that are small enough in (b) and (c). To unambiguously establish ETH behavior and determine for which class of operators it applies, an extension of our investigations is necessary. Published by the American Physical Society 2024

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Spectral fluctuations in the Sachdev-Ye-Kitaev model

We present a detailed quantitative analysis of spectral correlations in the Sachdev-Ye-Kitaev (SYK) model. We find that the deviations from universal Random Matrix Theory (RMT) behavior are due to a small number of long-wavelength fluctuations (of the order of the number of Majorana fermions N ) from one realization of the ensemble to the next one. These modes can be parameterized effectively in terms of Q-Hermite orthogonal polynomials, the main contribution being due to scale fluctuations for which we give a simple analytical estimate. Our numerical results for N = 32 show that only the lowest eight polynomials are needed to eliminate the nonuniversal part of the spectral fluctuations. The covariance matrix of the coefficients of this expansion can be obtained analytically from low-order double-trace moments. We evaluate the covariance matrix of the first six moments and find that it agrees with the numerics. We also analyze the spectral correlations in terms of a nonlinear σ-model, which is derived through a Fierz transformation, and evaluate the one and two-point spectral correlation functions to two-loop order. The wide correlator is given by the sum of the universal RMT result and corrections whose lowest-order term corresponds to scale fluctuations. However, the loop expansion of the σ-model results in an ill-behaved expansion of the resolvent, and it gives universal RMT fluctuations not only for q= 4 or higher even q-body interactions, but also for the q= 2 SYK model albeit with a much smaller Thouless energy while the correct result in this case should have been Poisson statistics. In our numerical studies we analyze the number variance and spectral form factor for N = 32 and q = 4. We show that the quadratic deviation of the number variance for large energies appears as a peak for small times in the spectral form factor. After eliminating the long-wavelength fluctuations, we find quantitative agreement with RMT up to an exponentially large number of level spacings for the number variance or exponentially short times in the case of the spectral form factor.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Covariance generation for the prompt neutron multiplicity of 239 Pu including the (n, γ f) process

Fission cross section of 239 Pu can be seen as a sum of the “immediate" fission and “two-step" (n,γf) reactions. In the Resolved Resonance Range of the reaction cross sections, the contribution of the (n,γf) process has an impact on the determination of the partial widths magnitude involved in the Reich-Moore approximation of the R-matrix theory. The present work aims to investigate this impact by using the CONRAD code and the partial width Γ γf for the (n,γf) reaction calculated by Lynn et al. A special attention will be paid to the covariance matrix obtained on ν p .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Double copy root of Hawking thermality

The Hawking radiation spectrum from a collapsing null shell can be derived via the double copy of a simpler gauge theory calculation. Analyzing the non-abelian Yang-Mills root of this process, we demonstrate that the radiation spectrum is thermal in the color charge eigenvalue 𝜆, not energy. Considering the 𝑆⁢𝑈⁡(𝑁 𝑐 ) gauge theory in the large 𝑁 𝑐 limit, we find the differential spectrum ⅆ⁢𝑁/ⅆ⁢𝜆 is a product of the gravitationally familiar Planck-like factor and the color phase space density, modeled here as the Wigner semicircle from random matrix theory. This reveals that apparent energy thermality in gravity is the direct dual of charge thermality in its underlying non-abelian gauge theory.

Carrasco, John Joseph M. [Northwestern University,↗
DOE OSTI2022

Calabi-Yau CFTs and random matrices

Using numerical methods for finding Ricci-flat metrics, we explore the spectrum of local operators in two-dimensional conformal field theories defined by sigma models on Calabi-Yau targets at large volume. Focusing on the examples of K3 and the quintic, we show that the spectrum, averaged over a region in complex structure moduli space, possesses the same statistical properties as the Gaussian orthogonal ensemble of random matrix theory.

superstring vacua↗
DOE OSTI2024

Density-matrix mean-field theory

Mean-field theories have proven to be efficient tools for exploring diverse phases of matter, complementing alternative methods that are more precise but also more computationally demanding. Conventional mean-field theories often fall short in capturing quantum fluctuations, which restricts their applicability to systems with significant quantum effects. In this article, we propose an improved mean-field theory, density-matrix mean-field theory (DMMFT). DMMFT constructs effective Hamiltonians, incorporating quantum environments shaped by entanglements, quantified by the reduced density matrices. Therefore, it offers a systematic and unbiased approach to account for the effects of fluctuations and entanglements in quantum ordered phases. As demonstrative examples, we show that DMMFT can not only quantitatively evaluate the renormalization of order parameters induced by quantum fluctuations, but can also detect the topological quantum phases. Additionally, we discuss the extensions of DMMFT for systems at finite temperatures and those with disorders. Our work provides an efficient approach to explore phases exhibiting unconventional quantum orders, which can be particularly beneficial for investigating frustrated spin systems in high spatial dimensions.

Physics↗
DOE OSTI2022

Intermediate scattering potential strength in electron-irradiated YBa 2 Cu 3 O 7-δ from London penetration depth measurements

Temperature-dependent London penetration depth, λ(T), of a high quality optimally-doped YBa 2 Cu 3 O 7-δ single crystal was measured using tunnel-diode-resonator technique. Controlled artificial disorder was induced by low-temperature 20 K irradiation by 2.5 MeV electrons at two large doses of 3.8 x 10 19 and 5.3 x 10 19 electrons per cm 2 . The irradiation caused significant suppression of the superconductor's critical temperature, T c , from 94.6 K to 90.0 K, and to 78.7 K, respectively. The low-temperature behavior of λ(T) evolves from a T-linear in pristine state to a T 2 behavior after irradiation, expected for a line-nodal d-wave superconductor. However, the original theory that explained such behavior assumed a unitary limit of the scattering potential, whereas usually in normal metals and semiconductors, Born scattering is sufficient to describe the experiment. To estimate the scattering potential strength, we calculated the superfluid density, ρ s (t = T/T c ) = λ 2 (0)/λ 2 (T), varying the amount and strength of non-magnetic scattering using a self-consistent t-matrix theory. Fitting the obtained curves to a power law, ρ s = 1 - Rt n , and to a polynomial, ρ s = 1 - At - Bt 2 , and comparing the coefficients n in one set and A and B in another with the experimental values, we estimate the phase shift to be around 70 and 65°, respectively. We correlate this result with the evolution of the density of states with nonmagnetic disorder.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Machine Learning for Neutron Resonance Evaluations [Slides]

The performance of nuclear reactors and other nuclear systems depends on a precise understanding of the neutron interaction cross sections for materials used in these systems. These cross sections exhibit a resonance structure whose shape is determined in part by the angular momentum quantum numbers of the resonances. The correct assignment of the quantum numbers of neutron resonances is therefore of paramount importance. In this presentation, we describe the application of machine learning to automate the quantum number assignments. Scikit-learn classifiers were trained on simulated resonance data whose statistical properties were chosen to mimic real data. We explored the use of several physics (and random matrix theory)-motivated features for training the classifiers, including the nearest neighbor spacing distribution, cumulative level distribution, and channel width distributions. Initial results demonstrated that we can determine resonance spin groups somewhat reliably. We are now investigating the application of our approach to 52 Cr resonance data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

140,142 Ce Neutron Cross Section Resolved Resonance Region Evaluation [Abstract]

A resolved resonance region evaluation of 140,142 Ce has been carried out by Oak Ridge National Laboratory. Requested by the US Nuclear Criticality Safety Program, this evaluation is based on recent high-resolution transmission and capture high-resolution measurements of nat Ce and 142 Ce conducted at JRC-GEEL at the Geel Linear Accelerator facility, as well as recently measured thermal constants available from the EXFOR database. Starting from the resonance parameters from the ENDF/B-VIII.0 library and following a preliminary R-matrix analysis, an updated set of resonance parameters and corresponding covariance information was derived by the fit of these experimental datasets using the Reich-Moore approximation of the R-matrix theory as implemented in the SAMMY code system. The resolved resonance region upper energy limit for 140 Ce was kept at 200 keV while the 142 Ce resonance region was extended from 13 to 26 keV. This new evaluation was found to be in good agreement not only with several integral quantities of interest to the reactor physics community, but also with the stellar Maxwellian-averaged cross section.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Effects of anisotropy and disorder on the superconducting properties of niobium

We report results for the superconducting transition temperature and anisotropic energy gap for pure niobium based on Eliashberg’s equations and electron and phonon band structures computed from density functional theory. The electronic band structure is used to construct the Fermi surface and calculate the Fermi velocity at each point on the Fermi surface. The phonon bands are in excellent agreement with inelastic neutron scattering data. The corresponding phonon density of states and electron–phonon coupling define the electron–phonon spectral function, α 2 F(p, p'; ω), and the corresponding electron–phonon pairing interaction, which is the basis for computing the superconducting properties. The electron–phonon spectral function is in good agreement with existing tunneling spectroscopy data except for the spectral weight of the longitudinal phonon peak at ℏω LO = 23 meV. We obtain an electron–phonon coupling constant of λ = 1.057, renormalized Coulomb interaction μ* = 0.218, and transition temperature T c = 9.33 K. The corresponding strong-coupling gap at T = 0 is modestly enhanced, Δ 0 = 1.55 meV, compared to the weak-coupling BCS value $Δ^{\text {wc}}_{0}$ = 1.78 k B T c = 1.43 meV. The superconducting gap function exhibits substantial anisotropy on the Fermi surface. We analyze the distribution of gap anisotropy and compute the suppression of the superconducting transition temperature using a self-consistent T-matrix theory for quasiparticle-impurity scattering to describe niobium doped with non-magnetic impurities. We compare these results with experimental results on niobium SRF cavities doped with nitrogen impurities.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

AdS 3 gravity and random CFT

We compute the path integral of three-dimensional gravity with negative cosmological constant on spaces which are topologically a torus times an interval. These are Euclidean wormholes, which smoothly interpolate between two asymptotically Euclidean AdS 3 regions with torus boundary. From our results we obtain the spectral correlations between BTZ black hole microstates near threshold, as well as extract the spectral form factor at fixed momentum, which has linear growth in time with small fluctuations around it. The low-energy limit of these correlations is precisely that of a double-scaled random matrix ensemble with Virasoro symmetry. Our findings suggest that if pure three-dimensional gravity has a holographic dual, then the dual is an ensemble which generalizes random matrix theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Hilbert series for covariants and their applications to minimal flavor violation

We elaborate how to apply the Hilbert series method to enumerating group covariants, which transform under any given representation, including but going beyond group invariants. Mathematically, group covariants form a module over the ring of the invariants. The number of independent covariants is given by the rank of the module, which can be computed by taking a ratio of two Hilbert series. In many cases, the rank equals the dimension of the group covariant representation. When this happens, we say that there is a rank saturation. We apply this technology to revisit the hypothesis of Minimal Flavor Violation in constructing Effective Field Theories beyond the Standard Model. We find that rank saturation is guaranteed in this case, leading to the important consequence that the MFV symmetry principle does not impose any restriction on the EFT, i.e. MFV SMEFT = SMEFT, in the absence of additional assumptions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

AdS 3 wormholes from a modular bootstrap

In recent work we computed the path integral of three-dimensional gravity with negative cosmological constant on spaces which are topologically a torus times an interval. Here we employ a modular bootstrap to show that the amplitude is completely fixed by consistency conditions and a few basic inputs from gravity. This bootstrap is notably for an ensemble of CFTs, rather than for a single instance. We also compare the 3d gravity result with the Narain ensemble. The former is well-approximated at low temperature by a random matrix theory ansatz, and we conjecture that this behavior is generic for an ensemble of CFTs at large central charge with a chaotic spectrum of heavy operators.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Emergent unitarity in de Sitter from matrix integrals

We study Jackiw-Teitelboim gravity with positive cosmological constant as a model for de Sitter quantum gravity. We focus on the quantum mechanics of the model at past and future infinity. There is a Hilbert space of asymptotic states and an infinite-time evolution operator between the far past and far future. This evolution is not unitary, although we find that it acts unitarily on a subspace up to non-perturbative corrections. These corrections come from processes which involve changes in the spatial topology, including the nucleation of baby universes. There is significant evidence that this 1+1 dimensional model is dual to a 0+0 dimensional matrix integral in the double-scaled limit. So the bulk quantum mechanics, including the Hilbert space and approximately unitary evolution, emerge from a classical integral. We find that this emergence is a robust consequence of the level repulsion of eigenvalues along with the double scaling limit, and so is rather universal in random matrix theory.

2D gravity↗