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At least 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Nonlinear dynamics and quantum chaos of a family of kicked p -spin models

Herein we introduce kicked p-spin models describing a family of transverse Ising-like models for an ensemble of spin-1/2 particles with all-to-all p-body interaction terms occurring periodically in time as delta-kicks. This is the natural generalization of the well-studied quantum kicked top (p = 2) [Haake, Kus', and Scharf, Z. Phys. B 65, 381 (1987)]. We fully characterize the classical nonlinear dynamics of these models, including the transition to global Hamiltonian chaos. The classical analysis allows us to build a classification for this family of models, distinguishing between p = 2 and p > 2, and between models with odd and even p's. Quantum chaos in these models is characterized in both kinematic and dynamic signatures. For the latter, we show numerically that the growth rate of the out-of-time-order correlator is dictated by the classical Lyapunov exponent. Finally, we argue that the classification of these models constructed in the classical system applies to the quantum system as well.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Spectral Filtering Induced by Non-Hermitian Evolution with Balanced Gain and Loss: Enhancing Quantum Chaos

Here, the dynamical signatures of quantum chaos in an isolated system are captured by the spectral form factor, which exhibits as a function of time a dip, a ramp, and a plateau, with the ramp being governed by the correlations in the level spacing distribution. While decoherence generally suppresses these dynamical signatures, the nonlinear non-Hermitian evolution with balanced gain and loss (BGL) in an energy-dephasing scenario can enhance manifestations of quantum chaos. In the Sachdev-Ye-Kitaev model and random matrix Hamiltonians, BGL increases the span of the ramp, lowering the dip as well as the value of the plateau, providing an experimentally realizable physical mechanism for spectral filtering. The chaos enhancement due to BGL is optimal over a family of filter functions that can be engineered with fluctuating Hamiltonians.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Scattering neutrinos, spin models, and permutations

We consider a class of Heisenberg all-to-all coupled spin models inspired by neutrino interactions in a supernova with N degrees of freedom. These models are characterized by a coupling matrix that is relatively simple in the sense that there are only a few, relative to N , nontrivial eigenvalues, in distinction to the classic Heisenberg spin-glass models, leading to distinct behavior in both the high-temperature and low-temperature regimes. When the momenta of the neutrinos are uniform and random in directions, we can calculate the large- N partition function for the quantum Heisenberg model. In particular, the high-temperature partition function predicts a non-Gaussian density of states, providing interesting counterexamples showing the limits of general theorems on the density of states for quantum spin models. We can repeat the same argument for classical Heisenberg models, also known as rotor models, and we find the high-temperature expansion is completely controlled by the eigenvalues of the coupling matrix, and again predicts non-Gaussian behavior for the density of states as long as the number of eigenvalues does not scale linearly with N . Indeed, we derive the amusing fact that these partition functions are essentially the generating function for counting permutations in the high-temperature regime. Finally, for the case relevant to neutrinos in a supernova, we identify the low-temperature phase as a unique state with the direction of the momenta of the neutrino dictating its coherent state in flavor-space, a state we dub the “flavor-momentum-locked” state. Published by the American Physical Society 2025

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Novel Phases and Dynamics of Multi-orbital Mott Insulators

The goal of this project is to gain theoretical insight into magnetism in the presence of spin-orbit coupling (SOC) for multi-orbital Mott insulators. Inspired by the exact solution of the Kitaev model that harbors a quantum spin liquid with novel excitations and struck by its relevance for materials with anisotropic orbital interactions, the PI will explore various new classes of 4d and 5d transition metal oxides. Starting with all electron Hamiltonians, the PI will derive minimal magnetic models. The aim will be to understand the role played by orbital frustration, even in the absence of any geometric frustration, in creating orbitally ordered as well as spin-orbital liquid phases. Orbital frustration arises primarily from the directional or anisotropic nature of d-orbitals in contrast to the isotropic nature of the spin degree of freedom. These models will be investigated by a variety of theoretical and numerical methods, including exact diagonalization, mean field theories, density matrix renormalization group and quantum Monte Carlo methods. Testable predictions for three experiments: nuclear magnetic resonance (NMR) and resonant x-ray scattering (RXS) to probe orbital ordering and pump-probe experiments to probe quantum dynamics will test the validity of these models for materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
NASA NTRS1973

Phase matrix induced symmetrics for multiple scattering using the matrix operator method

Entirely rigorous proofs of the symmetries induced by the phase matrix into the reflection and transmission operators used in the matrix operator theory are given. Results are obtained for multiple scattering in both homogeneous and inhomogeneous atmospheres. These results will be useful to researchers using the method since large savings in computer time and storage are obtainable.

Hitzfelder, S. J.↗
NASA NTRS1983

Direct structural parameter identification by modal test results

A direct identification procedure is proposed to obtain the mass and stiffness matrices based on the test measured eigenvalues and eigenvectors. The method is based on the theory of matrix perturbation in which the correct mass and stiffness matrices are expanded in terms of analytical values plus a modification matrix. The simplicity of the procedure enables real time operation during the structural testing.

Chen, J.-C.↗
NASA NTRS1990

Vibration transmission through rolling element bearings. I - Bearing stiffness formulation. II - System studies

How vibratory motion can be transmitted from the rotating shaft to the casing and other connecting structures in rotating mechanical equipment is addressed here by developing a new mathematical model of precision rolling element bearings. A new grating stiffness matrix is proposed in order to demonstrate a coupling between the shaft bending motion and the flexural motion of the casing plate. It is shown that the translational bearing stiffness coefficients currently used in rotor dynamic models are a small subset of the proposed matrix. The theory is validated by examples, and the proposed bearing formulation is then extended to demonstrate its superiority over existing models in vibration transmission analyses. It is shown that the model can easily be incorporated into analytical or numerical models typically used for dynamic analyses.

Lim, T. C.↗
NASA NTRS1991

Improved solution for ill-conditioned algebraic equations by epsilon decomposition

Matrix eigenvalue theory is presently used to examine the source of ill-conditioning in linear algebraic equations; the approach highlights the critical role played by the zero and near-zero eigenvalues and corresponding eigenvectors of poorly-conditioned systems. Insights derived from this approach are used to improve the recently developed epsilon-decomposition (E-D) solution procedure. The efficiency of E-D is significant for large matrices possessing small rank deficiency.

Ojalvo, Irving U.↗
NASA NTRS1995

An investigation of theories of failure for ceramic matrix composites

This final report is comprised of the abstract of a masters thesis research grant. The abstract of the thesis, 'An Investigation of Acoustic Emission Techniques for the Discrimination of Damage Mechanisms in Ceramic Matrix Composites', is as follows: In order to further advance the understanding of the mechanical behavior of ceramic matrix composites (CMS's), acoustic emission (AE) techniques were implemented to monitor and identify damage mechanisms in CMC's under tensile loading. In addition to real-time AE monitoring techniques, a data acquisition system was developed and implemented in order to capture AE waveforms resulting from stress-induced damage. Waveforms were inspected for multiple events, separated in distinct events, and then analyzed to determine waveform characteristics in the time and frequency domains. Waveform characteristics included peak amplitude, event duration, MARSE, energy, and dominant and centroidal frequency. In addition to conventional methods for determining a damage discrimination criteria, a study of the distribution and correlation of the waveform characteristics criteria and a study of the distribution and correlation of the waveform characteristics were performed to aid in the determination of a damage discrimination criteria. The damage discrimination criteria was tested for 'uniqueness', i.e., the effectiveness of the criteria to identify and monitor damage independent of the stress-strain relationship. Insitu radiography was used to substantiate the damage accumulation. A simulation test was also performed over the loading history to study the changes in the waveform characteristics of the system response from a constant excitation. This thesis demonstrates the use of waveform analysis to study the AE activity resulting from stress-induced damage in CMC's in conjunction with other nondestructive evaluation techniques to investigate the mechanical behavior of CMC's.

Hemann, John H.↗
NASA NTRS1995

An Investigation of Theories of Failure for Ceramic Matrix Composites

In order to further advance the understanding of the mechanical behavior of ceramic matrix composites (CMCs), acoustic emission (AE) techniques were imple mented to monitor and identify damage mechanisms in CMCs under tensile loading. In addition to real-time AE monitoring techniques, a data acquisition system was developed and implemented in order to capture AE waveforms resulting from stress-induced damage. Waveforms were inspected for multiple events, separated in distinct events, and then analyzed to determine waveform characteristics in the time and frequency domains. Waveform characteristics included peak amplitude, event duration, MARSE, energy, and dominant and centroidal frequency. In addition to conventional methods for determining a damage discrimination criteria, a study of the distribution and correlation the waveform characteristics was performed to aid in the determination of a damage discrimination criteria. The damage discrimination criteria was tested for "uniqueness", i.e., the effectiveness of the criteria to identify and monitor damage independent of the stress-strain relationship. Insitu radiography was used to substantiate the damage accumulation.

Hemann, John H.↗
NASA NTRS1988

Prediction of the microyield strength of polymer matrix composites

A theory for the prediction of the creep and the microyield strength of composite laminates with viscoelastic matrices has been developed and tested. Precise creep curves from three laminates with arbitrary orientations provide the necessary input data. The time-dependent lamina properties are derived for subsequent use with standard laminate codes. Both the level and the shape of creep and strain recovery curves can be predicted. Extensions of the theory to include the effects of microcracking are outlined.

Wolff, Ernest G.↗
NASA NTRS1974

On the use and computation of the Jordan canonical form in system theory

This paper investigates various aspects of the application of the Jordan canonical form of a matrix in system theory and develops a computational approach to determining the Jordan form for a given matrix. Applications include pole placement, controllability and observability studies, serving as an intermediate step in yielding other canonical forms, and theorem proving. The computational method developed in this paper is both simple and efficient. The method is based on the definition of a generalized eigenvector and a natural extension of Gauss elimination techniques. Examples are included for demonstration purposes.

Sridhar, B.↗