Search NASA⌕ Search

SEARCH · Search NASA

Results for “Hamiltonian dynamics”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Reshaping the Quantum Arrow of Time

While the microscopic laws of physics are often symmetric under time reversal, most natural processes that we observe are not. The emergent asymmetry between typical and time-reversed processes is referred to as the arrow of time. In quantum physics, an arrow of time emerges when a sequence of measurements is performed on a system. We introduce quantum control tools that can yield dynamics more consistent with time flowing backward than forward. The control tools are based on the explicit construction of a Hamiltonian that can replicate the stochastic trajectories of a monitored quantum system. Such a Hamiltonian can reverse the effect of monitoring and, via a feedback process, generate trajectories consistent with a reversed arrow of time. It can also be used to simulate the backward-in-time dynamics of an open quantum system. Finally, we design a feedback-driven continuous measurement engine powered by the energy pumped into the system by the monitoring process. We show that the engine can operate under experimentally realizable conditions with feedback delay and finite-efficiency measurements.

Entropy production↗
DOE OSTI2022

Quantum time dynamics employing the Yang-Baxter equation for circuit compression

Quantum time dynamics (QTD) is considered a promising problem for quantum supremacy on near-term quantum computers. However, QTD quantum circuits grow with increasing time simulations. This study focuses on simulating the time dynamics of one-dimensional (1D) integrable spin chains with nearest-neighbor interactions. We have proved the existence of a reflection symmetry in the quantum circuit employed for simulating the time evolution of certain classes of 1D Heisenberg model Hamiltonians by virtue of the quantum Yang-Baxter equation, and how this symmetry can be exploited to compress and produce a shallow quantum circuit. With this compression scheme, the depth of the quantum circuit becomes independent of step size and only depends on the number of spins. We show that the depth of the compressed circuit is rigorously a linear function of the system size for the studied Heisenberg model Hamiltonians in the present work. As a consequence, the number of CNOT gates in the compressed circuit only scales quadratically with the system size, which allows for the simulations of time dynamics of very large 1D spin chains. We derive the compressed circuit representations for different special cases of the Heisenberg Hamiltonian. We compare and demonstrate the effectiveness of this approach by performing simulations on quantum computers.

1-dimensional spin chains↗
DOE OSTI2024

Anomalies of non-invertible symmetries in (3+1)d

Anomalies of global symmetries are important tools for understanding the dynamics of quantum systems. We investigate anomalies of non-invertible symmetries in 3+1d using 4+1d bulk topological quantum field theories given by Abelian two-form gauge theories, with a 0-form permutation symmetry. Gauging the 0-form symmetry gives the 4+1d “inflow” symmetry topological field theory for the non-invertible symmetry. We find a two levels of anomalies: (1) the bulk may fail to have an appropriate set of loop excitations which can condense to trivialize the boundary dynamics, and (2) the “Frobenius-Schur indicator” of the non-invertible symmetry (generalizing the Frobenius-Schur indicator of 1+1d fusion categories) may be incompatible with trivial boundary dynamics. As a consequence we derive conditions for non-invertible symmetries in 3+1d to be compatible with symmetric gapped phases, and invertible gapped phases. Along the way, we see that the defects characterizing \mathbb{Z}_{4} ℤ 4 ordinary symmetry host worldvolume theories with time-reversal symmetry \mathsf{T} 𝖳 obeying the algebra \mathsf{T}^{2}=C 𝖳 2 = C or \mathsf{T}^{2}=(-1)^{F}C, 𝖳 2 = ( − 1 ) F C , with C C a unitary charge conjugation symmetry. We classify the anomalies of this symmetry algebra in 2+1d and further use these ideas to construct 2+1d topological orders with non-invertible time-reversal symmetry that permutes anyons. As a concrete realization of our general discussion, we construct new lattice Hamiltonian models in 3+1d with non-invertible symmetry, and constrain their dynamics.

Córdova, Clay↗
DOE OSTI2022

Predicting the structural basis of targeted protein degradation by integrating molecular dynamics simulations with structural mass spectrometry

Targeted protein degradation (TPD) is a promising approach in drug discovery for degrading proteins implicated in diseases. A key step in this process is the formation of a ternary complex where a heterobifunctional molecule induces proximity of an E3 ligase to a protein of interest (POI), thus facilitating ubiquitin transfer to the POI. In this work, we characterize 3 steps in the TPD process. (1) We simulate the ternary complex formation of SMARCA2 bromodomain and VHL E3 ligase by combining hydrogen-deuterium exchange mass spectrometry with weighted ensemble molecular dynamics (MD). (2) We characterize the conformational heterogeneity of the ternary complex using Hamiltonian replica exchange simulations and small-angle X-ray scattering. (3) We assess the ubiquitination of the POI in the context of the full Cullin-RING Ligase, confirming experimental ubiquitinomics results. Differences in degradation efficiency can be explained by the proximity of lysine residues on the POI relative to ubiquitin.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Generation, dynamics, and correlations of the fission fragments' angular momenta

The generation of angular momentum in fissioning nuclei is not well understood. The predictions of different models disagree, particularly concerning the correlation between the fragments' angular momenta. In this article, a time-dependent collective Hamiltonian model is proposed to treat the generation of the angular momentum in the fission fragments due to the quantum uncertainty principle as well as the dynamics of the collective wave function during and after scission. The model is constructed in the framework of the frozen Hartree-Fock approximation using a Skyrme energy functional to extract deformations of the fission fragments as well as the interactions in a derived collective Hamiltonian. The fission reactions studied are $^{240}$Pu $\rightarrow$ $^{132}$Sn+$^{108}$Ru and $^{240}$Pu $\rightarrow$ $^{144}$Ba+$^{96}$Sr. The model can account for a large part of the angular momentum found in experimental data. The orientation of the angular momentum of each fragment is found to be mainly in the plane perpendicular to the fission axis, in agreement with the experiment. The magnitudes of the angular momenta in the two fragments are nearly uncorrelated, in agreement with the recent experimental data of Wilson et al., Nature (London) 590, 566 (2021). Some of the conclusions of the traditional collective vibration model are supported by the present model but some are not. Surprisingly, it is found that the angular momenta of the fragments are slightly correlated positively as in a wriggling mode. As a result, it is also found that the presence of an octupole deformation in a fragment can significantly increase the generated angular momentum.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS2003

Quantum Adiabatic Algorithms and Large Spin Tunnelling

We provide a theoretical study of the quantum adiabatic evolution algorithm with different evolution paths proposed in this paper. The algorithm is applied to a random binary optimization problem (a version of the 3-Satisfiability problem) where the n-bit cost function is symmetric with respect to the permutation of individual bits. The evolution paths are produced, using the generic control Hamiltonians H (r) that preserve the bit symmetry of the underlying optimization problem. In the case where the ground state of H(0) coincides with the totally-symmetric state of an n-qubit system the algorithm dynamics is completely described in terms of the motion of a spin-n/2. We show that different control Hamiltonians can be parameterized by a set of independent parameters that are expansion coefficients of H (r) in a certain universal set of operators. Only one of these operators can be responsible for avoiding the tunnelling in the spin-n/2 system during the quantum adiabatic algorithm. We show that it is possible to select a coefficient for this operator that guarantees a polynomial complexity of the algorithm for all problem instances. We show that a successful evolution path of the algorithm always corresponds to the trajectory of a classical spin-n/2 and provide a complete characterization of such paths.

Boulatov, A.↗
DOE OSTI2022

Engineering an effective three-spin Hamiltonian in trapped-ion systems for applications in quantum simulation

Trapped-ion quantum simulators, in analog and digital modes, are considered a primary candidate to achieve quantum advantage in quantum simulation and quantum computation. The underlying controlled ion–laser interactions induce all-to-all two-spin interactions via the collective modes of motion through Cirac–Zoller or Mølmer–Sørensen schemes, leading to effective two-spin Hamiltonians, as well as two-qubit entangling gates. In this work, the Mølmer–Sørensen scheme is extended to induce three-spin interactions via tailored first- and second-order spin–motion couplings. The scheme enables engineering single-, two-, and three-spin interactions, and can be tuned via an enhanced protocol to simulate purely three-spin dynamics. Analytical results for the effective evolution are presented, along with detailed numerical simulations of the full dynamics to support the accuracy and feasibility of the proposed scheme for near-term applications. With a focus on quantum simulation, the advantage of a direct analog implementation of three-spin dynamics is demonstrated via the example of matter-gauge interactions in the U(1) lattice gauge theory within the quantum link model. The mapping of degrees of freedom and strategies for scaling the three-spin scheme to larger systems, are detailed, along with a discussion of the expected outcome of the simulation of the quantum link model given realistic fidelities in the upcoming experiments. The applications of the three-spin scheme go beyond the lattice gauge theory example studied here and include studies of static and dynamical phase diagrams of strongly interacting condensed-matter systems modeled by two- and three-spin Hamiltonians.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Light mesons with one dynamical gluon on the light front

We obtain the light meson mass spectroscopy from the light-front quantum chromodynamics (QCD) Hamiltonian, determined for their constituent quark-antiquark and quark-antiquark-gluon Fock components, together with a three-dimensional confinement. The eigenvectors of the light-front effective Hamiltonian provide a good quality description of the pion electromagnetic form factor, decay constant, and the valence quark distribution functions following QCD scale evolution. We also show that the pion's gluon densities can be probed through the pion-nucleus induced $J/ψ$ production data. Our pion parton distribution functions provide excellent agreement with $J/ψ$ production data from widely different experimental conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2006

Dynamic Theory of Relativistic Electrons Stochastic Heating by Whistler Mode Waves with Application to the Earth Magnetosphere

In the Hamiltonian approach an electron motion in a coherent packet of the whistler mode waves propagating along the direction of an ambient magnetic field is studied. The physical processes by which these particles are accelerated to high energy are established. Equations governing a particle motion by group symmetries of the problem were transformed in to a closed pair of nonlinear difference equations. The solutions of these equations have shown there exists the energetic threshold below that the electron motion is regular, and when the initial energy is above the threshold an electron moves stochastically. It is proved that the upper boundary of particle stochastic heating is conditioned by intrinsic property of the particle chaotic motion. Particle energy spectra and pitch angle electron scattering are described by the Fokker-Planck-Kolmogorov equations. It is shown that significant pitch angle diffusion occurs for the Earth radiation belt electrons with energies from a few keV up to a few MeV.

Khazanov, G. V.↗
NASA NTRS2007

Dynamic Theory of Relativistic Electrons Stochastic Heating by Whistler Mode Waves with Application to the Earth Magnetosphere

In the Hamiltonian approach an electron motion in a coherent packet of the whistler mode waves propagating along the direction of an ambient magnetic field is studied. The physical processes by which these particles are accelerated to high energy are established. Equations governing a particle motion were transformed in to a closed pair of nonlinear difference equations. The solutions of these equations have shown there exists the energetic threshold below that the electron motion is regular, and when the initial energy is above the threshold an electron moves stochastically. Particle energy spectra and pitch angle electron scattering are described by the Fokker-Planck-Kolmogorov equations. Calculating the stochastic diffusion of electrons due to a spectrum of whistler modes is presented. The parametric dependence of the diffusion coefficients on the plasma particle density, magnitude of wave field, and the strength of magnetic field is studies. It is shown that significant pitch angle diffusion occurs for the Earth radiation belt electrons with energies from a few keV up to a few MeV.

Khazanov, G. V.↗
DOE OSTI2022

Pulse-level noisy quantum circuits with QuTiP

The study of the impact of noise on quantum circuits is especially relevant to guide the progress of Noisy Intermediate-Scale Quantum (NISQ) computing. In this paper, we address the pulse-level simulation of noisy quantum circuits with the Quantum Toolbox in Python (QuTiP). We introduce new tools in qutip-qip, QuTiP's quantum information processing package. These tools simulate quantum circuits at the pulse level, leveraging QuTiP's quantum dynamics solvers and control optimization features. We show how quantum circuits can be compiled on simulated processors, with control pulses acting on a target Hamiltonian that describes the unitary evolution of the physical qubits. Various types of noise can be introduced based on the physical model, e.g., by simulating the Lindblad density-matrix dynamics or Monte Carlo quantum trajectories. In particular, the user can define environment-induced decoherence at the processor level and include noise simulation at the level of control pulses. We illustrate how the Deutsch-Jozsa algorithm is compiled and executed on a superconducting-qubit-based processor, on a spin-chain-based processor and using control optimization algorithms. We also show how to easily reproduce experimental results on cross-talk noise in an ion-based processor, and how a Ramsey experiment can be modeled with Lindblad dynamics. Finally, we illustrate how to integrate these features with other software frameworks.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Effect of off-diagonal elements in the Wannier Hamiltonian on DFT + DMFT for low-symmetry materials: Study of Li 2 MnO 3

Here, we study the effect of the off-diagonal elements of the Wannier Hamiltonian on the electronic structure of the low-symmetry material Li 2 MnO 3 ( C2/m ), using dynamical mean field theory calculations with a continuous-time quantum Monte Carlo impurity solver. The presence of significant off-diagonal elements leads to a pronounced suppression of the energy gap. The off-diagonal elements are largest when the Wannier projection is used based on the global coordinate, and they remain substantial even with the projection using the local coordinate close to the direction of Mn-O bonds. We show that the energy gap is enhanced by the diagonalization of the Mn d block in the full p-d Hamiltonian with the application of a unitary rotation matrix. Additionally, the inclusion of small double counting energy is crucial for achieving the experimental gap by reducing p-d hybridization. Furthermore, we establish the efficiency of a low-energy (d-only basis) model for studying the electronic structure of Li 2 MnO 3 , as the Wannier basis represents a hybridized state of Mn d and O p orbitals. These findings suggest an appropriate approach for investigating low-symmetry materials using the density functional theory plus dynamical mean field theory (DFT + DMFT) method. We also find that the antiferromagnetic ground state $\Gamma$ 2u is stable with U ≤ 2 eV within density functional theory+$U$ calculations, which is much smaller than the widely used U = 5 eV.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Exploration of lattice Hamiltonians for functional and structural discovery via Gaussian process-based exploration–exploitation

Statistical physics models ranging from simple lattice to complex quantum Hamiltonians are one of the mainstays of modern physics that have allowed both decades of scientific discovery and provided a universal framework to understand a broad range of phenomena from alloying to frustrated and phase separated materials to quantum systems. Traditionally, exploration of the phase diagrams corresponding to multidimensional parameter spaces of Hamiltonians was performed using a combination of basic physical principles, analytical approximations, and extensive numerical modeling. However, exploration of complex multidimensional parameter spaces is subject to the classic dimensionality problem, and the behaviors of interest concentrated on low dimensional manifolds remain undiscovered. Here, we demonstrate that a combination of exploration and exploration–exploitation with Gaussian process modeling and Bayesian optimization allows effective exploration of the parameter space for lattice Hamiltonians and effectively maps the regions at which specific macroscopic functionalities or local structures are maximized. We argue that this approach is general and can be further extended well beyond the lattice Hamiltonians to effectively explore the parameter space of more complex off-lattice and dynamic models.

42 ENGINEERING↗
DOE OSTI2021

Influence of solution phase environmental heterogeneity and fluctuations on vibronic spectra: Perylene diimide molecular chromophore complexes in solution

Ensembles of ab initio parameterized Frenkel-exciton model Hamiltonians for different perylene diimide dimer systems are used, together with various dissipative quantum dynamics approaches, to study the influence of the solvation environment and fluctuations in chromophore relative orientation and packing on the vibronic spectra of two different dimer systems: a π-stacked dimer in aqueous solution in which the relative chromophore geometry is strongly confined by a phosphate bridge and a side-by-side dimer in dichloromethane involving a more flexible alkyne bridge that allows quasi-free rotation of the chromophores relative to one another. These entirely first-principles calculations are found to accurately reproduce the main features of the experimental absorption spectra, providing a detailed mechanistic understanding of how the structural fluctuations and environmental interactions influence the vibronic dynamics and spectroscopy of solutions of these multi-chromophore complexes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1988

A study to evaluate STS heads-up ascent trajectory performance employing a minimum-Hamiltonian optimization strategy

A study was conducted to evaluate the performance implications of a heads-up ascent flight design for the Space Transportation System, as compared to the current heads-down flight mode. The procedure involved the use of the Minimum Hamiltonian Ascent Shuttle Trajectory Evaluation Program, which is a three-degree-of-freedom moment balance simulation of shuttle ascent. A minimum-Hamiltonian optimization strategy was employed to maximize injection weight as a function of maximum dynamic pressure constraint and Solid Rocket Motor burnrate. Performance Reference Mission Four trajectory groundrules were used for consistency. The major conclusions are that for heads-up ascent and a mission nominal design maximum dynamic pressure value of 680 psf, the optimum solid motor burnrate is 0.394 ips, which produces a performance enhancement of 4293 lbm relative to the baseline heads-down ascent, with 0.368 ips burnrate solid motors and a 680 psf dynamic pressure constraint. However, no performance advantage exists for heads-up flight if the current Solid Rocket Motor target burnrate of 0.368 ips is used. The advantage of heads-up ascent flight employing the current burnrate is that Space Shuttle Main Engine throttling for dynamic pressure control is not necessary.

Sinha, Sujit↗
NASA NTRS2004

Random Matrix Approach to Quantum Adiabatic Evolution Algorithms

We analyze the power of quantum adiabatic evolution algorithms (Q-QA) for solving random NP-hard optimization problems within a theoretical framework based on the random matrix theory (RMT). We present two types of the driven RMT models. In the first model, the driving Hamiltonian is represented by Brownian motion in the matrix space. We use the Brownian motion model to obtain a description of multiple avoided crossing phenomena. We show that the failure mechanism of the QAA is due to the interaction of the ground state with the "cloud" formed by all the excited states, confirming that in the driven RMT models. the Landau-Zener mechanism of dissipation is not important. We show that the QAEA has a finite probability of success in a certain range of parameters. implying the polynomial complexity of the algorithm. The second model corresponds to the standard QAEA with the problem Hamiltonian taken from the Gaussian Unitary RMT ensemble (GUE). We show that the level dynamics in this model can be mapped onto the dynamics in the Brownian motion model. However, the driven RMT model always leads to the exponential complexity of the algorithm due to the presence of the long-range intertemporal correlations of the eigenvalues. Our results indicate that the weakness of effective transitions is the leading effect that can make the Markovian type QAEA successful.

Boulatov, Alexei↗
NASA NTRS1997

Coupling of Sph and Finite Element Codes for Multi-Layer Orbital Debris Shield Design

Particle-based hydrodynamics models offer distinct advantages over Eulerian and Lagrangian hydrocodes in particular shock physics applications. Particle models are designed to avoid the mesh distortion and state variable diffusion problems which can hinder the effective use of Lagrangian and Eulerian codes respectively. However conventional particle-in-cell and smooth particle hydrodynamics methods employ particles which are actually moving interpolation points. A new particle-based modeling methodology, termed Hamiltonian particle hydrodynamics, was developed by Fahrenthold and Koo (1997) to provide an alternative, fully Lagrangian, energy-based approach to shock physics simulations. This alternative formulation avoids the tensile and boundary instabilities associated with standard smooth particle hydrodynamics formulations and the diffusive grid- to-particle mapping schemes characteristic of particle-in-cell methods. In the work described herein, the method of Fahrenthold and Koo has been extended, by coupling the aforementioned hydrodynamic particle model to a hexahedral finite element based description of the continuum dynamics. The resulting continuum model retains all of the features (including general contact-impact effects) of Hamiltonian particle hydrodynamics, while in addition accounting for tensile strength, plasticity, and damage effects important in the simulation of hypervelocity impact on orbital debris shielding. A three dimensional, vectorized, and autotasked implementation of the extended particle method described here has been coded for application to orbital debris shielding design. Source code for the pre-processor (PREP), analysis code (EXOS), post-processor (POST), and rezoner (ZONE), have been delivered separately, along with a User's Guide describing installation and application of the software.

Fahrenthold, Eric P.↗
DOE OSTI2022

Quantum dynamics of cold atomic gas with SU(1,1) symmetry

Motivated by recent advances in quantum dynamics, we investigate the dynamics of the system with SU(1,1) symmetry. Instead of performing the time-ordered integral for the evolution operator of the time-dependent Hamiltonian, we show that the time evolution operator can be expressed as an SU(1,1) group element. Since the SU(1,1) group describes the “rotation” on a hyperbolic surface, the dynamics can be visualized on a Poincaré disk, a stereographic projection of the upper hyperboloid. As an example, we present the trajectory of the revival of Bose-Einstein condensation and that of the scale-invariant Fermi gas on the Poincaré disk. Further considering quantum gases in an oscillating lattice, we also study the dynamics of the system with time-dependent single-particle dispersion.

74 ATOMIC AND MOLECULAR PHYSICS↗