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Results for “variational principle”

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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Nonequilibrium design strategies for functional colloidal assemblies

Here, we use a nonequilibrium variational principle to optimize the steady-state, shear-induced interconversion of self-assembled nanoclusters of DNA-coated colloids. Employing this principle within a stochastic optimization algorithm allows us to identify design strategies for functional materials. We find that far-from-equilibrium shear flow can significantly enhance the flux between specific colloidal states by decoupling trade-offs between stability and reactivity required by systems in equilibrium. For isolated nanoclusters, we find nonequilibrium strategies for amplifying transition rates by coupling a given reaction coordinate to the background shear flow. We also find that shear flow can be made to selectively break detailed balance and maximize probability currents by coupling orientational degrees of freedom to conformational transitions. For a microphase consisting of many nanoclusters, we study the flux of colloids hopping between clusters. We find that a shear flow can amplify the flux without a proportional compromise on the microphase structure. This approach provides a general means of uncovering design principles for nanoscale, autonomous, functional materials driven far from equilibrium.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Quantum simulation of excited states from parallel contracted quantum eigensolvers

Abstract Computing excited-state properties of molecules and solids is considered one of the most important near-term applications of quantum computers. While many of the current excited-state quantum algorithms differ in circuit architecture, specific exploitation of quantum advantage, or result quality, one common feature is their rooting in the Schrödinger equation. However, through contracting (or projecting) the eigenvalue equation, more efficient strategies can be designed for near-term quantum devices. Here we demonstrate that when combined with the Rayleigh–Ritz variational principle for mixed quantum states, the ground-state contracted quantum eigensolver (CQE) can be generalized to compute any number of quantum eigenstates simultaneously. We introduce two excited-state (anti-Hermitian) CQEs that perform the excited-state calculation while inheriting many of the remarkable features of the original ground-state version of the algorithm, such as its scalability. To showcase our approach, we study several model and chemical Hamiltonians and investigate the performance of different implementations.

Physics↗
DOE OSTI2025

Real-time scattering in Ising field theory using matrix product states

We study scattering in Ising field theory (IFT) using matrix product states and the time-dependent variational principle. IFT is a one-parameter family of strongly coupled nonintegrable quantum field theories in 1+1 dimensions, interpolating between massive free fermion theory and Zamolodchikov's integrable massive 𝐸 8 theory. Particles in IFT may scatter either elastically or inelastically. In the postcollision wave function, particle tracks from all final-state channels occur in superposition; processes of interest can be isolated by projecting the wave function onto definite particle sectors, or by evaluating energy density correlation functions. Using numerical simulations we determine the time delay of elastic scattering and the probability of inelastic particle production as a function of collision energy. We also study the mass and width of the lightest resonance near the 𝐸 8 point in detail. Close to both the free fermion and 𝐸 8 theories, our results for both elastic and inelastic scattering are in good agreement with expectations from form-factor perturbation theory. Using numerical computations to go beyond the regime accessible by perturbation theory, we find that the high-energy behavior of the two-to-two particle scattering probability in IFT is consistent with a conjecture of Zamolodchikov. Our results demonstrate the efficacy of tensor-network methods for simulating the real-time dynamics of strongly coupled quantum field theories in 1+1 dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Reduced-action-integral approach for photon-photon interactions in vacuum

Electromagnetic waves propagating through vacuum can polarize virtual electron–positron pairs; this polarization, in turn, nonlinearly modifies their propagation. A semi-classical nonlinear wave equation describing the propagation is derived from the Euler–Heisenberg Lagrangian density, which captures vacuum polarization effects up to the one-loop level. In this article, we present a reduced-actionintegral approach that enables rapid modeling of nonlinear phenomena arising from the Euler– Heisenberg Lagrangian. Application of the variational principle to the reduced action provides equations of motion for familiar light-pulse parameters, such as spot size, phase, polarization, and phase-front curvature, without requiring full-field simulations. Three examples demonstrate the utility of the approach: phase modulation, birefringence, and frequency mixing.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Quench dynamics of two-component dipolar fermions subject to a quasiperiodic potential

Motivated by recent experiments in fermionic polar gases, we study the nonequilibrium dynamics of two-component dipolar fermions subject to a quasiperiodic potential. We investigate the localization of charge and spin degrees of freedom time evolving with a long-range spin-SU(2) symmetric fermionic Hamiltonian by calculating experimentally accessible dynamical observables. To study the nonequilibrium dynamics, we start the time evolution with two initial states at half-filling: (i) product state with doublons |↑↓0↑↓0↑↓0↑↓0↑↓$\rangle$ and (ii) product state with singlons |↑↓↑↓↑↓↑↓↑↓$\rangle$. We carried out the real-time evolution via the fermionic Hamiltonian using exact diagonalization (ED) and the time-dependent variational principle (TDVP) for finite matrix product states (MPS), within experimentally relevant timescales. For the product state with doublons, we observe a delocalized to localized phase transition varying disorder strengths by monitoring the decay of charge imbalance with time. For the long-range interacting Hamiltonian of our focus, and in the presence of strong enough disorder, starting the time evolution with singlons we find a strong reduction in the spin delocalization, contrary to results of previous studies using the disordered short-range (on-site) Hubbard model with SU(2) symmetry. In addition to the quench dynamics, we also demonstrate the localization of charge and spin in the full energy spectrum of the long-range spin-SU(2) symmetric Hamiltonian by monitoring spin and charge autocorrelation functions. Finally, our predictions for localization of both charge and spin should be observable in ultracold experiments with fermionic dipolar atoms subject to a quasiperiodic potential.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Neutral excitations of quantum Hall states: A density matrix renormalization group study

We use the dynamical structure factors of the quantum Hall states at ν = 1 / 3 and 1 / 2 in the lowest Landau level to study their excitation spectrum. Using the density matrix renormalization group in combination with the time-dependent variational principle on an infinite cylinder geometry, we extract the low-energy properties. At ν = 1 / 3 , a sharp magnetoroton mode and the two-roton continuum are present and the finite-size effects can be understood using the fractional charge of the quasiparticle. At ν = 1 / 2 , we find low-energy modes with linear dispersion and the static structure factor s ¯ ( q ) ~ ( q ℓ ) 3 in the limit q ℓ → 0 . The properties of these modes agree quantitatively with the predictions of the composite-fermion theory placed on the infinite cylinder.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Accuracy of ghost rotationally invariant slave-boson and dynamical mean field theory as a function of the impurity-model bath size

Here, we compare the accuracy of the ghost rotationally invariant slave-boson (g-RISB) theory and dynamical mean field theory (DMFT) on the single-band Hubbard model, as a function of the number of bath sites in the embedding impurity Hamiltonian. Our benchmark calculations confirm that the accuracy of g-RISB can be systematically improved by increasing the number of bath sites, similar to DMFT. With a few bath sites, we observe that g-RISB is systematically more accurate than DMFT for the ground-state observables. On the other hand, the relative accuracy of these methods is generally comparable for the quasiparticle weight and the spectral function. As expected, we observe that g-RISB satisfies the variational principle in infinite dimensions, as the total energy decreases monotonically towards the exact value as a function of the number of bath sites, suggesting that the g-RISB wave function may approach the exact ground state in infinite dimensions. Our results suggest that the g-RISB is a promising method for first-principles simulations of strongly correlated matter, which can capture the behavior of both static and dynamical observables, at a relatively low computational cost.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Wave-function-based emulation for nucleon-nucleon scattering in momentum space

Emulators for low-energy nuclear physics can provide fast and accurate predictions of bound-state and scattering observables for applications that require repeated calculations with different parameters, such as Bayesian uncertainty quantification. In this paper, we extend a scattering emulator based on the Kohn variational principle (KVP) to momentum space (including coupled channels) with arbitrary boundary conditions, which enable the mitigation of spurious singularities known as Kohn anomalies. We test it on a modern chiral nucleon-nucleon (N N) interaction, including emulation of the coupled channels. We provide comparisons between a Lippmann-Schwinger equation emulator and our KVP momentum-space emulator for a representative set of neutron-proton (n p) scattering observables, and also introduce a quasi-spline-based approach for the KVP-based emulator. Furthermore, our findings show that while there are some trade-offs between accuracy and speed, all three emulators perform well. Self-contained Jupyter notebooks that generate the results and figures in this paper are publicly available.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Mixing effects on spectroscopy and partonic observables of heavy mesons with logarithmic confining potential in a light-front quark model

Using the variational principle, we systematically investigate the mass spectra and wave functions of both 1⁢𝑆 and 2⁢𝑆 state heavy pseudoscalar (𝑃) and vector (𝑉) mesons within the light-front quark model. This approach incorporates a Coulomb plus logarithmic confinement potential to accurately describe the constituent quark and antiquark dynamics. Additionally, spin hyperfine interactions are introduced perturbatively to compute the masses of pseudoscalar and vector mesons. The present analyses of the 1⁢𝑆 and 2⁢𝑆 states require the consideration of mixing between them to account for empirical constraints. These constraints include the mass gap Δ⁢𝑀 𝑃 >Δ⁢𝑀 𝑉 , where Δ⁢𝑀 𝑃⁡(𝑉) =𝑀$^{2⁢𝑆}_{𝑃⁡(𝑉)}$−𝑀$^{1⁢𝑆}_{𝑃⁡(𝑉)}$ and the hierarchy of the decay constants 𝑓 1⁢𝑆 >𝑓 2⁢𝑆 . We find the optimal value of the mixing angle to be 𝜃 =1⁢8°, significantly enhancing the consistency between our spectroscopic predictions and the experimental data compiled by the Particle Data Group. Furthermore, based on the predicted mass, the newly observed resonance 𝐵 𝐽⁡ (5840) could be assigned as a 2 1⁢ 𝑆 0 state in the 𝐵 meson family. The study also reports various pertinent observables, including twist-two distribution amplitudes, electromagnetic form factors, charge radii, 𝜉 moments, and transition form factors that are found to be consistent with both available lattice simulations and experimental data. In addition, our predicted branching ratios for the channels of 𝐵 + →𝜏 + ⁢𝜈 𝜏 as well as rare decays of 𝐵 0 and 𝐵$^0_𝑠$ appear in accordance with experimental data.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Tuning between continuous time crystals and many-body scars in long-range XYZ spin chains.

Persistent oscillatory dynamics in nonequilibrium many-body systems is a tantalizing manifestation of ergodicity breakdown that continues to attract much attention. Recent works have focused on two classes of such systems: discrete time crystals and quantum many-body scars (QMBS). While both systems host oscillatory dynamics, its origin is expected to be fundamentally different: discrete time crystal is a phase of matter which spontaneously breaks the Z 2 symmetry of the external periodic drive, while QMBS span a subspace of nonthermalizing eigenstates forming an su(2) algebra representation. Here, we ask a basic question: is there a physical system that allows us to tune between these two dynamical phenomena? In contrast to much previous work, we investigate the possibility of a continuous time crystal (CTC) in undriven, energy-conserving systems exhibiting prethermalization. We introduce a long-range XYZ spin model and show that it encompasses both a CTC phase as well as QMBS. We map out the dynamical phase diagram using numerical simulations based on exact diagonalization and time-dependent variational principle in the thermodynamic limit. We identify a regime where QMBS and CTC order coexist, and we discuss experimental protocols that reveal their similarities as well as key differences.

Bull, Kieran↗
DOE OSTI2022

A general framework for gravitational charges and holographic renormalization

We develop a general framework for constructing charges associated with diffeomorphisms in gravitational theories using covariant phase space techniques. This framework encompasses both localized charges associated with space–time subregions, as well as global conserved charges of the full space–time. Expressions for the charges include contributions from the boundary and corner terms in the subregion action, and are rendered unambiguous by appealing to the variational principle for the subregion, which selects a preferred form of the symplectic flux through the boundaries. The Poisson brackets of the charges on the subregion phase space are shown to reproduce the bracket of Barnich and Troessaert for open subsystems, thereby giving a novel derivation of this bracket from first principles. In the context of asymptotic boundaries, we show that the procedure of holographic renormalization can be always applied to obtain finite charges and fluxes once suitable counterterms have been found to ensure a finite action. This enables the study of larger asymptotic symmetry groups by loosening the boundary conditions imposed at infinity. We further present an algorithm for explicitly computing the counterterms that renormalize the action and symplectic potential, and, as an application of our framework, demonstrate that it reproduces known expressions for the charges of the generalized Bondi–Metzner–Sachs algebra.

Physics↗
DOE OSTI2020

Benchmarking Adaptive Variational Quantum Eigensolvers

By design, the variational quantum eigensolver (VQE) strives to recover the lowest-energy eigenvalue of a given Hamiltonian by preparing quantum states guided by the variational principle. In practice, the prepared quantum state is indirectly assessed by the value of the associated energy. Novel adaptive derivative-assembled pseudo-trotter (ADAPT) ansatz approaches and recent formal advances now establish a clear connection between the theory of quantum chemistry and the quantum state ansatz used to solve the electronic structure problem. Here we benchmark the accuracy of VQE and ADAPT-VQE to calculate the electronic ground states and potential energy curves for a few selected diatomic molecules, namely H 2 , NaH, and KH. Using numerical simulation, we find both methods provide good estimates of the energy and ground state, but only ADAPT-VQE proves to be robust to particularities in optimization methods. Another relevant finding is that gradient-based optimization is overall more economical and delivers superior performance than analogous simulations carried out with gradient-free optimizers. The results also identify small errors in the prepared state fidelity which show an increasing trend with molecular size.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗