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At least 253 records · Page 14

All sources NASA NTRS DOE OSTI

DOE OSTI2022

AGP-based unitary coupled cluster theory for quantum computers

Electronic structure methods typically benefit from symmetry breaking and restoration, specially in the strong correlation regime. Here, the same goes for ansätze on a quantum computer. We develop a unitary coupled cluster method based on the antisymmetrized geminal power (AGP)—a state formally equivalent to the number-projected Bardeen–Cooper–Schrieffer wavefunction. We demonstrate our method for the single-band Fermi–Hubbard Hamiltonian in one and two dimensions. We also explore post-selection as a state preparation step to obtain correlated AGP and prove that it scales no worse than O(√M) in the number of measurements, thereby making it a less expensive alternative to gauge integration to restore particle number symmetry.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

The response field and the saddle points of quantum mechanical path integrals

Highlights: • Moyal quantum mechanics and Marinov’s path integral. • Classical and semiclassical limits of Marinov’s path integral. • Oscillating functional integrals. • Instantons of the Marinov’s path integral. In quantum statistical mechanics, Moyal’s equation governs the time evolution of Wigner functions and of more general Weyl symbols that represent the density matrix of arbitrary mixed states. A formal solution to Moyal’s equation is given by Marinov’s path integral. In this paper we demonstrate that this path integral can be regarded as the natural link between several conceptual, geometric, and dynamical issues in quantum mechanics. A unifying perspective is achieved by highlighting the pivotal role which the response field, one of the integration variables in Marinov’s integral, plays for pure states even. The discussion focuses on how the integral’s semiclassical approximation relates to its strictly classical limit; unlike for Feynman type path integrals, the latter is well defined in the Marinov case. The topics covered include a random force representation of Marinov’s integral based upon the concept of “Airy averaging”, a related discussion of positivity-violating Wigner functions describing tunneling processes, and the role of the response field in maintaining quantum coherence and enabling interference phenomena. The double slit experiment for electrons and the Bohm–Aharonov effect are analyzed as illustrative examples. Furthermore, a surprising relationship between the instantons of the Marinov path integral over an analytically continued (“Wick rotated”) response field, and the complex instantons of Feynman-type integrals is found. The latter play a prominent role in recent work towards a Picard–Lefschetz theory applicable to oscillatory path integrals and the resurgence program.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2014

Two Dimensional Symmetric Correlation Functions of the S Operator and Two Dimensional Fourier Transforms: Considering the Line Coupling for P and R Lines of Linear Molecules

The refinement of the Robert-Bonamy (RB) formalism by considering the line coupling for isotropic Raman Q lines of linear molecules developed in our previous study [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] has been extended to infrared P and R lines. In these calculations, the main task is to derive diagonal and off-diagonal matrix elements of the Liouville operator iS1 − S2 introduced in the formalism. When one considers the line coupling for isotropic Raman Q lines where their initial and final rotational quantum numbers are identical, the derivations of off-diagonal elements do not require extra correlation functions of the ^S operator and their Fourier transforms except for those used in deriving diagonal elements. In contrast, the derivations for infrared P and R lines become more difficult because they require a lot of new correlation functions and their Fourier transforms. By introducing two dimensional correlation functions labeled by two tensor ranks and making variable changes to become even functions, the derivations only require the latters' two dimensional Fourier transforms evaluated at two modulation frequencies characterizing the averaged energy gap and the frequency detuning between the two coupled transitions. With the coordinate representation, it is easy to accurately derive these two dimensional correlation functions. Meanwhile, by using the sampling theory one is able to effectively evaluate their two dimensional Fourier transforms. Thus, the obstacles in considering the line coupling for P and R lines have been overcome. Numerical calculations have been carried out for the half-widths of both the isotropic Raman Q lines and the infrared P and R lines of C2H2 broadened by N2. In comparison with values derived from the RB formalism, new calculated values are significantly reduced and become closer to measurements.

infrared radiation↗

DOE OSTI2020

Relativistic Dynamics of Fluctuations and QCD Critical Point

Herein, we review the recent development on a systematic deterministic formalism describing dynamics of both bulk and fluctuations in an arbitrary relativistic hydrodynamic flow carrying conserved charges. In particular, we discuss the implementation of such general formalism near the QCD critical point.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Dynamical properties of a driven dissipative dimerized $S$ =1/2 chain

We consider the dynamical properties of a gapped quantum spin system coupled to the electric field of a laser, which drives the resonant excitation of specific phonon modes that modulate the magnetic interactions. Here, we deduce the quantum master equations governing the time-evolution of both the lattice and spin sectors, by developing a Lindblad formalism with bath operators providing an explicit description of their respective phonon-mediated damping terms. We investigate the nonequilibrium steady states (NESS) of the spin system established by a continuous driving, delineating parameter regimes in driving frequency, damping, and spin-phonon coupling for the establishment of physically meaningful NESS and their related nontrivial properties. Focusing on the regime of generic weak spin-phonon coupling, we characterize the NESS by their frequency and wave-vector content, explore their transient and relaxation behavior, and discuss the energy flow, the system temperature, and the critical role of the type of bath adopted. Our study lays a foundation for the quantitative modeling of experiments currently being designed to control coherent many-body spin states in quantum magnetic materials.

1-dimensional spin chains↗

DOE OSTI2023

Solving the nuclear pairing model with neural network quantum states

In this work, we present a variational Monte Carlo method that solves the nuclear many-body problem in the occupation number formalism exploiting an artificial neural network representation of the groundstate wave function. A memory-efficient version of the stochastic reconfiguration algorithm is developed to train the network by minimizing the expectation value of the Hamiltonian. We benchmark this approach against widely used nuclear many-body methods by solving a model used to describe pairing in nuclei for different types of interaction and different values of the interaction strength. Despite its polynomial computational cost, our method outperforms coupled-cluster and provides energies that are in excellent agreement with the numerically-exact full configuration interaction values.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Angular-momentum projection in coupled-cluster theory: Structure of 34 Mg

Single- reference coupled-cluster theory is an accurate and affordable computational method for the nuclear many-body problem. For open-shell nuclei, the reference state typically breaks rotational invariance and angular momentum must be restored as a good quantum number. We perform angular-momentum projection after variation and employ the disentangled coupled-cluster formalism and a Hermitian approach. We compare our results with benchmarks for 8 Be and 20 Ne using a two-nucleon interaction from chiral effective field theory and for pf-shell nuclei within the traditional shell model. We compute the rotational band in the exotic nucleus 34 Mg and find agreement with data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS1986

Comparison of abrasion model differences in heavy ion fragmentation - Optical versus geometric models

Two different abrasion formalisms, one based on an energy-independent geometric model and the other based on a quantum-mechanical optical model, are shown to yield comparable fragmentation cross section predictions when used as input to an abrasion-ablation frictional-spectator interaction fragmentation calculation which includes electromagnetic dissociation contributions. The results suggest that any dependence upon the incident ion's kinetic energy above 200 MeV/nucleon is weak. It is also noted that the larger surface diffusiveness of the optical model densities only affects nuclear cross sections for near-projectile-mass fragments, while for heavier nuclei, the sizable cross-section contributions from electromagnetic dissociation negate these differences.

Townsend, L. W.↗

NASA NTRS2012

Kuang's Semi-Classical Formalism for Electron Capture Cross-Sections in Ion-Ion Collisions at Approximately to MeV/amu: Application to ENA Modeling

Recent discovery by STEREO A/B of energetic neutral hydrogen is spurring an interest and need for reliable estimates of electron capture cross sections at few MeVs per nucleon as well as for multi-electron ions. Required accuracy in such estimates necessitates detailed and involved quantum-mechanical calculations or expensive numerical simulations. For ENA modeling and similar purposes, a semi-classical approach offers a middle-ground approach. Kuang's semiclassical formalism to calculate electron-capture cross sections for single and multi-electron ions is an elegant and efficient method, but has so far been applied to limited and specific laboratory measurements and at somewhat lower energies. Our goals are to test and extend Kuang s method to all ion-atom and ion-ion collisions relevant to ENA modeling, including multi-electron ions and for K-shell to K-shell transitions.

Barghouty, A. F.↗

DOE OSTI2025

The phase of the gravitational path integral

The gravitational path integral on S 2 × S 2 can be interpreted either as evaluating a contribution to the norm of the Hartle-Hawking wavefunction conditional on spatial S 1 × S 2 topology, or the pair creation rate of black holes in de Sitter. Both interpretations are distinguished at the quantum level. The former requires the path integral to be real and the latter to be imaginary. We develop a formalism to efficiently compute the phase of the gravitational path integral on Einstein spaces. We apply it to a broad class of spacetimes and in particular S 2 × S D−2 , finding it to be real and positive. We generalize some of the analysis to cases with charge and rotation.

AdS-CFT correspondence↗

DOE OSTI2021

Nonrad: Computing nonradiative capture coefficients from first principles

Point defects in semiconductor crystals provide a means for carriers to recombine nonradiatively. This recombination process impacts the performance of devices. We present the Nonrad code that implements the first-principles approach of Alkauskas et al. (2014) [8] for the evaluation of nonradiative capture coefficients based on a quantum-mechanical description of the capture process. An approach for evaluating electron-phonon coupling within the projector augmented wave formalism is presented. We also show that the common procedure of replacing Dirac delta functions with Gaussians can introduce errors into the resulting capture rate, and implement an alternative scheme to properly account for vibrational broadening. Finally, we assess the accuracy of using an analytic approximation to the Sommerfeld parameter by comparing with direct numerical evaluation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRSDate not supplied

Downfolding Complex Materials Problems Onto Model Hamiltonians for Quantum Computers

Simulating the properties of quantum materials is expected to be one of the exciting applications for quantum computers and where we hope to see advantages over classical hardware. The complexity of ab initio Hamiltonians describing the physics of application-relevant materials places them beyond the realm of possibility for solution on near-term hardware with a limited number of qubits. Various Hamiltonian approximations, including Hamiltonian downfolding, offers a possibility towards simulating complex materials on near-term hardware. This is accomplished by approximating the relevant physics of a given material through their representation by simpler model Hamiltonians, such as the Hubbard Hamiltonian or extensions of it. Here we employ a well-defined first-principles methodology for deriving downfolded multi-band extended Hubbard Hamiltonians of materials, capturing strong electronic correlation and electron-phonon coupling, based on the formalism of Wannier functions and the calculation of the screened Coulomb interaction. We demonstrate for a variety of systems that quantum simulation of these downfolded Hamiltonians reproduces key properties, thus establishing downfolding as a promising route to achieve near-term simulation of application-relevant systems on quantum hardware.

Antonios Markos Alvertis↗

NASA NTRSDate not supplied

Downfolding complex materials problems onto model Hamiltonians for quantum computers

Antonios M. Alvertis↗

DOE OSTI2020

Effective Hamiltonians derived from equation-of-motion coupled-cluster wave functions: Theory and application to the Hubbard and Heisenberg Hamiltonians

Effective Hamiltonians, which are commonly used for fitting experimental observables, provide a coarse-grained representation of exact many-electron states obtained in quantum chemistry calculations; however, the mapping between the two is not trivial. In this contribution, we apply Bloch’s formalism to equation-of-motion coupled-cluster (EOM-CC) wave functions to rigorously derive effective Hamiltonians in the Bloch’s and des Cloizeaux’ forms. We report the key equations and illustrate the theory by application to systems with two or three unpaired electrons, which give rise to electronic states of covalent and ionic characters. We show that the Hubbard and Heisenberg Hamiltonians can be extracted directly from the so-obtained effective Hamiltonians. By establishing a quantitative connection between many-body states and simple models, the approach facilitates the analysis of the correlated wave functions. We propose a simple diagnostic for assessing the validity of the model space choice based on the overlaps between the target- and model-space states. Finally, artifacts affecting the quality of electronic structure calculations such as spin contamination are also discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

Quantum and anharmonic effects in non-adiabatic transition state theory

Quantitative descriptions of non-adiabatic transition rates at intermediate temperatures are challenging due to the simultaneous importance of quantum and anharmonic effects. Here, in this paper, the interplay between quantum effects—for motion across or along the seam of crossing—and anharmonicity in the seam potential is considered within the weak coupling limit. The well-known expression for quantized 1-D motion across the seam (i.e., tunneling) in the linear terms approximation is derived in the thermal domain using the Lagrangian formalism, which is then applied to the case when tunneling is distributed along the seam of crossing (treating motion along the seam classically). For high-frequency quantum modes, a vibrationally adiabatic (VA) approach is developed that introduces to the non-adiabatic rate constant a factor associated with high-frequency wavefunction overlap; this approach treats the high-frequency motion along the seam quantum mechanically. To test these methodologies, the reaction N 2 O ↔ N 2 + O( 3 P) was chosen. CCSD(T)-F12b/cc-pVTZ-F12 explorations of the 3 A'- 1 A' seam of N 2 O revealed that seam anharmonicity has a strong effect on the rate constant (a factor of ~20 at 2000 K). Several quantum effects were found to be significant at intermediate/lower temperatures, including the quantum N–N vibration that was coupled with seam anharmonicity using the VA approach. Finally, a 1-D approximation to non-adiabatic instanton theory is presented to estimate the validity limit of the linear terms model at low temperatures (⁠~ 250 K for N 2 O). We recommend that the assumptions built into many statistical theories for non-adiabatic reactions—harmonic behavior, classical motion, linear terms, and weak coupling—should be verified on a case-by-case basis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Theory of Plasmonic Hot-Carrier Generation and Relaxation

Hot-carrier (HC) generation from (localized) surface plasmon decay has recently attracted much attention due to its promising applications in physical, chemical, materials, and energy science. However, the detailed mechanisms of plasmonic HC generation, relaxation, and trapping are less studied. In this work, we developed and applied a quantum-mechanical model and coupled master equation method to study the generation of HCs from plasmon decay and their following relaxation processes with different mechanisms treated on equal footing. First, a quantum-mechanical model for HC generation is developed. Its connection to existing semiclassical models and time-dependent density functional theory (TDDFT) is discussed. Second, the relaxation and lifetimes of HCs are investigated in the presence of electron–electron and electron–phonon interactions. A GW-like approximation is introduced to account for the electron–electron scattering. The numerical simulations on the Jellium nanoparticles with a size up to 1.6 nm demonstrate the electron–electron scattering and electron–phonon scattering dominate different time scale in the relaxation dynamics. We also generalize the model to study the extraction of HCs to attached molecules. The quantum yield of extracting HCs for other applications is found to be size-dependent. In general, the smaller size of NP improves the quantum yield, which is in agreement with recent experimental measurements. Even though we demonstrate this newly developed theoretical formalism with Jellium model, the theory applies to any other atomistic models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Squeezing quantum states in three-dimensional twisted crystals

Bloch's theorem provides a conventional starting point for describing wave propagation in periodic media, but in ordered materials where competing spatial periods coexist it is rendered ineffective, often with dramatic consequences. Here we develop an alternate approach that uses coherent free-particle vortex states to study quantum states in supertwisted crystals: three-dimensional stacks of atomically thin two-dimensional layers. Here, this formalism leads naturally to the representation of the spectrum using squeezed coherent states, and it reveals the crucial role of a Coriolis coupling in the equations of motion. This identifies an underlying noncommutative geometry and novel edge state structure in a family of complex ordered structures.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Four-Coordinate Fe N 2 and Imido Complexes Supported by a Hemilabile NNC Heteroscorpionate Ligand

Inspired by mechanistic proposals for N 2 reduction at the nitrogenase FeMo cofactor, we report herein a new, strongly σ-donating heteroscorpionate ligand featuring two weak-field pyrazoles and an alkyl donor. This ligand supports four-coordinate Fe(I)-N 2 , Fe(II)-Cl, and Fe(III)-imido complexes, which we have characterized using a variety of spectroscopic and computational methods. Structural and quantum mechanical analysis reveal the nature of the Fe–C bonds to be essentially invariant between the complexes, with conversion between the (formally) low-valent Fe-N 2 and high-valent Fe-imido complexes mediated by pyrazole hemilability. This presents a useful strategy for substrate reduction at such low-coordinate centers and suggests a mechanism by which FeMoco might accommodate the binding of both π-acidic and π-basic nitrogenous substrates.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗