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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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

Normal-ordered second-quantized Hamiltonian for molecular vibrations

A normal-ordered second-quantized form of the Hamiltonian is derived for quantum dynamics in a bound potential energy surface expressed as a Taylor series in an arbitrary set of orthogonal, delocalized coordinates centered at an arbitrary geometry. The constant, first-, and second-order excitation amplitudes of this Hamiltonian are identified as the ground-state energy, gradients, and frequencies, respectively, of the size-extensive vibrational self-consistent field (XVSCF) method or the self-consistent phonon method. They display the well-defined size dependence of V{sup 1−n/2}, where V is the volume and n is the number of coordinates associated with the amplitudes. It is used to rapidly derive the equations of XVSCF and vibrational many-body perturbation methods with the Møller–Plesset partitioning of the Hamiltonian.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Quantum simulation of second-quantized Hamiltonians in compact encoding

We describe methods for simulating general second-quantized Hamiltonians using the compact encoding, in which qubit states encode only the occupied modes in physical occupation number basis states. These methods apply to second-quantized Hamiltonians composed of a constant number of interactions, i.e., linear combinations of ladder operator monomials of fixed form. Compact encoding leads to qubit requirements that are optimal up to logarithmic factors. Here, we show how to use sparse Hamiltonian simulation methods for second-quantized Hamiltonians in compact encoding, give explicit implementations for the required oracles, and analyze the methods. We also describe several example applications including the free boson and fermion theories, the φ 4 -theory, and the massive Yukawa model, all in both equal-time and light-front quantization. Our methods provide a general-purpose tool for simulating second-quantized Hamiltonians, with optimal or near-optimal scaling with error and model parameters.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Quantum Computing and Second Quantization

Quantum computers are by their nature many particle quantum systems. Both the many-particle arrangement and being quantum are necessary for the existence of the entangled states, which are responsible for the parallelism of the quantum computers. Second quantization is a very important approximate method of describing such systems. This lecture will present the general idea of the second quantization, and discuss shortly some of the most important formulations of second quantization.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Second quantized scalar QED in homogeneous time-dependent electromagnetic fields

We formulate the second quantization of a charged scalar field in homogeneous, time-dependent electromagnetic fields, in which the Hamiltonian is an infinite system of decoupled, time-dependent oscillators for electric fields, but it is another infinite system of coupled, time-dependent oscillators for magnetic fields. We then employ the quantum invariant method to find various quantum states for the charged field. For time-dependent electric fields, a pair of quantum invariant operators for each oscillator with the given momentum plays the role of the time-dependent annihilation and the creation operators, constructs the exact quantum states, and gives the vacuum persistence amplitude as well as the pair-production rate. We also find the quantum invariants for the coupled oscillators for the charged field in time-dependent magnetic fields and advance a perturbation method when the magnetic fields change adiabatically. Finally, the quantum state and the pair production are discussed when a time-dependent electric field is present in parallel to the magnetic field.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1986

Second quantization techniques in the scattering of nonidentical composite bodies

Second quantization techniques for describing elastic and inelastic interactions between nonidentical composite bodies are presented and are applied to nucleus-nucleus collisions involving ground-state and one-particle-one-hole excitations. Evaluations of the resultant collision matrix elements are made through use of Wick's theorem.

Norbury, J. W.↗
NASA NTRS1993

Second quantization in bit-string physics

Using a new fundamental theory based on bit-strings, a finite and discrete version of the solutions of the free one particle Dirac equation as segmented trajectories with steps of length h/mc along the forward and backward light cones executed at velocity +/- c are derived. Interpreting the statistical fluctuations which cause the bends in these segmented trajectories as emission and absorption of radiation, these solutions are analogous to a fermion propagator in a second quantized theory. This allows us to interpret the mass parameter in the step length as the physical mass of the free particle. The radiation in interaction with it has the usual harmonic oscillator structure of a second quantized theory. How these free particle masses can be generated gravitationally using the combinatorial hierarchy sequence (3,10,137,2(sup 127) + 136), and some of the predictive consequences are sketched.

Noyes, H. Pierre↗
DOE OSTI2021

Finite-temperature many-body perturbation theory for electrons: Algebraic recursive definitions, second-quantized derivation, linked-diagram theorem, general-order algorithms, and grand canonical and canonical ensembles

A comprehensive and detailed account is presented for the finite-temperature many-body perturbation theory for electrons that expands in power series all thermodynamic functions on an equal footing. Algebraic recursions in the style of the Rayleigh–Schrödinger perturbation theory are derived for the grand potential, chemical potential, internal energy, and entropy in the grand canonical ensemble and for the Helmholtz energy, internal energy, and entropy in the canonical ensemble, leading to their sum-over-states analytical formulas at any arbitrary order. For the grand canonical ensemble, these sum-over-states formulas are systematically transformed to sum-over-orbitals reduced analytical formulas by the quantum-field-theoretical techniques of normal-ordered second quantization and Feynman diagrams extended to finite temperature. It is found that the perturbation corrections to energies entering the recursions have to be treated as a nondiagonal matrix, whose off-diagonal elements are generally nonzero within a subspace spanned by degenerate Slater determinants. They give rise to a unique set of linked diagrams—renormalization diagrams—whose resolvent lines are displaced upward, which are distinct from the well-known anomalous diagrams of which one or more resolvent lines are erased. A linked-diagram theorem is introduced that proves the size-consistency of the finite-temperature many-body perturbation theory at any order. General-order algorithms implementing the recursions establish the convergence of the perturbation series toward the finite-temperature full-configuration-interaction limit unless the series diverges. As a result, the normal-ordered Hamiltonian at finite temperature sheds light on the relationship between the finite-temperature Hartree–Fock and first-order many-body perturbation theories.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Finite-temperature many-body perturbation theory for anharmonic vibrations: Recursions, algebraic reduction, second-quantized reduction, diagrammatic rules, linked-diagram theorem, finite-temperature self-consistent field, and general-order algorithm

A unified theory is presented for finite-temperature many-body perturbation expansions of the anharmonic vibrational contributions to thermodynamic functions, i.e., the free energy, internal energy, and entropy. The theory is diagrammatically size-consistent at any order, as ensured by the linked-diagram theorem proved in this study, and, thus, applicable to molecular gases and solids on an equal footing. It is also a basis-set-free formalism, just like its underlying Bose–Einstein theory, capable of summing anharmonic effects over an infinite number of states analytically. It is formulated by the Rayleigh–Schrödinger-style recursions, generating sum-over-states formulas for the perturbation series, which unambiguously converges at the finite-temperature vibrational full-configuration-interaction limits. Two strategies are introduced to reduce these sum-over-states formulas into compact sum-over-modes analytical formulas. One is a purely algebraic method that factorizes each many-mode thermal average into a product of one-mode thermal averages, which are then evaluated by the thermal Born–Huang rules. Canonical forms of these rules are proposed, dramatically expediting the reduction process. The other is finite-temperature normal-ordered second quantization, which is fully developed in this study, including a proof of thermal Wick’s theorem and the derivation of a normal-ordered vibrational Hamiltonian at finite temperature. The latter naturally defines a finite-temperature extension of size-extensive vibrational self-consistent field theory. These reduced formulas can be represented graphically as Feynman diagrams with resolvent lines, which include anomalous and renormalization diagrams. Two order-by-order and one general-order algorithms of computing these perturbation corrections are implemented and applied up to the eighth order. The results show no signs of Kohn–Luttinger-type nonconvergence.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS1972

A second quantized model of anharmonicity.

A heuristic description is given for a simple harmonic oscillator as a basis for a model of anharmonicity. A formalism is applied in the process, which applies to complex excitation fields involving particle clusters and also facilitates a description of nonequilibrium multibody configurations by classical methods. The heuristic description is based on Streit's results (1965) and is free of linearization requirements in most physically interesting situations.

Rasetti, M.↗
DOE OSTI2019

Composite fermions in Fock space: Operator algebra, recursion relations, and order parameters

We develop recursion relations, in particle number, for all (unprojected) Jain composite fermion (CF) wave functions. These recursions generalize a similar recursion originally written down by Read for Laughlin states, in mixed first-second quantized notation. In contrast, our approach is purely second-quantized, giving rise to an algebraic, “pure guiding center” definition of CF states that de-emphasizes first quantized many-body wave functions. Key to the construction is a second-quantized representation of the flux attachment operator that maps any given fermion state to its CF counterpart. An algebra of generators of edge excitations is identified. In particular, in those cases where a well-studied parent Hamiltonian exists, its properties can be entirely understood in the present framework, and the identification of edge state generators can be understood as an instance of “microscopic bosonization.” Here, the intimate connection of Read's original recursion with “nonlocal order parameters” generalizes to the present situation, and we are able to give explicit second-quantized formulas for nonlocal order parameters associated with CF states.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2010

Third quantization

The basic ideas of second quantization and Fock space are extended to density operator states, used in treatments of open many-body systems. This can be done for fermions and bosons. While the former only requires the use of a non-orthogonal basis, the latter requires the introduction of a dual set of spaces. In both cases an operator algebra closely resembling the canonical one is developed and used to define the dual sets of bases. We here concentrated on the bosonic case where the unboundedness of the operators requires the definitions of dual spaces to support the pair of bases. Some applications, mainly to non-equilibrium steady states, will be mentioned.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Multinucleon structure and dynamics via quantum computing

We propose a framework for computing the structure and dynamics for second-quantized many-nucleon Hamiltonians on quantum computers. We develop an oracle-based Hamiltonian input model that computes the many-nucleon states and nonzero Hamiltonian matrix elements of the many-nucleon system. With our Fock-state based input model, we show how to implement the sparse matrix simulation algorithms to calculate the dynamics of the second-quantized many-nucleon Hamiltonian. Based on the dynamics simulation methods, we also present the methodology for structure calculations of the many-nucleon system. In this work, we provide an explicit circuit design of our input model of the second-quantized Hamiltonian within a direct encoding scheme that maps the occupation of each available single-particle state in the many-nucleon state to the state of specific qubit in a quantum register. Here, we analyze our method and provide the asymptotic cost in computing resources for structure and dynamics calculations of many-nucleon systems. For pedagogical purposes, we demonstrate our input model with two model problems in restricted model spaces.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

From Quantum Time to Manifestly Covariant QFT: On the Need for a Quantum-Action-Based Quantization

In quantum time (QT) schemes, time is promoted to a degree of freedom, allowing Lorentz covariance to be made explicit for single particles. We ask whether this can be lifted to QFT so that Lorentz covariance becomes manifest at the Hilbert-space level, rather than being hidden as in the standard canonical formulation. We address this question by proposing a second-quantized approach in which the elementary particle is the QT particle itself, leading naturally to the notion of spacetime field algebras and of quantum action. We show, however, that a naive many-body construction runs into inconsistencies. To pinpoint their origin we introduce a classical counterpart of the second-quantized formalism, spacetime classical mechanics (SCM), and prove a no-go theorem: Dirac quantization of SCM collapses back to standard QFT and therefore hides covariance. We circumvent this problem by presenting a quantum-action-based quantization that yields a spacetime version of quantum mechanics (SQM), making covariance manifest for (interacting) QFTs. Finally, we show that this resolution is tied to a genuine spacetime generalization of the notion of a quantum state, required by causality and closely connected to recent “states over time” proposals and, in dS/CFT–motivated settings, to microscopic notions of timelike entanglement and emergent time.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2011

Coupled tensorial forms of the second-order effective Hamiltonian for open-subshell atoms in jj-coupling

General expressions for the second-order effective atomic Hamiltonian are derived for open-subshell atoms in jj-coupling. The expansion terms are presented as N-body (N=0,1,2,3) effective operators given in the second quantization representation in coupled tensorial form. Two alternative coupled tensorial forms for each expansion term have been developed. To reduce the number of expressions of the effective Hamiltonian, the reduced matrix elements of antisymmetric two-particle wavefunctions are involved in the consideration. The general expressions presented allow the determination of the spin-angular part of expansion terms when studying correlation effects dealing with a number of problems in atomic structure calculations.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2011

Challenges of Theoretical Spectroscopy of Heavy and Superheavy Atoms and Ions

A review of methods of efficient accounting for correlation and relativistic effects is presented. A considerable part of efforts for these approaches must be devoted to coping with integrations over spin-angular variables, occurring in the matrix elements of the operators under consideration. Efficient methods to find the abovementioned quantities are described, based on the use of symmetry properties of operators and matrix elements in three spaces (orbital, spin and quasispin), on second quantization in coupled tensorial form, and on graphical technique. This allows to study and to generate fairly accurate their spectroscopic data practically for any atom and ion of periodical table.

74 ATOMIC AND MOLECULAR PHYSICS↗