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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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

Relativistic differential-difference momentum operators and noncommutative differential calculus

The relativistic kinetic momentum operators are introduced in the framework of the Quantum Mechanics (QM) in the Relativistic Configuration Space (RCS). These operators correspond to the half of the non-Euclidean distance in the Lobachevsky momentum space. In terms of kinetic momentum operators the relativistic kinetic energy is separated as the independent term of the total Hamiltonian. This relativistic kinetic energy term is not distinguishing in form from its nonrelativistic counterpart. The role of the plane wave (wave function of the motion with definite value of momentum and energy) plays the generating function for the matrix elements of the unitary irreps of Lorentz group (generalized Jacobi polynomials). The kinetic momentum operators are the interior derivatives in the framework of the noncommutative differential calculus over the commutative algebra generated by the coordinate functions over the RCS.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Irreducibility of the set of field operators in NC QFT

Irreducibility of the set of quantum field operators has been proved in noncommutative quantum field theory in the general case when time does not commute with spatial variables.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2012

On the variational noncommutative poisson geometry

We outline the notions and concepts of the calculus of variational multivectors within the Poisson formalism over the spaces of infinite jets of mappings from commutative (non)graded smooth manifolds to the factors of noncommutative associative algebras over the equivalence under cyclic permutations of the letters in the associative words. We state the basic properties of the variational Schouten bracket and derive an interesting criterion for (non)commutative differential operators to be Hamiltonian (and thus determine the (non)commutative Poisson structures). We place the noncommutative jet-bundle construction at hand in the context of the quantum string theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2012

Relativistic kinetic momentum operators, half-rapidities and noncommutative differential calculus

It is shown that the generating function for the matrix elements of irreps of Lorentz group is the common eigenfunction of the interior derivatives of the noncommutative differential calculus over the commutative algebra generated by the coordinate functions in the Relativistic Configuration Space (RCS). These derivatives commute and can be interpreted as the quantum mechanical operators of the relativistic momentum corresponding to the half of the non-Euclidean distance in the Lobachevsky momentum space (the mass shell).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2013

Factorization method for Schrödinger equation in relativistic configuration space and q-deformations

Review paper is devoted to the relativistic configuration space (RCS) concept, a version of the relativistic Quantum Mechanics in RCS, the generalization of the Dirac-Infeld-Hall factorization method in the framework of the noncommutative differential calculus natural for RCS, different versions of the deformed oscillators, emerging as the generalization of the harmonic oscillator for RCS. In the formulation of the Newton-Wigner postulates for the relativistic localized states the hypothesis of commutativity of the position operator components is silently accepted as an evident fact. In the present work it is shown that commutativity is not necessary condition and the alternative (noncommutative) approach to the relativistic position operator and localization concept can be realized in a framework of the physically as well as mathematically comprehensive scheme. The different generalizations of the Dirac-Infeld-Hall factorization method for this case are constructed. This method enables us to find out all possible generalizations of the most important nonrelativistic integrable case—the harmonic oscillator. It is shown also that the relativistic oscillator = q —oscillator.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

SO(2,3){sub ★} Noncommutative Gravity: Coupling with Matter Fields

In this paper, noncommutative gravity is treated as a gauge theory of the noncommutative SO(2,3){sub ⋆} group, while the noncommutativity is canonical. The Seiberg–Witten (SW) map is used to express noncommutative fields in terms of the corresponding commutative fields. In addition to pure gravity, we consider couplings to matter fields, in particular, to the Dirac and U(1) gauge field. The analysis can be extended to non Abelian gauge fields and scalar fields.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2011

Entropic uncertainty relations in multidimensional position and momentum spaces

Commutator-based entropic uncertainty relations in multidimensional position and momentum spaces are derived, twofold generalizing previous entropic uncertainty relations for one-mode states. They provide optimal lower bounds and imply the multidimensional variance-based uncertainty principle. The article concludes with an open conjecture.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

What the complex joint probabilities observed in weak measurements can tell us about quantum physics

Quantummechanics does not permit joint measurements of non-commuting observables. However, it is possible to measure the weak value of a projection operator, followed by the precise measurement of a different property. The results can be interpreted as complex joint probabilities of the two non-commuting measurement outcomes. Significantly, it is possible to predict the outcome of completely different measurements by combining the joint probabilities of the initial state with complex conditional probabilities relating the new measurement to the possible combinations of measurement outcomes used in the characterization of the quantum state. We can therefore conclude that the complex conditional probabilities observed in weak measurements describe fundamental state-independent relations between non-commuting properties that represent the most fundamental form of universal laws in quantum physics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Geospatial Analysis of Built Infrastructure and Modeled Household Driving Patterns

The level of access to opportunities for a location can be quantified in the amount of time it takes to travel from a departure point to the destinations that somebody would want or need to visit. Isochrone maps are geometric representations of the area accessible from a departure point within a set amount of time. Informed in part by the National Household Travel Survey, this report merges location data for amenities and opportunities across six frequent destination categories – employment, education, health, food, community, and transportation – with isochrone maps generated by the TravelTime API, whose departure points are census tract population-weighted centroids. Using a “Points-In-Polygon” analysis, destinations that fall within a census tract’s isochrone are tallied as accessible from the region within one of three time thresholds: 15-, 30-, and 45-minutes by the walking, cycling, public transit, and driving modes of travel. We find that access to a high number of jobs within a typical commute duration is negatively correlated with annual household vehicle miles traveled (VMT). The spatial distribution of our data suggests that the high household VMT frequently seen surrounding the edges of major cities may be related to worker commutes into the city core, and that the high household VMT frequently seen in rural tracts may be related to the longer travel distances required to access a variety of key opportunities from these areas.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2023

Equitable Employment Access Assessed Through the Mobility Energy Productivity (MEP) Metric

This paper examines commuting options for an underserved neighborhood in Columbus, Ohio to a major employment center. The analysis is based on an emerging metric called the Mobility Energy Productivity (MEP) metric developed by the National Renewable Energy Laboratory (NREL) on behalf the Department of Energy (DOE). The purpose of the analysis is twofold. The first is to quantify relative attractiveness of commute modes between the two locations, using a perspective that includes travel time, energy and cost, while providing an equity lens to compare commute options between privately owned vehicles and pooled transportation options. The second objective is to apply MEP in a specific origin-destination (O-D) scenario, whereas previously it has been used primarily as an aggregate metropolitan-wide statistical measure. In so doing, parameters in MEP are further customized and the methodology is refined to account for unique aspects of this case study. Four commute options between the neighborhood and the industry employment based are analyzed: drive alone option, public transit express bus (historical), public transit normal route (current), and a proposed shuttle specific to the O-D pair. This analysis identified issues applying MEP that required further customization: (1) deprecation functions customized to modes other than driving, (2) accounting for first-mile last-mile travel times with transit, (3) accounting for transit frequency without resorting to full simulation. The results provide quantitative insights on the employment accessibility between these two locations, both across modes, and as equity of job accessibility for those who can and cannot operate a personal vehicle.

ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2016

A bound on chaos

We conjecture a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom. Chaos can be diagnosed using an out-of-time-order correlation function closely related to the commutator of operators separated in time. We conjecture that the influence of chaos on this correlator can develop no faster than exponentially, with Lyapunov exponent λ L ≤ 2πk B T/ℏ. We give a precise mathematical argument, based on plausible physical assumptions, establishing this conjecture.

1/N Expansion↗
DOE OSTI2022

Quantization: History and problems

In this work, I explore the concept of quantization as a mapping from classical phase space functions to quantum operators. I discuss the early history of this notion of quantization with emphasis on the works of Schrödinger and Dirac, and how quantization fit into their overall understanding of quantum theory in the 1920's. Dirac, in particular, proposed a quantization map which should satisfy certain properties, including the property that quantum commutators should be related to classical Poisson brackets in a particular way. However, in 1946, Groenewold proved that Dirac's mapping was inconsistent, making the problem of defining a rigorous quantization map more elusive than originally expected. This result, known as the Groenewold-Van Hove theorem, is not often discussed in physics texts, but here I will give an account of the theorem and what it means for potential ``corrections” to Dirac's scheme. Other proposals for quantization have arisen over the years, the first major one being that of Weyl in 1927, which was later developed by many, including Groenewold, and which has since become known as Weyl Quantization in the mathematical literature. Another, known as Geometric Quantization, formulates quantization in differential-geometric terms by appealing to the character of classical phase spaces as symplectic manifolds; this approach began with the work of Souriau, Kostant, and Kirillov in the 1960's. I will describe these proposals for quantization and comment on their relation to Dirac's original program. Along the way, the problem of operator ordering and of quantizing in curvilinear coordinates will be described, since these are natural questions that immediately present themselves when thinking about quantization.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Quantum probabilities as Dempster-Shafer probabilities in the lattice of subspaces

The orthocomplemented modular lattice of subspaces L[H(d)], of a quantum system with d-dimensional Hilbert space H(d), is considered. A generalized additivity relation which holds for Kolmogorov probabilities is violated by quantum probabilities in the full lattice L[H(d)] (it is only valid within the Boolean subalgebras of L[H(d)]). This suggests the use of more general (than Kolmogorov) probability theories, and here the Dempster-Shafer probability theory is adopted. An operator D(H{sub 1},H{sub 2}), which quantifies deviations from Kolmogorov probability theory is introduced, and it is shown to be intimately related to the commutator of the projectors P(H{sub 1}),P(H{sub 2}), to the subspaces H{sub 1}, H{sub 2}. As an application, it is shown that the proof of the inequalities of Clauser, Horne, Shimony, and Holt for a system of two spin 1/2 particles is valid for Kolmogorov probabilities, but it is not valid for Dempster-Shafer probabilities. The violation of these inequalities in experiments supports the interpretation of quantum probabilities as Dempster-Shafer probabilities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2019

A complete quasiclassical map for the dynamics of interacting fermions

We present a strategy for mapping the dynamics of a fermionic quantum system to a set of classical dynamical variables. The approach is based on imposing the correspondence relation between the commutator and the Poisson bracket, preserving Heisenberg's equation of motion for one-body operators. In order to accommodate the effect of two-body terms, we further impose quantization on the spin-dependent occupation numbers in the classical equations of motion, with a parameter that is determined self-consistently. Expectation values for observables are taken with respect to an initial quasiclassical distribution that respects the original quantization of the occupation numbers. The proposed classical map becomes complete under the evolution of quadratic Hamiltonians and is extended for all even order observables. We show that the map provides an accurate description of the dynamics for an interacting quantum impurity model in the coulomb blockade regime, at both low and high temperatures. In conclusion, the numerical results are aided by a novel importance sampling scheme that employs a reference system to reduce significantly the sampling effort required to converge the classical calculations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Constructing Quantum Spin Liquids Using Combinatorial Gauge Symmetry

In this work, we introduce the notion of combinatorial gauge symmetry—a local transformation that includes single spin rotations plus permutations of spins (or swaps of their quantum states)—that preserve the commutation and anticommutation relations among the spins. We show that Hamiltonians with simple two-body interactions contain this symmetry if the coupling matrix is a Hadamard matrix, with the combinatorial gauge symmetry being associated with the automorphism of these matrices with respect to monomial transformations. Armed with this symmetry, we address the physical problem of how to build quantum spin liquids with physically accessible interactions. In addition to its intrinsic physical significance, the problem is also tied to that of how to build topological qubits.

36 MATERIALS SCIENCE↗
DOE OSTI2012

Parabosonic string and space-time non-commutativity

We investigate the para-quantum extension of the bosonic strings in a non-commutative space-time. We calculate the trilinear relations between the mass-center variables and the modes and we derive the Virasoro algebra where a new anomaly term due to the non-commutativity is obtained.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2012

Noncommutative Pfaffians associated with the orthogonal algebra

Commutators of Pfaffians associated with the orthogonal algebra are found in skew-symmetric and root realizations of o{sub N}. A generating function of Pfaffians is proved to satisfy the reflection equation. A relation between Pfaffians in skew-symmetric and root realizations of o{sub N} is established. Using these results we construct an integrable equation of Knizhnik-Zamolodchikov type using the Capelli central elements in U(o{sub N}), which are sums of squares of the considered Pfaffians. A classical limit of the obtained Knizhnik-Zamolodchikov type equation turns out to be a very specific system of equations of isomonodromic deformations. Bibliography: 18 titles.

97 MATHEMATICS AND COMPUTING↗