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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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Time operators and time crystals: self-adjointness by topology change

We investigate time operators in the context of quantum time crystals in ring systems. A generalized commutation relation called the generalized weak Weyl relation is used to derive a class of self-adjoint time operators for ring systems with a periodic time evolution: The conventional Aharonov–Bohm time operator is obtained by taking the infinite-radius limit. Then, we discuss the connection between time operators, time crystals and real-space topology. We also reveal the relationship between our time operators and a $ΡΤ$-symmetric time operator. These time operators are then used to derive several energy-time uncertainty relations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Zero curvature is a necessary and sufficient condition for a spin-orbital decomposition

There has been an extended debate regarding the existence of a spin-orbital decomposition of the angular momentum of photons and other massless particles. It was recently shown that there are both geometric and topological obstructions preventing any such decomposition. Here we show that any geometric connection on a particle’s state space induces a splitting of the angular momentum into two operators. These operators are well-defined angular momentum operators if and only if the connection has zero curvature. Massive particles have two canonical curved connections corresponding to boosts and rotations, respectively. Furthermore, these can be uniquely combined to produce a flat connection, and this gives a novel derivation of the Newton-Wigner position operator and the corresponding spin and orbital angular momenta for relativistic massive particles. When the mass is taken to zero, transverse boosts and rotations degenerate, leaving only a single connection for massless particles. This connection produces a commonly proposed splitting of the massless angular momentum into two operators. However, the connection is not flat, explaining why these operators do not satisfy the angular momentum commutation relations and are thus not true spin and orbital angular momentum operators.

Angular momentum↗
DOE OSTI2023

Quantum Langevin theory for two coupled phase-conjugated electromagnetic waves

We provide a general macroscopic phenomenological formula of quantum Langevin equations for two coupled phase-conjugated electromagnetic fields with linear loss (gain) and complex nonlinear coupling coefficient. The macroscopic phenomenological formula is obtained from the coupling matrix to preserve the field commutation relations and correlations, which does not require knowing the microscopic details of light-matter interaction and internal atomic structures. To validate this phenomenological formula, we take spontaneous four-wave mixing in a double-Λ four-level atomic system as an example to numerically confirm that our macroscopic phenomenological result is consistent with that obtained from the microscopic Heisenberg-Langevin theory. We find that a complex-valued nonlinear coupling coefficient can lead to noises even without linear gain or loss. Lastly, we apply the quantum Langevin equations to study the effects of linear gain and loss, complex phase mismatching, as well as complex nonlinear coupling coefficient in entangled photon pair (biphoton) generation, particularly to their temporal quantum correlations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

Complex-energy approach to sum rules within nuclear density functional theory

The linear response of the nucleus to an external field contains unique information about the effective interaction, correlations governing the behavior of the many-body system, and properties of its excited states. To characterize the response, it is useful to use its energy-weighted moments, or sum rules. By comparing computed sum rules with experimental values, the information content of the response can be utilized in the optimization process of the nuclear Hamiltonian or nuclear energy density functional (EDF). But the additional information comes at a price: compared to the ground state, computation of excited states is more demanding. To establish an efficient framework to compute energy-weighted sum rules of the response that is adaptable to the optimization of the nuclear EDF and large-scale surveys of collective strength, we have developed a new technique within the complex-energy finite-amplitude method (FAM) based on the quasiparticle random- phase approximation. The proposed sum-rule technique based on the complex-energy FAM is a tool of choice when optimizing effective interactions or energy functionals. The method is very efficient and well-adaptable to parallel computing. As a result, the FAM formulation is especially useful when standard theorems based on commutation relations involving the nuclear Hamiltonian and external field cannot be used.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2019

How low can vacuum energy go when your fields are finite-dimensional?

According to the holographic bound, there is only a finite density of degrees of freedom in space when gravity is taken into account. Conventional quantum field theory does not conform to this bound, since in this framework, infinitely many degrees of freedom may be localized to any given region of space. In this paper, we explore the viewpoint that quantum field theory may emerge from an underlying theory that is locally finite-dimensional, and we construct a locally finite-dimensional version of a Klein–Gordon scalar field using generalized Clifford algebras. Demanding that the finite-dimensional field operators obey a suitable version of the canonical commutation relations makes this construction essentially unique. Lastly, we then find that enforcing local finite dimensionality in a holographically consistent way leads to a huge suppression of the quantum contribution to vacuum energy, to the point that the theoretical prediction becomes plausibly consistent with observations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Four no-go theorems on the existence of spin and orbital angular momentum of massless bosons

The past decades have seen substantial interest in the so-called orbital angular momentum (OAM) of light, driven largely by its diverse range of applications. However, there are fundamental theoretical issues with decomposing the angular momentum of massless particles, such as photons, into spin (SAM) and orbital angular momentum parts. While the angular momentum of massive particles has a natural splitting into the Wigner SAM and OAM, there are numerous proposed splittings for photons and no consensus about which is correct. Moreover, it has been shown that most of the proposed SAM and OAM operators do not satisfy the defining commutation relations of angular momentum operators and are thus not legitimate splittings. Here, we prove that it is generally impossible to split the total angular momentum operator of massless bosons, such as photons and gravitons, into spin and orbital parts. We prove two further generalizations of this result, showing that there are no SAM-OAM splittings even if (1) the SAM operator generates non-internal symmetries or (2) if one allows the SAM and OAM operators to generate non-SO(3) symmetries.

Chern numbers↗
DOE OSTI2023

Adaptive estimation of quantum observables

The accurate estimation of quantum observables is a critical task in science. With progress on the hardware, measuring a quantum system will become increasingly demanding, particularly for variational protocols that require extensive sampling. Here, we introduce a measurement scheme that adaptively modifies the estimator based on previously obtained data. Our algorithm, which we call AEQuO, continuously monitors both the estimated average and the associated error of the considered observable, and determines the next measurement step based on this information. We allow both for overlap and non-bitwise commutation relations in the subsets of Pauli operators that are simultaneously probed, thereby maximizing the amount of gathered information. AEQuO comes in two variants: a greedy bucket-filling algorithm with good performance for small problem instances, and a machine learning-based algorithm with more favorable scaling for larger instances. The measurement configuration determined by these subroutines is further post-processed in order to lower the error on the estimator. We test our protocol on chemistry Hamiltonians, for which AEQuO provides error estimates that improve on all state-of-the-art methods based on various grouping techniques or randomized measurements, thus greatly lowering the toll of measurements in current and future quantum applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Source apportionment of VOCs, IVOCs and SVOCs by positive matrix factorization in suburban Livermore, California

Abstract. Gas- and particle-phase molecular markers provide highly specific information about the sources and atmospheric processes that contribute to air pollution. In urban areas, major sources of pollution are changing as regulation selectively mitigates some pollution sources and climate change impacts the surrounding environment. In this study, a comprehensive thermal desorption aerosol gas chromatograph (cTAG) was used to measure volatile, intermediate-volatility and semivolatile molecular markers every other hour over a 10 d period from 11 to 21 April 2018 in suburban Livermore, California. Source apportionment via positive matrix factorization (PMF) was performed to identify major sources of pollution. The PMF analysis identified 13 components, including emissions from gasoline, consumer products, biomass burning, secondary oxidation, aged regional transport and several factors associated with single compounds or specific events with unique compositions. The gasoline factor had a distinct morning peak in concentration but lacked a corresponding evening peak, suggesting commute-related traffic emissions are dominated by cold starts in residential areas. More monoterpene and monoterpenoid mass was assigned to consumer product emissions than biogenic sources, underscoring the increasing importance of volatile chemical products to urban emissions. Daytime isoprene concentrations were controlled by biogenic sunlight- and temperature-dependent processes, mediated by strong midday mixing, but gasoline was found to be the dominant and likely only source of isoprene at night. Biomass burning markers indicated residential wood burning activity remained an important pollution source even in the springtime. This study demonstrates that specific high-time-resolution molecular marker measurements across a wide range of volatility enable more comprehensive pollution source profiles than a narrower volatility range would allow.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2014

Oscillators in a (2+1)-dimensional noncommutative space

We study the Harmonic and Dirac Oscillator problem extended to a three-dimensional noncommutative space where the noncommutativity is induced by the shift of the dynamical variables with generators of SL(2,R) in a unitary irreducible representation considered in Falomir et al. [Phys. Rev. D 86, 105035 (2012)]. This redefinition is interpreted in the framework of the Levi's decomposition of the deformed algebra satisfied by the noncommutative variables. The Hilbert space gets the structure of a direct product with the representation space as a factor, where there exist operators which realize the algebra of Lorentz transformations. The spectrum of these models are considered in perturbation theory, both for small and large noncommutativity parameters, finding no constraints between coordinates and momenta noncommutativity parameters. Since the representation space of the unitary irreducible representations SL(2,R) can be realized in terms of spaces of square-integrable functions, we conclude that these models are equivalent to quantum mechanical models of particles living in a space with an additional compact dimension.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

The statistical properties of Klein-Gordon oscillator in noncommutative space

We study the relativistic spin-zero bosons influenced by the Klein-Gordon oscillator and an external magnetic field in noncommutative formulation. The problem is considered in two dimensions and is solved in an exact analytical manner. Having found the spectrum of the system, the statistical properties of an N-boson system are reported.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Comparing light-front quantization with instant-time quantization

Here in this paper we compare light-front quantization and instant-time quantization both at the level of operators and at the level of their Feynman diagram matrix elements. At the level of operators light-front quantization and instant-time quantization lead to equal light-front time commutation (or anticommutation) relations that appear to be quite different from equal instant-time commutation (or anticommutation) relations. Despite this we show that at unequal times instant-time and light-front commutation (or anticommutation) relations actually can be transformed into each other, with it only being the restriction to equal times that makes the commutation (or anticommutation) relations appear to be so different. While our results are valid for both bosons and fermions, for fermions there are subtleties associated with tip of the light cone contributions that need to be taken care of. At the level of Feynman diagrams we show for non-vacuum Feynman diagrams that the pole terms in four-dimensional light-front Feynman diagrams reproduce the widely used three-dimensional light-front on-shell Hamiltonian Fock space formulation in which the light-front energy and light-front momentum are on shell. Moreover, we show that the contributions of pole terms in non-vacuum instant-time and non-vacuum light-front Feynman diagrams are equal. However, because of circle at infinity contributions we show that this equivalence of pole terms fails for four-dimensional light-front vacuum tadpole diagrams. Then, and precisely because of these circle at infinity contributions, we show that light-front vacuum tadpole diagrams are not only nonzero, they quite remarkably are actually equal to the pure pole term instant-time vacuum tadpole diagrams. Light-front vacuum diagrams are not correctly describable by the on-shell Hamiltonian formalism, and thus not by the closely related infinite momentum frame prescription either. Thus for the light-front vacuum sector we must use the off-shell Feynman formalism as it contains information that is not accessible in the on-shell Hamiltonian Fock space approach. We show that light-front quantization is intrinsically nonlocal, and that for fermions this nonlocality is present in Ward identities. One can project fermion spinors into so-called good and bad components, and both of these components contribute in Ward identities. Central to our analysis is that the transformation from instant-time coordinates and fields to light-front coordinates and fields is a unitary, spacetime-dependent translation. Consequently, not only are instant-time quantization and light-front quantization equivalent, because of general coordinate invariance they are unitarily equivalent.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

The noncommutative Poisson bracket and the deformation of the family algebras

The family algebras are introduced by Kirillov in 2000. In this paper, we study the noncommutative Poisson bracket P on the classical family algebra C{sub τ}(g). We show that P controls the first-order 1-parameter formal deformation from C{sub τ}(g) to Q{sub τ}(g) where the latter is the quantum family algebra. Moreover, we will prove that the noncommutative Poisson bracket is in fact a Hochschild 2-coboundary, and therefore, the deformation is infinitesimally trivial. In the last part of this paper, we discuss the relation between Mackey’s analogue and the quantization problem of the family algebras.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Survey on nonlocal games and operator space theory

This review article is concerned with a recently uncovered connection between operator spaces, a noncommutative extension of Banach spaces, and quantum nonlocality, a striking phenomenon which underlies many of the applications of quantum mechanics to information theory, cryptography, and algorithms. Using the framework of nonlocal games, we relate measures of the nonlocality of quantum mechanics to certain norms in the Banach and operator space categories. We survey recent results that exploit this connection to derive large violations of Bell inequalities, study the complexity of the classical and quantum values of games and their relation to Grothendieck inequalities, and quantify the nonlocality of different classes of entangled states.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Testing a Model of Planck-Scale Quantum Geometry With Broadband Correlation of Colocated 40m Interferometers

The Holometer is designed to test for a Planck diffractive-scaling uncertainty in long-baseline position measurements due to an underlying noncommutative geometry normalized to relate Black hole entropy bounds of the Holographic principle to the now-finite number of position states. The experiment overlaps two independent 40 meter optical Michelson interferometers to detect the proposed uncertainty as a common broadband length fluctuation. 150 hours of instrument cross-correlation data are analyzed to test the prediction of a correlated noise magnitude of $7\times10^{−21}$ m/$\sqrt{\rm Hz}$ with an effective bandwidth of 750kHz. The interferometers each have a quantum-limited sensitivity of $2.5\times 10^{−18}$ m/$\sqrt{\rm Hz}$, but their correlation with a time-bandwidth product of $4\times 10^{11}$ digs between the noise floors in search for the covarying geometric jitter. The data presents an exclusion of 5 standard deviations for the tested model. This exclusion is defended through analysis of the calibration methods for the instrument as well as further sub shot noise characterization of the optical systems to limit spurious background-correlations from undermining the signal.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Continuous and Smooth Envelopes of Topological Algebras. Part 1

Since the first optical instruments were invented, an idea that the visible image of an object under observation depends on tools of observation became commonly assumed in physics. A way of formalizing this idea in mathematics is the construction that assigns to an arbitrary object A in a category K its envelope Env{sub Φ}{sup Ω}A in a given class of morphisms (a class of representations) Ω with respect to a given class of morphisms (a class of observation tools) Φ. It turns out that if we take a sufficiently wide category of topological algebras as K, then each choice of the classes Ω and Φ defines a “projection of functional analysis into geometry,” and the standard “geometric disciplines,” like complex geometry, differential geometry, and topology, become special cases of this construction. This gives a formal scheme of “categorical construction of geometries” with many interesting applications, in particular, “geometric generalizations of the Pontryagin duality” (to the classes of noncommutative groups). In this paper we describe this scheme in topology and in differential geometry.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Continuous and Smooth Envelopes of Topological Algebras. Part 2

Since the first optical instruments were invented, the idea that the visible image of an object under observation depends on tools of observation became commonly assumed in physics. A way of formalizing this idea in mathematics is the construction that assigns to an arbitrary object A in a category K its envelope Env{sub Φ}{sup Ω} A in a given class of morphisms (a class of representations) Ω with respect to a given class of morphisms (a class of observation tools) Φ. It turns out that if we take a sufficiently wide category of topological algebras as K, then each choice of the classes Ω and Φ defines a “projection of functional analysis into geometry,” and the standard “geometric disciplines,” like complex geometry, differential geometry, and topology, become special cases of this construction. This gives a formal scheme of “categorical construction of geometries” with many interesting applications, in particular, “geometric generalizations of the Pontryagin duality” (to the classes of noncommutative groups). In this paper we describe this scheme in topology and in differential geometry.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Binormal Matrices

A square complex matrix A is said to be binormal if the associated matrices A{sup *}A and AA{sup *} commute. This matrix class yields a meaningful finite-dimensional extension of the concept of normality. The paper can be regarded as a survey of properties of binormal matrices.

97 MATHEMATICS AND COMPUTING↗