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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 91 records · Page 5
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DOE OSTI2011

Coherent states for FLRW space-times in loop quantum gravity

We construct a class of coherent spin-network states that capture properties of curved space-times of the Friedmann-Lamaitre-Robertson-Walker type on which they are peaked. The data coded by a coherent state are associated to a cellular decomposition of a spatial (t=const) section with a dual graph given by the complete five-vertex graph, though the construction can be easily generalized to other graphs. The labels of coherent states are complex SL(2,C) variables, one for each link of the graph, and are computed through a smearing process starting from a continuum extrinsic and intrinsic geometry of the canonical surface. The construction covers both Euclidean and Lorentzian signatures; in the Euclidean case and in the limit of flat space we reproduce the simplicial 4-simplex semiclassical states used in spin foams.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2010

Schwarzschild-anti-de Sitter black holes within isothermal cavity: Thermodynamics, phase transitions, and the Dirichlet problem

The thermodynamics of Schwarzschild black holes within spherical isothermal cavities in anti-de Sitter (AdS) space is studied for arbitrary dimensions in the semiclassical approximation of the Euclidean path integral of quantum gravity. For such boundary conditions, known classical solutions are a hot AdS and two or no Schwarzschild-AdS depending on whether or not the wall-temperature of the cavity is above or below a minimum value. Earlier work in four dimensions with such boundary conditions showed that the larger and smaller holes have positive and negative specific heats and hence are locally thermodynamically stable and unstable, respectively. The standard area-law of entropy was known to hold too. We derive the area-law for arbitrary dimensions and show that qualitative behavior of local stability remains the same. Then using a careful analysis of the associated Dirichlet boundary-value problem we address global issues. We find that for wall-temperatures above a critical value a phase transition takes hot AdS to the larger Schwarzschild-AdS. The larger hole thus can be globally thermodynamically stable. We find that the smaller the cavity the higher the critical temperature for phase transition is and it always remains above the minimum temperature needed for the classical existence of the holes in that cavity. In the infinite limit of cavity this picture reduces to that considered by Hawking and Page. All these hold for arbitrary dimensions, however the case of five dimensions turns out to be special in that the Dirichlet problem can be solved exactly giving exact analytic expressions for the black-hole masses as functions of boundary variables (cavity-radius and temperature). This makes it possible to compute the on-shell Euclidean action as a function of boundary variables too from which other quantities of interest can be evaluated. In particular, we obtain the minimum temperature (for the holes to exist classically) and the critical temperature (for phase transition) as functions of the cavity-radius in five dimensions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2011

Canonical quantization of lattice Higgs-Maxwell-Chern-Simons fields: Osterwalder-Schrader positivity

A Euclidean representation is given for a canonically quantized relativistic Maxwell-Chern-Simons field on a lattice, which approximates a complex measure on a space of distributions. Using a path-space formula for the nonself-adjoint Hamiltonian, the relation between Euclidean Osterwalder-Schrader positivity, the Krein metric, and Gauss' law is examined.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2010

Quark propagator in the Nambu-Jona-Lasinio model in a self-consistent 1/N{sub c} expansion

The quark propagator is calculated in the Nambu-Jona-Lasinio model in a self-consistent 1/N{sub c}-expansion at next-to-leading order. The calculations are carried out iteratively in Euclidean space. The chiral quark condensate and its dependence on temperature and chemical potential is calculated directly and compared with the mean-field results. In the chiral limit, we find a second-order phase transition at finite temperature and zero chemical potential, in agreement with universality arguments. At zero temperature and finite chemical potential, the phase transition is first order. In comparison with the mean-field results, the critical temperature and chemical potential are slightly reduced. We determine spectral functions from the Euclidean propagators by employing the maximum-entropy method. Thereby quark and meson masses are estimated and decay channels identified. For testing this method, we also apply it to evaluate perturbative spectral functions, which can be calculated directly in Minkowski space. In most cases we find that the maximum-entropy method is able to reproduce the rough features of the spectral functions, but not the details.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2010

String wave function across a Kasner singularity

A collision of orbifold planes in 11 dimensions has been proposed as an explanation of the hot big bang. When the two planes are close to each other, the winding membranes become the lightest modes of the theory, and can be effectively described in terms of fundamental strings in a ten-dimensional background. Near the brane collision, the 11-dimensional metric is a Euclidean space times a 1+1-dimensional Milne universe. However, one may expect small perturbations to lead into a more general Kasner background. In this paper we extend the previous classical analysis of winding membranes to Kasner backgrounds, and using the Hamiltonian equations, solve for the wave function of loops with circular symmetry. The evolution across the singularity is regular, and explained in terms of the excitement of higher oscillation modes. We also show there is finite particle production and unitarity is preserved.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2010

Relativistic non-Hamiltonian mechanics

Relativistic particle subjected to a general four-force is considered as a nonholonomic system. The nonholonomic constraint in four-dimensional space-time represents the relativistic invariance by the equation for four-velocity u{sub {mu}u}{sup {mu}} + c{sup 2} = 0, where c is the speed of light in vacuum. In the general case, four-forces are non-potential, and the relativistic particle is a non-Hamiltonian system in four-dimensional pseudo-Euclidean space-time. We consider non-Hamiltonian and dissipative systems in relativistic mechanics. Covariant forms of the principle of stationary action and the Hamilton's principle for relativistic mechanics of non-Hamiltonian systems are discussed. The equivalence of these principles is considered for relativistic particles subjected to potential and non-potential forces. We note that the equations of motion which follow from the Hamilton's principle are not equivalent to the equations which follow from the variational principle of stationary action. The Hamilton's principle and the principle of stationary action are not compatible in the case of systems with nonholonomic constraint and the potential forces. The principle of stationary action for relativistic particle subjected to non-potential forces can be used if the Helmholtz conditions are satisfied. The Hamilton's principle and the principle of stationary action are equivalent only for a special class of relativistic non-Hamiltonian systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2010

Intrinsic geometry of quantum adiabatic evolution and quantum phase transitions

We elucidate the geometry of quantum adiabatic evolution. By minimizing the deviation from adiabaticity, we find a Riemannian metric tensor underlying adiabatic evolution. Equipped with this tensor, we identify a unified geometric description of quantum adiabatic evolution and quantum phase transitions that generalizes previous treatments to allow for degeneracy. The same structure is relevant for applications in quantum information processing, including adiabatic and holonomic quantum computing, where geodesics over the manifold of control parameters correspond to paths which minimize errors. We illustrate this geometric structure with examples, for which we explicitly find adiabatic geodesics. By solving the geodesic equations in the vicinity of a quantum critical point, we identify universal characteristics of optimal adiabatic passage through a quantum phase transition. In particular, we show that in the vicinity of a critical point describing a second-order quantum phase transition, the geodesic exhibits power-law scaling with an exponent given by twice the inverse of the product of the spatial and scaling dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2010

Phase transitions in a 3 dimensional lattice loop gas

We investigate, via Monte Carlo simulations, the phase structure of a system of closed, nonintersecting but otherwise noninteracting, loops in 3 Euclidean dimensions. The loops correspond to closed trajectories of massive particles and we find a phase transition as a function of their mass. We identify the order parameter as the average length of the loops at equilibrium. This order parameter exhibits a sharp increase as the mass is decreased through a critical value, the behavior seems to be a crossover transition. We believe that the model represents an effective description of the broken-symmetry sector of the 2+1 dimensional Abelian Higgs model, in the extreme strong coupling limit. The massive gauge bosons and the neutral scalars are decoupled, and the relevant low-lying excitations correspond to vortices and antivortices. The functional integral can be approximated by a sum over simple, closed vortex loop configurations. We present a novel fashion to generate nonintersecting closed loops, starting from a tetrahedral tessellation of three space. The two phases that we find admit the following interpretation: the usual Higgs phase and a novel phase which is heralded by the appearance of effectively infinitely long loops. We compute the expectation value of the Wilson loop operator and that of the Polyakov loop operator. The Wilson loop exhibits perimeter law behavior in both phases implying that the transition corresponds neither to the restoration of symmetry nor to confinement. The effective interaction between external charges is screened in both phases, however there is a dramatic increase in the polarization cloud in the novel phase as shown by the energy shift introduced by the Wilson loop.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2010

Model representations for systems of selfadjoint operators satisfying commutation relations

Model representations are constructed for a system {l_brace}B{sub k}{r_brace}{sub 1}{sup n} of bounded linear selfadjoint operators in a Hilbert space H such that; [B{sub k},B{sub s}] = i/2 {phi}*R{sub k,s}{sup -}{phi}, {sigma}{sub k}{phi}B{sub s} - {sigma}{sub s}{phi}B{sub k}=R{sub k,s}{sup +}{phi}, {sigma}{sub k}{phi}{phi}*{sigma}{sub s}-{sigma}{sub s}{phi}{phi}*{sigma}{sub k}=2iR{sub k,s}{sup -}, 1{<=}k, s{<=}n; where {phi} is a linear operator from H into a Hilbert space E and {l_brace}{sigma}{sub k},R{sub k,s}{sup {+-}}{r_brace}{sub 1}{sup n} are some selfadjoint operators in E. A realization of these models in function spaces on a Riemann surface is found and a full set of invariants for {l_brace}B{sub k}{r_brace}{sub 1}{sup n} is described. Bibliography: 11 titles.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

The geometry of the light-cone cell decomposition of moduli space

The moduli space of Riemann surfaces with at least two punctures can be decomposed into a cell complex by using a particular family of ribbon graphs called Nakamura graphs. We distinguish the moduli space with all punctures labelled from that with a single labelled puncture. In both cases, we describe a cell decomposition where the cells are parametrised by graphs or equivalence classes of finite sequences (tuples) of permutations. Each cell is a convex polytope defined by a system of linear equations and inequalities relating light-cone string parameters, quotiented by the automorphism group of the graph. We give explicit examples of the cell decomposition at low genus with few punctures.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2010

The formal path integral and quantum mechanics

Given an arbitrary Lagrangian function on R{sup d} and a choice of classical path, one can try to define Feynman's path integral supported near the classical path as a formal power series parameterized by 'Feynman diagrams', although these diagrams may diverge. We compute this expansion and show that it is (formally, if there are ultraviolet divergences) invariant under volume-preserving changes of coordinates. We prove that if the ultraviolet divergences cancel at each order, then our formal path integral satisfies a 'Fubini theorem' expressing the standard composition law for the time evolution operator in quantum mechanics. Moreover, we show that when the Lagrangian is inhomogeneous quadratic in velocity such that its homogeneous-quadratic part is given by a matrix with constant determinant, then the divergences cancel at each order. Thus, by 'cutting and pasting' and choosing volume-compatible local coordinates, our construction defines a Feynman-diagrammatic 'formal path integral' for the nonrelativistic quantum mechanics of a charged particle moving in a Riemannian manifold with an external electromagnetic field.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2010

Electric and magnetic screening masses at finite temperature from generalized Polyakov-line correlations in two-flavor lattice QCD

Screenings of the quark-gluon plasma in electric and magnetic sectors are studied on the basis of generalized Polyakov-line correlation functions in lattice QCD simulations with two flavors of improved Wilson quarks. Using the Euclidean-time reflection (R) and the charge conjugation (C), electric and magnetic screening masses are extracted in a gauge-invariant manner. Long distance behavior of the standard Polyakov-line correlation in the quark-gluon plasma is found to be dictated by the magnetic screening. Also, the ratio of the two screening masses agrees with that obtained from the dimensionally-reduced effective field theory and the N=4 supersymmetric Yang-Mills theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2015

Existence of a coupled system of fractional differential equations

We manage the existence and uniqueness of a fractional coupled system containing Schrödinger equations. Such a system appears in quantum mechanics. We confirm that the fractional system under consideration admits a global solution in appropriate functional spaces. The solution is shown to be unique. The method is based on analytic technique of the fixed point theory. The fractional differential operator is considered from the virtue of the Riemann-Liouville differential operator.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Invariant distributions on compact homogeneous spaces

In this paper, we study distributions on compact homogeneous spaces, including invariant distributions and also distributions admitting a sub-Riemannian structure. We first consider distributions of dimension 1 and 2 on compact homogeneous spaces. After this, we study the cases of compact homogeneous spaces of dimension 2, 3, and 4 in detail. Invariant distributions on simply connected compact homogeneous spaces are also treated. Bibliography: 18 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2010

Hadron-hadron interaction from SU(2) lattice QCD

We evaluate interhadron interactions in two-color lattice QCD from Bethe-Salpeter amplitudes on the Euclidean lattice. The simulations are performed in quenched SU(2) QCD with the plaquette gauge action at {beta}=2.45 and the Wilson quark action. We concentrate on S-wave scattering states of two scalar diquarks. Evaluating different flavor combinations with various quark masses, we try to find out the ingredients in hadronic interactions. Between two scalar diquarks (uC{gamma}{sub 5}d, the lightest baryon in SU(2) system), we observe repulsion in short-range region, even though present quark masses are not very light. We define and evaluate the quark-exchange part in the interaction, which is induced by adding quark-exchange diagrams, or equivalently, by introducing Pauli-blocking among some of quarks. The repulsive force in short-distance region arises only from the quark-exchange part and disappears when quark-exchange diagrams are omitted. We find that the strength of repulsion grows in light quark-mass regime, and its quark-mass dependence is similar to or slightly stronger than that of the color-magnetic interaction by one-gluon-exchange (OGE) processes. It is qualitatively consistent with the constituent-quark-model picture that a color-magnetic interaction among quarks is the origin of repulsion. We also find a universal long-range attractive force, which enters in any flavor channels of two scalar diquarks and whose interaction range and strength are quark-mass independent. The weak quark-mass dependence of interaction ranges in each component implies that meson-exchange contributions are small and subdominant, and the other contributions, e.g., flavor-exchange processes, color-Coulomb, or color-magnetic interactions, are considered to be predominant, in the quark-mass range we evaluated.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2010

Charm form factors in hadronic interactions

We calculate the form factors and the coupling constants in vertices with charm mesons, such as {rho}D*D*, in the framework of QCD sum rules. We first discuss the applications of these form factors in heavy ion collisions and in B decays. We then present an introduction to the method of QCD sum rules and describe how to work with the three-point function. We give special attention to the procedure employed to extrapolate results obtained in the deep euclidean region to the poles of the particles, located in the time-like region. Finally we present a table of ready-to-use parametrizations of all the form factors, which are relevant for the processes mentioned in the introduction. We also give the coupling constants.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗