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At least 1,531 records · Page 85
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DOE OSTI2013

Quantum graph as a quantum spectral filter

We study the transmission of a quantum particle along a straight input-output line to which a graph {Gamma} is attached at a point. In the point of contact we impose a singularity represented by a certain properly chosen scale-invariant coupling with a coupling parameter {alpha}. We show that the probability of transmission along the line as a function of the particle energy tends to the indicator function of the energy spectrum of {Gamma} as {alpha}{yields}{infinity}. This effect can be used for a spectral analysis of the given graph {Gamma}. Its applications include a control of a transmission along the line and spectral filtering. The result is illustrated with an example where {Gamma} is a loop exposed to a magnetic field. Two more quantum devices are designed using other special scale-invariant vertex couplings. They can serve as a band-stop filter and as a spectral separator, respectively.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Generalized plasma dispersion function: One-solve-all treatment, visualizations, and application to Landau damping

A unified, fast, and effective approach is developed for numerical calculation of the well-known plasma dispersion function with extensions from Maxwellian distribution to almost arbitrary distribution functions, such as the δ, flat top, triangular, κ or Lorentzian, slowing down, and incomplete Maxwellian distributions. The singularity and analytic continuation problems are also solved generally. Given that the usual conclusion γ∝∂f{sub 0}/∂v is only a rough approximation when discussing the distribution function effects on Landau damping, this approach provides a useful tool for rigorous calculations of the linear wave and instability properties of plasma for general distribution functions. The results are also verified via a linear initial value simulation approach. Intuitive visualizations of the generalized plasma dispersion function are also provided.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

First order deformations of the Fourier matrix

The N × N complex Hadamard matrices form a real algebraic manifold C{sub N}. The singularity at a point H ∈ C{sub N} is described by a filtration of cones T{sub H}{sup ×}C{sub N}⊂T{sub H}{sup ∘}C{sub N}⊂T{sub H}C{sub N}⊂T{sup ~}{sub H}C{sub N}, coming from the trivial, affine, smooth, and first order deformations. We study here these cones in the case where H = F{sub N} is the Fourier matrix, (w{sup ij}) with w = e{sup 2πi/N}, our main result being a simple description of T{sup ~}{sub H}C{sub N}. As a consequence, the rationality conjecture dim{sub R}(T{sup ~}{sub H}C{sub N})=dim{sub Q}(T{sup ~}{sub H}C{sub N}∩M{sub N}(Q)) holds at H = F{sub N}.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Dilaton field minimally coupled to 2+1 gravity; uniqueness of the static Chan-Mann black hole and new dilaton stationary metrics

Using the Schwarzschild coordinate frame for a static cyclic symmetric metric in 2+1 gravity coupled minimally to a dilaton logarithmically depending on the radial coordinate in the presence of an exponential potential, by solving first order linear Einstein equations, the general solution is derived and it is identified with the Chan–Mann dilaton solution. In these coordinates, a new stationary dilaton solution is obtained; it does not allow for a de Sitter–Anti-de Sitter limit at spatial infinity, where its structural functions increase indefinitely. On the other hand, it is horizonless and allows for a naked singularity at the origin of coordinates; moreover, one can identify at a large radial coordinate a (quasi-local) mass parameter and in the whole space a constant angular momentum. Via a general SL(2,R)–transformation, applied on the static cyclic symmetric metric, a family of stationary dilaton solutions has been generated. A particular SL(2,R)–transformation is identified, which gives rise to the rotating Chan–Mann dilaton solution. All the exhibited solutions have been characterized by their quasi-local energy, mass, and momentum through their series expansions at spatial infinity. The algebraic structure of the Ricci–energy-momentum, and Cotton tensors is given explicitly.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

A model for transonic plasma flow

A linear, two-dimensional model of a transonic plasma flow in equilibrium is constructed and given an explicit solution in the form of a complex Laplace integral. The solution indicates that the transonic state can be solved as an elliptic boundary value problem, as is done in the numerical code FLOW [Guazzotto et al., Phys. Plasmas 11, 604 (2004)]. Moreover, the presence of a hyperbolic region does not necessarily imply the presence of a discontinuity or any other singularity of the solution.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Transport on the surface of a topological insulator

We study theoretically dc and ac transport on the surface of a three-dimensional topological insulator when its time-reversal symmetry is broken. Starting with a Kubo formula, we derive an explicit expression for the dc Hall conductivity, valid for finite temperatures. At zero temperature this expression gives the dc half-quantum Hall conductivity, provided the Fermi level lies in the gap. Corrections when the Fermi level is outside the gap and scattering by impurities are quantified. The longitudinal conductivity is also examined. At finite frequencies, we find a modified Drude term in σ{sub xx}(ω) and logarithmic, frequency-dependent corrections in σ{sub yx}(ω). The ac Hall conductivity exhibits a robust logarithmic singularity for excitation energies equal to the gapwidth. For these energies, we also find that the power spectrum, which is pertinent to optical experiments, exhibits drastic increase. The Hall conductivity remains almost unaffected for temperatures up to approximately 300 K.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Extended space expectation values in quantum dynamical system evolutions

The time variant power series expansion for the expectation value of a given quantum dynamical operator is well-known and well-investigated issue in quantum dynamics. However, depending on the operator and Hamiltonian singularities this expansion either may not exist or may not converge for all time instances except the beginning of the evolution. This work focuses on this issue and seeks certain cures for the negativities. We work in the extended space obtained by adding all images of the initial wave function under the system Hamiltonian’s positive integer powers. This requires the introduction of certain appropriately defined weight operators. The resulting better convergence in the temporal power series urges us to call the new defined entities “extended space expectation values” even though they are constructed over certain weight operators and are somehow pseudo expectation values.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Comprehensive kinetic analysis of the plasma-wall transition layer in a strongly tilted magnetic field

The magnetized plasma-wall transition (MPWT) layer at the presence of the obliquity of the magnetic field to the wall consists of three sub-layers: the Debye sheath (DS), the magnetic pre-sheath (MPS), and the collisional pre-sheath (CPS) with characteristic lengths λ{sub D} (electron Debye length), ρ{sub i} (ion gyro-radius), and ℓ (the smallest relevant collision length), respectively. Tokamak plasmas are usually assumed to have the ordering λ{sub D}≪ρ{sub i}≪ℓ, when the above-mentioned sub-layers can be distinctly distinguished. In the limits of ε{sub Dm}(λ{sub D}/ρ{sub i})→0 and ε{sub mc}(ρ{sub i}/ℓ)→0 (“asymptotic three-scale (A3S) limits”), these sub-layers are precisely defined. Using the smallness of the tilting angle of the magnetic field to the wall, the ion distribution functions are found for three sub-regions in the analytic form. The equations and characteristic length-scales governing the transition (intermediate) regions between the neighboring sub-layers (CPS – MPS and MPS – DS) are derived, allowing to avoid the singularities arising from the ε{sub Dm}→0 and ε{sub mc}→0 approximations. The MPS entrance and the related kinetic form of the Bohm–Chodura condition are successfully defined for the first time. At the DS entrance, the Bohm condition maintains its usual form. The results encourage further study and understanding of physics of the MPWT layers in the modern plasma facilities.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Regularizing the molecular potential in electronic structure calculations. II. Many-body methods

In Paper I of this series [F. A. Bischoff, “Regularizing the molecular potential in electronic structure calculations. I. SCF methods,” J. Chem. Phys. 141, 184105 (2014)] a regularized molecular Hamilton operator for electronic structure calculations was derived and its properties in SCF calculations were studied. The regularization was achieved using a correlation factor that models the electron-nuclear cusp. In the present study we extend the regularization to correlated methods, in particular the exact solution of the two-electron problem, as well as second-order many body perturbation theory. The nuclear and electronic correlation factors lead to computations with a smaller memory footprint because the singularities are removed from the working equations, which allows coarser grid resolution while maintaining the precision. Numerical examples are given.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Quantum harmonic oscillator with superoscillating initial datum

In this paper, we study the evolution of superoscillating initial data for the quantum driven harmonic oscillator. Our main result shows that superoscillations are amplified by the harmonic potential and that the analytic solution develops a singularity in finite time. We also show that for a large class of solutions of the Schrödinger equation, superoscillating behavior at any given time implies superoscillating behavior at any other time.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Properties of hadronic systems according to the non-extensive self-consistent thermodynamics

The non-extensive self-consistent theory describing the thermodynamics of hadronic systems at high temperatures is used to derive some thermodynamical quantities, as pressure, entropy, speed of sound and trace-anomaly. The calculations are free of fitting parameters, and the results are compared to lattice QCD calculations, showing a good agreement between theory and data up to temperatures around 175 MeV. Above this temperature the effects of a singularity in the partition function at T{sub o} = 192 MeV results in a divergent behaviour in respect with the lattice calculation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

Griffiths phase, spin-phonon coupling, and exchange bias effect in double perovskite Pr{sub 2}CoMnO{sub 6}

The ceramic Pr{sub 2}CoMnO{sub 6} of double perovskite structure is prepared by a solid-state reaction and the magnetic properties, phonon behaviors are studied in detail. Two ferromagnetic transitions at T{sub C1} ∼ 172 K and T{sub C2} ∼ 140 K are observed in the temperature-dependent magnetization curves, respectively. Furthermore, a detail analysis on the magnetic susceptibility reveals that a short-range ferromagnetic clustered state exists above T{sub C1}, which can be well described as the Griffiths phase with a well-defined Griffiths temperature T{sub G} ∼ 210 K. The presence of the B-site antisite defects is considered to contribute to the observed Griffiths singularity. Temperature-dependent Raman scattering experiment reveals an obvious softening of the phonon mode involving stretching vibrations of the (Co/Mn)O{sub 6} octahedra in FM temperature regions, indicating a close correlation between magnetism and lattice in Pr{sub 2}CoMnO{sub 6}. On the other hand, it is found that the phonon softening extends up to T{sub G}, which further confirms the preformation of the short-range ferromagnetic clusters up to T{sub G}. Moreover, the field-cooling magnetic hysteresis loop reveals that exchange bias phenomena is present, which is supposed to origin from the exchange coupling between Co/Mn ordered ferromagnetic phases with antiferromagnetic antiphase boundaries caused by the partially Co/Mn antisite disorders. These findings give a systematic understanding on the magnetic interaction in Pr{sub 2}CoMnO{sub 6} which is closely related to the lattice and atomic distribution, and add special interest for application of this material.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Restricted Hartree Fock using complex-valued orbitals: A long-known but neglected tool in electronic structure theory

Restricted Hartree Fock using complex-valued orbitals (cRHF) is studied. We introduce an orbital pairing theorem, with which we obtain a concise connection between cRHF and real-valued RHF, and use it to uncover the close relationship between cRHF, unrestricted Hartree Fock, and generalized valence bond perfect pairing. This enables an intuition for cRHF, contrasting with the generally unintuitive nature of complex orbitals. We also describe an efficient computer implementation of cRHF and its corresponding stability analysis. By applying cRHF to the Be + H{sub 2} insertion reaction, a Woodward-Hoffmann violating reaction, and a symmetry-driven conical intersection, we demonstrate in genuine molecular systems that cRHF is capable of removing certain potential energy surface singularities that plague real-valued RHF and related methods. This complements earlier work that showed this capability in a model system. We also describe how cRHF is the preferred RHF method for certain radicaloid systems like singlet oxygen and antiaromatic molecules. For singlet O{sub 2}, we show that standard methods fail even at the equilibrium geometry. An implication of this work is that, regardless of their individual efficacies, cRHF solutions to the HF equations are fairly commonplace.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

The shallow water equations as a hybrid flow model for the numerical and experimental analysis of hydro power stations

The numerical analysis of hydro power stations is an important method of the hydraulic design and is used for the development and optimisation of hydro power stations in addition to the experiments with the physical submodel of a full model in the hydraulic laboratory. For the numerical analysis, 2D and 3D models are appropriate and commonly used.The 2D models refer mainly to the shallow water equations (SWE), since for this flow model a large experience on a wide field of applications for the flow analysis of numerous problems in hydraulic engineering already exists. Often, the flow model is verified by in situ measurements. In order to consider 3D flow phenomena close to singularities like weirs, hydro power stations etc. the development of a hybrid fluid model is advantageous to improve the quality and significance of the global model. Here, an extended hybrid flow model based on the principle of the SWE is presented. The hybrid flow model directly links the numerical model with the experimental data, which may originate from physical full models, physical submodels and in-situ measurements. Hence a wide field of application of the hybrid model emerges including the improvement of numerical models and the strong coupling of numerical and experimental analysis.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Interacting vacuum energy in the dark sector

We analyse three cosmological scenarios with interaction in the dark sector, which are particular cases of a general expression for the energy flux from vacuum to matter. In the first case the interaction leads to a transition from an unstable de Sitter phase to a radiation dominated universe, avoiding in this way the initial singularity. In the second case the interaction gives rise to a slow-roll power-law inflation. Finally, the third scenario is a concordance model for the late-time universe, with the vacuum term decaying into cold dark matter. We identify the physics behind these forms of interaction and show that they can be described as particular types of the modified Chaplygin gas.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

An efficient method for energy levels calculation using full symmetry and exact kinetic energy operator: Tetrahedral molecules

A simultaneous use of the full molecular symmetry and of an exact kinetic energy operator (KEO) is of key importance for accurate predictions of vibrational levels at a high energy range from a potential energy surface (PES). An efficient method that permits a fast convergence of variational calculations would allow iterative optimization of the PES parameters using experimental data. In this work, we propose such a method applied to tetrahedral AB{sub 4} molecules for which a use of high symmetry is crucial for vibrational calculations. A symmetry-adapted contracted angular basis set for six redundant angles is introduced. Simple formulas using this basis set for explicit calculation of the angular matrix elements of KEO and PES are reported. The symmetric form (six redundant angles) of vibrational KEO without the sin(q){sup −2} type singularity is derived. The efficient recursive algorithm based on the tensorial formalism is used for the calculation of vibrational matrix elements. A good basis set convergence for the calculations of vibrational levels of the CH{sub 4} molecule is demonstrated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Entropy density of an adiabatic relativistic Bose-Einstein condensate star

Inspired by recent works, we investigate how the thermodynamics parameters (entropy, temperature, number density, energy density, etc) of Bose-Einstein Condensate star scale with the structure of the star. Below the critical temperature in which the condensation starts to occur, we study how the entropy behaves with varying temperature till it reaches its own stability against gravitational collapse and singularity. Compared to photon gases (pressure is described by radiation) where the chemical potential, μ is zero, entropy of photon gases obeys the Stefan-Boltzmann Law for a small values of T while forming a spiral structure for a large values of T due to general relativity. The entropy density of Bose-Einstein Condensate is obtained following the similar sequence but limited under critical temperature condition. We adopt the scalar field equation of state in Thomas-Fermi limit to study the characteristics of relativistic Bose-Einstein condensate under varying temperature and entropy. Finally, we obtain the entropy density proportional to (σT{sup 3}-3T) which obeys the Stefan-Boltzmann Law in ultra-relativistic condition.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Phase change alloy viscosities down to T{sub g} using Adam-Gibbs-equation fittings to excess entropy data: A fragile-to-strong transition

A striking anomaly in the viscosity of Te{sub 85}Ge{sub 15} alloys noted by Greer and coworkers from the work of Neumann et al. is reminiscent of the equally striking comparison of liquid tellurium and water anomalies documented long ago by Kanno et al. In view of the power laws that are used to fit the data on water, we analyze the data on Te{sub 85}Ge{sub 15} using the Speedy-Angell power-law form, and find a good account with a singularity T{sub s} only 25 K below the eutectic temperature. However, the heat capacity data in this case are not diverging, but instead exhibit a sharp maximum like that observed in fast cooling in the Molinero-Moore model of water. Applying the Adam-Gibbs viscosity equation to these calorimetric data, we find that there must be a fragile-to-strong liquid transition at the heat capacity peak temperature, and then predict the 'strong' liquid course of the viscosity down to T{sub g} at 406 K (403.6 K at 20 K min{sup −1} in this study). Since crystallization can be avoided by moderately fast cooling in this case, we can check the validity of the extrapolation by making a direct measurement of fragility at T{sub g}, using differential scanning calorimetric techniques, and then comparing with the value from the extrapolated viscosity at T{sub g}. The agreement is encouraging, and prompts discussion of relations between water and phase change alloy anomalies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗