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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 307 records · Page 17
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DOE OSTI2013

Resonant electromagnetic scattering in anisotropic layered media

The resonant excitation of an electromagnetic guided mode of a slab structure by exterior radiation results in anomalous scattering behavior, including sharp energy-transmission anomalies and field amplification around the frequency of the slab mode. In the case of a periodically layered ambient medium, anisotropy serves to couple the slab mode to radiation. Exact expressions for scattering phenomena are proved by analyzing a pole of the full scattering matrix as it moves off the real frequency axis into the lower half complex plane under a detuning of the wavevector parallel to the slab. The real pole is the frequency of a perfect (infinite Q) guided mode, which becomes lossy as the frequency gains an imaginary part. This work extends results of Shipman and Venakides to evanescent source fields and two-dimensional parallel wavevector and demonstrates by example how the latter allows one to control independently the width and central frequency of a resonance by varying the angle of incidence of the source field. The analysis relies on two nondegeneracy conditions of the complex dispersion relation for slab modes (relating poles of the scattering matrix to wavevector), which were assumed in previous works and are proved in this work for layered media. One of them asserts that the dispersion relation near the wavevector κ and frequency ω of a perfect guided mode is the zero set of a simple eigenvalue ℓ(κ, ω), and the other relates ∂ℓ/∂ω to the total energy of the mode, thereby implying that this derivative is nonzero.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Spectral asymmetry of the massless Dirac operator on a 3-torus

Consider the massless Dirac operator on a 3-torus equipped with Euclidean metric and standard spin structure. It is known that the eigenvalues can be calculated explicitly: the spectrum is symmetric about zero and zero itself is a double eigenvalue. The aim of the paper is to develop a perturbation theory for the eigenvalue with smallest modulus with respect to perturbations of the metric. Here the application of perturbation techniques is hindered by the fact that eigenvalues of the massless Dirac operator have even multiplicity, which is a consequence of this operator commuting with the antilinear operator of charge conjugation (a peculiar feature of dimension 3). We derive an asymptotic formula for the eigenvalue with smallest modulus for arbitrary perturbations of the metric and present two particular families of Riemannian metrics for which the eigenvalue with smallest modulus can be evaluated explicitly. We also establish a relation between our asymptotic formula and the eta invariant.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Magnetic field induced dynamical chaos

In this article, we have studied the dynamics of a particle having charge in the presence of a magnetic field. The motion of the particle is confined in the x–y plane under a two dimensional nonlinear potential. We have shown that constant magnetic field induced dynamical chaos is possible even for a force which is derived from a simple potential. For a given strength of the magnetic field, initial position, and velocity of the particle, the dynamics may be regular, but it may become chaotic when the field is time dependent. Chaotic dynamics is very often if the field is time dependent. Origin of chaos has been explored using the Hamiltonian function of the dynamics in terms of action and angle variables. Applicability of the present study has been discussed with a few examples.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Phase transitions and magnetocaloric and transport properties in off-stoichiometric GdNi{sub 2}Mn{sub x}

The structural, magnetic, magnetocaloric, transport, and magnetoresistance properties of the rare-earth intermetallic compounds GdNi{sub 2}Mn{sub x} (0.5 ≤ x ≤ 1.5) have been studied. The compounds with x = 0.5 and 0.6 crystallize in the cubic MgCu{sub 2} type phase, whereas samples with x ≥ 0.8 form a mixed MgCu{sub 2} and rhombohedral PuNi{sub 3} phase. A second order magnetic phase transition from a ferromagnetic to paramagnetic state was observed near the Curie temperature (T{sub C}). The GdNi{sub 2}Mn{sub x} (0.5 ≤ x ≤ 1.5) compounds order in a ferrimagnetic structure in the ground state. The largest observed values of magnetic entropy changes (at T{sub C} for ΔH = 5T) were 3.9, 3.5, and 3.1 J/kg K for x = 0.5, 0.6, and 0.8, respectively. The respective relative values of the cooling power were 395, 483, and 220 J/kg. These values are greater than some well-known prototype magnetocaloric materials such as Gd (400 J/kg) and Gd{sub 5}Si{sub 2}Ge{sub 2} (240 J/kg). Analysis of the resistivity data showed a T{sup 2} dependence at low temperatures, suggesting strong electron-phonon interactions, whereas at higher temperatures s-d scattering was dominated by the electron-phonon contribution, resulting in a slow increase in resistivity. Magnetoresistance values of ∼−1.1% were found for x = 0.5 near T{sub C}, and −7% for x = 1.5 near T = 80 K.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Generalized spectral method for near-field optical microscopy

Electromagnetic interaction between a sub-wavelength particle (the “probe”) and a material surface (the “sample”) is studied theoretically. The interaction is shown to be governed by a series of resonances corresponding to surface polariton modes localized near the probe. The resonance parameters depend on the dielectric function and geometry of the probe as well as on the surface reflectivity of the material. Calculation of such resonances is carried out for several types of axisymmetric probes: spherical, spheroidal, and pear-shaped. For spheroids, an efficient numerical method is developed, capable of handling cases of large or strongly momentum-dependent surface reflectivity. Application of the method to highly resonant materials, such as aluminum oxide (by itself or covered with graphene), reveals a rich structure of multi-peak spectra and nonmonotonic approach curves, i.e., the probe-sample distance dependence. These features also strongly depend on the probe shape and optical constants of the model. For less resonant materials such as silicon oxide, the dependence is weak, so that the spheroidal model is reliable. The calculations are done within the quasistatic approximation with radiative damping included perturbatively.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Control of excitons in multi-layer van der Waals heterostructures

We report an experimental study of excitons in a double quantum well van der Waals heterostructure made of atomically thin layers of MoS{sub 2} and hexagonal boron nitride. The emission of neutral and charged excitons is controlled by gate voltage, temperature, and both the helicity and the power of optical excitation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Optical spectroscopy and band gap analysis of hybrid improper ferroelectric Ca{sub 3}Ti{sub 2}O{sub 7}

We bring together optical absorption spectroscopy, photoconductivity, and first principles calculations to reveal the electronic structure of the room temperature ferroelectric Ca{sub 3}Ti{sub 2}O{sub 7}. The 3.94 eV direct gap in Ca{sub 3}Ti{sub 2}O{sub 7} is charge transfer in nature and noticeably higher than that in CaTiO{sub 3} (3.4 eV), a finding that we attribute to dimensional confinement in the n = 2 member of the Ruddlesden-Popper series. While Sr substitution introduces disorder and broadens the gap edge slightly, oxygen deficiency reduces the gap to 3.7 eV and gives rise to a broad tail that persists to much lower energies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

Effects of an additional dimension in the Young experiment

The results of the Young experiment can be analyzed either by classical or Quantum Physics. The later one though leads to a more complete interpretation, based on two different patterns that appear when one works either with single or double slits. Here we show that the two patterns can be derived from a single principle, in the context of General Relativity, if one assumes an additional spatial dimension to the four known today. The found equations yield the same results as those in Quantum Mechanics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

Combinatorial theory of the semiclassical evaluation of transport moments. I. Equivalence with the random matrix approach

To study electronic transport through chaotic quantum dots, there are two main theoretical approaches. One involves substituting the quantum system with a random scattering matrix and performing appropriate ensemble averaging. The other treats the transport in the semiclassical approximation and studies correlations among sets of classical trajectories. There are established evaluation procedures within the semiclassical evaluation that, for several linear and nonlinear transport moments to which they were applied, have always resulted in the agreement with random matrix predictions. We prove that this agreement is universal: any semiclassical evaluation within the accepted procedures is equivalent to the evaluation within random matrix theory. The equivalence is shown by developing a combinatorial interpretation of the trajectory sets as ribbon graphs (maps) with certain properties and exhibiting systematic cancellations among their contributions. Remaining trajectory sets can be identified with primitive (palindromic) factorisations whose number gives the coefficients in the corresponding expansion of the moments of random matrices. The equivalence is proved for systems with and without time reversal symmetry.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

On quantum Rényi entropies: A new generalization and some properties

The Rényi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies, or mutual information, and have found many applications in information theory and beyond. Various generalizations of Rényi entropies to the quantum setting have been proposed, most prominently Petz's quasi-entropies and Renner's conditional min-, max-, and collision entropy. However, these quantum extensions are incompatible and thus unsatisfactory. We propose a new quantum generalization of the family of Rényi entropies that contains the von Neumann entropy, min-entropy, collision entropy, and the max-entropy as special cases, thus encompassing most quantum entropies in use today. We show several natural properties for this definition, including data-processing inequalities, a duality relation, and an entropic uncertainty relation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Matrix elements for type 1 unitary irreducible representations of the Lie superalgebra gl(m|n)

Using our recent results on eigenvalues of invariants associated to the Lie superalgebra gl(m|n), we use characteristic identities to derive explicit matrix element formulae for all gl(m|n) generators, particularly non-elementary generators, on finite dimensional type 1 unitary irreducible representations. We compare our results with existing works that deal with only subsets of the class of type 1 unitary representations, all of which only present explicit matrix elements for elementary generators. Our work therefore provides an important extension to existing methods, and thus highlights the strength of our techniques which exploit the characteristic identities.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Complex dynamics of a delayed discrete neural network of two nonidentical neurons

In this paper, we discover that a delayed discrete Hopfield neural network of two nonidentical neurons with self-connections and no self-connections can demonstrate chaotic behaviors. To this end, we first transform the model, by a novel way, into an equivalent system which has some interesting properties. Then, we identify the chaotic invariant set for this system and show that the dynamics of this system within this set is topologically conjugate to the dynamics of the full shift map with two symbols. This confirms chaos in the sense of Devaney. Our main results generalize the relevant results of Huang and Zou [J. Nonlinear Sci. 15, 291–303 (2005)], Kaslik and Balint [J. Nonlinear Sci. 18, 415–432 (2008)] and Chen et al. [Sci. China Math. 56(9), 1869–1878 (2013)]. We also give some numeric simulations to verify our theoretical results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Chaotic vibrations of the duffing system with fractional damping

We examined the Duffing system with a fractional damping term. Calculating the basins of attraction, we demonstrate a broad spectrum of non-linear behaviour connected with sensitivity to the initial conditions and chaos. To quantify dynamical response of the system, we propose the statistical 0-1 test as well as the maximal Lyapunov exponent; the application of the latter encounter a few difficulties because of the memory effect due to the fractional derivative. The results are confirmed by bifurcation diagrams, phase portraits, and Poincaré sections.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Generalization of Abel's mechanical problem: The extended isochronicity condition and the superposition principle

This paper presents a simple but nontrivial generalization of Abel's mechanical problem, based on the extended isochronicity condition and the superposition principle. There are two primary aims. The first one is to reveal the linear relation between the transit-time T and the travel-length X hidden behind the isochronicity problem that is usually discussed in terms of the nonlinear equation of motion (d{sup 2}X)/(dt{sup 2}) +(dU)/(dX) =0 with U(X) being an unknown potential. Second, the isochronicity condition is extended for the possible Abel-transform approach to designing the isochronous trajectories of charged particles in spectrometers and/or accelerators for time-resolving experiments. Our approach is based on the integral formula for the oscillatory motion by Landau and Lifshitz [Mechanics (Pergamon, Oxford, 1976), pp. 27–29]. The same formula is used to treat the non-periodic motion that is driven by U(X). Specifically, this unknown potential is determined by the (linear) Abel transform X(U) ∝ A[T(E)], where X(U) is the inverse function of U(X), A=(1/√(π))∫{sub 0}{sup E}dU/√(E−U) is the so-called Abel operator, and T(E) is the prescribed transit-time for a particle with energy E to spend in the region of interest. Based on this Abel-transform approach, we have introduced the extended isochronicity condition: typically, τ = T{sub A}(E) + T{sub N}(E) where τ is a constant period, T{sub A}(E) is the transit-time in the Abel type [A-type] region spanning X > 0 and T{sub N}(E) is that in the Non-Abel type [N-type] region covering X < 0. As for the A-type region in X > 0, the unknown inverse function X{sub A}(U) is determined from T{sub A}(E) via the Abel-transform relation X{sub A}(U) ∝ A[T{sub A}(E)]. In contrast, the N-type region in X < 0 does not ensure this linear relation: the region is covered with a predetermined potential U{sub N}(X) of some arbitrary choice, not necessarily obeying the Abel-transform relation. In discussing the isochronicity problem, there has been no attempt of N-type regions that are practically of full use for the charged-particle spectrometers and/or accelerators. In this Abel-transform approach, the superposition principle simplifies the derivation of X{sub A}(U) satisfying the extended isochronicity condition. Although the extended isochronicity condition inevitably discards the low-energy particles, there is no problem for handling accelerated particles because they do not involve the small-amplitude oscillations around the potential minimum. We present analytic examples of X{sub A}(U) that are instructive. In Appendix B, Urabe's criterion is interpreted in the time domain, using the Abel-transform approach.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

A parametric approach to supersymmetric quantum mechanics in the solution of Schrödinger equation

We study exact solutions of the Schrödinger equation for some potentials. We introduce a parametric approach to supersymmetric quantum mechanics to calculate energy eigenvalues and corresponding wave functions exactly. As an application we solve Schrödinger equation for the generalized Morse potential, modified Hulthen potential, deformed Rosen-Morse potential and Poschl-Teller potential. The method is simple and effective to get the results.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Signature candidate of quantum chaos far from the semiclassical regime

We numerically investigated the entanglement product in the simplest coupled kicked top model with the spin j = 1. Different from the dynamical pattern of entanglement in the semiclassical regime, two similar initial states may have discordant entanglement oscillations. A candidate of the quantum signature of this classical chaotic system was proposed. The potential antimonotonic relation between the rank correlation coefficient qualifying the concordant of two entanglement evolutions and the stationary entanglement was preliminarily revealed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Statistical mechanics based on fractional classical and quantum mechanics

The purpose of this work is to study some problems in statistical mechanics based on the fractional classical and quantum mechanics. At first stage we have presented the thermodynamical properties of the classical ideal gas and the system of N classical oscillators. In both cases, the Hamiltonian contains fractional exponents of the phase space (position and momentum). At the second stage, in the context of the fractional quantum mechanics, we have calculated the thermodynamical properties for the black body radiation, studied the Bose-Einstein statistics with the related problem of the condensation and the Fermi-Dirac statistics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗