Solitons in a one-dimensional Wigner crystal

DOE PAGES

Pustilnik, M.; Matveev, K. A.

2015-04-16

In one-dimensional quantum systems with strong long-range repulsion particles arrange in a quasi-periodic chain, the Wigner crystal. Here, we demonstrate that besides the familiar phonons, such one-dimensional Wigner crystal supports an additional mode of elementary excitations, which can be identified with solitons in the classical limit. Furthermore, we compute the corresponding excitation spectrum and argue that the solitons have a parametrically small decay rate at low energies. Finally, we discuss implications of our results for the behavior of the dynamic structure factor.

The continuous spin representations of the Poincare and super-Poincare groups and their construction by the Inonu-Wigner group contraction

NASA Astrophysics Data System (ADS)

Khan, Abu M. A. S.

We study the continuous spin representation (CSR) of the Poincare group in arbitrary dimensions. In d dimensions, the CSRs are characterized by the length of the light-cone vector and the Dynkin labels of the SO(d-3) short little group which leaves the light-cone vector invariant. In addition to these, a solid angle Od-3 which specifies the direction of the light-cone vector is also required to label the states. We also find supersymmetric generalizations of the CSRs. In four dimensions, the supermultiplet contains one bosonic and one fermionic CSRs which transform into each other under the action of the supercharges. In a five dimensional case, the supermultiplet contains two bosonic and two fermionic CSRs which is like N = 2 supersymmetry in four dimensions. When constructed using Grassmann parameters, the light-cone vector becomes nilpotent. This makes the representation finite dimensional, but at the expense of introducing central charges even though the representation is massless. This leads to zero or negative norm states. The nilpotent constructions are valid only for even dimensions. We also show how the CSRs in four dimensions can be obtained from five dimensions by the combinations of Kaluza-Klein (KK) dimensional reduction and the Inonu-Wigner group contraction. The group contraction is a singular transformation. We show that the group contraction is equivalent to imposing periodic boundary condition along one direction and taking a double singular limit. In this form the contraction parameter is interpreted as the inverse KK radius. We apply this technique to both five dimensional regular massless and massive representations. For the regular massless case, we find that the contraction gives the CSR in four dimensions under a double singular limit and the representation wavefunction is the Bessel function. For the massive case, we use Majorana's infinite component theory as a model for the SO(4) little group. In this case, a triple singular limit is required to yield any CSR in four dimensions. The representation wavefunction is the Bessel function, as expected, but the scale factor is not the length of the light-cone vector. The amplitude and the scale factor are implicit functions of the parameter y which is a ratio of the internal and external coordinates. We also state under what conditions our solutions become identical to Wigner's solution.

Wigner distribution function and entropy of the damped harmonic oscillator within the theory of the open quantum systems

NASA Technical Reports Server (NTRS)

Isar, Aurelian

1995-01-01

The harmonic oscillator with dissipation is studied within the framework of the Lindblad theory for open quantum systems. By using the Wang-Uhlenbeck method, the Fokker-Planck equation, obtained from the master equation for the density operator, is solved for the Wigner distribution function, subject to either the Gaussian type or the delta-function type of initial conditions. The obtained Wigner functions are two-dimensional Gaussians with different widths. Then a closed expression for the density operator is extracted. The entropy of the system is subsequently calculated and its temporal behavior shows that this quantity relaxes to its equilibrium value.

Analysis of geometric phase effects in the quantum-classical Liouville formalism.

PubMed

Ryabinkin, Ilya G; Hsieh, Chang-Yu; Kapral, Raymond; Izmaylov, Artur F

2014-02-28

We analyze two approaches to the quantum-classical Liouville (QCL) formalism that differ in the order of two operations: Wigner transformation and projection onto adiabatic electronic states. The analysis is carried out on a two-dimensional linear vibronic model where geometric phase (GP) effects arising from a conical intersection profoundly affect nuclear dynamics. We find that the Wigner-then-Adiabatic (WA) QCL approach captures GP effects, whereas the Adiabatic-then-Wigner (AW) QCL approach does not. Moreover, the Wigner transform in AW-QCL leads to an ill-defined Fourier transform of double-valued functions. The double-valued character of these functions stems from the nontrivial GP of adiabatic electronic states in the presence of a conical intersection. In contrast, WA-QCL avoids this issue by starting with the Wigner transform of single-valued quantities of the full problem. As a consequence, GP effects in WA-QCL can be associated with a dynamical term in the corresponding equation of motion. Since the WA-QCL approach uses solely the adiabatic potentials and non-adiabatic derivative couplings as an input, our results indicate that WA-QCL can capture GP effects in two-state crossing problems using first-principles electronic structure calculations without prior diabatization or introduction of explicit phase factors.

Analysis of geometric phase effects in the quantum-classical Liouville formalism

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ryabinkin, Ilya G.; Izmaylov, Artur F.; Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6

2014-02-28

We analyze two approaches to the quantum-classical Liouville (QCL) formalism that differ in the order of two operations: Wigner transformation and projection onto adiabatic electronic states. The analysis is carried out on a two-dimensional linear vibronic model where geometric phase (GP) effects arising from a conical intersection profoundly affect nuclear dynamics. We find that the Wigner-then-Adiabatic (WA) QCL approach captures GP effects, whereas the Adiabatic-then-Wigner (AW) QCL approach does not. Moreover, the Wigner transform in AW-QCL leads to an ill-defined Fourier transform of double-valued functions. The double-valued character of these functions stems from the nontrivial GP of adiabatic electronic statesmore » in the presence of a conical intersection. In contrast, WA-QCL avoids this issue by starting with the Wigner transform of single-valued quantities of the full problem. As a consequence, GP effects in WA-QCL can be associated with a dynamical term in the corresponding equation of motion. Since the WA-QCL approach uses solely the adiabatic potentials and non-adiabatic derivative couplings as an input, our results indicate that WA-QCL can capture GP effects in two-state crossing problems using first-principles electronic structure calculations without prior diabatization or introduction of explicit phase factors.« less

Efficient solution of the Wigner-Liouville equation using a spectral decomposition of the force field

NASA Astrophysics Data System (ADS)

Van de Put, Maarten L.; Sorée, Bart; Magnus, Wim

2017-12-01

The Wigner-Liouville equation is reformulated using a spectral decomposition of the classical force field instead of the potential energy. The latter is shown to simplify the Wigner-Liouville kernel both conceptually and numerically as the spectral force Wigner-Liouville equation avoids the numerical evaluation of the highly oscillatory Wigner kernel which is nonlocal in both position and momentum. The quantum mechanical evolution is instead governed by a term local in space and non-local in momentum, where the non-locality in momentum has only a limited range. An interpretation of the time evolution in terms of two processes is presented; a classical evolution under the influence of the averaged driving field, and a probability-preserving quantum-mechanical generation and annihilation term. Using the inherent stability and reduced complexity, a direct deterministic numerical implementation using Chebyshev and Fourier pseudo-spectral methods is detailed. For the purpose of illustration, we present results for the time-evolution of a one-dimensional resonant tunneling diode driven out of equilibrium.

Scattering of charge and spin excitations and equilibration of a one-dimensional Wigner crystal

DOE Office of Scientific and Technical Information (OSTI.GOV)

Matveev, K. A.; Andreev, A. V.; Klironomos, A. D.

2014-07-01

We study scattering of charge and spin excitations in a system of interacting electrons in one dimension. At low densities, electrons form a one-dimensional Wigner crystal. To a first approximation, the charge excitations are the phonons in the Wigner crystal, and the spin excitations are described by the Heisenberg model with nearest-neighbor exchange coupling. This model is integrable and thus incapable of describing some important phenomena, such as scattering of excitations off each other and the resulting equilibration of the system. We obtain the leading corrections to this model, including charge-spin coupling and the next-nearest-neighbor exchange in the spin subsystem.more » We apply the results to the problem of equilibration of the one-dimensional Wigner crystal and find that the leading contribution to the equilibration rate arises from scattering of spin excitations off each other. We discuss the implications of our results for the conductance of quantum wires at low electron densities« less

Observation and spectroscopy of a two-electron Wigner molecule in an ultraclean carbon nanotube

NASA Astrophysics Data System (ADS)

Pecker, S.; Kuemmeth, F.; Secchi, A.; Rontani, M.; Ralph, D. C.; McEuen, P. L.; Ilani, S.

2013-09-01

Two electrons on a string form a simple model system where Coulomb interactions are expected to play an interesting role. In the presence of strong interactions, these electrons are predicted to form a Wigner molecule, separating to the ends of the string. This spatial structure is believed to be clearly imprinted on the energy spectrum, yet so far a direct measurement of such a spectrum in a controllable one-dimensional setting is still missing. Here we use an ultraclean carbon nanotube to realize this system in a tunable potential. Using tunnelling spectroscopy we measure the addition spectra of two interacting carriers, electrons or holes, and identify seven low-energy states characterized by their exchange symmetries. The formation of a Wigner molecule is evident from a tenfold quenching of the fundamental excitation energy as compared with the non-interacting value. Our ability to tune the two-carrier state in space and to study it for both electrons and holes provides an unambiguous demonstration of this strongly interacting quantum ground state.

Pair Formation of Hard Core Bosons in Flat Band Systems

NASA Astrophysics Data System (ADS)

Mielke, Andreas

2018-05-01

Hard core bosons in a large class of one or two dimensional flat band systems have an upper critical density, below which the ground states can be described completely. At the critical density, the ground states are Wigner crystals. If one adds a particle to the system at the critical density, the ground state and the low lying multi particle states of the system can be described as a Wigner crystal with an additional pair of particles. The energy band for the pair is separated from the rest of the multi-particle spectrum. The proofs use a Gerschgorin type of argument for block diagonally dominant matrices. In certain one-dimensional or tree-like structures one can show that the pair is localised, for example in the chequerboard chain. For this one-dimensional system with periodic boundary condition the energy band for the pair is flat, the pair is localised.

Wigner's quantum phase-space current in weakly-anharmonic weakly-excited two-state systems

NASA Astrophysics Data System (ADS)

Kakofengitis, Dimitris; Steuernagel, Ole

2017-09-01

There are no phase-space trajectories for anharmonic quantum systems, but Wigner's phase-space representation of quantum mechanics features Wigner current J . This current reveals fine details of quantum dynamics —finer than is ordinarily thought accessible according to quantum folklore invoking Heisenberg's uncertainty principle. Here, we focus on the simplest, most intuitive, and analytically accessible aspects of J. We investigate features of J for bound states of time-reversible, weakly-anharmonic one-dimensional quantum-mechanical systems which are weakly-excited. We establish that weakly-anharmonic potentials can be grouped into three distinct classes: hard, soft, and odd potentials. We stress connections between each other and the harmonic case. We show that their Wigner current fieldline patterns can be characterised by J's discrete stagnation points, how these arise and how a quantum system's dynamics is constrained by the stagnation points' topological charge conservation. We additionally show that quantum dynamics in phase space, in the case of vanishing Planck constant ℏ or vanishing anharmonicity, does not pointwise converge to classical dynamics.

Evidence for a Peierls phase-transition in a three-dimensional multiple charge-density waves solid

PubMed Central

Mansart, Barbara; Cottet, Mathieu J. G.; Penfold, Thomas J.; Dugdale, Stephen B.; Tediosi, Riccardo; Chergui, Majed; Carbone, Fabrizio

2012-01-01

The effect of dimensionality on materials properties has become strikingly evident with the recent discovery of graphene. Charge ordering phenomena can be induced in one dimension by periodic distortions of a material’s crystal structure, termed Peierls ordering transition. Charge-density waves can also be induced in solids by strong coulomb repulsion between carriers, and at the extreme limit, Wigner predicted that crystallization itself can be induced in an electrons gas in free space close to the absolute zero of temperature. Similar phenomena are observed also in higher dimensions, but the microscopic description of the corresponding phase transition is often controversial, and remains an open field of research for fundamental physics. Here, we photoinduce the melting of the charge ordering in a complex three-dimensional solid and monitor the consequent charge redistribution by probing the optical response over a broad spectral range with ultrashort laser pulses. Although the photoinduced electronic temperature far exceeds the critical value, the charge-density wave is preserved until the lattice is sufficiently distorted to induce the phase transition. Combining this result with ab initio electronic structure calculations, we identified the Peierls origin of multiple charge-density waves in a three-dimensional system for the first time. PMID:22451898

Physical scales in the Wigner-Boltzmann equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Nedjalkov, M., E-mail: mixi@iue.tuwien.ac.at; Selberherr, S.; Ferry, D.K.

2013-01-15

The Wigner-Boltzmann equation provides the Wigner single particle theory with interactions with bosonic degrees of freedom associated with harmonic oscillators, such as phonons in solids. Quantum evolution is an interplay of two transport modes, corresponding to the common coherent particle-potential processes, or to the decoherence causing scattering due to the oscillators. Which evolution mode will dominate depends on the scales of the involved physical quantities. A dimensionless formulation of the Wigner-Boltzmann equation is obtained, where these scales appear as dimensionless strength parameters. A notion called scaling theorem is derived, linking the strength parameters to the coupling with the oscillators. Itmore » is shown that an increase of this coupling is equivalent to a reduction of both the strength of the electric potential, and the coherence length. Secondly, the existence of classes of physically different, but mathematically equivalent setups of the Wigner-Boltzmann evolution is demonstrated. - Highlights: Black-Right-Pointing-Pointer Dimensionless parameters determine the ratio of quantum or classical WB evolution. Black-Right-Pointing-Pointer The scaling theorem evaluates the decoherence effect due to scattering. Black-Right-Pointing-Pointer Evolution processes are grouped into classes of equivalence.« less

Discrete Wigner formalism for qubits and noncontextuality of Clifford gates on qubit stabilizer states

NASA Astrophysics Data System (ADS)

Kocia, Lucas; Love, Peter

2017-12-01

We show that qubit stabilizer states can be represented by non-negative quasiprobability distributions associated with a Wigner-Weyl-Moyal formalism where Clifford gates are positive state-independent maps. This is accomplished by generalizing the Wigner-Weyl-Moyal formalism to three generators instead of two—producing an exterior, or Grassmann, algebra—which results in Clifford group gates for qubits that act as a permutation on the finite Weyl phase space points naturally associated with stabilizer states. As a result, a non-negative probability distribution can be associated with each stabilizer state's three-generator Wigner function, and these distributions evolve deterministically to one another under Clifford gates. This corresponds to a hidden variable theory that is noncontextual and local for qubit Clifford gates while Clifford (Pauli) measurements have a context-dependent representation. Equivalently, we show that qubit Clifford gates can be expressed as propagators within the three-generator Wigner-Weyl-Moyal formalism whose semiclassical expansion is truncated at order ℏ0 with a finite number of terms. The T gate, which extends the Clifford gate set to one capable of universal quantum computation, requires a semiclassical expansion of the propagator to order ℏ1. We compare this approach to previous quasiprobability descriptions of qubits that relied on the two-generator Wigner-Weyl-Moyal formalism and find that the two-generator Weyl symbols of stabilizer states result in a description of evolution under Clifford gates that is state-dependent, in contrast to the three-generator formalism. We have thus extended Wigner non-negative quasiprobability distributions from the odd d -dimensional case to d =2 qubits, which describe the noncontextuality of Clifford gates and contextuality of Pauli measurements on qubit stabilizer states.

Reactive scattering with row-orthonormal hyperspherical coordinates. 4. Four-dimensional-space Wigner rotation function for pentaatomic systems.

PubMed

Kuppermann, Aron

2011-05-14

The row-orthonormal hyperspherical coordinate (ROHC) approach to calculating state-to-state reaction cross sections and bound state levels of N-atom systems requires the use of angular momentum tensors and Wigner rotation functions in a space of dimension N - 1. The properties of those tensors and functions are discussed for arbitrary N and determined for N = 5 in terms of the 6 Euler angles involved in 4-dimensional space.

Linear canonical transformations of coherent and squeezed states in the Wigner phase space

NASA Technical Reports Server (NTRS)

Han, D.; Kim, Y. S.; Noz, Marilyn E.

1988-01-01

It is shown that classical linear canonical transformations are possible in the Wigner phase space. Coherent and squeezed states are shown to be linear canonical transforms of the ground-state harmonic oscillator. It is therefore possible to evaluate the Wigner functions for coherent and squeezed states from that for the harmonic oscillator. Since the group of linear canonical transformations has a subgroup whose algebraic property is the same as that of the (2+1)-dimensional Lorentz group, it may be possible to test certain properties of the Lorentz group using optical devices. A possible experiment to measure the Wigner rotation angle is discussed.

Observation and Spectroscopy of a Two-Electron Wigner Molecule in Ultra-Clean Carbon Nanotubes

NASA Astrophysics Data System (ADS)

Pecker, Sharon; Kuemmeth, Ferdinand; Secchi, Andrea; Rontani, Massimo; Ralph, Dan; McEuen, Paul; Ilani, Shahal

2013-03-01

Coulomb interactions can have a decisive effect on the ground state of electronic systems. The simplest system in which interactions can play an interesting role is that of two electrons on a string. In the presence of strong interactions the two electrons are predicted to form a Wigner molecule, separating to the ends of the string due to their mutual repulsion. This spatial structure is believed to be clearly imprinted on the energy spectrum, yet to date a direct measurement of such a spectrum in a controllable one-dimensional setting is still missing. Here we use an ultra-clean suspended carbon nanotube to realize this strongly-correlated system in a tunable potential. Using tunneling spectroscopy we measure the excitation spectra of two interacting carriers, electrons or holes. Seven quantum states are identified, characterized by their spin and isospin quantum numbers. These states are seen to fall into two distinctive multiplets according to their exchange symmetries. Interestingly, we find that the splitting between multiplets is quenched by an order of magnitude compared to the non-interacting value. This quenching is shown to be a direct manifestation of the formation of a strongly-interacting Wigner-molecule ground state.

Stochastic solution to quantum dynamics

NASA Technical Reports Server (NTRS)

John, Sarah; Wilson, John W.

1994-01-01

The quantum Liouville equation in the Wigner representation is solved numerically by using Monte Carlo methods. For incremental time steps, the propagation is implemented as a classical evolution in phase space modified by a quantum correction. The correction, which is a momentum jump function, is simulated in the quasi-classical approximation via a stochastic process. The technique, which is developed and validated in two- and three- dimensional momentum space, extends an earlier one-dimensional work. Also, by developing a new algorithm, the application to bound state motion in an anharmonic quartic potential shows better agreement with exact solutions in two-dimensional phase space.

Electron ptychographic phase imaging of light elements in crystalline materials using Wigner distribution deconvolution

DOE PAGES

Yang, Hao; MacLaren, Ian; Jones, Lewys; ...

2017-04-01

Recent development in fast pixelated detector technology has allowed a two dimensional diffraction pattern to be recorded at every probe position of a two dimensional raster scan in a scanning transmission electron microscope (STEM), forming an information-rich four dimensional (4D) dataset. Electron ptychography has been shown to enable efficient coherent phase imaging of weakly scattering objects from a 4D dataset recorded using a focused electron probe, which is optimised for simultaneous incoherent Z-contrast imaging and spectroscopy in STEM. Thus coherent phase contrast and incoherent Z-contrast imaging modes can be efficiently combined to provide a good sensitivity of both light andmore » heavy elements at atomic resolution. Here, we explore the application of electron ptychography for atomic resolution imaging of strongly scattering crystalline specimens, and present experiments on imaging crystalline specimens including samples containing defects, under dynamical channelling conditions using an aberration corrected microscope. A ptychographic reconstruction method called Wigner distribution deconvolution (WDD) was implemented. Our experimental results and simulation results suggest that ptychography provides a readily interpretable phase image and great sensitivity for imaging light elements at atomic resolution in relatively thin crystalline materials.« less

Uniform electron gases. III. Low-density gases on three-dimensional spheres.

PubMed

Agboola, Davids; Knol, Anneke L; Gill, Peter M W; Loos, Pierre-François

2015-08-28

By combining variational Monte Carlo (VMC) and complete-basis-set limit Hartree-Fock (HF) calculations, we have obtained near-exact correlation energies for low-density same-spin electrons on a three-dimensional sphere (3-sphere), i.e., the surface of a four-dimensional ball. In the VMC calculations, we compare the efficacies of two types of one-electron basis functions for these strongly correlated systems and analyze the energy convergence with respect to the quality of the Jastrow factor. The HF calculations employ spherical Gaussian functions (SGFs) which are the curved-space analogs of Cartesian Gaussian functions. At low densities, the electrons become relatively localized into Wigner crystals, and the natural SGF centers are found by solving the Thomson problem (i.e., the minimum-energy arrangement of n point charges) on the 3-sphere for various values of n. We have found 11 special values of n whose Thomson sites are equivalent. Three of these are the vertices of four-dimensional Platonic solids - the hyper-tetrahedron (n = 5), the hyper-octahedron (n = 8), and the 24-cell (n = 24) - and a fourth is a highly symmetric structure (n = 13) which has not previously been reported. By calculating the harmonic frequencies of the electrons around their equilibrium positions, we also find the first-order vibrational corrections to the Thomson energy.

Eugene P. Wigner's Visionary Contributions to Generations-I through IV Fission Reactors

NASA Astrophysics Data System (ADS)

Carré, Frank

2014-09-01

Among Europe's greatest scientists who fled to Britain and America in the 1930s, Eugene P. Wigner made instrumental advances in reactor physics, reactor design and technology, and spent nuclear fuel processing for both purposes of developing atomic weapons during world-war II and nuclear power afterwards. Wigner who had training in chemical engineering and self-education in physics first gained recognition for his remarkable articles and books on applications of Group theory to Quantum mechanics, Solid state physics and other topics that opened new branches of Physics.

Evidence for a New Intermediate Phase in a Strongly Correlated 2D System near Wigner Crystallization

NASA Astrophysics Data System (ADS)

Gao, Xuan; Qiu, Richard; Goble, Nicholas; Serafin, Alex; Yin, Liang; Xia, Jian-Sheng; Sullivan, Neil; Pfeiffer, Loren; West, Ken

How the two dimensional (2D) quantum Wigner crystal (WC) transforms into the metallic liquid phase remains an outstanding problem in physics. In theories considering the 2D WC to liquid transition in the clean limit, it was suggested that a number of intermediate phases might exist. We have studied the transformation between the metallic fluid phase and the low magnetic field reentrant insulating phase (RIP) which was interpreted as due to the WC [Qiu et al., PRL 108, 106404 (2012)], in a strongly correlated 2D hole system in GaAs quantum well with large interaction parameter rs (~20-30) and high mobility. Instead of a sharp transition, we found that increasing density (or lowering rs) drives the RIP into a state where the incipient RIP coexists with Fermi liquid. This apparent mixture phase intermediate between Fermi liquid and WC also exhibits a non-trivial temperature dependent resistivity behavior which can be qualitatively understood by the reversed melting of WC in the mixture, in analogy to the Pomeranchuk effect in the solid-liquid mixture of Helium-3. X.G. thanks NSF (DMR-0906415) for supporting work at CWRU. Experiments at the NHMFL High B/T Facility were supported by NSF Grant 0654118 and the State of Florida. L.P. thanks the Gordon and Betty Moore Foundation and NSF MRSEC (DMR-0819860) for support.

Strong Correlation and Topological States in Orbital-Active Dirac Materials

NASA Astrophysics Data System (ADS)

Xu, Shenglong; Wu, Congjun

Two dimensional Dirac materials, starting with graphene, have drawn tremendous research interests in the past decade. Instead of focusing on the pz orbital as in graphene, we go a step further and study its two orbitals counterpart, namely the px and py orbitals on a honeycomb lattice. The model applies to both optical lattices and several solid state systems including organic material, fluoridated tin film, BiX/SBX (X=H.F.CI.Br). In the band structure, besides the well known Dirac points in the graphene band structure, the orbital degrees of freedom give rise to flat bands as well as quadratic band touching points. These new features provide an even wider playground for searching exotic states of matter. With help of mean field theory and functional renormalization group (FRG) method, we explore the effects of interaction on the system and investigate the consequential interesting states such as ferromagnetism, Wigner crystallization, quantum anomalous Hall states and f-wave superconductivity.

Melting of Wigner Crystal on Helium in Quasi-One-Dimensional Geometry

NASA Astrophysics Data System (ADS)

Ikegami, Hiroki; Akimoto, Hikota; Kono, Kimitoshi

2015-05-01

We discuss melting of a Wigner crystal formed on a free surface of superfluid He, in quasi-one-dimensional (Q1D) channels of width between 5 and 15 m. We reexamine our previous transport data (Ikegami et al. in Phys Rev B 82:201104(R), 2010), in particular, by estimating the number of electrons across the channel in a more accurate way with the aid of numerical calculations of distributions of the electrons in the channels. The results of reexamination indicate more convincingly that the melting of the Wigner crystal in the Q1D geometry is understood by the finite size effect on the Kosterlitz-Thouless-Halperin-Nelson-Young melting process. We also present technical details of the transport measurements of the electrons in a Q1D geometry, including a fabrication method of devices used for the transport measurements, numerical simulations of response of the devices, and a procedure for analyzing transport data.

Effect of boundary treatments on quantum transport current in the Green's function and Wigner distribution methods for a nano-scale DG-MOSFET

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jiang Haiyan; Department of Mathematics and Statistics, University of North Carolina at Charlotte, Charlotte, NC 28223-0001; Cai Wei

2010-06-20

In this paper, we conduct a study of quantum transport models for a two-dimensional nano-size double gate (DG) MOSFET using two approaches: non-equilibrium Green's function (NEGF) and Wigner distribution. Both methods are implemented in the framework of the mode space methodology where the electron confinements below the gates are pre-calculated to produce subbands along the vertical direction of the device while the transport along the horizontal channel direction is described by either approach. Each approach handles the open quantum system along the transport direction in a different manner. The NEGF treats the open boundaries with boundary self-energy defined by amore » Dirichlet to Neumann mapping, which ensures non-reflection at the device boundaries for electron waves leaving the quantum device active region. On the other hand, the Wigner equation method imposes an inflow boundary treatment for the Wigner distribution, which in contrast ensures non-reflection at the boundaries for free electron waves entering the device active region. In both cases the space-charge effect is accounted for by a self-consistent coupling with a Poisson equation. Our goals are to study how the device boundaries are treated in both transport models affects the current calculations, and to investigate the performance of both approaches in modeling the DG-MOSFET. Numerical results show mostly consistent quantum transport characteristics of the DG-MOSFET using both methods, though with higher transport current for the Wigner equation method, and also provide the current-voltage (I-V) curve dependence on various physical parameters such as the gate voltage and the oxide thickness.« less

Uniform electron gases. III. Low-density gases on three-dimensional spheres

DOE Office of Scientific and Technical Information (OSTI.GOV)

Agboola, Davids; Knol, Anneke L.; Gill, Peter M. W., E-mail: peter.gill@anu.edu.au

2015-08-28

By combining variational Monte Carlo (VMC) and complete-basis-set limit Hartree-Fock (HF) calculations, we have obtained near-exact correlation energies for low-density same-spin electrons on a three-dimensional sphere (3-sphere), i.e., the surface of a four-dimensional ball. In the VMC calculations, we compare the efficacies of two types of one-electron basis functions for these strongly correlated systems and analyze the energy convergence with respect to the quality of the Jastrow factor. The HF calculations employ spherical Gaussian functions (SGFs) which are the curved-space analogs of Cartesian Gaussian functions. At low densities, the electrons become relatively localized into Wigner crystals, and the natural SGFmore » centers are found by solving the Thomson problem (i.e., the minimum-energy arrangement of n point charges) on the 3-sphere for various values of n. We have found 11 special values of n whose Thomson sites are equivalent. Three of these are the vertices of four-dimensional Platonic solids — the hyper-tetrahedron (n = 5), the hyper-octahedron (n = 8), and the 24-cell (n = 24) — and a fourth is a highly symmetric structure (n = 13) which has not previously been reported. By calculating the harmonic frequencies of the electrons around their equilibrium positions, we also find the first-order vibrational corrections to the Thomson energy.« less

Three Dimensional Imaging of the Nucleon

NASA Astrophysics Data System (ADS)

More, Jai; Mukherjee, Asmita; Nair, Sreeraj

2018-05-01

We study the Wigner distributions of quarks and gluons in light-front dressed quark model using the overlap of light front wave functions (LFWFs). We take the target to be a dressed quark, this is a composite spin -1/2 state of quark dressed with a gluon. This state allows us to calculate the quark and gluon Wigner distributions analytically in terms of LFWFs using Hamiltonian perturbation theory. We analyze numerically the Wigner distributions of quark and gluon and report their nature in the contour plots. We use an improved numerical technique to remove the cutoff dependence of the Fourier transformed integral over \\varvec{Δ}_\\perp.

Exact and quasi-classical density matrix and Wigner functions for a particle in the box and half space

NASA Technical Reports Server (NTRS)

Akhundova, E. A.; Dodonov, V. V.; Manko, V. I.

1993-01-01

The exact expressions for density matrix and Wigner functions of quantum systems are known only in special cases. Corresponding Hamiltonians are quadratic forms of Euclidean coordinates and momenta. In this paper we consider the problem of one-dimensional free particle movement in the bounded region 0 is less than x is less than a (including the case a = infinity).

Correlation lengths of the wigner-crystal order in a two-dimensional electron system at high magnetic fields.

PubMed

Ye, P D; Engel, L W; Tsui, D C; Lewis, R M; Pfeiffer, L N; West, K

2002-10-21

The insulator terminating the fractional quantum Hall series at low Landau level filling nu is generally taken to be a pinned Wigner crystal (WC), and exhibits a microwave resonance that is interpreted as a WC pinning mode. For a high quality sample at several densities, n, we find maxima in resonance peak frequency, f(pk), vs magnetic field, B. L, the correlation length of WC order, is calculated from f(pk). For each n, L vs nu tends at low nu toward a line with positive intercept; the fit is accurate over as much as a factor of 5 range of nu. The linear behavior is interpreted as due to B compressing the electron wave functions, to alter the effective electron-impurity interaction.

Wigner-Seitz local-environment study of the high-T/sub c/ superconductors

DOE Office of Scientific and Technical Information (OSTI.GOV)

Melamud, M.; Bennett, L.H.; Watson, R.E.

The near-neighbor environments and the bonding of atoms in the high-T/sub c/ superconductors are studied using a Wigner-Seitz-cell contruction. Assuming metallic radii for the atoms, it is shown that the Ba, Y, and La atoms have large coordination numbers, implying a three-dimensional bonding scheme. The La-Cu-O type (approx. =40 K) and the Y-Ba-Cu-O type (approx. =90 K) superconductors both display the same bonding characteristics.

Quantum mechanics on phase space and the Coulomb potential

NASA Astrophysics Data System (ADS)

Campos, P.; Martins, M. G. R.; Vianna, J. D. M.

2017-04-01

Symplectic quantum mechanics (SMQ) makes possible to derive the Wigner function without the use of the Liouville-von Neumann equation. In this formulation of the quantum theory the Galilei Lie algebra is constructed using the Weyl (or star) product with Q ˆ = q ⋆ = q +iħ/2∂p , P ˆ = p ⋆ = p -iħ/2∂q, and the Schrödinger equation is rewritten in phase space; in consequence physical applications involving the Coulomb potential present some specific difficulties. Within this context, in order to treat the Schrödinger equation in phase space, a procedure based on the Levi-Civita (or Bohlin) transformation is presented and applied to two-dimensional (2D) hydrogen atom. Amplitudes of probability in phase space and the correspondent Wigner quasi-distribution functions are derived and discussed.

Wigner analysis of three dimensional pupil with finite lateral aperture

PubMed Central

Chen, Hsi-Hsun; Oh, Se Baek; Zhai, Xiaomin; Tsai, Jui-Chang; Cao, Liang-Cai; Barbastathis, George; Luo, Yuan

2015-01-01

A three dimensional (3D) pupil is an optical element, most commonly implemented on a volume hologram, that processes the incident optical field on a 3D fashion. Here we analyze the diffraction properties of a 3D pupil with finite lateral aperture in the 4-f imaging system configuration, using the Wigner Distribution Function (WDF) formulation. Since 3D imaging pupil is finite in both lateral and longitudinal directions, the WDF of the volume holographic 4-f imager theoretically predicts distinct Bragg diffraction patterns in phase space. These result in asymmetric profiles of diffracted coherent point spread function between degenerate diffraction and Bragg diffraction, elucidating the fundamental performance of volume holographic imaging. Experimental measurements are also presented, confirming the theoretical predictions. PMID:25836443

An embedding of the universal Askey-Wilson algebra into Uq (sl2) ⊗Uq (sl2) ⊗Uq (sl2)

NASA Astrophysics Data System (ADS)

Huang, Hau-Wen

2017-09-01

The Askey-Wilson algebras were used to interpret the algebraic structure hidden in the Racah-Wigner coefficients of the quantum algebra Uq (sl2). In this paper, we display an injection of a universal analog △q of Askey-Wilson algebras into Uq (sl2) ⊗Uq (sl2) ⊗Uq (sl2) behind the application. Moreover we establish the decomposition rules for 3-fold tensor products of irreducible Verma Uq (sl2)-modules and of finite-dimensional irreducible Uq (sl2)-modules into the direct sums of finite-dimensional irreducible △q-modules. As an application, we derive a formula for the Racah-Wigner coefficients of Uq (sl2).

Variational model for one-dimensional quantum magnets

NASA Astrophysics Data System (ADS)

Kudasov, Yu. B.; Kozabaranov, R. V.

2018-04-01

A new variational technique for investigation of the ground state and correlation functions in 1D quantum magnets is proposed. A spin Hamiltonian is reduced to a fermionic representation by the Jordan-Wigner transformation. The ground state is described by a new non-local trial wave function, and the total energy is calculated in an analytic form as a function of two variational parameters. This approach is demonstrated with an example of the XXZ-chain of spin-1/2 under a staggered magnetic field. Generalizations and applications of the variational technique for low-dimensional magnetic systems are discussed.

Wigner phase space distribution via classical adiabatic switching

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bose, Amartya; Makri, Nancy; Department of Physics, University of Illinois, 1110 W. Green Street, Urbana, Illinois 61801

2015-09-21

Evaluation of the Wigner phase space density for systems of many degrees of freedom presents an extremely demanding task because of the oscillatory nature of the Fourier-type integral. We propose a simple and efficient, approximate procedure for generating the Wigner distribution that avoids the computational difficulties associated with the Wigner transform. Starting from a suitable zeroth-order Hamiltonian, for which the Wigner density is available (either analytically or numerically), the phase space distribution is propagated in time via classical trajectories, while the perturbation is gradually switched on. According to the classical adiabatic theorem, each trajectory maintains a constant action if themore » perturbation is switched on infinitely slowly. We show that the adiabatic switching procedure produces the exact Wigner density for harmonic oscillator eigenstates and also for eigenstates of anharmonic Hamiltonians within the Wentzel-Kramers-Brillouin (WKB) approximation. We generalize the approach to finite temperature by introducing a density rescaling factor that depends on the energy of each trajectory. Time-dependent properties are obtained simply by continuing the integration of each trajectory under the full target Hamiltonian. Further, by construction, the generated approximate Wigner distribution is invariant under classical propagation, and thus, thermodynamic properties are strictly preserved. Numerical tests on one-dimensional and dissipative systems indicate that the method produces results in very good agreement with those obtained by full quantum mechanical methods over a wide temperature range. The method is simple and efficient, as it requires no input besides the force fields required for classical trajectory integration, and is ideal for use in quasiclassical trajectory calculations.« less

Quantitative Tomography for Continuous Variable Quantum Systems

NASA Astrophysics Data System (ADS)

Landon-Cardinal, Olivier; Govia, Luke C. G.; Clerk, Aashish A.

2018-03-01

We present a continuous variable tomography scheme that reconstructs the Husimi Q function (Wigner function) by Lagrange interpolation, using measurements of the Q function (Wigner function) at the Padua points, conjectured to be optimal sampling points for two dimensional reconstruction. Our approach drastically reduces the number of measurements required compared to using equidistant points on a regular grid, although reanalysis of such experiments is possible. The reconstruction algorithm produces a reconstructed function with exponentially decreasing error and quasilinear runtime in the number of Padua points. Moreover, using the interpolating polynomial of the Q function, we present a technique to directly estimate the density matrix elements of the continuous variable state, with only a linear propagation of input measurement error. Furthermore, we derive a state-independent analytical bound on this error, such that our estimate of the density matrix is accompanied by a measure of its uncertainty.

Pressure-temperature phase diagram of a charge-ordered organic conductor studied by C13 NMR

NASA Astrophysics Data System (ADS)

Itou, T.; Miyagawa, K.; Nakamura, J.; Kanoda, K.; Hiraki, K.; Takahashi, T.

2014-07-01

We performed C13 NMR measurements on the quasi-one-dimensional (Q1D) charge-ordered system (DI-DCNQI)2Ag under ambient and applied pressure to clarify the pressure-temperature phase diagram. For pressures up to 15 kbar, the NMR spectra exhibit complicated splitting at low temperatures, indicating a "generalized 3D Wigner crystal" state. In this pressure region, we find that increased pressure causes a decrease in the charge disproportionation ratio, along with a decrease in the transition temperature of the generalized 3D Wigner crystal. In the high-pressure region, near 20 kbar, where a 1D confined liquid crosses over to a 3D Fermi liquid at high temperatures, the ground state is replaced by a nonmagnetic insulating state that is qualitatively different from the generalized 3D Wigner crystal.

Dissipative quantum transport in silicon nanowires based on Wigner transport equation

NASA Astrophysics Data System (ADS)

Barraud, Sylvain

2011-11-01

In this work, we present a one-dimensional model of quantum electron transport for silicon nanowire transistor that makes use of the Wigner function formalism and that takes into account the carrier scattering. Effect of scattering on the current-voltage (I-V) characteristics is assessed using both the relaxation time approximation and the Boltzmann collision operator. Similarly to the classical transport theory, the scattering mechanisms are included in the Wigner formulation through the addition of a collision term in the Liouville equation. As compared to the relaxation time, the Boltzmann collision operator approach is considered to be more realistic because it provides a better description of the scattering events. Within the Fermi golden rule approximation, the standard collision term is described for both acoustic phonon and surface-roughness interactions. It is introduced in the discretized version of the Liouville equation to obtain the Wigner distribution function and the current density. The model is then applied to study the impact of each scattering mechanism on short-channel electrical performance of silicon nanowire transistors for different gate lengths and nanowire widths.

Time-varying higher order spectra

NASA Astrophysics Data System (ADS)

Boashash, Boualem; O'Shea, Peter

1991-12-01

A general solution for the problem of time-frequency signal representation of nonlinear FM signals is provided, based on a generalization of the Wigner-Ville distribution. The Wigner- Ville distribution (WVD) is a second order time-frequency representation. That is, it is able to give ideal energy concentration for quadratic phase signals and its ensemble average is a second order time-varying spectrum. The same holds for Cohen's class of time-frequency distributions, which are smoothed versions of the WVD. The WVD may be extended so as to achieve ideal energy concentration for higher order phase laws, and such that the expectation is a time-varying higher order spectrum. The usefulness of these generalized Wigner-Ville distributions (GWVD) is twofold. Firstly, because they achieve ideal energy concentration for polynomial phase signals, they may be used for optimal instantaneous frequency estimation. Second, they are useful for discriminating between nonstationary processes of differing higher order moments. In the same way that the WVD is generalized, we generalize Cohen's class of TFDs by defining a class of generalized time-frequency distributions (GTFDs) obtained by a two dimensional smoothing of the GWVD. Another results derived from this approach is a method based on higher order spectra which allows the separation of cross-terms and auto- terms in the WVD.

Wigner tomography of multispin quantum states

NASA Astrophysics Data System (ADS)

Leiner, David; Zeier, Robert; Glaser, Steffen J.

2017-12-01

We study the tomography of multispin quantum states in the context of finite-dimensional Wigner representations. An arbitrary operator can be completely characterized and visualized using multiple shapes assembled from linear combinations of spherical harmonics [A. Garon, R. Zeier, and S. J. Glaser, Phys. Rev. A 91, 042122 (2015), 10.1103/PhysRevA.91.042122]. We develop a general methodology to experimentally recover these shapes by measuring expectation values of rotated axial spherical tensor operators and provide an interpretation in terms of fictitious multipole potentials. Our approach is experimentally demonstrated for quantum systems consisting of up to three spins using nuclear magnetic resonance spectroscopy.

Anomalous Quasiparticle Reflection from the Surface of a ^{3}He-^{4}He Dilute Solution.

PubMed

Ikegami, Hiroki; Kim, Kitak; Sato, Daisuke; Kono, Kimitoshi; Choi, Hyoungsoon; Monarkha, Yuriy P

2017-11-10

A free surface of a dilute ^{3}He-^{4}He liquid mixture is a unique system where two Fermi liquids with distinct dimensions coexist: a three-dimensional (3D) ^{3}He Fermi liquid in the bulk and a two-dimensional (2D) ^{3}He Fermi liquid at the surface. To investigate a novel effect generated by the interaction between the two Fermi liquids, the mobility of a Wigner crystal of electrons formed on the free surface of the mixture is studied. An anomalous enhancement of the mobility, compared with the case where the 3D and 2D systems do not interact with each other, is observed. The enhancement is explained by the nontrivial reflection of 3D quasiparticles from the surface covered with the 2D ^{3}He system.

Nonrelativistic limits of colored gravity in three dimensions

NASA Astrophysics Data System (ADS)

Joung, Euihun; Li, Wenliang

2018-05-01

The three-dimensional nonrelativistic isometry algebras, namely Galilei and Newton-Hooke algebras, are known to admit double central extensions, which allows for nondegenerate bilinear forms hence for action principles through Chern-Simons formulation. In three-dimensional colored gravity, the same central extension helps the theory evade the multigraviton no-go theorems by enlarging the color-decorated isometry algebra. We investigate the nonrelativistic limits of three-dimensional colored gravity in terms of generalized İnönü-Wigner contractions.

Pauli structures arising from confined particles interacting via a statistical potential

NASA Astrophysics Data System (ADS)

Batle, Josep; Ciftja, Orion; Farouk, Ahmed; Alkhambashi, Majid; Abdalla, Soliman

2017-09-01

There have been suggestions that the Pauli exclusion principle alone can lead a non-interacting (free) system of identical fermions to form crystalline structures dubbed Pauli crystals. Single-shot imaging experiments for the case of ultra-cold systems of free spin-polarized fermionic atoms in a two-dimensional harmonic trap appear to show geometric arrangements that cannot be characterized as Wigner crystals. This work explores this idea and considers a well-known approach that enables one to treat a quantum system of free fermions as a system of classical particles interacting with a statistical interaction potential. The model under consideration, though classical in nature, incorporates the quantum statistics by endowing the classical particles with an effective interaction potential. The reasonable expectation is that possible Pauli crystal features seen in experiments may manifest in this model that captures the correct quantum statistics as a first order correction. We use the Monte Carlo simulated annealing method to obtain the most stable configurations of finite two-dimensional systems of confined particles that interact with an appropriate statistical repulsion potential. We consider both an isotropic harmonic and a hard-wall confinement potential. Despite minor differences, the most stable configurations observed in our model correspond to the reported Pauli crystals in single-shot imaging experiments of free spin-polarized fermions in a harmonic trap. The crystalline configurations observed appear to be different from the expected classical Wigner crystal structures that would emerge should the confined classical particles had interacted with a pair-wise Coulomb repulsion.

Path-integral approach to the Wigner-Kirkwood expansion.

PubMed

Jizba, Petr; Zatloukal, Václav

2014-01-01

We study the high-temperature behavior of quantum-mechanical path integrals. Starting from the Feynman-Kac formula, we derive a functional representation of the Wigner-Kirkwood perturbation expansion for quantum Boltzmann densities. As shown by its applications to different potentials, the presented expansion turns out to be quite efficient in generating analytic form of the higher-order expansion coefficients. To put some flesh on the bare bones, we apply the expansion to obtain basic thermodynamic functions of the one-dimensional anharmonic oscillator. Further salient issues, such as generalization to the Bloch density matrix and comparison with the more customary world-line formulation, are discussed.

Applicability, Indispensability, and Underdetermination: Puzzling Over Wigner's `Unreasonable Effectiveness of Mathematics'

NASA Astrophysics Data System (ADS)

Gelfert, Axel

2014-05-01

In his influential 1960 paper `The Unreasonable Effectiveness of Mathematics in the Natural Sciences', Eugene P. Wigner raises the question of why something that was developed without concern for empirical facts—mathematics—should turn out to be so powerful in explaining facts about the natural world. Recent philosophy of science has developed `Wigner's puzzle' in two different directions: First, in relation to the supposed indispensability of mathematical facts to particular scientific explanations and, secondly, in connection with the idea that aesthetic criteria track theoretical desiderata such as empirical success. An important aspect of Wigner's article has, however, been overlooked in these debates: his worries about the underdetermination of physical theories by mathematical frameworks. The present paper argues that, by restoring this aspect of Wigner's argument to its proper place, Wigner's puzzle may become an instructive case study for the teaching of core issues in the philosophy of science and its history.

Bath-induced correlations in an infinite-dimensional Hilbert space

NASA Astrophysics Data System (ADS)

Nizama, Marco; Cáceres, Manuel O.

2017-09-01

Quantum correlations between two free spinless dissipative distinguishable particles (interacting with a thermal bath) are studied analytically using the quantum master equation and tools of quantum information. Bath-induced coherence and correlations in an infinite-dimensional Hilbert space are shown. We show that for temperature T> 0 the time-evolution of the reduced density matrix cannot be written as the direct product of two independent particles. We have found a time-scale that characterizes the time when the bath-induced coherence is maximum before being wiped out by dissipation (purity, relative entropy, spatial dispersion, and mirror correlations are studied). The Wigner function associated to the Wannier lattice (where the dissipative quantum walks move) is studied as an indirect measure of the induced correlations among particles. We have supported the quantum character of the correlations by analyzing the geometric quantum discord.

Optimally cloned binary coherent states

NASA Astrophysics Data System (ADS)

Müller, C. R.; Leuchs, G.; Marquardt, Ch.; Andersen, U. L.

2017-10-01

Binary coherent state alphabets can be represented in a two-dimensional Hilbert space. We capitalize this formal connection between the otherwise distinct domains of qubits and continuous variable states to map binary phase-shift keyed coherent states onto the Bloch sphere and to derive their quantum-optimal clones. We analyze the Wigner function and the cumulants of the clones, and we conclude that optimal cloning of binary coherent states requires a nonlinearity above second order. We propose several practical and near-optimal cloning schemes and compare their cloning fidelity to the optimal cloner.

In situ realization of particlelike scattering states in a microwave cavity

NASA Astrophysics Data System (ADS)

Böhm, Julian; Brandstötter, Andre; Ambichl, Philipp; Rotter, Stefan; Kuhl, Ulrich

2018-02-01

We realize scattering states in a lossy and chaotic two-dimensional microwave cavity which follow bundles of classical particle trajectories. To generate such particlelike scattering states, we measure the system's complex transmission matrix and apply an adapted Wigner-Smith time-delay formalism to it. The necessary shaping of the incident wave is achieved in situ using phase- and amplitude-regulated microwave antennas. Our experimental findings pave the way for establishing spatially confined communication channels that avoid possible intruders or obstacles in wave-based communication systems.

New Interpretation of the Wigner Function

NASA Technical Reports Server (NTRS)

Daboul, Jamil

1996-01-01

I define a two-sided or forward-backward propagator for the pseudo-diffusion equation of the 'squeezed' Q function. This propagator leads to squeezing in one of the phase-space variables and anti-squeezing in the other. By noting that the Q function is related to the Wigner function by a special case of the above propagator, I am led to a new interpretation of the Wigner function.

Equivalence between contextuality and negativity of the Wigner function for qudits

NASA Astrophysics Data System (ADS)

Delfosse, Nicolas; Okay, Cihan; Bermejo-Vega, Juan; Browne, Dan E.; Raussendorf, Robert

2017-12-01

Understanding what distinguishes quantum mechanics from classical mechanics is crucial for quantum information processing applications. In this work, we consider two notions of non-classicality for quantum systems, negativity of the Wigner function and contextuality for Pauli measurements. We prove that these two notions are equivalent for multi-qudit systems with odd local dimension. For a single qudit, the equivalence breaks down. We show that there exist single qudit states that admit a non-contextual hidden variable model description and whose Wigner functions are negative.

Measurement of complete and continuous Wigner functions for discrete atomic systems

NASA Astrophysics Data System (ADS)

Tian, Yali; Wang, Zhihui; Zhang, Pengfei; Li, Gang; Li, Jie; Zhang, Tiancai

2018-01-01

We measure complete and continuous Wigner functions of a two-level cesium atom in both a nearly pure state and highly mixed states. We apply the method [T. Tilma et al., Phys. Rev. Lett. 117, 180401 (2016), 10.1103/PhysRevLett.117.180401] of strictly constructing continuous Wigner functions for qubit or spin systems. We find that the Wigner function of all pure states of a qubit has negative regions and the negativity completely vanishes when the purity of an arbitrary mixed state is less than 2/3 . We experimentally demonstrate these findings using a single cesium atom confined in an optical dipole trap, which undergoes a nearly pure dephasing process. Our method can be applied straightforwardly to multi-atom systems for measuring the Wigner function of their collective spin state.

Combining neural networks and signed particles to simulate quantum systems more efficiently

NASA Astrophysics Data System (ADS)

Sellier, Jean Michel

2018-04-01

Recently a new formulation of quantum mechanics has been suggested which describes systems by means of ensembles of classical particles provided with a sign. This novel approach mainly consists of two steps: the computation of the Wigner kernel, a multi-dimensional function describing the effects of the potential over the system, and the field-less evolution of the particles which eventually create new signed particles in the process. Although this method has proved to be extremely advantageous in terms of computational resources - as a matter of fact it is able to simulate in a time-dependent fashion many-body systems on relatively small machines - the Wigner kernel can represent the bottleneck of simulations of certain systems. Moreover, storing the kernel can be another issue as the amount of memory needed is cursed by the dimensionality of the system. In this work, we introduce a new technique which drastically reduces the computation time and memory requirement to simulate time-dependent quantum systems which is based on the use of an appropriately tailored neural network combined with the signed particle formalism. In particular, the suggested neural network is able to compute efficiently and reliably the Wigner kernel without any training as its entire set of weights and biases is specified by analytical formulas. As a consequence, the amount of memory for quantum simulations radically drops since the kernel does not need to be stored anymore as it is now computed by the neural network itself, only on the cells of the (discretized) phase-space which are occupied by particles. As its is clearly shown in the final part of this paper, not only this novel approach drastically reduces the computational time, it also remains accurate. The author believes this work opens the way towards effective design of quantum devices, with incredible practical implications.

Geometrical comparison of two protein structures using Wigner-D functions.

PubMed

Saberi Fathi, S M; White, Diana T; Tuszynski, Jack A

2014-10-01

In this article, we develop a quantitative comparison method for two arbitrary protein structures. This method uses a root-mean-square deviation characterization and employs a series expansion of the protein's shape function in terms of the Wigner-D functions to define a new criterion, which is called a "similarity value." We further demonstrate that the expansion coefficients for the shape function obtained with the help of the Wigner-D functions correspond to structure factors. Our method addresses the common problem of comparing two proteins with different numbers of atoms. We illustrate it with a worked example. © 2014 Wiley Periodicals, Inc.

Compressive sensing for sparse time-frequency representation of nonstationary signals in the presence of impulsive noise

NASA Astrophysics Data System (ADS)

Orović, Irena; Stanković, Srdjan; Amin, Moeness

2013-05-01

A modified robust two-dimensional compressive sensing algorithm for reconstruction of sparse time-frequency representation (TFR) is proposed. The ambiguity function domain is assumed to be the domain of observations. The two-dimensional Fourier bases are used to linearly relate the observations to the sparse TFR, in lieu of the Wigner distribution. We assume that a set of available samples in the ambiguity domain is heavily corrupted by an impulsive type of noise. Consequently, the problem of sparse TFR reconstruction cannot be tackled using standard compressive sensing optimization algorithms. We introduce a two-dimensional L-statistics based modification into the transform domain representation. It provides suitable initial conditions that will produce efficient convergence of the reconstruction algorithm. This approach applies sorting and weighting operations to discard an expected amount of samples corrupted by noise. The remaining samples serve as observations used in sparse reconstruction of the time-frequency signal representation. The efficiency of the proposed approach is demonstrated on numerical examples that comprise both cases of monocomponent and multicomponent signals.

Weak values of a quantum observable and the cross-Wigner distribution.

PubMed

de Gosson, Maurice A; de Gosson, Serge M

2012-01-09

We study the weak values of a quantum observable from the point of view of the Wigner formalism. The main actor here is the cross-Wigner transform of two functions, which is in disguise the cross-ambiguity function familiar from radar theory and time-frequency analysis. It allows us to express weak values using a complex probability distribution. We suggest that our approach seems to confirm that the weak value of an observable is, as conjectured by several authors, due to the interference of two wavefunctions, one coming from the past, and the other from the future.

Wigner functions for nonclassical states of a collection of two-level atoms

NASA Technical Reports Server (NTRS)

Agarwal, G. S.; Dowling, Jonathan P.; Schleich, Wolfgang P.

1993-01-01

The general theory of atomic angular momentum states is used to derive the Wigner distribution function for atomic angular momentum number states, coherent states, and squeezed states. These Wigner functions W(theta,phi) are represented as a pseudo-probability distribution in spherical coordinates theta and phi on the surface of a sphere of radius the square root of j(j +1) where j is the total angular momentum.

Physics of the Lorentz Group

NASA Astrophysics Data System (ADS)

Başkal, Sibel

2015-11-01

This book explains the Lorentz mathematical group in a language familiar to physicists. While the three-dimensional rotation group is one of the standard mathematical tools in physics, the Lorentz group of the four-dimensional Minkowski space is still very strange to most present-day physicists. It plays an essential role in understanding particles moving at close to light speed and is becoming the essential language for quantum optics, classical optics, and information science. The book is based on papers and books published by the authors on the representations of the Lorentz group based on harmonic oscillators and their applications to high-energy physics and to Wigner functions applicable to quantum optics. It also covers the two-by-two representations of the Lorentz group applicable to ray optics, including cavity, multilayer and lens optics, as well as representations of the Lorentz group applicable to Stokes parameters and the Poincaré sphere on polarization optics.

Spin-dependent analysis of two-dimensional electron liquids

NASA Astrophysics Data System (ADS)

Bulutay, C.; Tanatar, B.

2002-05-01

Two-dimensional electron liquid (2D EL) at full Fermi degeneracy is revisited, giving special attention to the spin-polarization effects. First, we extend the recently proposed classical-map hypernetted-chain (CHNC) technique to the 2D EL, while preserving the simplicity of the original proposal. An efficient implementation of CHNC is given utilizing Lado's quadrature expressions for the isotropic Fourier transforms. Our results indicate that the paramagnetic phase stays to be the ground state until the Wigner crystallization density, even though the energy separation with the ferromagnetic and other partially polarized states become minute. We analyze compressibility and spin stiffness variations with respect to density and spin polarization, the latter being overlooked until now. Spin-dependent static structure factor and pair-distribution functions are computed; agreement with the available quantum Monte Carlo data persists even in the strong-coupling regime of the 2D EL.

Complexes of dipolar excitons in layered quasi-two-dimensional nanostructures

NASA Astrophysics Data System (ADS)

Bondarev, Igor V.; Vladimirova, Maria R.

2018-04-01

We discuss neutral and charged complexes (biexcitons and trions) formed by indirect excitons in layered quasi-two-dimensional semiconductor heterostructures. Indirect excitons—long-lived neutral Coulomb-bound pairs of electrons and holes of different layers—have been known for semiconductor coupled quantum wells and have recently been reported for van der Waals heterostructures such as double bilayer graphene and transition-metal dichalcogenides. Using the configuration space approach, we derive the analytical expressions for the trion and biexciton binding energies as a function of interlayer distance. The method captures essential kinematics of complex formation to reveal significant binding energies, up to a few tens of meV for typical interlayer distances ˜3 -5 Å , with the trion binding energy always being greater than that of the biexciton. Our results can contribute to the understanding of more complex many-body phenomena such as exciton Bose-Einstein condensation and Wigner-like electron-hole crystallization in layered semiconductor heterostructures.

Direct measurement of the biphoton Wigner function through two-photon interference

PubMed Central

Douce, T.; Eckstein, A.; Walborn, S. P.; Khoury, A. Z.; Ducci, S.; Keller, A.; Coudreau, T.; Milman, P.

2013-01-01

The Hong-Ou-Mandel (HOM) experiment was a benchmark in quantum optics, evidencing the non–classical nature of photon pairs, later generalized to quantum systems with either bosonic or fermionic statistics. We show that a simple modification in the well-known and widely used HOM experiment provides the direct measurement of the Wigner function. We apply our results to one of the most reliable quantum systems, consisting of biphotons generated by parametric down conversion. A consequence of our results is that a negative value of the Wigner function is a sufficient condition for non-gaussian entanglement between two photons. In the general case, the Wigner function provides all the required information to infer entanglement using well known necessary and sufficient criteria. The present work offers a new vision of the HOM experiment that further develops its possibilities to realize fundamental tests of quantum mechanics using simple optical set-ups. PMID:24346262

Signatures of chaos in the Brillouin zone.

PubMed

Barr, Aaron; Barr, Ariel; Porter, Max D; Reichl, Linda E

2017-10-01

When the classical dynamics of a particle in a finite two-dimensional billiard undergoes a transition to chaos, the quantum dynamics of the particle also shows manifestations of chaos in the form of scarring of wave functions and changes in energy level spacing distributions. If we "tile" an infinite plane with such billiards, we find that the Bloch states on the lattice undergo avoided crossings, energy level spacing statistics change from Poisson-like to Wigner-like, and energy sheets of the Brillouin zone begin to "mix" as the classical dynamics of the billiard changes from regular to chaotic behavior.

Signal analysis by means of time-frequency (Wigner-type) distributions -- Applications to sonar and radar echoes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gaunaurd, G.; Strifors, H.C.

1996-09-01

Time series data have been traditionally analyzed in either the time or the frequency domains. For signals with a time-varying frequency content, the combined time-frequency (TF) representations, based on the Cohen class of (generalized) Wigner distributions (WD`s) offer a powerful analysis tool. Using them, it is possible to: (1) trace the time-evolution of the resonance features usually present in a standard sonar cross section (SCS), or in a radar cross section (RCS) and (2) extract target information that may be difficult to even notice in an ordinary SCS or RCS. After a brief review of the fundamental properties of themore » WD, the authors discuss ways to reduce or suppress the cross term interference that appears in the WD of multicomponent systems. These points are illustrated with a variety of three-dimensional (3-D) plots of Wigner and pseudo-Wigner distributions (PWD), in which the strength of the distribution is depicted as the height of a Wigner surface with height scales measured by various color shades or pseudocolors. The authors also review studies they have made of the echoes returned by conducting or dielectric targets in the atmosphere, when they are illuminated by broadband radar pings. A TF domain analysis of these impulse radar returns demonstrates their superior informative content. These plots allow the identification of targets in an easier and clearer fashion than by the conventional RCS of narrowband systems. The authors show computed and measured plots of WD and PWD of various types of aircraft to illustrate the classification advantages of the approach at any aspect angle. They also show analogous results for metallic objects buried underground, in dielectric media, at various depths.« less

Simple procedure for phase-space measurement and entanglement validation

NASA Astrophysics Data System (ADS)

Rundle, R. P.; Mills, P. W.; Tilma, Todd; Samson, J. H.; Everitt, M. J.

2017-08-01

It has recently been shown that it is possible to represent the complete quantum state of any system as a phase-space quasiprobability distribution (Wigner function) [Phys. Rev. Lett. 117, 180401 (2016), 10.1103/PhysRevLett.117.180401]. Such functions take the form of expectation values of an observable that has a direct analogy to displaced parity operators. In this work we give a procedure for the measurement of the Wigner function that should be applicable to any quantum system. We have applied our procedure to IBM's Quantum Experience five-qubit quantum processor to demonstrate that we can measure and generate the Wigner functions of two different Bell states as well as the five-qubit Greenberger-Horne-Zeilinger state. Because Wigner functions for spin systems are not unique, we define, compare, and contrast two distinct examples. We show how the use of these Wigner functions leads to an optimal method for quantum state analysis especially in the situation where specific characteristic features are of particular interest (such as for spin Schrödinger cat states). Furthermore we show that this analysis leads to straightforward, and potentially very efficient, entanglement test and state characterization methods.

Graded-index fibers, Wigner-distribution functions, and the fractional Fourier transform.

PubMed

Mendlovic, D; Ozaktas, H M; Lohmann, A W

1994-09-10

Two definitions of a fractional Fourier transform have been proposed previously. One is based on the propagation of a wave field through a graded-index medium, and the other is based on rotating a function's Wigner distribution. It is shown that both definitions are equivalent. An important result of this equivalency is that the Wigner distribution of a wave field rotates as the wave field propagates through a quadratic graded-index medium. The relation with ray-optics phase space is discussed.

Sequential measurement of conjugate variables as an alternative quantum state tomography.

PubMed

Di Lorenzo, Antonio

2013-01-04

It is shown how it is possible to reconstruct the initial state of a one-dimensional system by sequentially measuring two conjugate variables. The procedure relies on the quasicharacteristic function, the Fourier transform of the Wigner quasiprobability. The proper characteristic function obtained by Fourier transforming the experimentally accessible joint probability of observing "position" then "momentum" (or vice versa) can be expressed as a product of the quasicharacteristic function of the two detectors and that unknown of the quantum system. This allows state reconstruction through the sequence (1) data collection, (2) Fourier transform, (3) algebraic operation, and (4) inverse Fourier transform. The strength of the measurement should be intermediate for the procedure to work.

Modeling some two-dimensional relativistic phenomena using an educational interactive graphics software

NASA Astrophysics Data System (ADS)

Sastry, G. P.; Ravuri, Tushar R.

1990-11-01

This paper describes several relativistic phenomena in two spatial dimensions that can be modeled using the collision program of Spacetime Software. These include the familiar aberration, the Doppler effect, the headlight effect, and the invariance of the speed of light in vacuum, in addition to the rather unfamiliar effects like the dragging of light in a moving medium, reflection at moving mirrors, Wigner rotation of noncommuting boosts, and relativistic rotation of shrinking and expanding rods. All these phenomena are exhibited by tracings of composite computer printouts of the collision movie. It is concluded that an interactive educational graphics software with pleasing visuals can have considerable investigative power packed within it.

Modulational Instability of Cylindrical and Spherical NLS Equations. Statistical Approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grecu, A. T.; Grecu, D.; Visinescu, Anca

2010-01-21

The modulational (Benjamin-Feir) instability for cylindrical and spherical NLS equations (c/s NLS equations) is studied using a statistical approach (SAMI). A kinetic equation for a two-point correlation function is written and analyzed using the Wigner-Moyal transform. The linear stability of the Fourier transform of the two-point correlation function is studied and an implicit integral form for the dispersion relation is found. This is solved for different expressions of the initial spectrum (delta-spectrum, Lorentzian, Gaussian), and in the case of a Lorentzian spectrum the total growth of the instability is calculated. The similarities and differences with the usual one-dimensional NLS equationmore » are emphasized.« less

Two-dimensional solid-phase extraction strategy for the selective enrichment of aminoglycosides in milk.

PubMed

Shen, Aijin; Wei, Jie; Yan, Jingyu; Jin, Gaowa; Ding, Junjie; Yang, Bingcheng; Guo, Zhimou; Zhang, Feifang; Liang, Xinmiao

2017-03-01

An orthogonal two-dimensional solid-phase extraction strategy was established for the selective enrichment of three aminoglycosides including spectinomycin, streptomycin, and dihydrostreptomycin in milk. A reversed-phase liquid chromatography material (C 18 ) and a weak cation-exchange material (TGA) were integrated in a single solid-phase extraction cartridge. The feasibility of two-dimensional clean-up procedure that experienced two-step adsorption, two-step rinsing, and two-step elution was systematically investigated. Based on the orthogonality of reversed-phase and weak cation-exchange procedures, the two-dimensional solid-phase extraction strategy could minimize the interference from the hydrophobic matrix existing in traditional reversed-phase solid-phase extraction. In addition, high ionic strength in the extracts could be effectively removed before the second dimension of weak cation-exchange solid-phase extraction. Combined with liquid chromatography and tandem mass spectrometry, the optimized procedure was validated according to the European Union Commission directive 2002/657/EC. A good performance was achieved in terms of linearity, recovery, precision, decision limit, and detection capability in milk. Finally, the optimized two-dimensional clean-up procedure incorporated with liquid chromatography and tandem mass spectrometry was successfully applied to the rapid monitoring of aminoglycoside residues in milk. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Ground-state properties of anyons in a one-dimensional lattice

NASA Astrophysics Data System (ADS)

Tang, Guixin; Eggert, Sebastian; Pelster, Axel

2015-12-01

Using the Anyon-Hubbard Hamiltonian, we analyze the ground-state properties of anyons in a one-dimensional lattice. To this end we map the hopping dynamics of correlated anyons to an occupation-dependent hopping Bose-Hubbard model using the fractional Jordan-Wigner transformation. In particular, we calculate the quasi-momentum distribution of anyons, which interpolates between Bose-Einstein and Fermi-Dirac statistics. Analytically, we apply a modified Gutzwiller mean-field approach, which goes beyond a classical one by including the influence of the fractional phase of anyons within the many-body wavefunction. Numerically, we use the density-matrix renormalization group by relying on the ansatz of matrix product states. As a result it turns out that the anyonic quasi-momentum distribution reveals both a peak-shift and an asymmetry which mainly originates from the nonlocal string property. In addition, we determine the corresponding quasi-momentum distribution of the Jordan-Wigner transformed bosons, where, in contrast to the hard-core case, we also observe an asymmetry for the soft-core case, which strongly depends on the particle number density.

Positive Wigner functions render classical simulation of quantum computation efficient.

PubMed

Mari, A; Eisert, J

2012-12-07

We show that quantum circuits where the initial state and all the following quantum operations can be represented by positive Wigner functions can be classically efficiently simulated. This is true both for continuous-variable as well as discrete variable systems in odd prime dimensions, two cases which will be treated on entirely the same footing. Noting the fact that Clifford and Gaussian operations preserve the positivity of the Wigner function, our result generalizes the Gottesman-Knill theorem. Our algorithm provides a way of sampling from the output distribution of a computation or a simulation, including the efficient sampling from an approximate output distribution in the case of sampling imperfections for initial states, gates, or measurements. In this sense, this work highlights the role of the positive Wigner function as separating classically efficiently simulable systems from those that are potentially universal for quantum computing and simulation, and it emphasizes the role of negativity of the Wigner function as a computational resource.

EMD-WVD time-frequency distribution for analysis of multi-component signals

NASA Astrophysics Data System (ADS)

Chai, Yunzi; Zhang, Xudong

2016-10-01

Time-frequency distribution (TFD) is two-dimensional function that indicates the time-varying frequency content of one-dimensional signals. And The Wigner-Ville distribution (WVD) is an important and effective time-frequency analysis method. The WVD can efficiently show the characteristic of a mono-component signal. However, a major drawback is the extra cross-terms when multi-component signals are analyzed by WVD. In order to eliminating the cross-terms, we decompose signals into single frequency components - Intrinsic Mode Function (IMF) - by using the Empirical Mode decomposition (EMD) first, then use WVD to analyze each single IMF. In this paper, we define this new time-frequency distribution as EMD-WVD. And the experiment results show that the proposed time-frequency method can solve the cross-terms problem effectively and improve the accuracy of WVD time-frequency analysis.

Particle statistics and lossy dynamics of ultracold atoms in optical lattices

NASA Astrophysics Data System (ADS)

Yago Malo, J.; van Nieuwenburg, E. P. L.; Fischer, M. H.; Daley, A. J.

2018-05-01

Experimental control over ultracold quantum gases has made it possible to investigate low-dimensional systems of both bosonic and fermionic atoms. In closed one-dimensional systems there are many similarities in the dynamics of local quantities for spinless fermions and strongly interacting "hard-core" bosons, which on a lattice can be formalized via a Jordan-Wigner transformation. In this study, we analyze the similarities and differences for spinless fermions and hard-core bosons on a lattice in the presence of particle loss. The removal of a single fermion causes differences in local quantities compared with the bosonic case because of the different particle exchange symmetry in the two cases. We identify deterministic and probabilistic signatures of these dynamics in terms of local particle density, which could be measured in ongoing experiments with quantum gas microscopes.

The many-body Wigner Monte Carlo method for time-dependent ab-initio quantum simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sellier, J.M., E-mail: jeanmichel.sellier@parallel.bas.bg; Dimov, I.

2014-09-15

The aim of ab-initio approaches is the simulation of many-body quantum systems from the first principles of quantum mechanics. These methods are traditionally based on the many-body Schrödinger equation which represents an incredible mathematical challenge. In this paper, we introduce the many-body Wigner Monte Carlo method in the context of distinguishable particles and in the absence of spin-dependent effects. Despite these restrictions, the method has several advantages. First of all, the Wigner formalism is intuitive, as it is based on the concept of a quasi-distribution function. Secondly, the Monte Carlo numerical approach allows scalability on parallel machines that is practicallymore » unachievable by means of other techniques based on finite difference or finite element methods. Finally, this method allows time-dependent ab-initio simulations of strongly correlated quantum systems. In order to validate our many-body Wigner Monte Carlo method, as a case study we simulate a relatively simple system consisting of two particles in several different situations. We first start from two non-interacting free Gaussian wave packets. We, then, proceed with the inclusion of an external potential barrier, and we conclude by simulating two entangled (i.e. correlated) particles. The results show how, in the case of negligible spin-dependent effects, the many-body Wigner Monte Carlo method provides an efficient and reliable tool to study the time-dependent evolution of quantum systems composed of distinguishable particles.« less

Wigner functions defined with Laplace transform kernels.

PubMed

Oh, Se Baek; Petruccelli, Jonathan C; Tian, Lei; Barbastathis, George

2011-10-24

We propose a new Wigner-type phase-space function using Laplace transform kernels--Laplace kernel Wigner function. Whereas momentum variables are real in the traditional Wigner function, the Laplace kernel Wigner function may have complex momentum variables. Due to the property of the Laplace transform, a broader range of signals can be represented in complex phase-space. We show that the Laplace kernel Wigner function exhibits similar properties in the marginals as the traditional Wigner function. As an example, we use the Laplace kernel Wigner function to analyze evanescent waves supported by surface plasmon polariton. © 2011 Optical Society of America

Two-Dimensional Optical Processing Of One-Dimensional Acoustic Data

NASA Astrophysics Data System (ADS)

Szu, Harold H.

1982-10-01

The concept of carrier-mean-frequency-selective convolution is introduced to solve the undersea problem of passive acoustic surveillance (PAS) and compared with the conventional notion of difference-frequency Doppler-corrected correlation. The former results in the cross-Wigner distribution function (WD), and the latter results in the cross-ambiguity function (AF). When the persistent time of a sound emitter is more important than the characteristic tone of the sound emitter, WD will be more useful than AF for PAS activity detection, and vice versa. Their mutual relationships with the instantaneous power spectrum (IPS) show the importance of the phase information that must be kept in any 2-D representation of a 1 -D signal. If a square-law detector is used, or an unsymmetric version of WD or AF is gener-ated, then one must produce the other 2-D representations directly, rather than transform one to the other.

Pseudoclassical Foldy-Wouthuysen transformation and canonical quantization of (D-2n)-dimensional relativistic particle with spin in an external electromagnetic field

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grigoryan, G.V.; Grigoryan, R.P.

1995-09-01

The canonical quantization of a (D=2n)-dimensional Dirac particle with spin in an arbitrary external electromagnetic field is performed in a gauge that makes it possible to describe simultaneously particles and antiparticles (both massive and massless) already at the classical level. A pseudoclassical Foldy-Wouthuysen transformation is used to find the canonical (Newton-Wigner) coordinates. The connection between this quantization scheme and Blount`s picture describing the behavior of a Dirac particle in an external electromagnetic field is discussed.

A study of methods to predict and measure the transmission of sound through the walls of light aircraft

NASA Technical Reports Server (NTRS)

Bernhard, R. J.; Bolton, J. S.; Gardner, B.; Mickol, J.; Mollo, C.; Bruer, C.

1986-01-01

Progress was made in the following areas: development of a numerical/empirical noise source identification procedure using bondary element techniques; identification of structure-borne noise paths using structural intensity and finite element methods; development of a design optimization numerical procedure to be used to study active noise control in three-dimensional geometries; measurement of dynamic properties of acoustical foams and incorporation of these properties in models governing three-dimensional wave propagation in foams; and structure-borne sound path identification by use of the Wigner distribution.

Real-space Wigner-Seitz Cells Imaging of Potassium on Graphite via Elastic Atomic Manipulation

PubMed Central

Yin, Feng; Koskinen, Pekka; Kulju, Sampo; Akola, Jaakko; Palmer, Richard E.

2015-01-01

Atomic manipulation in the scanning tunnelling microscopy, conventionally a tool to build nanostructures one atom at a time, is here employed to enable the atomic-scale imaging of a model low-dimensional system. Specifically, we use low-temperature STM to investigate an ultra thin film (4 atomic layers) of potassium created by epitaxial growth on a graphite substrate. The STM images display an unexpected honeycomb feature, which corresponds to a real-space visualization of the Wigner-Seitz cells of the close-packed surface K atoms. Density functional simulations indicate that this behaviour arises from the elastic, tip-induced vertical manipulation of potassium atoms during imaging, i.e. elastic atomic manipulation, and reflects the ultrasoft properties of the surface under strain. The method may be generally applicable to other soft e.g. molecular or biomolecular systems. PMID:25651973

Quantum dynamical simulation of the scattering of Ar from a frozen LiF(100) surface based on a first principles interaction potential

DOE Office of Scientific and Technical Information (OSTI.GOV)

Azuri, Asaf; Pollak, Eli, E-mail: eli.pollak@weizmann.ac.il

2015-07-07

In-plane two and three dimensional diffraction patterns are computed for the vertical scattering of an Ar atom from a frozen LiF(100) surface. Suitable collimation of the incoming wavepacket serves to reveal the quantum mechanical diffraction. The interaction potential is based on a fit to an ab initio potential calculated using density functional theory with dispersion corrections. Due to the potential coupling found between the two horizontal surface directions, there are noticeable differences between the quantum angular distributions computed for two and three dimensional scattering. The quantum results are compared to analogous classical Wigner computations on the same surface and withmore » the same conditions. The classical dynamics largely provides the envelope for the quantum diffractive scattering. The classical results also show that the corrugation along the [110] direction of the surface is smaller than along the [100] direction, in qualitative agreement with experimental observations of unimodal and bimodal scattering for the [110] and [100] directions, respectively.« less

Spin-orbit coupling and transport in strongly correlated two-dimensional systems

NASA Astrophysics Data System (ADS)

Huang, Jian; Pfeiffer, L. N.; West, K. W.

2017-05-01

Measuring the magnetoresistance (MR) of ultraclean GaAs two-dimensional holes for a large rs range of 20-50, two striking behaviors in relation to the spin-orbit coupling (SOC) emerge in response to strong electron-electron interaction. First, in exact correspondence to the zero-field metal-to-insulator transition (MIT), the sign of the MR switches from being positive in the metallic regime to being negative in the insulating regime when the carrier density crosses the critical density pc of MIT (rs˜39 ). Second, as the SOC-driven correction Δ ρ to the MR decreases with reducing carrier density (or the in-plane wave vector), it exhibits an upturn in the close proximity just above pc where rs is beyond 30, indicating a substantially enhanced SOC effect. This peculiar behavior echoes with a trend of delocalization long suspected for the SOC-interaction interplay. Meanwhile, for p 40 , in contrast to the common belief that a magnet field enhances Wigner crystallization, the negative MR is likely linked to enhanced interaction.

The Wigner function in the relativistic quantum mechanics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kowalski, K., E-mail: kowalski@uni.lodz.pl; Rembieliński, J.

2016-12-15

A detailed study is presented of the relativistic Wigner function for a quantum spinless particle evolving in time according to the Salpeter equation. - Highlights: • We study the Wigner function for a quantum spinless relativistic particle. • We discuss the relativistic Wigner function introduced by Zavialov and Malokostov. • We introduce relativistic Wigner function based on the standard definition. • We find analytic expressions for relativistic Wigner functions.

Local and nonlocal order parameters in the Kitaev chain

NASA Astrophysics Data System (ADS)

Chitov, Gennady Y.

2018-02-01

We have calculated order parameters for the phases of the Kitaev chain with interaction and dimerization at a special symmetric point applying the Jordan-Wigner and other duality transformations. We use string order parameters (SOPs) defined via the correlation functions of the Majorana string operators. The SOPs are mapped onto the local order parameters of some dual Hamiltonians and easily calculated. We have shown that the phase diagram of the interacting dimerized chain comprises the phases with the conventional local order as well as the phases with nonlocal SOPs. From the results for the critical indices, we infer the two-dimensional Ising universality class of criticality at the particular symmetry point where the model is exactly solvable.

Mean-field approximation for spacing distribution functions in classical systems

NASA Astrophysics Data System (ADS)

González, Diego Luis; Pimpinelli, Alberto; Einstein, T. L.

2012-01-01

We propose a mean-field method to calculate approximately the spacing distribution functions p(n)(s) in one-dimensional classical many-particle systems. We compare our method with two other commonly used methods, the independent interval approximation and the extended Wigner surmise. In our mean-field approach, p(n)(s) is calculated from a set of Langevin equations, which are decoupled by using a mean-field approximation. We find that in spite of its simplicity, the mean-field approximation provides good results in several systems. We offer many examples illustrating that the three previously mentioned methods give a reasonable description of the statistical behavior of the system. The physical interpretation of each method is also discussed.

A new model for two-dimensional numerical simulation of pseudo-2D gas-solids fluidized beds

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Tingwen; Zhang, Yongmin

2013-10-11

Pseudo-two dimensional (pseudo-2D) fluidized beds, for which the thickness of the system is much smaller than the other two dimensions, is widely used to perform fundamental studies on bubble behavior, solids mixing, or clustering phenomenon in different gas-solids fluidization systems. The abundant data from such experimental systems are very useful for numerical model development and validation. However, it has been reported that two-dimensional (2D) computational fluid dynamic (CFD) simulations of pseudo-2D gas-solids fluidized beds usually predict poor quantitative agreement with the experimental data, especially for the solids velocity field. In this paper, a new model is proposed to improve themore » 2D numerical simulations of pseudo-2D gas-solids fluidized beds by properly accounting for the frictional effect of the front and back walls. Two previously reported pseudo-2D experimental systems were simulated with this model. Compared to the traditional 2D simulations, significant improvements in the numerical predictions have been observed and the predicted results are in better agreement with the available experimental data.« less

The hyperbolic step potential: Anti-bound states, SUSY partners and Wigner time delays

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gadella, M.; Kuru, Ş.; Negro, J., E-mail: jnegro@fta.uva.es

We study the scattering produced by a one dimensional hyperbolic step potential, which is exactly solvable and shows an unusual interest because of its asymmetric character. The analytic continuation of the scattering matrix in the momentum representation has a branch cut and an infinite number of simple poles on the negative imaginary axis which are related with the so called anti-bound states. This model does not show resonances. Using the wave functions of the anti-bound states, we obtain supersymmetric (SUSY) partners which are the series of Rosen–Morse II potentials. We have computed the Wigner reflection and transmission time delays formore » the hyperbolic step and such SUSY partners. Our results show that the more bound states a partner Hamiltonian has the smaller is the time delay. We also have evaluated time delays for the hyperbolic step potential in the classical case and have obtained striking similitudes with the quantum case. - Highlights: • The scattering matrix of hyperbolic step potential is studied. • The scattering matrix has a branch cut and an infinite number of poles. • The poles are associated to anti-bound states. • Susy partners using antibound states are computed. • Wigner time delays for the hyperbolic step and partner potentials are compared.« less

A numerical study of three-dimensional flame propagation over thin solids in purely forced concurrent flow including gas-phase radiation

NASA Astrophysics Data System (ADS)

Feier, Ioan I., Jr.

The effect of flame radiation on concurrent-flow flame spread over a thin solid sample of finite width in a low-speed wind tunnel is modeled using three-dimensional full Navier-Stokes equations and three-dimensional flame radiation transfer equations. The formulation includes the conservation of mass, momentum, energy, and species: fuel vapor, oxygen, carbon dioxide and water vapor. The SN discrete ordinates method is used to solve the radiation transfer equation with a mean absorption coefficient kappa = Ckappa p, where kappap is the Planck mean absorption coefficient of the gas mixture. The varying parameter C has a value between 0 and 1; C represents the strength of flame radiation. In addition, the solid fuel absorptivity alpha is varied to ascertain the effect of flame radiation heat feedback to the solid. The flow tunnel modeled has a dimension of 10x10x30 cm, the solid fuel has a width of 6-cm with two 1-cm inert strips as edges. Incoming forced flow velocity (5 cm/s) of 21% oxygen is assumed. For comparison with the three-dimensional results, corresponding two-dimensional computations are also performed. Detailed spatial flame profiles, solid surface profiles, and heat fluxes are presented. Increasing the flame radiation strength decreases the flame length. Although flame radiation provides an additional heat transfer mechanism to preheat the solid, it is insufficient to offset the decreased convective heating due to the shorter flame; the net effect is a slower spread rate. The percentage of unreacted fuel vapor that escapes from the flame is under 2%. It is theorized that some of the pyrolyzed fuel vapor diffuses sideway and reacts at the flame edges. A radiative energy balance is analyzed also. Flame radiative feedback to the solid plays a more important role in two-dimensional flames. With high solid fuel absorptivity, a peak in the flame spread rate occurs at an intermediate value of flame radiation strength---due to the competition between two mechanisms: gas-radiation heat loss weakening the flame and the radiative feedback boosting the solid pyrolysis. Two-dimensional calculations suggest that a larger percentage of unreacted fuel vapor can escape from the flame when the flame radiation strength is high.

Impact of high-frequency pumping on anomalous finite-size effects in three-dimensional topological insulators

NASA Astrophysics Data System (ADS)

Pervishko, Anastasiia A.; Yudin, Dmitry; Shelykh, Ivan A.

2018-02-01

Lowering of the thickness of a thin-film three-dimensional topological insulator down to a few nanometers results in the gap opening in the spectrum of topologically protected two-dimensional surface states. This phenomenon, which is referred to as the anomalous finite-size effect, originates from hybridization between the states propagating along the opposite boundaries. In this work, we consider a bismuth-based topological insulator and show how the coupling to an intense high-frequency linearly polarized pumping can further be used to manipulate the value of a gap. We address this effect within recently proposed Brillouin-Wigner perturbation theory that allows us to map a time-dependent problem into a stationary one. Our analysis reveals that both the gap and the components of the group velocity of the surface states can be tuned in a controllable fashion by adjusting the intensity of the driving field within an experimentally accessible range and demonstrate the effect of light-induced band inversion in the spectrum of the surface states for high enough values of the pump.

From the Weyl quantization of a particle on the circle to number–phase Wigner functions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Przanowski, Maciej, E-mail: maciej.przanowski@p.lodz.pl; Brzykcy, Przemysław, E-mail: 800289@edu.p.lodz.pl; Tosiek, Jaromir, E-mail: jaromir.tosiek@p.lodz.pl

2014-12-15

A generalized Weyl quantization formalism for a particle on the circle is shown to supply an effective method for defining the number–phase Wigner function in quantum optics. A Wigner function for the state ϱ{sup ^} and the kernel K for a particle on the circle is defined and its properties are analysed. Then it is shown how this Wigner function can be easily modified to give the number–phase Wigner function in quantum optics. Some examples of such number–phase Wigner functions are considered.

Linear canonical transformations of coherent and squeezed states in the Wigner phase space. II - Quantitative analysis

NASA Technical Reports Server (NTRS)

Han, D.; Kim, Y. S.; Noz, Marilyn E.

1989-01-01

It is possible to calculate expectation values and transition probabilities from the Wigner phase-space distribution function. Based on the canonical transformation properties of the Wigner function, an algorithm is developed for calculating these quantities in quantum optics for coherent and squeezed states. It is shown that the expectation value of a dynamical variable can be written in terms of its vacuum expectation value of the canonically transformed variable. Parallel-axis theorems are established for the photon number and its variant. It is also shown that the transition probability between two squeezed states can be reduced to that of the transition from one squeezed state to vacuum.

Electrons in one dimension

PubMed Central

Berggren, K.-F.; Pepper, M.

2010-01-01

In this article, we present a summary of the current status of the study of the transport of electrons confined to one dimension in very low disorder GaAs–AlGaAs heterostructures. By means of suitably located gates and application of a voltage to ‘electrostatically squeeze’ the electronic wave functions, it is possible to produce a controllable size quantization and a transition from two-dimensional transport. If the length of the electron channel is sufficiently short, then transport is ballistic and the quantized subbands each have a conductance equal to the fundamental quantum value 2e2/h, where the factor of 2 arises from the spin degeneracy. This mode of conduction is discussed, and it is shown that a number of many-body effects can be observed. These effects are discussed as in the spin-incoherent regime, which is entered when the separation of the electrons is increased and the exchange energy is less than kT. Finally, results are presented in the regime where the confinement potential is decreased and the electron configuration relaxes to minimize the electron–electron repulsion to move towards a two-dimensional array. It is shown that the ground state is no longer a line determined by the size quantization alone, but becomes two distinct rows arising from minimization of the electrostatic energy and is the precursor of a two-dimensional Wigner lattice. PMID:20123751

Phonon mediated quantum spin simulator made from a two-dimensional Wigner crystal in Penning traps

NASA Astrophysics Data System (ADS)

Wang, Joseph; Keith, Adam; Freericks, J. K.

2013-03-01

Motivated by recent advances in quantum simulations in a Penning trap, we give a theoretical description for the use of two-dimensional cold ions in a rotating trap as a quantum emulator. The collective axial phonon modes and planar modes are studied in detail, including all effects of the rotating frame. We show the character of the phonon modes and spectrum, which is crucial for engineering exotic spin interactions. In the presence of laser-ion coupling with these coherent phonon excitations, we show theoretically how the spin-spin Hamiltonian can be generated. Specifically, we notice certain parameter regimes in which the level of frustration between spins can be engineered by the coupling to the planar modes. This may be relevant to the quantum simulation of spin-glass physics or other disordered problems. This work was supported under ARO grant number W911NF0710576 with funds from the DARPA OLE Program. J. K. F. also acknowledges the McDevitt bequest at Georgetown University. A. C. K. also acknowledges support of the National Science Foundation under grant

Quantum Monte Carlo Studies of Interaction-Induced Localization in Quantum Dots and Wires

NASA Astrophysics Data System (ADS)

Devrim Güçlü, A.

2009-03-01

We investigate interaction-induced localization of electrons in both quantum dots and inhomogeneous quantum wires using variational and diffusion quantum Monte Carlo methods. Quantum dots and wires are highly tunable systems that enable the study of the physics of strongly correlated electrons. With decreasing electronic density, interactions become stronger and electrons are expected to localize at their classical positions, as in Wigner crystallization in an infinite 2D system. (1) Dots: We show that the addition energy shows a clear progression from features associated with shell structure to those caused by commensurability of a Wigner crystal. This cross-over is, then, a signature of localization; it occurs near rs˜20. For higher values of rs, the configuration symmetry of the quantum dot becomes fully consistent with the classical ground state. (2) Wires: We study an inhomogeneous quasi-one-dimensional system -- a wire with two regions, one at low density and the other high. We find that strong localization occurs in the low density quantum point contact region as the gate potential is increased. The nature of the transition from high to low density depends on the density gradient -- if it is steep, a barrier develops between the two regions, causing Coulomb blockade effects. We find no evidence for ferromagnetic spin polarization for the range of parameters studied. The picture emerging here is in good agreement with the experimental measurements of tunneling between two wires. Collaborators: C. J. Umrigar (Cornell), Hong Jiang (Fritz Haber Institut), Amit Ghosal (IISER Calcutta), and H. U. Baranger (Duke).

Entropy and wigner functions

PubMed

Manfredi; Feix

2000-10-01

The properties of an alternative definition of quantum entropy, based on Wigner functions, are discussed. Such a definition emerges naturally from the Wigner representation of quantum mechanics, and can easily quantify the amount of entanglement of a quantum state. It is shown that smoothing of the Wigner function induces an increase in entropy. This fact is used to derive some simple rules to construct positive-definite probability distributions which are also admissible Wigner functions.

Communication: phase transitions, criticality, and three-phase coexistence in constrained cell models.

PubMed

Nayhouse, Michael; Kwon, Joseph Sang-Il; Orkoulas, G

2012-05-28

In simulation studies of fluid-solid transitions, the solid phase is usually modeled as a constrained system in which each particle is confined to move in a single Wigner-Seitz cell. The constrained cell model has been used in the determination of fluid-solid coexistence via thermodynamic integration and other techniques. In the present work, the phase diagram of such a constrained system of Lennard-Jones particles is determined from constant-pressure simulations. The pressure-density isotherms exhibit inflection points which are interpreted as the mechanical stability limit of the solid phase. The phase diagram of the constrained system contains a critical and a triple point. The temperature and pressure at the critical and the triple point are both higher than those of the unconstrained system due to the reduction in the entropy caused by the single occupancy constraint.

Propagation of partially coherent fields through planar dielectric boundaries using angle-impact Wigner functions I. Two dimensions.

PubMed

Petruccelli, Jonathan C; Alonso, Miguel A

2007-09-01

We examine the angle-impact Wigner function (AIW) as a computational tool for the propagation of nonparaxial quasi-monochromatic light of any degree of coherence past a planar boundary between two homogeneous media. The AIWs of the reflected and transmitted fields in two dimensions are shown to be given by a simple ray-optical transformation of the incident AIW plus a series of corrections in the form of differential operators. The radiometric and leading six correction terms are studied for Gaussian Schell-model fields of varying transverse width, transverse coherence, and angle of incidence.

Eugene P. Wigner - in the light of unexpected events

NASA Astrophysics Data System (ADS)

Koblinger, L.

2014-09-01

In the first part of the paper, Wigner's humane attitude is overviewed based on the author's personal impressions and on selected quotations from Wigner and his contemporaries. The second part briefly summarizes Wigner's contribution to the development of nuclear science and technology.

Stability and Physical Accuracy Analysis of the Numerical Solutions to Wigner-Poisson Modeling of Resonant Tunneling Diodes

DTIC Science & Technology

2013-03-22

discrete Wigner function is periodic in momentum space. The periodicity follows from the Fourier transform of the density matrix. The inverse...resonant-tunneling diode . The Green function method has been one of alternatives. Another alternative was to utilize the Wigner function . The Wigner ... function approach to the simulation of a resonant-tunneling diode offers many advantages. In the limit of the classical physics the Wigner equation

Quantum transport in d-dimensional lattices

DOE PAGES

Manzano, Daniel; Chuang, Chern; Cao, Jianshu

2016-04-28

We show that both fermionic and bosonic uniform d-dimensional lattices can be reduced to a set of independent one-dimensional chains. This reduction leads to the expression for ballistic energy fluxes in uniform fermionic and bosonic lattices. By the use of the Jordan–Wigner transformation we can extend our analysis to spin lattices, proving the coexistence of both ballistic and non-ballistic subspaces in any dimension and for any system size. Lastly, we then relate the nature of transport to the number of excitations in the homogeneous spin lattice, indicating that a single excitation always propagates ballistically and that the non-ballistic behaviour ofmore » uniform spin lattices is a consequence of the interaction between different excitations.« less

Wigner distribution functions for complex dynamical systems: the emergence of the Wigner-Boltzmann equation.

PubMed

Sels, Dries; Brosens, Fons

2013-10-01

The equation of motion for the reduced Wigner function of a system coupled to an external quantum system is presented for the specific case when the external quantum system can be modeled as a set of harmonic oscillators. The result is derived from the Wigner function formulation of the Feynman-Vernon influence functional theory. It is shown how the true self-energy for the equation of motion is connected with the influence functional for the path integral. Explicit expressions are derived in terms of the bare Wigner propagator. Finally, we show under which approximations the resulting equation of motion reduces to the Wigner-Boltzmann equation.

Mean-field approximation for spacing distribution functions in classical systems.

PubMed

González, Diego Luis; Pimpinelli, Alberto; Einstein, T L

2012-01-01

We propose a mean-field method to calculate approximately the spacing distribution functions p((n))(s) in one-dimensional classical many-particle systems. We compare our method with two other commonly used methods, the independent interval approximation and the extended Wigner surmise. In our mean-field approach, p((n))(s) is calculated from a set of Langevin equations, which are decoupled by using a mean-field approximation. We find that in spite of its simplicity, the mean-field approximation provides good results in several systems. We offer many examples illustrating that the three previously mentioned methods give a reasonable description of the statistical behavior of the system. The physical interpretation of each method is also discussed. © 2012 American Physical Society

Assessment of Muscle Fatigue from TF Distributions of SEMG Signals

DTIC Science & Technology

2008-06-01

Wigner - Ville distribution ( WVD ) holds the...techniques used to build a TF distribution of SEMG signals, namely spectrogram, Wigner - Ville , Choi- Williams and smoothed pseudo Wigner - Ville . SEMG signals...spectrogram but also other Cohen’s class TF distributions , such as the Choi-Williams distribution (CWD) and the smoothed pseudo Wigner - Ville distribution

Battle Damage Assessment Using Inverse Synthetic Aperture Radar (ISAR)

DTIC Science & Technology

2004-12-01

are many forms of bilinear TFT. The most basic is the Wigner - Ville Distribution ( WVD ), which is defined as the Fourier transform of the time...resolution (compared to WVD — which is known (Chen [2]) to possess the best time-frequency resolution). Two well-known distributions in this category...resolution limit imposed by the STFT. Examples of some of these TFT schemes include the Continuous Wavelet Transform (CWT), the bilinear Wigner - Ville

Analysis of the coupled electron-ripplon oscillations resonance spectra in the Wigner solid at different temperatures and modeling of the excitation process

NASA Astrophysics Data System (ADS)

Syvokon, V. E.; Sharapova, I. V.

2018-05-01

The spectrum of coupled electron-ripplon oscillations in a Wigner crystal on the surface of superfluid helium at various temperatures and excitation voltages, leading to spectrum distortion, was studied experimentally. It was shown that at all temperatures, increasing excitation voltage leads to the appearance of non-axisymmetric vibrational modes, which indicates distortions of the crystal lattice. The possibility of excitation of the non-axisymmetric modes in a cell was demonstrated by modeling electronic crystal oscillations using the molecular dynamics method. At several fixed frequencies, the amplitudes of the response of the electronic crystal to external excitation were measured as a function of the magnitude of excitation voltage, and jumps were detected at certain critical voltages. Using the Lindemann criterion, a correlation was found between the critical stress and stability limit of the crystal lattice. It was concluded that when the critical voltage is reached, dynamic melting of the electronic crystal occurs.

Observation of Wigner crystal phase and ripplon-limited mobility behavior in monolayer CVD MoS2 with grain boundary.

PubMed

Chen, Jyun-Hong; Zhong, Yuan-Liang; Li, Lain-Jong; Chen, Chii-Dong

2018-06-01

Two-dimensional electron gas (2DEG) is crucial in condensed matter physics and is present on the surface of liquid helium and at the interface of semiconductors. Monolayer MoS 2 of 2D materials also contains 2DEG in an atomic layer as a field effect transistor (FET) ultrathin channel. In this study, we synthesized double triangular MoS 2 through a chemical vapor deposition method to obtain grain boundaries for forming a ripple structure in the FET channel. When the temperature was higher than approximately 175 K, the temperature dependence of the electron mobility μ was consistent with those in previous experiments and theoretical predictions. When the temperature was lower than approximately 175 K, the mobility behavior decreased with the temperature; this finding was also consistent with that of the previous experiments. We are the first research group to explain the decreasing mobility behavior by using the Wigner crystal phase and to discover the temperature independence of ripplon-limited mobility behavior at lower temperatures. Although these mobility behaviors have been studied on the surface of liquid helium through theories and experiments, they have not been previously analyzed in 2D materials and semiconductors. We are the first research group to report the similar temperature-dependent mobility behavior of the surface of liquid helium and the monolayer MoS 2 .

Observation of Wigner crystal phase and ripplon-limited mobility behavior in monolayer CVD MoS2 with grain boundary

NASA Astrophysics Data System (ADS)

Chen, Jyun-Hong; Zhong, Yuan-Liang; Li, Lain-Jong; Chen, Chii-Dong

2018-06-01

Two-dimensional electron gas (2DEG) is crucial in condensed matter physics and is present on the surface of liquid helium and at the interface of semiconductors. Monolayer MoS2 of 2D materials also contains 2DEG in an atomic layer as a field effect transistor (FET) ultrathin channel. In this study, we synthesized double triangular MoS2 through a chemical vapor deposition method to obtain grain boundaries for forming a ripple structure in the FET channel. When the temperature was higher than approximately 175 K, the temperature dependence of the electron mobility μ was consistent with those in previous experiments and theoretical predictions. When the temperature was lower than approximately 175 K, the mobility behavior decreased with the temperature; this finding was also consistent with that of the previous experiments. We are the first research group to explain the decreasing mobility behavior by using the Wigner crystal phase and to discover the temperature independence of ripplon-limited mobility behavior at lower temperatures. Although these mobility behaviors have been studied on the surface of liquid helium through theories and experiments, they have not been previously analyzed in 2D materials and semiconductors. We are the first research group to report the similar temperature-dependent mobility behavior of the surface of liquid helium and the monolayer MoS2.

Time-Frequency Domain Analysis of Helicopter Transmission Vibration

DTIC Science & Technology

1991-08-01

Wigner - Ville distribution ( WVD ) have be reported, including speech...FREQUENCY DISTRIBUTIONS . 8 6. THE WIGNER - VILLE DISTRIBUTION . 9 6.1 History. 9 6.2 Definition. 9 6.3 Discrete-Time/Frequency Wigner - Ville Distribution . 10...signals are examined to indicate how various forms of modulation are portrayed using the Wigner - Ville distribution . Practical examples A signal is

Rovibrational states of Wigner molecules in spherically symmetric confining potentials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cioslowski, Jerzy

2016-08-07

The strong-localization limit of three-dimensional Wigner molecules, in which repulsively interacting particles are confined by a weak spherically symmetric potential, is investigated. An explicit prescription for computation of rovibrational wavefunctions and energies that are asymptotically exact at this limit is presented. The prescription is valid for systems with arbitrary angularly-independent interparticle and confining potentials, including those involving Coulombic and screened (i.e., Yukawa/Debye) interactions. The necessary derivations are greatly simplified by explicit constructions of the Eckart frame and the parity-adapted primitive wavefunctions. The performance of the new formalism is illustrated with the three- and four-electron harmonium atoms at their strong-correlation limits.more » In particular, the involvement of vibrational modes with the E symmetry is readily pinpointed as the origin of the “anomalous” weak-confinement behavior of the {sup 1}S{sub +} state of the four-electron species that is absent in its {sup 1}D{sub +} companion of the strong-confinement regime.« less

Pseudo Wigner-Ville Distribution, Computer Program and its Applications to Time-Frequency Domain Problems

DTIC Science & Technology

1993-03-01

representation is needed to characterize such signature. Pseudo Wigner - Ville distribution is ideally suited for portraying non-stationary signal in the...features jointly in time and frequency. 14, SUBJECT TERIMS 15. NUMBER OF PAGES Pseudo Wigner - Ville Distribution , Analytic Signal, 83 Hilbert Transform...D U C T IO N ............................................................................ . 1 II. PSEUDO WIGNER - VILLE DISTRIBUTION

Wavelet-Based Signal Processing for Monitoring Discomfort and Fatigue

DTIC Science & Technology

2008-06-01

Wigner - Ville distribution ( WVD ), the short-time Fourier transform (STFT) or spectrogram, the Choi-Williams distribution (CWD), the smoothed pseudo Wigner ...has the advantage of being computationally less expensive than other standard techniques, such as the Wigner - Ville distribution ( WVD ), the spectrogram...slopes derived from the spectrogram and the smoothed pseudo Wigner - Ville distribution . Furthermore, slopes derived from the filter bank

Double Wigner distribution function of a first-order optical system with a hard-edge aperture.

PubMed

Pan, Weiqing

2008-01-01

The effect of an apertured optical system on Wigner distribution can be expressed as a superposition integral of the input Wigner distribution function and the double Wigner distribution function of the apertured optical system. By introducing a hard aperture function into a finite sum of complex Gaussian functions, the double Wigner distribution functions of a first-order optical system with a hard aperture outside and inside it are derived. As an example of application, the analytical expressions of the Wigner distribution for a Gaussian beam passing through a spatial filtering optical system with an internal hard aperture are obtained. The analytical results are also compared with the numerical integral results, and they show that the analytical results are proper and ascendant.

Phase diagram of two-dimensional hard ellipses.

PubMed

Bautista-Carbajal, Gustavo; Odriozola, Gerardo

2014-05-28

We report the phase diagram of two-dimensional hard ellipses as obtained from replica exchange Monte Carlo simulations. The replica exchange is implemented by expanding the isobaric ensemble in pressure. The phase diagram shows four regions: isotropic, nematic, plastic, and solid (letting aside the hexatic phase at the isotropic-plastic two-step transition [E. P. Bernard and W. Krauth, Phys. Rev. Lett. 107, 155704 (2011)]). At low anisotropies, the isotropic fluid turns into a plastic phase which in turn yields a solid for increasing pressure (area fraction). Intermediate anisotropies lead to a single first order transition (isotropic-solid). Finally, large anisotropies yield an isotropic-nematic transition at low pressures and a high-pressure nematic-solid transition. We obtain continuous isotropic-nematic transitions. For the transitions involving quasi-long-range positional ordering, i.e., isotropic-plastic, isotropic-solid, and nematic-solid, we observe bimodal probability density functions. This supports first order transition scenarios.

Ultra-directional source of longitudinal acoustic waves based on a two-dimensional solid/solid phononic crystal

DOE Office of Scientific and Technical Information (OSTI.GOV)

Morvan, B.; Tinel, A.; Sainidou, R.

2014-12-07

Phononic crystals (PC) can be used to control the dispersion properties of acoustic waves, which are essential to direct their propagation. We use a PC-based two-dimensional solid/solid composite to demonstrate experimentally and theoretically the spatial filtering of a monochromatic non-directional wave source and its emission in a surrounding water medium as an ultra-directional beam with narrow angular distribution. The phenomenon relies on square-shaped equifrequency contours (EFC) enabling self-collimation of acoustic waves within the phononic crystal. Additionally, the angular width of collimated beams is controlled via the EFC size-shrinking when increasing frequency.

Advanced Beamforming Concepts: Source Localization Using the Bispectrum, Gabor Transform, Wigner-Ville Distribution, and Nonstationary Signal Representation

DTIC Science & Technology

1991-12-01

TRANSFORM, WIGNER - VILLE DISTRIBUTION , AND NONSTATIONARY SIGNAL REPRESENTATIONS 6. AUTHOR(S) J. C. Allen 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS...bispectrum yields a bispectral direction finder. Estimates of time-frequency distributions produce Wigner - Ville and Gabor direction-finders. Some types...Beamforming Concepts: Source Localization Using the Bispectrum, Gabor Transform, Wigner - Ville Distribution , and Nonstationary Signal Representations

The origin of non-classical effects in a one-dimensional superposition of coherent states

NASA Technical Reports Server (NTRS)

Buzek, V.; Knight, P. L.; Barranco, A. Vidiella

1992-01-01

We investigate the nature of the quantum fluctuations in a light field created by the superposition of coherent fields. We give a physical explanation (in terms of Wigner functions and phase-space interference) why the 1-D superposition of coherent states in the direction of the x-quadrature leads to the squeezing of fluctuations in the y-direction, and show that such a superposition can generate the squeezed vacuum and squeezed coherent states.

Features of the use of time-frequency distributions for controlling the mixture-producing aggregate

NASA Astrophysics Data System (ADS)

Fedosenkov, D. B.; Simikova, A. A.; Fedosenkov, B. A.

2018-05-01

The paper submits and argues the information on filtering properties of the mixing unit as a part of the mixture-producing aggregate. Relevant theoretical data concerning a channel transfer function of the mixing unit and multidimensional material flow signals are adduced here. Note that ordinary one-dimensional material flow signals are defined in terms of time-frequency distributions of Cohen’s class representations operating with Gabor wavelet functions. Two time-frequencies signal representations are written about in the paper to show how one can solve controlling problems as applied to mixture-producing systems: they are the so-called Rihaczek and Wigner-Ville distributions. In particular, the latter illustrates low-pass filtering properties that are practically available in any of low-pass elements of a physical system.

Generalized Weyl-Wigner map and Vey quantum mechanics

NASA Astrophysics Data System (ADS)

Dias, Nuno Costa; Prata, João Nuno

2001-12-01

The Weyl-Wigner map yields the entire structure of Moyal quantum mechanics directly from the standard operator formulation. The covariant generalization of Moyal theory, also known as Vey quantum mechanics, was presented in the literature many years ago. However, a derivation of the formalism directly from standard operator quantum mechanics, clarifying the relation between the two formulations, is still missing. In this article we present a covariant generalization of the Weyl order prescription and of the Weyl-Wigner map and use them to derive Vey quantum mechanics directly from the standard operator formulation. The procedure displays some interesting features: it yields all the key ingredients and provides a more straightforward interpretation of the Vey theory including a direct implementation of unitary operator transformations as phase space coordinate transformations in the Vey idiom. These features are illustrated through a simple example.

Wigner functions for noncommutative quantum mechanics: A group representation based construction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chowdhury, S. Hasibul Hassan, E-mail: shhchowdhury@gmail.com; Department of Mathematics and Statistics, Concordia University, Montréal, Québec H3G 1M8; Ali, S. Twareque, E-mail: twareque.ali@concordia.ca

This paper is devoted to the construction and analysis of the Wigner functions for noncommutative quantum mechanics, their marginal distributions, and star-products, following a technique developed earlier, viz, using the unitary irreducible representations of the group G{sub NC}, which is the three fold central extension of the Abelian group of ℝ{sup 4}. These representations have been exhaustively studied in earlier papers. The group G{sub NC} is identified with the kinematical symmetry group of noncommutative quantum mechanics of a system with two degrees of freedom. The Wigner functions studied here reflect different levels of non-commutativity—both the operators of position and thosemore » of momentum not commuting, the position operators not commuting and finally, the case of standard quantum mechanics, obeying the canonical commutation relations only.« less

Semiclassical propagation: Hilbert space vs. Wigner representation

NASA Astrophysics Data System (ADS)

Gottwald, Fabian; Ivanov, Sergei D.

2018-03-01

A unified viewpoint on the van Vleck and Herman-Kluk propagators in Hilbert space and their recently developed counterparts in Wigner representation is presented. Based on this viewpoint, the Wigner Herman-Kluk propagator is conceptually the most general one. Nonetheless, the respective semiclassical expressions for expectation values in terms of the density matrix and the Wigner function are mathematically proven here to coincide. The only remaining difference is a mere technical flexibility of the Wigner version in choosing the Gaussians' width for the underlying coherent states beyond minimal uncertainty. This flexibility is investigated numerically on prototypical potentials and it turns out to provide neither qualitative nor quantitative improvements. Given the aforementioned generality, utilizing the Wigner representation for semiclassical propagation thus leads to the same performance as employing the respective most-developed (Hilbert-space) methods for the density matrix.

Wigner functions for fermions in strong magnetic fields

NASA Astrophysics Data System (ADS)

Sheng, Xin-li; Rischke, Dirk H.; Vasak, David; Wang, Qun

2018-02-01

We compute the covariant Wigner function for spin-(1/2) fermions in an arbitrarily strong magnetic field by exactly solving the Dirac equation at non-zero fermion-number and chiral-charge densities. The Landau energy levels as well as a set of orthonormal eigenfunctions are found as solutions of the Dirac equation. With these orthonormal eigenfunctions we construct the fermion field operators and the corresponding Wigner-function operator. The Wigner function is obtained by taking the ensemble average of the Wigner-function operator in global thermodynamical equilibrium, i.e., at constant temperature T and non-zero fermion-number and chiral-charge chemical potentials μ and μ_5, respectively. Extracting the vector and axial-vector components of the Wigner function, we reproduce the currents of the chiral magnetic and separation effect in an arbitrarily strong magnetic field.

An Energy Analysis of the Pseudo Wigner-Ville Distribution in Support of Machinery Monitoring and Diagnostics

DTIC Science & Technology

1992-06-01

AD-A256 202 NAVAL POSTGRADUATE SCHOOL Monterey, California THESIS - _ ’. AN ENERGY ANALYSIS OF THE PSEUDO WIGNER - VILLE DISTRIBUTION IN SUPPORT OF...NO 11 TITLE (Include Security Classification) AN ENERGY ANALYSIS OF THE PSEUDO WIGNER - VILLE DISTRIBUTION IN SUPPORT OF MACHINERY MONITORING AND...block number) FIELD GROUP SUB-GROUP machinery monitoring, transient, pseudo wigner - ville distribution , machinery diagnostics 19 ABSTRACT (Continue on

Detection and Estimation of Multi-Pulse LFMCW Radar Signals

DTIC Science & Technology

2010-01-01

the Hough transform (HT) of the Wigner - Ville distribution ( WVD ), has been shown to be equivalent to the generalized likelihood ratio test (GLRT...virginia.edu Abstract— The Wigner - Ville Hough transform (WVHT) has been applied to detect and estimate the parameters of linear frequency-modulated...well studied in the literature. One of the most prominent techniques is the Wigner - Ville Hough Transform [8], [9]. The Wigner - Ville Hough transform (WVHT

Out-of-time-ordered correlators in a quantum Ising chain

NASA Astrophysics Data System (ADS)

Lin, Cheng-Ju; Motrunich, Olexei I.

2018-04-01

Out-of-time-ordered correlators (OTOC) have been proposed to characterize quantum chaos in generic systems. However, they can also show interesting behavior in integrable models, resembling the OTOC in chaotic systems in some aspects. Here we study the OTOC for different operators in the exactly-solvable one-dimensional quantum Ising spin chain. The OTOC for spin operators that are local in terms of the Jordan-Wigner fermions has a "shell-like" structure: After the wavefront passes, the OTOC approaches its original value in the long-time limit, showing no signature of scrambling; the approach is described by a t-1 power law at long time t . On the other hand, the OTOC for spin operators that are nonlocal in the Jordan-Wigner fermions has a "ball-like" structure, with its value reaching zero in the long-time limit, looking like a signature of scrambling; the approach to zero, however, is described by a slow power law t-1 /4 for the Ising model at the critical coupling. These long-time power-law behaviors in the lattice model are not captured by conformal field theory calculations. The mixed OTOC with both local and nonlocal operators in the Jordan-Wigner fermions also has a "ball-like" structure, but the limiting values and the decay behavior appear to be nonuniversal. In all cases, we are not able to define a parametrically large window around the wavefront to extract the Lyapunov exponent.

Wigner Distribution Functions as a Tool for Studying Gas Phase Alkali Metal Plus Noble Gas Collisions

DTIC Science & Technology

2014-03-27

ii List of Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii I...t, E) Wigner Distribution Function ii List of Acronyms Acronym Definition WDF Wigner Distribution Function PES Potential Energy Surface DPAL Diode

Two-Dimensional Nanoporous Networks Formed by Liquid-to-Solid Transfer of Hydrogen-Bonded Macrocycles Built from DNA Bases.

PubMed

Bilbao, Nerea; Destoop, Iris; De Feyter, Steven; González-Rodríguez, David

2016-01-11

We present an approach that makes use of DNA base pairing to produce hydrogen-bonded macrocycles whose supramolecular structure can be transferred from solution to a solid substrate. A hierarchical assembly process ultimately leads to two-dimensional nanostructured porous networks that are able to host size-complementary guests. © 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Strength functions, entropies, and duality in weakly to strongly interacting fermionic systems.

PubMed

Angom, D; Ghosh, S; Kota, V K B

2004-01-01

We revisit statistical wave function properties of finite systems of interacting fermions in the light of strength functions and their participation ratio and information entropy. For weakly interacting fermions in a mean-field with random two-body interactions of increasing strength lambda, the strength functions F(k) (E) are well known to change, in the regime where level fluctuations follow Wigner's surmise, from Breit-Wigner to Gaussian form. We propose an ansatz for the function describing this transition which we use to investigate the participation ratio xi(2) and the information entropy S(info) during this crossover, thereby extending the known behavior valid in the Gaussian domain into much of the Breit-Wigner domain. Our method also allows us to derive the scaling law lambda(d) approximately 1/sqrt[m] ( m is number of fermions) for the duality point lambda= lambda(d), where F(k) (E), xi(2), and S(info) in both the weak ( lambda=0 ) and strong mixing ( lambda= infinity ) basis coincide. As an application, the ansatz function for strength functions is used in describing the Breit-Wigner to Gaussian transition seen in neutral atoms CeI to SmI with valence electrons changing from 4 to 8.

Possibility to Probe Negative Values of a Wigner Function in Scattering of a Coherent Superposition of Electronic Wave Packets by Atoms.

PubMed

Karlovets, Dmitry V; Serbo, Valeriy G

2017-10-27

Within a plane-wave approximation in scattering, an incoming wave packet's Wigner function stays positive everywhere, which obscures such purely quantum phenomena as nonlocality and entanglement. With the advent of the electron microscopes with subnanometer-sized beams, one can enter a genuinely quantum regime where the latter effects become only moderately attenuated. Here we show how to probe negative values of the Wigner function in scattering of a coherent superposition of two Gaussian packets with a nonvanishing impact parameter between them (a Schrödinger's cat state) by atomic targets. For hydrogen in the ground 1s state, a small parameter of the problem, a ratio a/σ_{⊥} of the Bohr radius a to the beam width σ_{⊥}, is no longer vanishing. We predict an azimuthal asymmetry of the scattered electrons, which is found to be up to 10%, and argue that it can be reliably detected. The production of beams with the not-everywhere-positive Wigner functions and the probing of such quantum effects can open new perspectives for noninvasive electron microscopy, quantum tomography, particle physics, and so forth.

Formation of Schrödinger-cat states in the Morse potential: Wigner function picture.

PubMed

Foldi, Peter; Czirjak, Attila; Molnar, Balazs; Benedict, Mihaly

2002-04-22

We investigate the time evolution of Morse coherent states in the potential of the NO molecule. We present animated wave functions and Wigner functions of the system exhibiting spontaneous formation of Schrödinger-cat states at certain stages of the time evolution. These nonclassical states are coherent superpositions of two localized states corresponding to two di.erent positions of the center of mass. We analyze the degree of nonclassicality as the function of the expectation value of the position in the initial state. Our numerical calculations are based on a novel, essentially algebraic treatment of the Morse potential.

Wigner-Hough/Radon Transform for GPS Post-Correlation Integration (Preprint)

DTIC Science & Technology

2007-09-01

Wigner - Ville distribution ( WVD ) is a well known method to estimate instantaneous frequency, which appears as a...Barbarossa, 1996]. In this method, the Wigner - Ville distribution ( WVD ) is used to represent the signal energy in the time-frequency plane while the...its Wigner - Ville 4 distribution or WVD is computed as: ∫ +∞ ∞− −−+= τττ τπ detxtxftW fj 2* ) 2 () 2 (),( (4) where * stands for complex

Monolayer adsorption of noble gases on graphene

NASA Astrophysics Data System (ADS)

Maiga, Sidi M.; Gatica, Silvina M.

2018-02-01

We report our results of simulations of the adsorption of noble gases (Kr, Ar, Xe) on graphene. For Kr, we consider two configurations: supported and free-standing graphene, where atoms are adsorbed only on one or two sides of the graphene. For Ar and Xe, we studied only the case of supported graphene. For the single-side adsorption, we calculated the two-dimensional gas-liquid critical temperature for each adsorbate. We determined the different phases of the monolayers and constructed the phase diagrams. We found two-dimensional incommensurate solid phases for krypton, argon and xenon, and a two-dimensional commensurate solid phase for krypton. For double side adsorption of Kr, we do not see evidence of an ordering transition driven by the interlayer forces.

Data Mining for New Two- and One-Dimensional Weakly Bonded Solids and Lattice-Commensurate Heterostructures.

PubMed

Cheon, Gowoon; Duerloo, Karel-Alexander N; Sendek, Austin D; Porter, Chase; Chen, Yuan; Reed, Evan J

2017-03-08

Layered materials held together by weak interactions including van der Waals forces, such as graphite, have attracted interest for both technological applications and fundamental physics in their layered form and as an isolated single-layer. Only a few dozen single-layer van der Waals solids have been subject to considerable research focus, although there are likely to be many more that could have superior properties. To identify a broad spectrum of layered materials, we present a novel data mining algorithm that determines the dimensionality of weakly bonded subcomponents based on the atomic positions of bulk, three-dimensional crystal structures. By applying this algorithm to the Materials Project database of over 50,000 inorganic crystals, we identify 1173 two-dimensional layered materials and 487 materials that consist of weakly bonded one-dimensional molecular chains. This is an order of magnitude increase in the number of identified materials with most materials not known as two- or one-dimensional materials. Moreover, we discover 98 weakly bonded heterostructures of two-dimensional and one-dimensional subcomponents that are found within bulk materials, opening new possibilities for much-studied assembly of van der Waals heterostructures. Chemical families of materials, band gaps, and point groups for the materials identified in this work are presented. Point group and piezoelectricity in layered materials are also evaluated in single-layer forms. Three hundred and twenty-five of these materials are expected to have piezoelectric monolayers with a variety of forms of the piezoelectric tensor. This work significantly extends the scope of potential low-dimensional weakly bonded solids to be investigated.

Real-Time Time-Frequency Two-Dimensional Imaging of Ultrafast Transient Signals in Solid-State Organic Materials

PubMed Central

Takeda, Jun; Ishida, Akihiro; Makishima, Yoshinori; Katayama, Ikufumi

2010-01-01

In this review, we demonstrate a real-time time-frequency two-dimensional (2D) pump-probe imaging spectroscopy implemented on a single shot basis applicable to excited-state dynamics in solid-state organic and biological materials. Using this technique, we could successfully map ultrafast time-frequency 2D transient absorption signals of β-carotene in solid films with wide temporal and spectral ranges having very short accumulation time of 20 ms per unit frame. The results obtained indicate the high potential of this technique as a powerful and unique spectroscopic tool to observe ultrafast excited-state dynamics of organic and biological materials in solid-state, which undergo rapid photodegradation. PMID:22399879

Wigner functions on non-standard symplectic vector spaces

NASA Astrophysics Data System (ADS)

Dias, Nuno Costa; Prata, João Nuno

2018-01-01

We consider the Weyl quantization on a flat non-standard symplectic vector space. We focus mainly on the properties of the Wigner functions defined therein. In particular we show that the sets of Wigner functions on distinct symplectic spaces are different but have non-empty intersections. This extends previous results to arbitrary dimension and arbitrary (constant) symplectic structure. As a by-product we introduce and prove several concepts and results on non-standard symplectic spaces which generalize those on the standard symplectic space, namely, the symplectic spectrum, Williamson's theorem, and Narcowich-Wigner spectra. We also show how Wigner functions on non-standard symplectic spaces behave under the action of an arbitrary linear coordinate transformation.

Simulation of wave packet tunneling of interacting identical particles

NASA Astrophysics Data System (ADS)

Lozovik, Yu. E.; Filinov, A. V.; Arkhipov, A. S.

2003-02-01

We demonstrate a different method of simulation of nonstationary quantum processes, considering the tunneling of two interacting identical particles, represented by wave packets. The used method of quantum molecular dynamics (WMD) is based on the Wigner representation of quantum mechanics. In the context of this method ensembles of classical trajectories are used to solve quantum Wigner-Liouville equation. These classical trajectories obey Hamiltonian-like equations, where the effective potential consists of the usual classical term and the quantum term, which depends on the Wigner function and its derivatives. The quantum term is calculated using local distribution of trajectories in phase space, therefore, classical trajectories are not independent, contrary to classical molecular dynamics. The developed WMD method takes into account the influence of exchange and interaction between particles. The role of direct and exchange interactions in tunneling is analyzed. The tunneling times for interacting particles are calculated.

Probing the antiferromagnetic long-range order with Glauber spin states

NASA Technical Reports Server (NTRS)

Cabrera, Guillermo G.

1994-01-01

It is well known that the ground state of low-dimensional antiferromagnets deviates from Neel states due to strong quantum fluctuations. Even in the presence of long-range order, those fluctuations produce a substantial reduction of the magnetic moment from its saturation value. Numerical simulations in anisotropic antiferromagnetic chains suggest that quantum fluctuations over Neel order appear in the form of localized reversal of pairs of neighboring spins. In this paper, we propose a coherent state representation for the ground state to describe the above situation. In the one-dimensional case, our wave function corresponds to a two-mode Glauber state, when the Neel state is used as a reference, while the boson fields are associated to coherent flip of spin pairs. The coherence manifests itself through the antiferromagnetic long-range order that survives the action of quantum fluctuations. The present representation is different from the standard zero-point spin wave state, and is asymptotically exact in the limit of strong anisotropy. The fermionic version of the theory, obtained through the Jordan-Wigner transformation, is also investigated.

What is the Brillouin zone of an anisotropic photonic crystal?

NASA Astrophysics Data System (ADS)

Sivarajah, P.; Maznev, A. A.; Ofori-Okai, B. K.; Nelson, K. A.

2016-02-01

The concept of the Brillouin zone (BZ) in relation to a photonic crystal fabricated in an optically anisotropic material is explored both experimentally and theoretically. In experiment we used femtosecond laser pulses to excite THz polaritons and image their propagation in lithium niobate and lithium tantalate photonic crystal (PhC) slabs. We directly measured the dispersion relation inside PhCs and observed that the lowest band gap expected to form at the BZ boundary forms inside the BZ in the anisotropic lithium niobate PhC. Our analysis shows that in an anisotropic material the BZ—defined as the Wigner-Seitz cell in the reciprocal lattice—is no longer bounded by Bragg planes and thus does not conform to the original definition of the BZ by Brillouin. We construct an alternative Brillouin zone defined by Bragg planes and show its utility in identifying features of the dispersion bands. We show that for an anisotropic two-dimensional PhC without dispersion, the Bragg plane BZ can be constructed by applying the Wigner-Seitz method to a stretched or compressed reciprocal lattice. We also show that in the presence of the dispersion in the underlying material or in a slab waveguide, the Bragg planes are generally represented by curved surfaces rather than planes. The concept of constructing a BZ with Bragg planes should prove useful in understanding the formation of dispersion bands in anisotropic PhCs and in selectively tailoring their optical properties.

Evaluation of a Delay-Doppler Imaging Algorithm Based on the Wigner-Ville Distribution

DTIC Science & Technology

1989-10-18

exchanging the frequency and time variables. 2.3 PROPERTIES OF THE WIGNER - VILLE DISTRIBUTION A partial list of the properties of the WVD is provided...ESD-TH-89-163 N Technical Report (N R55 00 Lfl Evaluation of a Delay-Doppler Imaging Algorithm Based on the Wigner - Ville Distribution K.I. Schultz 18...DOPPLER IMAGING ALGORITHM BASED ON THE WIGNER - VILLE DISTRIBUTION K.I. SCHULTZ Group 52 TECHNICAL REPORT 855 18 OCTOBER 1989 Approved for public release

Prognosis of Electrical Faults in Permanent Magnet AC Machines using the Hidden Markov Model

DTIC Science & Technology

2010-11-10

time resolution and high frequency resolution Tiling is variable Wigner Ville Distribution Defined as W (t, ω) = ∫ s(t + τ 2 )s∗(t − τ 2 )e−jωτdτ...smoothed version of the Wigner distribution Amount of smoothing is controlled by σ Smoothing comes with a tradeoff of reduced resolution UNCLAS: Dist A...the Wigner or Choi-Williams distributions Although for Wigner and Choi-Williams distributions the probabilities are close for the early fault

Wigner Functions for Arbitrary Quantum Systems.

PubMed

Tilma, Todd; Everitt, Mark J; Samson, John H; Munro, William J; Nemoto, Kae

2016-10-28

The possibility of constructing a complete, continuous Wigner function for any quantum system has been a subject of investigation for over 50 years. A key system that has served to illustrate the difficulties of this problem has been an ensemble of spins. Here we present a general and consistent framework for constructing Wigner functions exploiting the underlying symmetries in the physical system at hand. The Wigner function can be used to fully describe any quantum system of arbitrary dimension or ensemble size.

Photodetachment cross sections of negative ions - The range of validity of the Wigner threshold law

NASA Technical Reports Server (NTRS)

Farley, John W.

1989-01-01

The threshold behavior of the photodetachment cross section of negative ions as a function of photon frequency is usually described by the Wigner law. This paper reports the results of a model calculation using the zero-core-contribution (ZCC) approximation. Theoretical expressions for the leading correction to the Wigner law are developed, giving the range of validity of the Wigner law and the expected accuracy. The results are relevant to extraction of electron affinities from experimental photodetachment data.

Contextuality and Wigner-function negativity in qubit quantum computation

NASA Astrophysics Data System (ADS)

Raussendorf, Robert; Browne, Dan E.; Delfosse, Nicolas; Okay, Cihan; Bermejo-Vega, Juan

2017-05-01

We describe schemes of quantum computation with magic states on qubits for which contextuality and negativity of the Wigner function are necessary resources possessed by the magic states. These schemes satisfy a constraint. Namely, the non-negativity of Wigner functions must be preserved under all available measurement operations. Furthermore, we identify stringent consistency conditions on such computational schemes, revealing the general structure by which negativity of Wigner functions, hardness of classical simulation of the computation, and contextuality are connected.

Monte Carlo sampling of Wigner functions and surface hopping quantum dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kube, Susanna; Lasser, Caroline; Weber, Marcus

2009-04-01

The article addresses the achievable accuracy for a Monte Carlo sampling of Wigner functions in combination with a surface hopping algorithm for non-adiabatic quantum dynamics. The approximation of Wigner functions is realized by an adaption of the Metropolis algorithm for real-valued functions with disconnected support. The integration, which is necessary for computing values of the Wigner function, uses importance sampling with a Gaussian weight function. The numerical experiments agree with theoretical considerations and show an error of 2-3%.

Generalized Reduction Formula for Discrete Wigner Functions of Multiqubit Systems

NASA Astrophysics Data System (ADS)

Srinivasan, K.; Raghavan, G.

2018-03-01

Density matrices and Discrete Wigner Functions are equally valid representations of multiqubit quantum states. For density matrices, the partial trace operation is used to obtain the quantum state of subsystems, but an analogous prescription is not available for discrete Wigner Functions. Further, the discrete Wigner function corresponding to a density matrix is not unique but depends on the choice of the quantum net used for its reconstruction. In the present work, we derive a reduction formula for discrete Wigner functions of a general multiqubit state which works for arbitrary quantum nets. These results would be useful for the analysis and classification of entangled states and the study of decoherence purely in a discrete phase space setting and also in applications to quantum computing.

Experimental extractions of particle position from inline holograms using single coefficient of Wigner-Ville analysis

NASA Astrophysics Data System (ADS)

Widjaja, Joewono; Dawprateep, Saowaros; Chuamchaitrakool, Porntip

2017-07-01

Extractions of particle positions from inline holograms using a single coefficient of Wigner-Ville distribution (WVD) are experimentally verified. WVD analysis of holograms gives local variation of fringe frequency. Regardless of an axial position of particles, one of the WVD coefficients has the unique characteristics of having the lowest amplitude and being located on a line with a slope inversely proportional to the particle position. Experimental results obtained using two image sensors with different resolutions verify the feasibility of the present method.

Local Sampling of the Wigner Function at Telecom Wavelength with Loss-Tolerant Detection of Photon Statistics.

PubMed

Harder, G; Silberhorn, Ch; Rehacek, J; Hradil, Z; Motka, L; Stoklasa, B; Sánchez-Soto, L L

2016-04-01

We report the experimental point-by-point sampling of the Wigner function for nonclassical states created in an ultrafast pulsed type-II parametric down-conversion source. We use a loss-tolerant time-multiplexed detector based on a fiber-optical setup and a pair of photon-number-resolving avalanche photodiodes. By capitalizing on an expedient data-pattern tomography, we assess the properties of the light states with outstanding accuracy. The method allows us to reliably infer the squeezing of genuine two-mode states without any phase reference.

Preparative isolation of flavonoid glycosides from Sphaerophysa salsula using hydrophilic interaction solid-phase extraction coupled with two-dimensional preparative liquid chromatography.

PubMed

Jiao, Lijin; Tao, Yanduo; Wang, Weidong; Shao, Yun; Mei, Lijuan; Wang, Qilan; Dang, Jun

2017-10-01

An offline preparative two-dimensional reversed-phase liquid chromatography/hydrophilic interaction liquid chromatography coupled with hydrophilic interaction solid-phase extraction method was developed for the preparative isolation of flavonoid glycosides from a crude sample of Sphaerophysa salsula. First, the non-flavonoids were removed using an XAmide solid-phase extraction cartridge. Based on the separation results of three different chromatographic stationary phases, the first-dimensional preparation was performed on an XAqua C18 prep column, and 15 fractions were obtained from the 5.2 g target sample. Then, three representative fractions were selected for additional purification on an XAmide preparative column to further isolate the flavonoid glycosides. In all, eight flavonoid glycosides were isolated in purities over 97%. The results demonstrated that the two-dimensional liquid chromatography method used in this study was effective for the preparative separation of flavonoid glycosides from Sphaerophysa salsula. Additionally, this method showed great potential for the separation of flavonoid glycosides from other plant materials. © 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Semiclassical Wigner theory of photodissociation in three dimensions: Shedding light on its basis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arbelo-González, W.; CNRS, Institut des Sciences Moléculaires, UMR 5255, 33405 Talence; Université Bordeaux, Institut des Sciences Moléculaires, UMR 5255, 33405 Talence

2015-04-07

The semiclassical Wigner theory (SCWT) of photodissociation dynamics, initially proposed by Brown and Heller [J. Chem. Phys. 75, 186 (1981)] in order to describe state distributions in the products of direct collinear photodissociations, was recently extended to realistic three-dimensional triatomic processes of the same type [Arbelo-González et al., Phys. Chem. Chem. Phys. 15, 9994 (2013)]. The resulting approach, which takes into account rotational motions in addition to vibrational and translational ones, was applied to a triatomic-like model of methyl iodide photodissociation and its predictions were found to be in nearly quantitative agreement with rigorous quantum results, but at a muchmore » lower computational cost, making thereby SCWT a potential tool for the study of polyatomic reaction dynamics. Here, we analyse the main reasons for this agreement by means of an elementary model of fragmentation explicitly dealing with the rotational motion only. We show that our formulation of SCWT makes it a semiclassical approximation to an approximate planar quantum treatment of the dynamics, both of sufficient quality for the whole treatment to be satisfying.« less

Relativistic features and time delay of laser-induced tunnel ionization

NASA Astrophysics Data System (ADS)

Yakaboylu, Enderalp; Klaiber, Michael; Bauke, Heiko; Hatsagortsyan, Karen Z.; Keitel, Christoph H.

2013-12-01

The electron dynamics in the classically forbidden region during relativistic tunnel ionization is investigated. The classical forbidden region in the relativistic regime is identified by defining a gauge-invariant total-energy operator. Introducing position-dependent energy levels inside the tunneling barrier, we demonstrate that the relativistic tunnel ionization can be well described by a one-dimensional intuitive picture. This picture predicts that, in contrast to the well-known nonrelativistic regime, the ionized electron wave packet arises with a momentum shift along the laser's propagation direction. This is compatible with results from a strong-field approximation calculation where the binding potential is assumed to be zero ranged. Further, the tunneling time delay, stemming from Wigner's definition, is investigated for model configurations of tunneling and compared with results obtained from the exact propagator. By adapting Wigner's time delay definition to the ionization process, the tunneling time is investigated in the deep-tunneling and in the near-threshold-tunneling regimes. It is shown that while in the deep-tunneling regime signatures of the tunneling time delay are not measurable at remote distance, they are detectable, however, in the latter regime.

The Bargmann-Wigner equations in spherical space

NASA Astrophysics Data System (ADS)

McKeon, D. G. C.; Sherry, T. N.

2006-01-01

The Bargmann-Wigner formalism is adapted to spherical surfaces embedded in three to eleven dimensions. This is demonstrated to generate wave equations in spherical space for a variety of antisymmetric tensor fields. Some of these equations are gauge invariant for particular values of the parameters characterizing them. For spheres embedded in three, four, and five dimensions, this gauge invariance can be generalized so as to become non-Abelian. This non-Abelian gauge invariance is shown to be a property of second-order models for two index antisymmetric tensor fields in any number of dimensions. The O(3) model is quantized and the two-point function is shown to vanish at the one-loop order.

Comparison of qubit and qutrit like entangled squeezed and coherent states of light

NASA Astrophysics Data System (ADS)

Najarbashi, G.; Mirzaei, S.

2016-10-01

Squeezed state of light is one of the important subjects in quantum optics which is generated by optical nonlinear interactions. In this paper, we especially focus on qubit like entangled squeezed states (ESS's) generated by beam splitters, phase-shifter and cross Kerr nonlinearity. Moreover the Wigner function of two-mode qubit and qutrit like ESS are investigated. We will show that the distances of peaks of Wigner functions for two-mode ESS are entanglement sensitive and can be a witness for entanglement. Like the qubit cases, monogamy inequality is fulfilled for qutrit like ESS. These trends are compared with those obtained for qubit and qutrit like entangled coherent states (ECS).

Comparative Study of Entanglement and Wigner Function for Multi-Qubit GHZ-Squeezed State

NASA Astrophysics Data System (ADS)

Siyouri, Fatima-Zahra

2017-12-01

In this paper we address the possibility of using the Wigner function to capture the quantum entanglement present in a multi-qubit system. For that purpose, we calculate both the degree of entanglement and the Wigner function for mixed tripartite squeezed states of Greenberger-Horne-Zeilinger (GHZ) type then we compare their behaviors. We show that the role of Wigner function in detecting and quantifying bipartite quantum correlation [Int. J. Mod. Phys. B 30 (2016) 1650187] may be generalized to the multipartite case.

Computer-Generated, Three-Dimensional Character Animation.

ERIC Educational Resources Information Center

Van Baerle, Susan Lynn

This master's thesis begins by discussing the differences between 3-D computer animation of solid three-dimensional, or monolithic, objects, and the animation of characters, i.e., collections of movable parts with soft pliable surfaces. Principles from two-dimensional character animation that can be transferred to three-dimensional character…

Visualization Skills: A Prerequisite to Advanced Solid Modeling

ERIC Educational Resources Information Center

Gow, George

2007-01-01

Many educators believe that solid modeling software has made teaching two- and three-dimensional visualization skills obsolete. They claim that the visual tools built into the solid modeling software serve as a replacement for the CAD operator's personal visualization skills. They also claim that because solid modeling software can produce…

Autonomous Non-Linear Classification of LPI Radar Signal Modulations

DTIC Science & Technology

2007-09-01

Wigner - Ville distribution ( WVD ), the Choi-Williams distribution (CWD) and a Quadrature...accomplished using the images from the Wigner - Ville distribution and the Choi-Williams distribution for polyphase modulations. For the WVD images, radon...this work. Four detection techniques including the Wigner - Ville distribution ( WVD ), the Choi-Williams distribution (CWD), Quadrature Mirror

ELINT Signal Processing Using Choi-Williams Distribution on Reconfigurable Computers for Detection and Classification of LPI Emitters

DTIC Science & Technology

2008-03-01

WVD Wigner - Ville Distribution xiv THIS PAGE INTENTIONALLY LEFT BLANK xv ACKNOWLEDGMENTS Many thanks to David Caliga of SRC Computer for his...11 2. Wigner - Ville Distribution .................................................................11 3. Choi-Williams... Ville Distribution ...................................12 Table 3. C Code Output for Wigner - Ville Distribution

Field theoretic perspectives of the Wigner function formulation of the chiral magnetic effect

NASA Astrophysics Data System (ADS)

Wu, Yan; Hou, De-fu; Ren, Hai-cang

2017-11-01

We assess the applicability of the Wigner function formulation in its present form to the chiral magnetic effect and note some issues regarding the conservation and the consistency of the electric current in the presence of an inhomogeneous and time-dependent axial chemical potential. The problems are rooted in the ultraviolet divergence of the underlying field theory associated with the axial anomaly and can be fixed with the Pauli-Villars regularization of the Wigner function. The chiral magnetic current with a nonconstant axial chemical potential is calculated with the regularized Wigner function and the phenomenological implications are discussed.

Semiclassical propagator of the Wigner function.

PubMed

Dittrich, Thomas; Viviescas, Carlos; Sandoval, Luis

2006-02-24

Propagation of the Wigner function is studied on two levels of semiclassical propagation: one based on the Van Vleck propagator, the other on phase-space path integration. Leading quantum corrections to the classical Liouville propagator take the form of a time-dependent quantum spot. Its oscillatory structure depends on whether the underlying classical flow is elliptic or hyperbolic. It can be interpreted as the result of interference of a pair of classical trajectories, indicating how quantum coherences are to be propagated semiclassically in phase space. The phase-space path-integral approach allows for a finer resolution of the quantum spot in terms of Airy functions.

Positive phase space distributions and uncertainty relations

NASA Technical Reports Server (NTRS)

Kruger, Jan

1993-01-01

In contrast to a widespread belief, Wigner's theorem allows the construction of true joint probabilities in phase space for distributions describing the object system as well as for distributions depending on the measurement apparatus. The fundamental role of Heisenberg's uncertainty relations in Schroedinger form (including correlations) is pointed out for these two possible interpretations of joint probability distributions. Hence, in order that a multivariate normal probability distribution in phase space may correspond to a Wigner distribution of a pure or a mixed state, it is necessary and sufficient that Heisenberg's uncertainty relation in Schroedinger form should be satisfied.

Electrostatic attraction of coupled Wigner crystals: finite temperature effects.

PubMed

Lau, A W; Pincus, P; Levine, D; Fertig, H A

2001-05-01

In this paper we present a unified physical picture for the electrostatic attraction between two coupled planar Wigner crystals at finite temperature. This model may facilitate our conceptual understanding of counterion-mediated attractions between (highly) similarly charged planes. By adopting an elastic theory, we show that the total attractive force between them can be (approximately) decomposed into a short-ranged and a long-ranged component. They are evaluated below the melting temperature of the Wigner crystals. In particular, we analyze the temperature dependence of the short-ranged attraction, arising from ground-state configuration, and we argue that thermal fluctuations may drastically reduce its strength. Also, the long-range force agrees exactly with that based on the charge-fluctuation approach. Furthermore, we take quantum contributions to the long-ranged (fluctuation-induced) attraction into account and show how the fractional power law, which scales as d(-7/2) for large interplanar distance d at zero temperature, crosses over to the classical regime d(-3) via an intermediate regime of d(-2).

Large angle solid state position sensitive x-ray detector system

DOEpatents

Kurtz, David S.; Ruud, Clay O.

1998-01-01

A method and apparatus for x-ray measurement of certain properties of a solid material. In distinction to known methods and apparatus, this invention employs a specific fiber-optic bundle configuration, termed a reorganizer, itself known for other uses, for coherently transmitting visible light originating from the scintillation of diffracted x-radiation from the solid material gathered along a substantially one dimensional linear arc, to a two-dimensional photo-sensor array. The two-dimensional photodetector array, with its many closely packed light sensitive pixels, is employed to process the information contained in the diffracted radiation and present the information in the form of a conventional x-ray diffraction spectrum. By this arrangement, the angular range of the combined detector faces may be increased without loss of angular resolution. Further, the prohibitively expensive coupling together of a large number of individual linear diode photodetectors, which would be required to process signals generated by the diffracted radiation, is avoided.

Triple Resonance Solid State NMR Experiments with Reduced Dimensionality Evolution Periods

NASA Astrophysics Data System (ADS)

Astrof, Nathan S.; Lyon, Charles E.; Griffin, Robert G.

2001-10-01

Two solid state NMR triple resonance experiments which utilize the simultaneous incrementation of two chemical shift evolution periods to obtain a spectrum with reduced dimensionality are described. The CON CA experiment establishes the correlation of 13Ci-1 to 13Cαi and 15Ni by simultaneously encoding the 13COi-1 and 15Ni chemical shifts. The CAN COCA experiment establishes the correlation 13Cai and 15COi to 13Cαi-1 and 15Ni-1 within a single experiment by simultaneous encoding of the 13Cαi and 15Ni chemical shifts. This experiment establishes sequential amino acid correlations in close analogy to the solution state HNCA experiment. Reduced dimensionality 2D experiments are a practical alternative to recording multiple 3D data sets for the purpose of obtaining sequence-specific resonance assignments of peptides and proteins in the solid state.

Physical scales in the Wigner–Boltzmann equation

PubMed Central

Nedjalkov, M.; Selberherr, S.; Ferry, D.K.; Vasileska, D.; Dollfus, P.; Querlioz, D.; Dimov, I.; Schwaha, P.

2013-01-01

The Wigner–Boltzmann equation provides the Wigner single particle theory with interactions with bosonic degrees of freedom associated with harmonic oscillators, such as phonons in solids. Quantum evolution is an interplay of two transport modes, corresponding to the common coherent particle-potential processes, or to the decoherence causing scattering due to the oscillators. Which evolution mode will dominate depends on the scales of the involved physical quantities. A dimensionless formulation of the Wigner–Boltzmann equation is obtained, where these scales appear as dimensionless strength parameters. A notion called scaling theorem is derived, linking the strength parameters to the coupling with the oscillators. It is shown that an increase of this coupling is equivalent to a reduction of both the strength of the electric potential, and the coherence length. Secondly, the existence of classes of physically different, but mathematically equivalent setups of the Wigner–Boltzmann evolution is demonstrated. PMID:23504194

Experimental eavesdropping attack against Ekert's protocol based on Wigner's inequality

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bovino, F. A.; Colla, A. M.; Castagnoli, G.

2003-09-01

We experimentally implemented an eavesdropping attack against the Ekert protocol for quantum key distribution based on the Wigner inequality. We demonstrate a serious lack of security of this protocol when the eavesdropper gains total control of the source. In addition we tested a modified Wigner inequality which should guarantee a secure quantum key distribution.

The motion of a cloud of solid spherical particles falling in a cellular flow field at low Stokes number

NASA Astrophysics Data System (ADS)

Marchetti, Benjamin; Bergougnoux, Laurence; Guazzelli, Elisabeth

2017-11-01

We present a jointed experimental and numerical study examining the influence of vortical structures on the settling of a cloud of solid spherical particles under the action of gravity at low Stokes numbers. The two-dimensional model experiment uses electro-convection to generate a two-dimensional array of controlled vortices which mimics a simplified vortical flow. Particle image-velocimetry and tracking are used to examine the motion of the cloud within this vortical flow. The cloud motion is compared to the predictions of a two-way-coupling numerical simulation.

A surface curvature oscillation model for vapour-liquid-solid growth of periodic one-dimensional nanostructures

NASA Astrophysics Data System (ADS)

Wang, Hui; Wang, Jian-Tao; Cao, Ze-Xian; Zhang, Wen-Jun; Lee, Chun-Sing; Lee, Shuit-Tong; Zhang, Xiao-Hong

2015-03-01

While the vapour-liquid-solid process has been widely used for growing one-dimensional nanostructures, quantitative understanding of the process is still far from adequate. For example, the origins for the growth of periodic one-dimensional nanostructures are not fully understood. Here we observe that morphologies in a wide range of periodic one-dimensional nanostructures can be described by two quantitative relationships: first, inverse of the periodic spacing along the length direction follows an arithmetic sequence; second, the periodic spacing in the growth direction varies linearly with the diameter of the nanostructure. We further find that these geometric relationships can be explained by considering the surface curvature oscillation of the liquid sphere at the tip of the growing nanostructure. The work reveals the requirements of vapour-liquid-solid growth. It can be applied for quantitative understanding of vapour-liquid-solid growth and to design experiments for controlled growth of nanostructures with custom-designed morphologies.

Exact steady state of a Kerr resonator with one- and two-photon driving and dissipation: Controllable Wigner-function multimodality and dissipative phase transitions

NASA Astrophysics Data System (ADS)

Bartolo, Nicola; Minganti, Fabrizio; Casteels, Wim; Ciuti, Cristiano

2016-09-01

We present exact results for the steady-state density matrix of a general class of driven-dissipative systems consisting of a nonlinear Kerr resonator in the presence of both coherent (one-photon) and parametric (two-photon) driving and dissipation. Thanks to the analytical solution, obtained via the complex P -representation formalism, we are able to explore any regime, including photon blockade, multiphoton resonant effects, and a mesoscopic regime with large photon density and quantum correlations. We show how the interplay between one- and two-photon driving provides a way to control the multimodality of the Wigner function in regimes where the semiclassical theory exhibits multistability. We also study the emergence of dissipative phase transitions in the thermodynamic limit of large photon numbers.

Breakdown of the Wigner-Mattis theorem in semiconductor carbon-nanotube quantum dots

NASA Astrophysics Data System (ADS)

Rontani, Massimo; Secchi, Andrea; Manghi, Franca

2009-03-01

The Wigner-Mattis theorem states the ground state of two bound electrons, in the absence of the magnetic field, is always a spin-singlet. We predict the opposite result --a triplet- for two electrons in a quantum dot defined in a semiconductor carbon nanotube. The claim is supported by extensive many-body calculations based on the accurate configuration interaction code DONRODRIGO (www.s3.infm.t/donrodrigo). The crux of the matter is the peculiar two-valley structure of low-energy states, which encodes a pseudo-spin degree of freedom. The spin polarization of the ground state corresponds to a pseudo-spin singlet, which is selected by the inter-valley short-range Coulomb interaction. Single-electron excitation spectra and STM wave function images may validate this scenario, as shown by our numerical simulations.

Decoherence and Fidelity in Teleportation of Coherent Photon-Added Two-Mode Squeezed Thermal States

NASA Astrophysics Data System (ADS)

Li, Heng-Mei; Yuan, Hong-Chun; Wan, Zhi-Long; Wang, Zhen

2018-04-01

We theoretically introduce a kind of non-Gaussian entangled resources, i.e., coherent photon-added two-mode squeezed thermal states (CPA-TMSTS), by successively performing coherent photon addition operation to the two-mode squeezed thermal states. The normalization factor related to bivariate Hermite polynomials is obtained. Based upon it, the nonclassicality and decoherence process are analyzed by virtue of the Wigner function. It is shown that the coherent photon addition operation is an effective way in generating partial negative values of Wigner function, which clearly manifests the nonclassicality and non-Gaussianity of the target states. Additionally, the fidelity in teleporting coherent states using CPA-TMSTS as entangled resource is quantified both analytically and numerically. It is found that the CPA-TMSTS is an entangled resource of high-efficiency and high-fidelity in quantum teleportation.

Eigenvalue distributions for a class of covariance matrices with application to Bienenstock-Cooper-Munro neurons under noisy conditions.

PubMed

Bazzani, Armando; Castellani, Gastone C; Cooper, Leon N

2010-05-01

We analyze the effects of noise correlations in the input to, or among, Bienenstock-Cooper-Munro neurons using the Wigner semicircular law to construct random, positive-definite symmetric correlation matrices and compute their eigenvalue distributions. In the finite dimensional case, we compare our analytic results with numerical simulations and show the effects of correlations on the lifetimes of synaptic strengths in various visual environments. These correlations can be due either to correlations in the noise from the input lateral geniculate nucleus neurons, or correlations in the variability of lateral connections in a network of neurons. In particular, we find that for fixed dimensionality, a large noise variance can give rise to long lifetimes of synaptic strengths. This may be of physiological significance.

State-specific tunneling lifetimes from classical trajectories: H-atom dissociation in electronically excited pyrrole

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xie, Weiwei; Domcke, Wolfgang; Farantos, Stavros C.

A trajectory method of calculating tunneling probabilities from phase integrals along straight line tunneling paths, originally suggested by Makri and Miller [J. Chem. Phys. 91, 4026 (1989)] and recently implemented by Truhlar and co-workers [Chem. Sci. 5, 2091 (2014)], is tested for one- and two-dimensional ab initio based potentials describing hydrogen dissociation in the {sup 1}B{sub 1} excited electronic state of pyrrole. The primary observables are the tunneling rates in a progression of bending vibrational states lying below the dissociation barrier and their isotope dependences. Several initial ensembles of classical trajectories have been considered, corresponding to the quasiclassical and themore » quantum mechanical samplings of the initial conditions. It is found that the sampling based on the fixed energy Wigner density gives the best agreement with the quantum mechanical dissociation rates.« less

Detection and Parameter Estimation of Chirped Radar Signals.

DTIC Science & Technology

2000-01-10

Wigner - Ville distribution ( WVD ): The WVD belongs to the Cohen’s class of energy distributions ...length. 28 6. Pseudo Wigner - Ville distribution (PWVD): The PWVD introduces a time-window to the WVD definition, thereby reducing the interferences...Frequency normalized to sampling frequency 26 Figure V.2: Wigner - Ville distribution ; time normalized to the pulse length 28 Figure V.3:

Fixed and Data Adaptive Kernels in Cohen’s Class of Time-Frequency Distributions

DTIC Science & Technology

1992-09-01

translated into its associated analytic signal by using the techniques discussed in Chapter Four. 1. Wigner - Ville Distribution function PS = wvd (data,winlen...step,begin,theend) % PS = wvd (data,winlen,step,begin,theend) % ’wvd.ml returns the Wigner - Ville time-frequency distribution % for the input data...12 IV. FIXED KERNEL DISTRIBUTIONS .................................................................. 19 A. WIGNER - VILLE DISTRIBUTION

Uncertainty relations with the generalized Wigner-Yanase-Dyson skew information

NASA Astrophysics Data System (ADS)

Fan, Yajing; Cao, Huaixin; Wang, Wenhua; Meng, Huixian; Chen, Liang

2018-07-01

The uncertainty principle in quantum mechanics is a fundamental relation with different forms, including Heisenberg's uncertainty relation and Schrödinger's uncertainty relation. We introduce the generalized Wigner-Yanase-Dyson correlation and the related quantities. Various properties of them are discussed. Finally, we establish several generalizations of uncertainty relation expressed in terms of the generalized Wigner-Yanase-Dyson skew information.

Sampling in the light of Wigner distribution.

PubMed

Stern, Adrian; Javidi, Bahram

2004-03-01

We propose a new method for analysis of the sampling and reconstruction conditions of real and complex signals by use of the Wigner domain. It is shown that the Wigner domain may provide a better understanding of the sampling process than the traditional Fourier domain. For example, it explains how certain non-bandlimited complex functions can be sampled and perfectly reconstructed. On the basis of observations in the Wigner domain, we derive a generalization to the Nyquist sampling criterion. By using this criterion, we demonstrate simple preprocessing operations that can adapt a signal that does not fulfill the Nyquist sampling criterion. The preprocessing operations demonstrated can be easily implemented by optical means.

Nanometer-sized materials for solid-phase extraction of trace elements.

PubMed

Hu, Bin; He, Man; Chen, Beibei

2015-04-01

This review presents a comprehensive update on the state-of-the-art of nanometer-sized materials in solid-phase extraction (SPE) of trace elements followed by atomic-spectrometry detection. Zero-dimensional nanomaterials (fullerene), one-dimensional nanomaterials (carbon nanotubes, inorganic nanotubes, and nanowires), two-dimensional nanomaterials (nanofibers), and three-dimensional nanomaterials (nanoparticles, mesoporous nanoparticles, magnetic nanoparticles, and dendrimers) for SPE are discussed, with their application for trace-element analysis and their speciation in different matrices. A variety of other novel SPE sorbents, including restricted-access sorbents, ion-imprinted polymers, and metal-organic frameworks, are also discussed, although their applications in trace-element analysis are relatively scarce so far.

Real time correlation function in a single phase space integral beyond the linearized semiclassical initial value representation.

PubMed

Liu, Jian; Miller, William H

2007-06-21

It is shown how quantum mechanical time correlation functions [defined, e.g., in Eq. (1.1)] can be expressed, without approximation, in the same form as the linearized approximation of the semiclassical initial value representation (LSC-IVR), or classical Wigner model, for the correlation function [cf. Eq. (2.1)], i.e., as a phase space average (over initial conditions for trajectories) of the Wigner functions corresponding to the two operators. The difference is that the trajectories involved in the LSC-IVR evolve classically, i.e., according to the classical equations of motion, while in the exact theory they evolve according to generalized equations of motion that are derived here. Approximations to the exact equations of motion are then introduced to achieve practical methods that are applicable to complex (i.e., large) molecular systems. Four such methods are proposed in the paper--the full Wigner dynamics (full WD) and the second order WD based on "Wigner trajectories" [H. W. Lee and M. D. Scully, J. Chem. Phys. 77, 4604 (1982)] and the full Donoso-Martens dynamics (full DMD) and the second order DMD based on "Donoso-Martens trajectories" [A. Donoso and C. C. Martens, Phys. Rev. Lett. 8722, 223202 (2001)]--all of which can be viewed as generalizations of the original LSC-IVR method. Numerical tests of the four versions of this new approach are made for two anharmonic model problems, and for each the momentum autocorrelation function (i.e., operators linear in coordinate or momentum operators) and the force autocorrelation function (nonlinear operators) have been calculated. These four new approximate treatments are indeed seen to be significant improvements to the original LSC-IVR approximation.

FRAUD/SABOTAGE Killing Nuclear-Reactors Need Modeling!!!: "Super"alloys GENERIC ENDEMIC Wigner's-Disease/.../IN-stability: Ethics? SHMETHICS!!!

NASA Astrophysics Data System (ADS)

Asphahani, Aziz; Siegel, Sidney; Siegel, Edward

2010-03-01

Carbides solid-state chemistry domination of old/new nuclear- reactors/spent-fuel-casks/refineries/jet/missile/rocket-engines in austenitic/FCC Ni/Fe-based(so miscalled)``super"alloys(182/82; Hastelloy-X,600,304/304L-SSs,...,690!!!) GENERIC ENDEMIC EXTANT detrimental(synonyms): Wigner's-diseas(WD)[J.Appl.Phys.17,857 (1946)]/Ostwald-ripening/spinodal-decomposition/overageing- embrittlement/thermal-leading-to-mechanical(TLTM)-INstability: Mayo[Google:``If Leaks Could Kill"; at flickr.com search on ``Giant-Magnotoresistance"; find: Siegel[J.Mag.Mag.Mtls.7,312 (1978)]<<<``Fert"-"Gruenberg"(1988/89)2007-physics Nobel/Wolf/ Japan-prizes]necessitating NRC-inspections of 40+25 = 65 Westin- ``KLouse PWRs(12/2006)]-Lai[Met.Trans.AIME,9A,827(1978)]-Sabol- Stickler[Phys.Stat.Sol.(1970)]-Ashpahani[Intl.Conf. H in Metals, Paris(1977]-Russell[Prog.Mtls.Sci.(1983)]-Pollard[last UCS rept. (9/1995)]-Lofaro[BNL/DOE/NRC Repts.]-Pringle[Nuclear-Power:From Physics to Politics(1979)]-Hoffman[animatedsoftware.com], what DOE/NRC MISlabels as ``butt-welds" ``stress-corrosion cracking" endpoint's ROOT-CAUSE ULTIMATE-ORIGIN is WD overageing-embritt- lement caused brittle-fracture cracking from early/ongoing AEC/ DOE-n"u"tional-la"v"atories sabotage!!!

FRAUD/SABOTAGE Killing Nuclear-Reactors Need Modeling!!!: ``Super'' alloys GENERIC ENDEMIC Wigner's-Disease/.../IN-stability: Ethics? SHMETHICS!!!

NASA Astrophysics Data System (ADS)

O'Grady, Joseph; Bument, Arlden; Siegel, Edward

2011-03-01

Carbides solid-state chemistry domination of old/new nuclear-reactors/spent-fuel-casks/refineries/jet/missile/rocket-engines is austenitic/FCC Ni/Fe-based (so miscalled)"super"alloys(182/82;Hastelloy-X,600,304/304L-SSs,...690!!!) GENERIC ENDEMIC EXTANT detrimental(synonyms): Wigner's-disease(WD) [J.Appl.Phys.17,857 (46)]/Ostwald-ripening/spinodal-decomposition/overageing-embrittlement/thermal-leading-to-mechanical(TLTM)-INstability: Mayo[Google: fLeaksCouldKill > ; - Siegel [ J . Mag . Mag . Mtls . 7 , 312 (78) = atflickr . comsearchonGiant - Magnotoresistance [Fert" [PRL(1988)]-"Gruenberg"[PRL(1989)] 2007-Nobel]necessitating NRC inspections on 40+25=65 Westin"KL"ouse PWRs(12/2006)]-Lai [Met.Trans.AIME, 9A,827(78)]-Sabol-Stickler[Phys.Stat.Sol.(70)]-Ashpahani[ Intl.Conf. Hydrogen in Metals, Paris(1977]-Russell [Prog.Mtls.Sci.(1983)]-Pollard [last UCS rept.(9/1995)]-Lofaro [BNL/DOE/NRC Repts.]-Pringle [ Nuclear-Power:From Physics to Politics(1979)]-Hoffman [animatedsoftware.com], what DOE/NRC MISlabels as "butt-welds" "stress-corrosion cracking" endpoint's ROOT-CAUSE ULTIMATE-ORIGIN is WD overageing-embrittlement caused brittle-fracture cracking from early/ongoing AEC/DOE-n"u"tional-la"v"atories sabotage!!!

Hartree-Fock mass formulas and extrapolation to new mass data

NASA Astrophysics Data System (ADS)

Goriely, S.; Samyn, M.; Heenen, P.-H.; Pearson, J. M.; Tondeur, F.

2002-08-01

The two previously published Hartree-Fock (HF) mass formulas, HFBCS-1 and HFB-1 (HF-Bogoliubov), are shown to be in poor agreement with new Audi-Wapstra mass data. The problem lies first with the prescription adopted for the cutoff of the single-particle spectrum used with the δ-function pairing force, and second with the Wigner term. We find an optimal mass fit if the spectrum is cut off both above EF+15 MeV and below EF-15 MeV, EF being the Fermi energy of the nucleus in question. In addition to the Wigner term of the form VW exp(-λ|N-Z|/A) already included in the two earlier HF mass formulas, we find that a second Wigner term linear in |N-Z| leads to a significant improvement in lighter nuclei. These two features are incorporated into our new Hartree-Fock-Bogoliubov model, which leads to much improved extrapolations. The 18 parameters of the model are fitted to the 2135 measured masses for N,Z>=8 with an rms error of 0.674 MeV. With this parameter set a complete mass table, labeled HFB-2, has been constructed, going from one drip line to the other, up to Z=120. The new pairing-cutoff prescription favored by the new mass data leads to weaker neutron-shell gaps in neutron-rich nuclei.

Correlations and sum rules in a half-space for a quantum two-dimensional one-component plasma

NASA Astrophysics Data System (ADS)

Jancovici, B.; Šamaj, L.

2007-05-01

This paper is the continuation of a previous one (Šamaj and Jancovici, 2007 J. Stat. Mech. P02002); for a nearly classical quantum fluid in a half-space bounded by a plain plane hard wall (no image forces), we had generalized the Wigner Kirkwood expansion of the equilibrium statistical quantities in powers of Planck's constant \\hbar . As a model system for a more detailed study, we consider the quantum two-dimensional one-component plasma: a system of charged particles of one species, interacting through the logarithmic Coulomb potential in two dimensions, in a uniformly charged background of opposite sign, such that the total charge vanishes. The corresponding classical system is exactly solvable in a variety of geometries, including the present one of a half-plane, when βe2 = 2, where β is the inverse temperature and e is the charge of a particle: all the classical n-body densities are known. In the present paper, we have calculated the expansions of the quantum density profile and truncated two-body density up to order \\hbar ^2 (instead of only to order \\hbar as in the previous paper). These expansions involve the classical n-body densities up to n = 4; thus we obtain exact expressions for these quantum expansions in this special case. For the quantum one-component plasma, two sum rules involving the truncated two-body density (and, for one of them, the density profile) have been derived, a long time ago, by using heuristic macroscopic arguments: one sum rule concerns the asymptotic form along the wall of the truncated two-body density; the other one concerns the dipole moment of the structure factor. In the two-dimensional case at βe2 = 2, we now have explicit expressions up to order \\hbar^2 for these two quantum densities; thus we can microscopically check the sum rules at this order. The checks are positive, reinforcing the idea that the sum rules are correct.

A coupled sharp-interface immersed boundary-finite-element method for flow-structure interaction with application to human phonation.

PubMed

Zheng, X; Xue, Q; Mittal, R; Beilamowicz, S

2010-11-01

A new flow-structure interaction method is presented, which couples a sharp-interface immersed boundary method flow solver with a finite-element method based solid dynamics solver. The coupled method provides robust and high-fidelity solution for complex flow-structure interaction (FSI) problems such as those involving three-dimensional flow and viscoelastic solids. The FSI solver is used to simulate flow-induced vibrations of the vocal folds during phonation. Both two- and three-dimensional models have been examined and qualitative, as well as quantitative comparisons, have been made with established results in order to validate the solver. The solver is used to study the onset of phonation in a two-dimensional laryngeal model and the dynamics of the glottal jet in a three-dimensional model and results from these studies are also presented.

Broadband Time-Frequency Analysis Using a Multicomputer

DTIC Science & Technology

2004-09-30

FFT 512 pt Waterfall WVD display 8© 2004 Mercury Computer Systems, Inc. Smoothed Pseudo Wigner - Ville Distribution One of many interference reduction...The Wigner - Ville distribution , the scalogram, and the discrete Gabor transform are among the most well-known of these methods. Due to specific...based upon FFT Accumulation Method • Continuous Wavelet Transform (Scalogram) • Discrete Wigner - Ville Distribution with a selected set of interference

STAP for SAR

DTIC Science & Technology

2003-04-01

Wigner - Ville Distribution ( WVD ) of the signal. This distribution is a signal representation consisting in the mapping of the... Wigner - Ville distribution The aim of this section is to show how time-frequency representation by WVD of the echoes received by a SAR provides a...frequency analysis by Wigner - Ville distribution ". IEE Proc., Pt. F., Vol. 139, no. 1, February 1992, pp. 89-97. 3-17 [BFA94] S. Barbarossa, A.

Supersymmetrical bounding of asymmetric states and quantum phase transitions by anti-crossing of symmetric states

PubMed Central

Afzal, Muhammad Imran; Lee, Yong Tak

2016-01-01

Von Neumann and Wigner theorized the bounding and anti-crossing of eigenstates. Experiments have demonstrated that owing to anti-crossing and similar radiation rates, the graphene-like resonance of inhomogeneously strained photonic eigenstates can generate a pseudomagnetic field, bandgaps and Landau levels, whereas exponential or dissimilar rates induce non-Hermicity. Here, we experimentally demonstrate higher-order supersymmetry and quantum phase transitions by resonance between similar one-dimensional lattices. The lattices consisted of inhomogeneous strain-like phases of triangular solitons. The resonance created two-dimensional, inhomogeneously deformed photonic graphene. All parent eigenstates were annihilated. Eigenstates of mildly strained solitons were annihilated at similar rates through one tail and generated Hermitian bounded eigenstates. The strongly strained solitons with positive phase defects were annihilated at exponential rates through one tail, which bounded eigenstates through non-Hermitianally generated exceptional points. Supersymmetry was evident, with preservation of the shapes and relative phase differences of the parent solitons. Localizations of energies generated from annihilations of mildly and strongly strained soliton eigenstates were responsible for geometrical (Berry) and topological phase transitions, respectively. Both contributed to generating a quantum Zeno phase, whereas only strong twists generated topological (Anderson) localization. Anti-bunching-like condensation was also observed. PMID:27966596

Decoherence and surface hopping: When can averaging over initial conditions help capture the effects of wave packet separation?

NASA Astrophysics Data System (ADS)

Subotnik, Joseph E.; Shenvi, Neil

2011-06-01

Fewest-switches surface hopping (FSSH) is a popular nonadiabatic dynamics method which treats nuclei with classical mechanics and electrons with quantum mechanics. In order to simulate the motion of a wave packet as accurately as possible, standard FSSH requires a stochastic sampling of the trajectories over a distribution of initial conditions corresponding, e.g., to the Wigner distribution of the initial quantum wave packet. Although it is well-known that FSSH does not properly account for decoherence effects, there is some confusion in the literature about whether or not this averaging over a distribution of initial conditions can approximate some of the effects of decoherence. In this paper, we not only show that averaging over initial conditions does not generally account for decoherence, but also why it fails to do so. We also show how an apparent improvement in accuracy can be obtained for a fortuitous choice of model problems, even though this improvement is not possible, in general. For a basic set of one-dimensional and two-dimensional examples, we find significantly improved results using our recently introduced augmented FSSH algorithm.

Semiclassical relation between open trajectories and periodic orbits for the Wigner time delay.

PubMed

Kuipers, Jack; Sieber, Martin

2008-04-01

The Wigner time delay of a classically chaotic quantum system can be expressed semiclassically either in terms of pairs of scattering trajectories that enter and leave the system or in terms of the periodic orbits trapped inside the system. We show how these two pictures are related on the semiclassical level. We start from the semiclassical formula with the scattering trajectories and derive from it all terms in the periodic orbit formula for the time delay. The main ingredient in this calculation are correlations between scattering trajectories which are due to trajectories that approach the trapped periodic orbits closely. The equivalence between the two pictures is also demonstrated by considering correlation functions of the time delay. A corresponding calculation for the conductance gives no periodic orbit contributions in leading order.

Center-of-Mass Tomography and Wigner Function for Multimode Photon States

NASA Astrophysics Data System (ADS)

Dudinets, Ivan V.; Man'ko, Vladimir I.

2018-06-01

Tomographic probability representation of multimode electromagnetic field states in the scheme of center-of-mass tomography is reviewed. Both connection of the field state Wigner function and observable Weyl symbols with the center-of-mass tomograms as well as connection of the Grönewold kernel with the center-of-mass tomographic kernel determining the noncommutative product of the tomograms are obtained. The dual center-of-mass tomogram of the photon states are constructed and the dual tomographic kernel is obtained. The models of other generalized center-of-mass tomographies are discussed. Example of two-mode even and odd Schrödinger cat states is presented in details.

Flame propagation in two-dimensional solids: Particle-resolved studies with complex plasmas

NASA Astrophysics Data System (ADS)

Yurchenko, S. O.; Yakovlev, E. V.; Couëdel, L.; Kryuchkov, N. P.; Lipaev, A. M.; Naumkin, V. N.; Kislov, A. Yu.; Ovcharov, P. V.; Zaytsev, K. I.; Vorob'ev, E. V.; Morfill, G. E.; Ivlev, A. V.

2017-10-01

Using two-dimensional (2D) complex plasmas as an experimental model system, particle-resolved studies of flame propagation in classical 2D solids are carried out. Combining experiments, theory, and molecular dynamics simulations, we demonstrate that the mode-coupling instability operating in 2D complex plasmas reveals all essential features of combustion, such as an activated heat release, two-zone structure of the self-similar temperature profile ("flame front"), as well as thermal expansion of the medium and temperature saturation behind the front. The presented results are of relevance for various fields ranging from combustion and thermochemistry, to chemical physics and synthesis of materials.

Two-dimensional periodic structures in solid state laser resonator

NASA Astrophysics Data System (ADS)

Okulov, Alexey Y.

1991-07-01

Transverse effects in nonlinear optical devices are being widely investigated. Recently, synchronization of a laser set by means of the Talbot effect has been demonstrated experimentally. This paper considers a Talbot cavity formed by a solid-state amplifying laser separated from the output mirror by a free space interval. This approach involves the approximation of the nonlinear medium as a thin layer, within which the diffraction is negligible. The other part of a resonator is empty, and the wave field is transformed by the Fresnel-Kirchoff integral. As a result, the dynamics of the transverse (and temporal) structure is computed by a successively iterated nonlinear local map (one- or two-dimensional) and a linear nonlocal map (generally speaking, infinitely dimensional).

A device adaptive inflow boundary condition for Wigner equations of quantum transport

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jiang, Haiyan; Lu, Tiao; Cai, Wei, E-mail: wcai@uncc.edu

2014-02-01

In this paper, an improved inflow boundary condition is proposed for Wigner equations in simulating a resonant tunneling diode (RTD), which takes into consideration the band structure of the device. The original Frensley inflow boundary condition prescribes the Wigner distribution function at the device boundary to be the semi-classical Fermi–Dirac distribution for free electrons in the device contacts without considering the effect of the quantum interaction inside the quantum device. The proposed device adaptive inflow boundary condition includes this effect by assigning the Wigner distribution to the value obtained from the Wigner transform of wave functions inside the device atmore » zero external bias voltage, thus including the dominant effect on the electron distribution in the contacts due to the device internal band energy profile. Numerical results on computing the electron density inside the RTD under various incident waves and non-zero bias conditions show much improvement by the new boundary condition over the traditional Frensley inflow boundary condition.« less

Fokker-Planck equation of the reduced Wigner function associated to an Ohmic quantum Langevin dynamics

NASA Astrophysics Data System (ADS)

Colmenares, Pedro J.

2018-05-01

This article has to do with the derivation and solution of the Fokker-Planck equation associated to the momentum-integrated Wigner function of a particle subjected to a harmonic external field in contact with an ohmic thermal bath of quantum harmonic oscillators. The strategy employed is a simplified version of the phenomenological approach of Schramm, Jung, and Grabert of interpreting the operators as c numbers to derive the quantum master equation arising from a twofold transformation of the Wigner function of the entire phase space. The statistical properties of the random noise comes from the integral functional theory of Grabert, Schramm, and Ingold. By means of a single Wigner transformation, a simpler equation than that mentioned before is found. The Wigner function reproduces the known results of the classical limit. This allowed us to rewrite the underdamped classical Langevin equation as a first-order stochastic differential equation with time-dependent drift and diffusion terms.

Higher-order stochastic differential equations and the positive Wigner function

NASA Astrophysics Data System (ADS)

Drummond, P. D.

2017-12-01

General higher-order stochastic processes that correspond to any diffusion-type tensor of higher than second order are obtained. The relationship of multivariate higher-order stochastic differential equations with tensor decomposition theory and tensor rank is explained. Techniques for generating the requisite complex higher-order noise are proved to exist either using polar coordinates and γ distributions, or from products of Gaussian variates. This method is shown to allow the calculation of the dynamics of the Wigner function, after it is extended to a complex phase space. The results are illustrated physically through dynamical calculations of the positive Wigner distribution for three-mode parametric downconversion, widely used in quantum optics. The approach eliminates paradoxes arising from truncation of the higher derivative terms in Wigner function time evolution. Anomalous results of negative populations and vacuum scattering found in truncated Wigner quantum simulations in quantum optics and Bose-Einstein condensate dynamics are shown not to occur with this type of stochastic theory.

Quantum to classical transition in the Hořava-Lifshitz quantum cosmology

NASA Astrophysics Data System (ADS)

Bernardini, A. E.; Leal, P.; Bertolami, O.

2018-02-01

A quasi-Gaussian quantum superposition of Hořava-Lifshitz (HL) stationary states is built in order to describe the transition of the quantum cosmological problem to the related classical dynamics. The obtained HL phase-space superposed Wigner function and its associated Wigner currents describe the conditions for the matching between classical and quantum phase-space trajectories. The matching quantum superposition parameter is associated to the total energy of the classical trajectory which, at the same time, drives the engendered Wigner function to the classical stationary regime. Through the analysis of the Wigner flows, the quantum fluctuations that distort the classical regime can be quantified as a measure of (non)classicality. Finally, the modifications to the Wigner currents due to the inclusion of perturbative potentials are computed in the HL quantum cosmological context. In particular, the inclusion of a cosmological constant provides complementary information that allows for connecting the age of the Universe with the overall stiff matter density profile.

Lamb Waves Decomposition and Mode Identification Using Matching Pursuit Method

DTIC Science & Technology

2009-01-01

Wigner - Ville distribution ( WVD ). However, WVD suffers from severe interferences, called cross-terms. Cross- terms are the area of a time-frequency...transform (STFT), wavelet transform, Wigner - Ville distribution , matching pursuit decomposition, etc. 1 Report Documentation Page Form ApprovedOMB No...MP decomposition using chirplet dictionary was applied to a simulated S0 mode Lamb wave shown previously in Figure 2a. Wigner - Ville distribution of

Feature Extraction for Bearing Prognostics and Health Management (PHM) - A Survey (Preprint)

DTIC Science & Technology

2008-05-01

Envelope analysis • Cepstrum analysis • Higher order spectrum • Short-time Fourier Transform (STFT) • Wigner - Ville distribution ( WVD ) • Empirical mode...techniques are the short-time Fourier transform (STFT), the Wigner - Ville distribution , and the wavelet transform. In this paper we categorize wavelets...diagnosis have shown in many publications, for example, [22]. b) Wigner – Ville distribution : The afore-mentioned STFT is conceptually simple. However

Simulation of Devices with Molecular Potentials

DTIC Science & Technology

2013-12-22

10] W. R. Frensley, Wigner - function model of a resonant-tunneling semiconductor de- vice, Phys. Rev. B, 36 (1987), pp. 1570–1580. 6 [11] M. J...develop the principal investigator’s Wigner -Poisson code and extend that code to deal with longer devices and more complex barrier profiles. Over...Research Triangle Park, NC 27709-2211 Molecular Confirmation, Sparse Interpolation, Wigner -Poisson Equation, Parallel Algorithms REPORT DOCUMENTATION PAGE 11

Elastic and viscoelastic effects in rubber/air acoustic band gap structures: A theoretical and experimental study

NASA Astrophysics Data System (ADS)

Merheb, B.; Deymier, P. A.; Jain, M.; Aloshyna-Lesuffleur, M.; Mohanty, S.; Berker, A.; Greger, R. W.

2008-09-01

The transmission of acoustic waves through centimeter-scale elastic and viscoelastic two-dimensional silicone rubber/air phononic crystal structures is investigated theoretically and experimentally. We introduce a finite difference time domain method for two-dimensional elastic and viscoelastic composite structures. Elastic fluid-solid phononic crystals composed of a two-dimensional array of cylindrical air inclusions in a solid rubber matrix, as well as an array of rubber cylinders in an air matrix, are shown to behave similarly to fluid-fluid composite structures. These systems exhibit very wide band gaps in their transmission spectra that extend to frequencies in the audible range of the spectrum. This effect is associated with the very low value of the transverse speed of sound in rubber compared to that of the longitudinal polarization. The difference in transmission between elastic and viscoelastic rubber/air crystals results from attenuation of transmission over a very wide frequency range, leaving only narrow passing bands at very low frequencies. These phononic crystals demonstrate the practical design of elastic or viscoelastic solid rubber/air acoustic band gap sound barriers with small dimensions.

Exploration and exploitation of homologous series of bis(acrylamido)alkanes containing pyridyl and phenyl groups: β-sheet versus two-dimensional layers in solid-state photochemical [2 + 2] reactions.

PubMed

Garai, Mousumi; Biradha, Kumar

2015-09-01

The homologous series of phenyl and pyridyl substituted bis(acrylamido)alkanes have been synthesized with the aim of systematic analysis of their crystal structures and their solid-state [2 + 2] reactivities. The changes in the crystal structures with respect to a small change in the molecular structure, that is by varying alkyl spacers between acrylamides and/or by varying the end groups (phenyl, 2-pyridyl, 3-pyridyl, 4-pyridyl) on the C-terminal of the amide, were analyzed in terms of hydrogen-bonding interference (N-H⋯Npy versus N-H⋯O=C) and network geometries. In this series, a greater tendency towards the formation of N-H⋯O hydrogen bonds (β-sheets and two-dimensional networks) over N-H⋯N hydrogen bonds was observed. Among all the structures seven structures were found to have the required alignments of double bonds for the [2 + 2] reaction such that the formations of single dimer, double dimer and polymer are facilitated. However, only four structures were found to exhibit such a solid-state [2 + 2] reaction to form a single dimer and polymers. The two-dimensional hydrogen-bonding layer via N-H⋯O hydrogen bonds was found to promote solid-state [2 + 2] photo-polymerization in a single-crystal-to-single-crystal manner. Such two-dimensional layers were encountered only when the spacer between acryl amide moieties is butyl. Only four out of the 16 derivatives were found to form hydrates, two each from 2-pyridyl and 4-pyridyl derivatives. The water molecules in these structures govern the hydrogen-bonding networks by the formation of an octameric water cluster and one-dimensional zigzag water chains. The trends in the melting points and densities were also analyzed.

Time-resolved two-window measurement of Wigner functions for coherent backscatter from a turbid medium

NASA Astrophysics Data System (ADS)

Reil, Frank; Thomas, John E.

2002-05-01

For the first time we are able to observe the time-resolved Wigner function of enhanced backscatter from a random medium using a novel two-window technique. This technique enables us to directly verify the phase-conjugating properties of random media. An incident divergent beam displays a convergent enhanced backscatter cone. We measure the joint position and momentum (x, p) distributions of the light field as a function of propagation time in the medium. The two-window technique allows us to independently control the resolutions for position and momentum, thereby surpassing the uncertainty limit associated with Fourier transform pairs. By using a low-coherence light source in a heterodyne detection scheme, we observe enhanced backscattering resolved by path length in the random medium, providing information about the evolution of optical coherence as a function of penetration depth in the random medium.

Parametrically coupled fermionic oscillators: Correlation functions and phase-space description

NASA Astrophysics Data System (ADS)

Ghosh, Arnab

2015-01-01

A fermionic analog of a parametric amplifier is used to describe the joint quantum state of the two interacting fermionic modes. Based on a two-mode generalization of the time-dependent density operator, time evolution of the fermionic density operator is determined in terms of its two-mode Wigner and P function. It is shown that the equation of motion of the Wigner function corresponds to a fermionic analog of Liouville's equation. The equilibrium density operator for fermionic fields developed by Cahill and Glauber is thus extended to a dynamical context to show that the mathematical structures of both the correlation functions and the weight factors closely resemble their bosonic counterpart. It has been shown that the fermionic correlation functions are marked by a characteristic upper bound due to Fermi statistics, which can be verified in the matter wave counterpart of photon down-conversion experiments.

Maple procedures for the coupling of angular momenta. IX. Wigner D-functions and rotation matrices

NASA Astrophysics Data System (ADS)

Pagaran, J.; Fritzsche, S.; Gaigalas, G.

2006-04-01

The Wigner D-functions, Dpqj(α,β,γ), are known for their frequent use in quantum mechanics. Defined as the matrix elements of the rotation operator Rˆ(α,β,γ) in R and parametrized in terms of the three Euler angles α, β, and γ, these functions arise not only in the transformation of tensor components under the rotation of the coordinates, but also as the eigenfunctions of the spherical top. In practice, however, the use of the Wigner D-functions is not always that simple, in particular, if expressions in terms of these and other functions from the theory of angular momentum need to be simplified before some computations can be carried out in detail. To facilitate the manipulation of such Racah expressions, here we present an extension to the RACAH program [S. Fritzsche, Comput. Phys. Comm. 103 (1997) 51] in which the properties and the algebraic rules of the Wigner D-functions and reduced rotation matrices are implemented. Care has been taken to combine the standard knowledge about the rotation matrices with the previously implemented rules for the Clebsch-Gordan coefficients, Wigner n-j symbols, and the spherical harmonics. Moreover, the application of the program has been illustrated below by means of three examples. Program summaryTitle of program:RACAH Catalogue identifier:ADFv_9_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADFv_9_0 Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Catalogue identifier of previous version: ADFW, ADHW, title RACAH Journal reference of previous version(s): S. Fritzsche, Comput. Phys. Comm. 103 (1997) 51; S. Fritzsche, S. Varga, D. Geschke, B. Fricke, Comput. Phys. Comm. 111 (1998) 167; S. Fritzsche, T. Inghoff, M. Tomaselli, Comput. Phys. Comm. 153 (2003) 424. Does the new version supersede the previous one: Yes, in addition to the spherical harmonics and recoupling coefficients, the program now supports also the occurrence of the Wigner rotation matrices in the algebraic expressions to be evaluated. Licensing provisions:None Computer for which the program is designed and others on which it is operable: All computers with a license for the computer algebra package Maple [Maple is a registered trademark of Waterloo Maple Inc.] Installations:University of Kassel (Germany) Operating systems under which the program has been tested: Linux 8.2+ Program language used:MAPLE, Release 8 and 9 Memory required to execute with typical data:10-50 MB No. of lines in distributed program, including test data, etc.:52 653 No. of bytes in distributed program, including test data, etc.:1 195 346 Distribution format:tar.gzip Nature of the physical problem: The Wigner D-functions and (reduced) rotation matrices occur very frequently in physical applications. They are known not only as the (infinite) representation of the rotation group but also to obey a number of integral and summation rules, including those for their orthogonality and completeness. Instead of the direct computation of these matrices, therefore, one first often wishes to find algebraic simplifications before the computations can be carried out in practice. Reasons for new version: The RACAH program has been found an efficient tool during recent years, in order to evaluate and simplify expressions from Racah's algebra. Apart from the Wigner n-j symbols ( j=3,6,9) and spherical harmonics, we now extended the code to allow for Wigner rotation matrices. This extension will support the study of those quantum processes especially where different axis of quantization occurs in course of the theoretical deviations. Summary of revisions: In a revised version of the RACAH program [S. Fritzsche, Comput. Phys. Comm. 103 (1997) 51; S. Fritzsche, T. Inghoff, M. Tomaselli, Comput. Phys. Comm. 153 (2003) 424], we now also support the occurrence of the Wigner D-functions and reduced rotation matrices. By following our previous design, the (algebraic) properties of these rotation matrices as well as a number of summation and integration rules are implemented to facilitate the algebraic simplification of expressions from the theories of angular momentum and the spherical tensor operators. Restrictions onto the complexity of the problem: The definition as well as the properties of the rotation matrices, as used in our implementation, are based mainly on the book of Varshalovich et al. [D.A. Varshalovich, A.N. Moskalev, V.K. Khersonskii, Quantum Theory of Angular Momentum, World Scientific, Singapore, 1988], Chapter 4. From this monograph, most of the relations involving the Wigner D-functions and rotation matrices are taken into account although, in practice, only a rather selected set was needed to be implemented explicitly owing to the symmetries of these functions. In the integration over the rotation matrices, products of up to three Wigner D-functions or reduced matrices (with the same angular arguments) are recognized and simplified properly; for the integration over a solid angle, however, the domain of integration must be specified for the Euler angles α and γ. This restriction arose because MAPLE does not generate a constant of integration when the limits in the integral are omitted. For any integration over the angle β the range of the integration, if omitted, is always taken from 0 to π. Unusual features of the program: The RACAH program is designed for interactive use that allows a quick and algebraic evaluation of (complex) expression from Racah's algebra. It is based on a number of well-defined data structures that are now extended to incorporate the Wigner rotation matrices. For these matrices, the transformation properties, sum rules, recursion relations, as well as a variety of special function expansions have been added to the previous functionality of the RACAH program. Moreover, the knowledge about the orthogonality as well as the completeness of the Wigner D-functions is also implemented. Typical running time:All the examples presented in Section 4 take only a few seconds on a 1.5 GHz Pentium Pro computer.

Professor Louis Michel (1923-1999)

NASA Astrophysics Data System (ADS)

Zak, J.

2001-04-01

Professor Louis Michel was born on May 4, 1923 in Roanne, France and died of aneurysm on December 30, 1999 in Bures-Sur-Yvette, France. With the untimely and sudden death of Louis Michel the world physics community has lost one of its most prominent members. The extraordinary popularity and respect to Louis as a scientist and a man was demonstrated in his funeral ceremony at l'Eglise de Bures-Sur-Yvette when many people from all over the world came to part from him. Many obituaries appeared in Louis' memory in different journals and among them Physics Today, Cern Courier, Physics Reports, in the Bulletin of the French Embassy in Israel and others. It is certainly impossible in this short lecture to give an adequate description of Prof. Michel's contributions in physics but if one looks for a way to identify a niche that Louis occupies in science of the 20th century, this can best be done by his relation to Eugene Wigner whom Louis much admired. On July 16, 1996 Prof. Michel gave the Wigner Memorial Lecture at the 21st International Colloquium on Group Theoretical Methods in Physics. 1 This was the first Colloquium after Wigner's death (who died on January 1, 1995). Wigner had a very great influence on Louis which started during Louis' membership at the Institute of Advanced Studies at Princeton in the years 1953-55. For Louis Wigner was (in Louis' words) a "model in science: a complete physicist, drawing, when necessary, from his deep mathematical culture". In my view, on the world arena of science, Prof. Michel was one of Wigner's successors in the field of symmetries in physics, and many of us would agree that the above quotation applies equally well to Louis himself. In his famous book "Group Theory" Wigner thanks in the Preface 4 people, with one of them being Louis Michel, and I quote: "The author also wishes to thank his colleagues for many stimulating discussions on the role of group theory in quantum mechanics as well as on more specific subjects. He wishes to record his deep indebtedness to Drs. Bargmann, Michel, Wightman, and, last but not least, J. von Neumann". Louis was very proud to find himself in Wigner's book and in the Wigner Memorial Lecture of 1996 he writes: "One of the greatest surprises of my life was to find my name among the four persons to whom 'He wishes to record his deep indebtedness'". In 1994 Louis Michel has received the Wigner Medal...

Computation of turbulence and dispersion of cork in the NETL riser

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jiradilok, Veeraya; Gidaspow, Dimitri; Breault, R.W.

The knowledge of dispersion coefficients is essential for reliable design of gasifiers. However, a literature review had shown that dispersion coefficients in fluidized beds differ by more than five orders of magnitude. This study presents a comparison of the computed axial solids dispersion coefficients for cork particles to the NETL riser cork data. The turbulence properties, the Reynolds stresses, the granular temperature spectra and the radial and axial gas and solids dispersion coefficients are computed. The standard kinetic theory model described in Gidaspow’s 1994 book, Multiphase Flow and Fluidization, Academic Press and the IIT and Fluent codes were used tomore » compute the measured axial solids volume fraction profiles for flow of cork particles in the NETL riser. The Johnson–Jackson boundary conditions were used. Standard drag correlations were used. This study shows that the computed solids volume fractions for the low flux flow are within the experimental error of those measured, using a two-dimensional model. At higher solids fluxes the simulated solids volume fractions are close to the experimental measurements, but deviate significantly at the top of the riser. This disagreement is due to use of simplified geometry in the two-dimensional simulation. There is a good agreement between the experiment and the three-dimensional simulation for a high flux condition. This study concludes that the axial and radial gas and solids dispersion coefficients in risers operating in the turbulent flow regime can be computed using a multiphase computational fluid dynamics model.« less

Modes of surface premelting in colloidal crystals composed of attractive particles

NASA Astrophysics Data System (ADS)

Li, Bo; Wang, Feng; Zhou, Di; Peng, Yi; Ni, Ran; Han, Yilong

2016-03-01

Crystal surfaces typically melt into a thin liquid layer at temperatures slightly below the melting point of the crystal. Such surface premelting is prevalent in all classes of solids and is important in a variety of metallurgical, geological and meteorological phenomena. Premelting has been studied using X-ray diffraction and differential scanning calorimetry, but the lack of single-particle resolution makes it hard to elucidate the underlying mechanisms. Colloids are good model systems for studying phase transitions because the thermal motions of individual micrometre-sized particles can be tracked directly using optical microscopy. Here we use colloidal spheres with tunable attractions to form equilibrium crystal-vapour interfaces, and study their surface premelting behaviour at the single-particle level. We find that monolayer colloidal crystals exhibit incomplete premelting at their perimeter, with a constant liquid-layer thickness. In contrast, two- and three-layer crystals exhibit conventional complete melting, with the thickness of the surface liquid diverging as the melting point is approached. The microstructures of the surface liquids differ in certain aspects from what would be predicted by conventional premelting theories. Incomplete premelting in the monolayer crystals is triggered by a bulk isostructural solid-solid transition and truncated by a mechanical instability that separately induces homogeneous melting within the bulk. This finding is in contrast to the conventional assumption that two-dimensional crystals melt heterogeneously from their free surfaces (that is, at the solid-vapour interface). The unexpected bulk melting that we observe for the monolayer crystals is accompanied by the formation of grain boundaries, which supports a previously proposed grain-boundary-mediated two-dimensional melting theory. The observed interplay between surface premelting, bulk melting and solid-solid transitions challenges existing theories of surface premelting and two-dimensional melting.

Large angle solid state position sensitive x-ray detector system

DOEpatents

Kurtz, D.S.; Ruud, C.O.

1998-03-03

A method and apparatus for x-ray measurement of certain properties of a solid material are disclosed. In distinction to known methods and apparatus, this invention employs a specific fiber-optic bundle configuration, termed a reorganizer, itself known for other uses, for coherently transmitting visible light originating from the scintillation of diffracted x-radiation from the solid material gathered along a substantially one dimensional linear arc, to a two-dimensional photo-sensor array. The two-dimensional photodetector array, with its many closely packed light sensitive pixels, is employed to process the information contained in the diffracted radiation and present the information in the form of a conventional x-ray diffraction spectrum. By this arrangement, the angular range of the combined detector faces may be increased without loss of angular resolution. Further, the prohibitively expensive coupling together of a large number of individual linear diode photodetectors, which would be required to process signals generated by the diffracted radiation, is avoided. 7 figs.

Large angle solid state position sensitive x-ray detector system

DOEpatents

Kurtz, D.S.; Ruud, C.O.

1998-07-21

A method and apparatus are disclosed for x-ray measurement of certain properties of a solid material. In distinction to known methods and apparatus, this invention employs a specific fiber-optic bundle configuration, termed a reorganizer, itself known for other uses, for coherently transmitting visible light originating from the scintillation of diffracted x-radiation from the solid material gathered along a substantially one dimensional linear arc, to a two-dimensional photo-sensor array. The two-dimensional photodetector array, with its many closely packed light sensitive pixels, is employed to process the information contained in the diffracted radiation and present the information in the form of a conventional x-ray diffraction spectrum. By this arrangement, the angular range of the combined detector faces may be increased without loss of angular resolution. Further, the prohibitively expensive coupling together of a large number of individual linear diode photodetectors, which would be required to process signals generated by the diffracted radiation, is avoided. 7 figs.

Generalized isobaric multiplet mass equation and its application to the Nolen-Schiffer anomaly

NASA Astrophysics Data System (ADS)

Dong, J. M.; Zhang, Y. H.; Zuo, W.; Gu, J. Z.; Wang, L. J.; Sun, Y.

2018-02-01

The Wigner isobaric multiplet mass equation (IMME) is the most fundamental prediction in nuclear physics with the concept of isospin. However, it was deduced based on the Wigner-Eckart theorem with the assumption that all charge-violating interactions can be written as tensors of rank two. In the present work, the charge-symmetry breaking (CSB) and charge-independent breaking (CIB) components of the nucleon-nucleon force, which contribute to the effective interaction in nuclear medium, are established in the framework of Brueckner theory with AV18 and AV14 bare interactions. Because such charge-violating components can no longer be expressed as an irreducible tensor due to density dependence, its matrix element cannot be analytically reduced by the Wigner-Eckart theorem. With an alternative approach, we derive a generalized IMME (GIMME) that modifies the coefficients of the original IMME. As the first application of GIMME, we study the long-standing question of the origin of the Nolen-Schiffer anomaly (NSA) found in the Coulomb displacement energy of mirror nuclei. We find that the naturally emerged CSB term in GIMME is largely responsible for explaining the NSA.

Nondestructive Integrity Evaluation of PC Pile Using Wigner-Ville Distribution Method

NASA Astrophysics Data System (ADS)

Ni, Sheng-Huoo; Lo, Kuo-Feng; Huang, Yan-Hong

Nondestructive evaluation (NDE) techniques have been used for years to provide a quality control of the construction for both drilled shafts and driven concrete piles. This trace is typically made up of transient pulses reflected from structural features of the pile or changes in its surrounding environment. It is often analyzed in conjunction with the spectral response, mobility curve, arrival time, etc. The Wigner-Ville Distribution is a new numerical analysis tool for signal process technique in the time-frequency domain and it can offer assistance and enhance signal characteristics for better resolution both easily and quickly. In this study, five single pre-cast concrete piles have been tested and evaluated by both sonic echo method and Wigner-Ville distribution (WVD). Furthermore, two difficult problems in nondestructive evaluation problems are discussed and solved: the first one is with a pile with slight defect, whose necking area percentage is less than 10%, and the other is a pile with multiple defects. The results show that WVD can not only recognize the characteristics easily, but also locate the defects more clearly than the traditional pile integrity testing method.

Under-the-barrier dynamics in laser-induced relativistic tunneling.

PubMed

Klaiber, Michael; Yakaboylu, Enderalp; Bauke, Heiko; Hatsagortsyan, Karen Z; Keitel, Christoph H

2013-04-12

The tunneling dynamics in relativistic strong-field ionization is investigated with the aim to develop an intuitive picture for the relativistic tunneling regime. We demonstrate that the tunneling picture applies also in the relativistic regime by introducing position dependent energy levels. The quantum dynamics in the classically forbidden region features two time scales, the typical time that characterizes the probability density's decay of the ionizing electron under the barrier (Keldysh time) and the time interval which the electron spends inside the barrier (Eisenbud-Wigner-Smith tunneling time). In the relativistic regime, an electron momentum shift as well as a spatial shift along the laser propagation direction arise during the under-the-barrier motion which are caused by the laser magnetic field induced Lorentz force. The momentum shift is proportional to the Keldysh time, while the wave-packet's spatial drift is proportional to the Eisenbud-Wigner-Smith time. The signature of the momentum shift is shown to be present in the ionization spectrum at the detector and, therefore, observable experimentally. In contrast, the signature of the Eisenbud-Wigner-Smith time delay disappears at far distances for pure quasistatic tunneling dynamics.

Initial-value semiclassical propagators for the Wigner phase space representation: Formulation based on the interpretation of the Moyal equation as a Schrödinger equation.

PubMed

Koda, Shin-ichi

2015-12-28

We formulate various semiclassical propagators for the Wigner phase space representation from a unified point of view. As is shown in several studies, the Moyal equation, which is an equation of motion for the Wigner distribution function, can be regarded as the Schrödinger equation of an extended Hamiltonian system where its "position" and "momentum" correspond to the middle point of two points of the original phase space and the difference between them, respectively. Then we show that various phase-space semiclassical propagators can be formulated just by applying existing semiclassical propagators to the extended system. As a result, a phase space version of the Van Vleck propagator, the initial-value Van Vleck propagator, the Herman-Kluk propagator, and the thawed Gaussian approximation are obtained. In addition, we numerically compare the initial-value phase-space Van Vleck propagator, the phase-space Herman-Kluk propagator, and the classical mechanical propagation as approximation methods for the time propagation of the Wigner distribution function in terms of both accuracy and convergence speed. As a result, we find that the convergence speed of the Van Vleck propagator is far slower than others as is the case of the Hilbert space, and the Herman-Kluk propagator keeps its accuracy for a long period compared with the classical mechanical propagation while the convergence speed of the latter is faster than the former.

On the simulation of indistinguishable fermions in the many-body Wigner formalism

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sellier, J.M., E-mail: jeanmichel.sellier@gmail.com; Dimov, I.

2015-01-01

The simulation of quantum systems consisting of interacting, indistinguishable fermions is an incredible mathematical problem which poses formidable numerical challenges. Many sophisticated methods addressing this problem are available which are based on the many-body Schrödinger formalism. Recently a Monte Carlo technique for the resolution of the many-body Wigner equation has been introduced and successfully applied to the simulation of distinguishable, spinless particles. This numerical approach presents several advantages over other methods. Indeed, it is based on an intuitive formalism in which quantum systems are described in terms of a quasi-distribution function, and highly scalable due to its Monte Carlo nature.more » In this work, we extend the many-body Wigner Monte Carlo method to the simulation of indistinguishable fermions. To this end, we first show how fermions are incorporated into the Wigner formalism. Then we demonstrate that the Pauli exclusion principle is intrinsic to the formalism. As a matter of fact, a numerical simulation of two strongly interacting fermions (electrons) is performed which clearly shows the appearance of a Fermi (or exchange–correlation) hole in the phase-space, a clear signature of the presence of the Pauli principle. To conclude, we simulate 4, 8 and 16 non-interacting fermions, isolated in a closed box, and show that, as the number of fermions increases, we gradually recover the Fermi–Dirac statistics, a clear proof of the reliability of our proposed method for the treatment of indistinguishable particles.« less

Fully coupled six-dimensional calculations of the water dimer vibration-rotation-tunneling states with split Wigner pseudospectral approach. II. Improvements and tests of additional potentials

NASA Astrophysics Data System (ADS)

Fellers, R. S.; Braly, L. B.; Saykally, R. J.; Leforestier, C.

1999-04-01

The SWPS method is improved by the addition of H.E.G. contractions for generating a more compact basis. An error in the definition of the internal fragment axis system used in our previous calculation is described and corrected. Fully coupled 6D (rigid monomers) VRT states are computed for several new water dimer potential surfaces and compared with experiment and our earlier SWPS results. This work sets the stage for refinement of such potential surfaces via regression analysis of VRT spectroscopic data.

Application of the Fractional Fourier Transform and S-Method in Doppler Radar Tomography

DTIC Science & Technology

2010-08-01

Distribution Series WVD - Wigner - Ville Distribution xi DSTO–RR–0357 xii DSTO–RR...for chirped signals include bilinear tech- niques such as the Wigner - Ville Distribution ( WVD ), the Cohen’s class, and the time- frequency distribution ...2which is also known as ”‘ Wigner - Ville Distribution ”’ 3Assuming the integration extent in (13) is from −∞ to +∞ and using the property of the Dirac

Code Optimization for the Choi-Williams Distribution for ELINT Applications

DTIC Science & Technology

2009-12-01

Probability of Intercept N Number of Samples NPS Naval Postgraduate School SNR Signal To Noise Ratio WVD Wigner - Ville Distribution xvi THIS PAGE...Many of the optimizations developed can be applied to the computation of the Wigner - Ville distribution as well. This work is highly applicable in the...made can also be used to increase the speed at which the Wigner - Ville distribution (another signal processing algorithm) can be computed. These

Unconventional Signal Processing Using the Cone Kernel Time-Frequency Representation.

DTIC Science & Technology

1992-10-30

Wigner - Ville distribution ( WVD ), the Choi- Williams distribution , and the cone kernel distribution were compared with the spectrograms. Results were...ambiguity function. Figures A-18(c) and (d) are the Wigner - Ville Distribution ( WVD ) and CK-TFR Doppler maps. In this noiseless case all three exhibit...kernel is the basis for the well known Wigner - Ville distribution . In A-9(2), the cone kernel defined by Zhao, Atlas and Marks [21 is described

Review of Vibration-Based Helicopters Health and Usage Monitoring Methods

DTIC Science & Technology

2001-04-05

FM4, NA4, NA4*, NB4 and NB48* (Polyshchuk et al., 1998). The Wigner - Ville distribution ( WVD ) is a joint time-frequency signal analysis. The WVD is one...signal processing methodologies that are of relevance to vibration based damage detection (e.g., Wavelet Transform and Wigner - Ville distribution ) will be...operation cost, reduce maintenance flights, and increase flight safety. Key Words: HUMS; Wavelet Transform; Wigner - Ville distribution ; O&S; Machinery

Ultra-Wideband Radar Transient Detection using Time-Frequency and Wavelet Transforms.

DTIC Science & Technology

1992-12-01

if p==2, mesh(flipud(abs(spdatamatrix).A2)) end 2. Wigner - Ville Distribution function P = wvd (data,winlenstep,begintheendp) % Filename: wvd.m % Title...short time Fourier transform (STFT), the Instantaneous Power Spectrum and the Wigner - Ville distribution , and time-scale methods, such as the a trous...such as the short time Fourier transform (STFT), the Instantaneous Power Spectrum and the Wigner - Ville distribution [1], and time-scale methods, such

A New Approach in Time-Frequency Analysis with Applications to Experimental High Range Resolution Radar Data

DTIC Science & Technology

2003-11-01

Distributions In contrast to the linear time-frequency transforms such as the short-time Fourier transform, the Wigner - Ville distribution ( WVD ) is...23 9 Results of nine TFDs: (a) Wigner - Ville distribution , (b) Born-Jordan distribution , (c) Choi-Williams distribution , (d) bilinear TFD...are applied in the Wigner - Ville class of time-frequency transforms and the reassignment methods, which are applied to any time-frequency distribution

Focusing ISAR Images using Fast Adaptive Time-Frequency and 3D Motion Detection on Simulated and Experimental Radar Data

DTIC Science & Technology

2005-06-01

Time Fourier Transform WVD Wigner - Ville Distribution GA Genetic Algorithm PSO Particle Swarm Optimization JEM Jet Engine Modulation CPI...of the Wigner - Ville Distribution ( WVD ), cross-terms appear in the time-frequency image. As shown in Figure 9, which is a WVD of range bin 31 of...14 Figure 9. Wigner - Ville Distribution of Unfocused Range Bin 31 (After [3] and [5].) ...15

Elimination of interference component in Wigner-Ville distribution for the signal with 1/f spectral characteristic.

PubMed

Chan, H L; Lin, J L; Huang, H H; Wu, C P

1997-09-01

A new technique for interference-term suppression in Wigner-Ville distribution (WVD) is proposed for the signal with 1/f spectrum shape. The spectral characteristic of the signal is altered by f alpha filtering before time-frequency analysis and compensated after analysis. With the utilization of the proposed technique in smoothed pseudo Wigner-Ville distribution, an excellent suppression of interference component can be achieved.

Deformation quantization of fermi fields

DOE Office of Scientific and Technical Information (OSTI.GOV)

Galaviz, I.; Garcia-Compean, H.; Departamento de Fisica, Centro de Investigacion y de Estudios Avanzados del IPN, P.O. Box 14-740, 07000 Mexico, D.F.

2008-04-15

Deformation quantization for any Grassmann scalar free field is described via the Weyl-Wigner-Moyal formalism. The Stratonovich-Weyl quantizer, the Moyal *-product and the Wigner functional are obtained by extending the formalism proposed recently in [I. Galaviz, H. Garcia-Compean, M. Przanowski, F.J. Turrubiates, Weyl-Wigner-Moyal Formalism for Fermi Classical Systems, arXiv:hep-th/0612245] to the fermionic systems of infinite number of degrees of freedom. In particular, this formalism is applied to quantize the Dirac free field. It is observed that the use of suitable oscillator variables facilitates considerably the procedure. The Stratonovich-Weyl quantizer, the Moyal *-product, the Wigner functional, the normal ordering operator, and finally,more » the Dirac propagator have been found with the use of these variables.« less

An equation for pressure of a two-dimensional Yukawa liquid

NASA Astrophysics Data System (ADS)

Feng, Yan; Li, Wei; Wang, Qiaoling; Lin, Wei; Goree, John; Liu, Bin

2016-10-01

Thermodynamic behavior of two-dimensional (2D) dusty plasmas has been studied experimentally and theoretically recently. As a crucial parameter in thermodynamics, the pressure of dusty plasmas arises from frequent collisions of individual dust particles. Here, equilibrium molecular dynamical simulations were performed to study the pressure of 2D Yukawa liquids. A simple analytical expression for the pressure of a 2D Yukawa liquid is found by fitting the obtained pressure data over a wide range of temperatures, from the coldest close to the melting point, to the hottest about 70 times higher than the melting points. The obtained expression verifies that the pressure can be written as the sum of a potential term which is a simple multiple of the Coulomb potential energy at a distance of Wigner-Seitz radius, and a kinetic term which is a multiple of the one for an ideal gas. Dimensionless coefficients for each of these terms are found empirically, by fitting. The resulting analytical expression, with its empirically determined coefficients, is plotted as isochors, or curves of constant area. These results should be applicable to 2D dusty plasmas. Work in China supported by by the National Natural Science Foundation of China under Grant No. 11505124, the 1000 Youth Talents Plan, and startup funds from Soochow University. Work in the US supported by DOE & NSF.

Spin polarization of two-dimensional electron system in parabolic potential

NASA Astrophysics Data System (ADS)

Miyake, Takashi; Totsuji, Chieko; Nakanishi, Kenta; Tsuruta, Kenji; Totsuji, Hiroo

2008-09-01

We analyze the ground state of the two-dimensional quantum system of electrons confined in a parabolic potential with the system size around 100 at 0 K. We map the system onto a classical system on the basis of the classical-map hypernetted-chain (CHNC) method which has been proven to work in the integral-equation-based analyses of uniform systems and apply classical Monte Carlo and molecular dynamics simulations. We find that, when we decrease the strength of confinement keeping the number of confined electrons fixed, the energy of the spin-polarized state with somewhat lower average density becomes smaller than that of the spin-unpolarized state with somewhat higher average density. This system thus undergoes the transition from the spin-unpolarized state to the spin polarized state and the corresponding critical value of r estimated from the average density is as low as r∼0.4 which is much smaller than the r value for the Wigner lattice formation. When we compare the energies of spin-unpolarized and spin-polarized states for given average density, our data give the critical r value for the transition between unpolarized and polarized states around 10 which is close to but still smaller than the known possibility of polarization at r∼27. The advantage of our method is a direct applicability to geometrically complex systems which are difficult to analyze by integral equations and this is an example.

Quantitative characterization of solid epoxy resins using comprehensive two dimensional liquid chromatography coupled with electrospray ionization-time of flight mass spectrometry.

PubMed

Julka, Samir; Cortes, Hernan; Harfmann, Robert; Bell, Bruce; Schweizer-Theobaldt, Andreas; Pursch, Matthias; Mondello, Luigi; Maynard, Shawn; West, David

2009-06-01

A comprehensive multidimensional liquid chromatography system coupled to Electrospray Ionization-Mass Spectrometry (LCxLC-ESI-MS) was developed for detailed characterization and quantitation of solid epoxy resin components. The two orthogonal modes of separation selected were size exclusion chromatography (SEC) in the first dimension and liquid chromatography at critical conditions (LCCC) in the second dimension. Different components present in the solid epoxy resins were separated and quantitated for the first time based on the functional groups and molecular weight heterogeneity. Coupling LCxLC separations with mass spectrometry enabled the identification of components resolved in the two-dimensional space. Several different functional group families of compounds were separated and identified, including epoxy-epoxy and epoxy-alpha-glycol functional oligomers, and their individual molecular weight ranges were determined. Repeatability obtained ranged from 0.5% for the main product to 21% for oligomers at the 0.4% concentration level.

Understanding squeezing of quantum states with the Wigner function

NASA Technical Reports Server (NTRS)

Royer, Antoine

1994-01-01

The Wigner function is argued to be the only natural phase space function evolving classically under quadratic Hamiltonians with time-dependent bilinear part. This is used to understand graphically how certain quadratic time-dependent Hamiltonians induce squeezing of quantum states. The Wigner representation is also used to generalize Ehrenfest's theorem to the quantum uncertainties. This makes it possible to deduce features of the quantum evolution, such as squeezing, from the classical evolution, whatever the Hamiltonian.

Local symmetries and order-disorder transitions in small macroscopic Wigner islands.

PubMed

Coupier, Gwennou; Guthmann, Claudine; Noat, Yves; Jean, Michel Saint

2005-04-01

The influence of local order on the disordering scenario of small Wigner islands is discussed. A first disordering step is put in evidence by the time correlation functions and is linked to individual excitations resulting in configuration transitions, which are very sensitive to the local symmetries. This is followed by two other transitions, corresponding to orthoradial and radial diffusion, for which both individual and collective excitations play a significant role. Finally, we show that, contrary to large systems, the focus that is commonly made on collective excitations for such small systems through the Lindemann criterion has to be made carefully in order to clearly identify the relative contributions in the whole disordering process.

The use of the Wigner Distribution to analyze structural impulse responses

NASA Technical Reports Server (NTRS)

Wahl, T. J.; Bolton, J. S.

1990-01-01

In this paper it is argued that the time-frequency analysis of structural impulse responses may be used to reveal the wave types carrying significant energy through a structure. Since each wave type is characterized by its own dispersion relation, each wave type may be associated with particular features appearing in the time-frequency domain representation of an impulse response. Here the Wigner Distribution is introduced as a means for obtaining appropriate time-frequency representations of impulse responses. Practical aspects of the calculation of the Wigner Distribution are discussed and examples of its application to the analysis of structural impulse responses are given. These examples will show that the Wigner Distribution may be conveniently used to distinguish between the contributions of various waves types to a total structural response.

Detection of volatile spoilage metabolites in fermented cucumbers using nontargeted, comprehensive two-dimensional gas chromatography-time-of-flight mass spectrometry (GCxGC-TOFMS)

USDA-ARS?s Scientific Manuscript database

A nontargeted, comprehensive two-dimensional gas chromatography-time-of-flight mass spectrometry (GCxGC-TOFMS) method was developed for the analysis of fermented cucumber volatiles before and after anaerobic spoilage. Volatiles extracted by solid-phase microextraction were separated on a polyethyle...

Wigner distributions for an electron

NASA Astrophysics Data System (ADS)

Kumar, Narinder; Mondal, Chandan

2018-06-01

We study the Wigner distributions for a physical electron, which reveal the multidimensional images of the electron. The physical electron is considered as a composite system of a bare electron and photon. The Wigner distributions for unpolarized, longitudinally polarized and transversely polarized electron are presented in transverse momentum plane as well as in impact-parameter plane. The spin-spin correlations between the bare electron and the physical electron are discussed. We also evaluate all the leading twist generalized transverse momentum distributions (GTMDs) for electron.

Dissipative transport in superlattices within the Wigner function formalism

DOE PAGES

Jonasson, O.; Knezevic, I.

2015-07-30

Here, we employ the Wigner function formalism to simulate partially coherent, dissipative electron transport in biased semiconductor superlattices. We introduce a model collision integral with terms that describe energy dissipation, momentum relaxation, and the decay of spatial coherences (localization). Based on a particle-based solution to the Wigner transport equation with the model collision integral, we simulate quantum electronic transport at 10 K in a GaAs/AlGaAs superlattice and accurately reproduce its current density vs field characteristics obtained in experiment.

A Computer Program for the Prediction of Solid Propellant Rocket Motor Performance. Volume 3

DTIC Science & Technology

1975-07-01

following losses: two-dimensional/two-phase (coupled), nozzle erosion, kinetics, boundary layer, combustion efficiency, submergence . The program...loss •Two dimensional or divergence less •Finite Rate Kinetics loss •Boundary Layer Loss •Combustion Efficiency - • Submergence Loss •Erosion...counted twice. The iforcmcr.tioned assumptions are describ- ed In Section US, The submergence efficiency, ijgno* ^* rased on an empirical

Global Search of a Three-dimensional Low Solidity Circular Cascade Diffuser for Centrifugal Blowers by Meta-model Assisted Optimization

NASA Astrophysics Data System (ADS)

Sakaguchi, Daisaku; Sakue, Daiki; Tun, Min Thaw

2018-04-01

A three-dimensional blade of a low solidity circular cascade diffuser in centrifugal blowers is designed by means of a multi-point optimization technique. The optimization aims at improving static pressure coefficient at a design point and at a small flow rate condition. Moreover, a clear definition of secondary flow expressed by positive radial velocity at hub side is taken into consideration in constraints. The number of design parameters for three-dimensional blade reaches to 10 in this study, such as a radial gap, a radial chord length and mean camber angle distribution of the LSD blade with five control points, control point between hub and shroud with two design freedom. Optimization results show clear Pareto front and selected optimum design shows good improvement of pressure rise in diffuser at small flow rate conditions. It is found that three-dimensional blade has advantage to stabilize the secondary flow effect with improving pressure recovery of the low solidity circular cascade diffuser.

Hydraulic separation of plastic wastes: Analysis of liquid-solid interaction.

PubMed

Moroni, Monica; Lupo, Emanuela; La Marca, Floriana

2017-08-01

The separation of plastic wastes in mechanical recycling plants is the process that ensures high-quality secondary raw materials. An innovative device employing a wet technology for particle separation is presented in this work. Due to the combination of the characteristic flow pattern developing within the apparatus and density, shape and size differences among two or more polymers, it allows their separation into two products, one collected within the instrument and the other one expelled through its outlet ducts. The kinematic investigation of the fluid flowing within the apparatus seeded with a passive tracer was conducted via image analysis for different hydraulic configurations. The two-dimensional turbulent kinetic energy results strictly connected to the apparatus separation efficacy. Image analysis was also employed to study the behaviour of mixtures of passive tracer and plastic particles with different physical characteristics in order to understand the coupling regime between fluid and solid phases. The two-dimensional turbulent kinetic energy analysis turned out to be fundamental to this aim. For the tested operating conditions, two-way coupling takes place, i.e., the fluid exerts an influence on the plastic particle and the opposite occurs too. Image analysis confirms the outcomes from the investigation of the two-phase flow via non-dimensional numbers (particle Reynolds number, Stokes number and solid phase volume fraction). Copyright © 2017 Elsevier Ltd. All rights reserved.

Ginzburg-Landau theory for the solid-liquid interface of bcc elements. II - Application to the classical one-component plasma, the Wigner crystal, and He-4

NASA Technical Reports Server (NTRS)

Zeng, X. C.; Stroud, D.

1989-01-01

The previously developed Ginzburg-Landau theory for calculating the crystal-melt interfacial tension of bcc elements to treat the classical one-component plasma (OCP), the charged fermion system, and the Bose crystal. For the OCP, a direct application of the theory of Shih et al. (1987) yields for the surface tension 0.0012(Z-squared e-squared/a-cubed), where Ze is the ionic charge and a is the radius of the ionic sphere. Bose crystal-melt interface is treated by a quantum extension of the classical density-functional theory, using the Feynman formalism to estimate the relevant correlation functions. The theory is applied to the metastable He-4 solid-superfluid interface at T = 0, with a resulting surface tension of 0.085 erg/sq cm, in reasonable agreement with the value extrapolated from the measured surface tension of the bcc solid in the range 1.46-1.76 K. These results suggest that the density-functional approach is a satisfactory mean-field theory for estimating the equilibrium properties of liquid-solid interfaces, given knowledge of the uniform phases.

The Wigner distribution and 2D classical maps

NASA Astrophysics Data System (ADS)

Sakhr, Jamal

2017-07-01

The Wigner spacing distribution has a long and illustrious history in nuclear physics and in the quantum mechanics of classically chaotic systems. In this paper, a novel connection between the Wigner distribution and 2D classical mechanics is introduced. Based on a well-known correspondence between the Wigner distribution and the 2D Poisson point process, the hypothesis that typical pseudo-trajectories of a 2D ergodic map have a Wignerian nearest-neighbor spacing distribution (NNSD) is put forward and numerically tested. The standard Euclidean metric is used to compute the interpoint spacings. In all test cases, the hypothesis is upheld, and the range of validity of the hypothesis appears to be robust in the sense that it is not affected by the presence or absence of: (i) mixing; (ii) time-reversal symmetry; and/or (iii) dissipation.

Wigner in Hungary

NASA Astrophysics Data System (ADS)

Marx, George

2002-04-01

Eugene P. Wigner was born into a well-to-do family in Budapest 100 years ago. .He attended the Fasori Lutheran Gymnasium, which educated - among others - John von Neumann, and John Harsanyi,Nobel-laureate in economics. Wigner was influenced by his math teacher, László Rátz who taught calculus in high school. World War I, revolutions and counter/revolutions, kingdom, republic, soviet type council republic followed each other in dizzying sequence, so Wigner decided to continue his university studies in Berlin, where quantum mechanics was discussed and developed in the 1920s. After his Ph.D. Wigner worked in Budapest and in Berlin, and he elaborated the foundations of quantum mechanics based on symmetry principles. He wrote his book on symmetries during a summer holiday in Hungary, and this later brought him the Nobel Prize. Wigner moved to the U.S. in 1930, where he enjoyed the excellent working conditions and recognition. He revisited his homeland only in the 1970s, where his ideas about the future attracted huge audiences at the Academy of Sciences, at universities, and in the Physical Society. He received high honors from his home country - a bit belatedly. The principal focus of his attention was the quantum-mechanical concept of measurement, the role of human consciousness. But even in his last years, in the 1980s, he most enjoyed his visits to high schools - attending physics classes, discussing the future of science in human society with teachers and students.

Performance analysis of three-dimensional-triple-level cell and two-dimensional-multi-level cell NAND flash hybrid solid-state drives

NASA Astrophysics Data System (ADS)

Sakaki, Yukiya; Yamada, Tomoaki; Matsui, Chihiro; Yamaga, Yusuke; Takeuchi, Ken

2018-04-01

In order to improve performance of solid-state drives (SSDs), hybrid SSDs have been proposed. Hybrid SSDs consist of more than two types of NAND flash memories or NAND flash memories and storage-class memories (SCMs). However, the cost of hybrid SSDs adopting SCMs is more expensive than that of NAND flash only SSDs because of the high bit cost of SCMs. This paper proposes unique hybrid SSDs with two-dimensional (2D) horizontal multi-level cell (MLC)/three-dimensional (3D) vertical triple-level cell (TLC) NAND flash memories to achieve higher cost-performance. The 2D-MLC/3D-TLC hybrid SSD achieves up to 31% higher performance than the conventional 2D-MLC/2D-TLC hybrid SSD. The factors of different performance between the proposed hybrid SSD and the conventional hybrid SSD are analyzed by changing its block size, read/write/erase latencies, and write unit of 3D-TLC NAND flash memory, by means of a transaction-level modeling simulator.

The transition to the metallic state in low density hydrogen

DOE PAGES

McMinis, Jeremy; Morales, Miguel A.; Ceperley, David M.; ...

2015-11-18

Solid atomic hydrogen is one of the simplest systems to undergo a metal-insulator transition. Near the transition, the electronic degrees of freedom become strongly correlated and their description provides a difficult challenge for theoretical methods. As a result, the order and density of the phase transition are still subject to debate. In this work we use diffusion quantum Monte Carlo to benchmark the transition between the paramagnetic and anti-ferromagnetic phases of ground state body centered cubic atomic hydrogen. We locate the density of the transition by computing the equation of state for these two phases and identify the phase transitionmore » order by computing the band gap near the phase transition. These benchmark results show that the phase transition is continuous and occurs at a Wigner-Seitz radius of r s = 2.27(3)a 0. As a result, we compare our results to previously reported density functional theory, Hedin s GW approximation, and dynamical mean field theory results.« less

Three-dimensional fractional-spin gravity

NASA Astrophysics Data System (ADS)

Boulanger, Nicolas; Sundell, Per; Valenzuela, Mauricio

2014-02-01

Using Wigner-deformed Heisenberg oscillators, we construct 3D Chern-Simons models consisting of fractional-spin fields coupled to higher-spin gravity and internal nonabelian gauge fields. The gauge algebras consist of Lorentz-tensorial Blencowe-Vasiliev higher-spin algebras and compact internal algebras intertwined by infinite-dimensional generators in lowest-weight representations of the Lorentz algebra with fractional spin. In integer or half-integer non-unitary cases, there exist truncations to gl(ℓ , ℓ ± 1) or gl(ℓ|ℓ ± 1) models. In all non-unitary cases, the internal gauge fields can be set to zero. At the semi-classical level, the fractional-spin fields are either Grassmann even or odd. The action requires the enveloping-algebra representation of the deformed oscillators, while their Fock-space representation suffices on-shell. The project was funded in part by F.R.S.-FNRS " Ulysse" Incentive Grant for Mobility in Scientific Research.

Strain, curvature, and twist measurements in digital holographic interferometry using pseudo-Wigner-Ville distribution based method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rajshekhar, G.; Gorthi, Sai Siva; Rastogi, Pramod

2009-09-15

Measurement of strain, curvature, and twist of a deformed object play an important role in deformation analysis. Strain depends on the first order displacement derivative, whereas curvature and twist are determined by second order displacement derivatives. This paper proposes a pseudo-Wigner-Ville distribution based method for measurement of strain, curvature, and twist in digital holographic interferometry where the object deformation or displacement is encoded as interference phase. In the proposed method, the phase derivative is estimated by peak detection of pseudo-Wigner-Ville distribution evaluated along each row/column of the reconstructed interference field. A complex exponential signal with unit amplitude and the phasemore » derivative estimate as the argument is then generated and the pseudo-Wigner-Ville distribution along each row/column of this signal is evaluated. The curvature is estimated by using peak tracking strategy for the new distribution. For estimation of twist, the pseudo-Wigner-Ville distribution is evaluated along each column/row (i.e., in alternate direction with respect to the previous one) for the generated complex exponential signal and the corresponding peak detection gives the twist estimate.« less

Eugene Wigner and Fundamental Symmetry Principles

Science.gov Websites

, DOE Technical Report, April 19, 1944 Effect of the Temperature of the Moderator on the Velocity , 1949 The Magnitude of the Eta Effect, DOE Technical Report, April 25, 1951 Wigner Honored: Eugene

A fast and accurate algorithm for QTAIM integration in solids.

PubMed

Otero-de-la-Roza, A; Luaña, Víctor

2011-01-30

A new algorithm is presented for the calculation of atomic properties, in the sense of the quantum theory of atoms in molecules. This new method, named QTREE, applies to solid-state densities and allows the computation of the atomic properties of all the atoms in the crystal in seconds to minutes. The basis of the method is the recursive subdivision of a symmetry-reduced wedge of the Wigner-Seitz cell, which in turn is expressed as a union of tetrahedra, plus the use of β-spheres to improve the performance. A considerable speedup is thus achieved compared with traditional quadrature-based schemes, justified by the poor performance of the latter because of the particular features of atomic basins in solids. QTREE can use both analytical or interpolated densities, calculates all the atomic properties available, and converges to the correct values in the limit of infinite precision. Several gradient path tracing and integration techniques are tested. Basin volumes and charges for a selected set of 11 crystals are determined as a test of the new method. Copyright © 2010 Wiley Periodicals, Inc.

Anharmonic, dimensionality and size effects in phonon transport

NASA Astrophysics Data System (ADS)

Thomas, Iorwerth O.; Srivastava, G. P.

2017-12-01

We have developed and employed a numerically efficient semi- ab initio theory, based on density-functional and relaxation-time schemes, to examine anharmonic, dimensionality and size effects in phonon transport in three- and two-dimensional solids of different crystal symmetries. Our method uses third- and fourth-order terms in crystal Hamiltonian expressed in terms of a temperature-dependent Grüneisen’s constant. All input to numerical calculations are generated from phonon calculations based on the density-functional perturbation theory. It is found that four-phonon processes make important and measurable contribution to lattice thermal resistivity above the Debye temperature. From our numerical results for bulk Si, bulk Ge, bulk MoS2 and monolayer MoS2 we find that the sample length dependence of phonon conductivity is significantly stronger in low-dimensional solids.

Softly-confined water cluster between freestanding graphene sheets

NASA Astrophysics Data System (ADS)

Agustian, Rifan; Akaishi, Akira; Nakamura, Jun

2018-01-01

Confined water could adopt new forms not seen in the open air, such as a two-dimensional (2D) square ice trapped between two graphene sheets [Algara-Siller et al., Nature 519, 443-445 (2015)]. In this study, in order to investigate how the flexibility of graphene affects the confined structure of water molecules, we employed classical molecular dynamics simulations with Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) potential to produce a soft-confining property of graphene. We discovered various solid-like structures of water molecules ranging from two-dimensional to three-dimensional structure encapsulated between two freestanding graphene sheets even at room temperature (300K). A small amount of water encapsulation leads to a layered two-dimensional form with triangular structure. On the other hand, large amounts of water molecules take a three-dimensional flying-saucer-like form with the square ice intra-layer structure. There is also a metastable state where both two-dimensional and three-dimensional structures coexist.

Relativistic effects in photoionization: Wigner time delay for the noble gases and IIB atoms

NASA Astrophysics Data System (ADS)

Banerjee, Sourav; Deshmukh, Pranawa; Dolmatov, Valeriy; Kheifets, Anatoli; Manson, Steven

2017-04-01

Time delay in atomic photoionization has been observed in several experiments, and various theoretical and experimental approaches are developing rapidly to obtain a better understanding of this phenomena. Theoretical methods that account for many body correlations include the relativistic random phase approximation (RRPA) and its non-relativistic analogue, RPAE. Calculations using RRPA are performed and the impact of relativistic interactions on Wigner time delay are explored via comparison of this result with RPAE results. In addition, results on Wigner time delay for Zn Cd and Hg are presented.

Dimension of quantum phase space measured by photon correlations

NASA Astrophysics Data System (ADS)

Leuchs, Gerd; Glauber, Roy J.; Schleich, Wolfgang P.

2015-06-01

We show that the different values 1, 2 and 3 of the normalized second-order correlation function {g}(2)(0) corresponding to a coherent state, a thermal state and a highly squeezed vacuum originate from the different dimensionality of these states in phase space. In particular, we derive an exact expression for {g}(2)(0) in terms of the ratio of the moments of the classical energy evaluated with the Wigner function of the quantum state of interest and corrections proportional to the reciprocal of powers of the average number of photons. In this way we establish a direct link between {g}(2)(0) and the shape of the state in phase space. Moreover, we illuminate this connection by demonstrating that in the semi-classical limit the familiar photon statistics of a thermal state arise from an area in phase space weighted by a two-dimensional Gaussian, whereas those of a highly squeezed state are governed by a line-integral of a one-dimensional Gaussian. We dedicate this article to Margarita and Vladimir Man’ko on the occasion of their birthdays. The topic of our contribution is deeply rooted in and motivated by their love for non-classical light, quantum mechanical phase space distribution functions and orthogonal polynomials. Indeed, through their articles, talks and most importantly by many stimulating discussions and intensive collaborations with us they have contributed much to our understanding of physics. Happy birthday to you both!

The Total Gaussian Class of Quasiprobabilities and its Relation to Squeezed-State Excitations

NASA Technical Reports Server (NTRS)

Wuensche, Alfred

1996-01-01

The class of quasiprobabilities obtainable from the Wigner quasiprobability by convolutions with the general class of Gaussian functions is investigated. It can be described by a three-dimensional, in general, complex vector parameter with the property of additivity when composing convolutions. The diagonal representation of this class of quasiprobabilities is connected with a generalization of the displaced Fock states in direction of squeezing. The subclass with real vector parameter is considered more in detail. It is related to the most important kinds of boson operator ordering. The properties of a specific set of discrete excitations of squeezed coherent states are given.

Critical slowing down in driven-dissipative Bose-Hubbard lattices

NASA Astrophysics Data System (ADS)

Vicentini, Filippo; Minganti, Fabrizio; Rota, Riccardo; Orso, Giuliano; Ciuti, Cristiano

2018-01-01

We explore theoretically the dynamical properties of a first-order dissipative phase transition in coherently driven Bose-Hubbard systems, describing, e.g., lattices of coupled nonlinear optical cavities. Via stochastic trajectory calculations based on the truncated Wigner approximation, we investigate the dynamical behavior as a function of system size for one-dimensional (1D) and 2D square lattices in the regime where mean-field theory predicts nonlinear bistability. We show that a critical slowing down emerges for increasing number of sites in 2D square lattices, while it is absent in 1D arrays. We characterize the peculiar properties of the collective phases in the critical region.

Correlated sequential tunneling through a double barrier for interacting one-dimensional electrons

NASA Astrophysics Data System (ADS)

Thorwart, M.; Egger, R.; Grifoni, M.

2005-07-01

The problem of resonant tunneling through a quantum dot weakly coupled to spinless Tomonaga-Luttinger liquids has been studied. We compute the linear conductance due to sequential tunneling processes upon employing a master equation approach. Besides the previously used lowest-order golden rule rates describing uncorrelated sequential tunneling processes, we systematically include higher-order correlated sequential tunneling (CST) diagrams within the standard Weisskopf-Wigner approximation. We provide estimates for the parameter regions where CST effects can be important. Focusing mainly on the temperature dependence of the peak conductance, we discuss the relation of these findings to previous theoretical and experimental results.

Fully coupled six-dimensional calculations of the water dimer vibration-rotation-tunneling states with split Wigner pseudospectral approach. II. Improvements and tests of additional potentials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Fellers, R.S.; Braly, L.B.; Saykally, R.J.

The SWPS method is improved by the addition of H.E.G. contractions for generating a more compact basis. An error in the definition of the internal fragment axis system used in our previous calculation is described and corrected. Fully coupled 6D (rigid monomers) VRT states are computed for several new water dimer potential surfaces and compared with experiment and our earlier SWPS results. This work sets the stage for refinement of such potential surfaces via regression analysis of VRT spectroscopic data. {copyright} {ital 1999 American Institute of Physics.}

Breit-Wigner Approximation and the Distributionof Resonances

NASA Astrophysics Data System (ADS)

Petkov, Vesselin; Zworski, Maciej

For operators with a discrete spectrum, {λj2}, the counting function of λj's, N (λ), trivially satisfies N ( λ+δ ) -N ( λ-δ ) =∑jδλj((λ-δ,λ+δ]). In scattering situations the natural analogue of the discrete spectrum is given by resonances, λj∈+, and of N (λ), by the scattering phase, s(λ). The relation between the two is now non-trivial and we prove that where ω+ is the harmonic measure of the upper of half plane and δ can be taken dependent on λ. This provides a precise high energy version of the Breit-Wigner approximation, and relates the properties of s (λ) to the distribution of resonances close to the real axis.

Waveguide quantum electrodynamics in squeezed vacuum

NASA Astrophysics Data System (ADS)

You, Jieyu; Liao, Zeyang; Li, Sheng-Wen; Zubairy, M. Suhail

2018-02-01

We study the dynamics of a general multiemitter system coupled to the squeezed vacuum reservoir and derive a master equation for this system based on the Weisskopf-Wigner approximation. In this theory, we include the effect of positions of the squeezing sources which is usually neglected in the previous studies. We apply this theory to a quasi-one-dimensional waveguide case where the squeezing in one dimension is experimentally achievable. We show that while dipole-dipole interaction induced by ordinary vacuum depends on the emitter separation, the two-photon process due to the squeezed vacuum depends on the positions of the emitters with respect to the squeezing sources. The dephasing rate, decay rate, and the resonance fluorescence of the waveguide-QED in the squeezed vacuum are controllable by changing the positions of emitters. Furthermore, we demonstrate that the stationary maximum entangled NOON state for identical emitters can be reached with arbitrary initial state when the center-of-mass position of the emitters satisfies certain conditions.

Effect of propellant deformation on ignition and combustion processes in solid propellant cracks

NASA Technical Reports Server (NTRS)

Kumar, M.; Kuo, K. K.

1980-01-01

A comprehensive theoretical model was formulated to study the development of convective burning in a solid propellant crack which continually deforms due to burning and pressure loading. In the theoretical model, the effect of interrelated structural deformation and combustion processes was taken into account by considering (1) transient, one dimensional mass, momentum, and energy conservation equations in the gas phase; (2) a transient, one dimensional heat conduction equation in the solid phase; and (3) quasi-static deformation of the two dimensional, linear viscoelastic propellant crack caused by pressure loading. Partial closures may generate substantial local pressure peaks along the crack, implying a strong coupling between chamber pressurization, crack combustion, and propellant deformation, especially when the cracks are narrow and the chamber pressurization rates high. The maximum pressure in the crack cavity is generally higher than that in the chamber. The initial flame-spreading process is not affected by propellant deformation.

Comparison of deterministic and stochastic methods for time-dependent Wigner simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shao, Sihong, E-mail: sihong@math.pku.edu.cn; Sellier, Jean Michel, E-mail: jeanmichel.sellier@parallel.bas.bg

2015-11-01

Recently a Monte Carlo method based on signed particles for time-dependent simulations of the Wigner equation has been proposed. While it has been thoroughly validated against physical benchmarks, no technical study about its numerical accuracy has been performed. To this end, this paper presents the first step towards the construction of firm mathematical foundations for the signed particle Wigner Monte Carlo method. An initial investigation is performed by means of comparisons with a cell average spectral element method, which is a highly accurate deterministic method and utilized to provide reference solutions. Several different numerical tests involving the time-dependent evolution ofmore » a quantum wave-packet are performed and discussed in deep details. In particular, this allows us to depict a set of crucial criteria for the signed particle Wigner Monte Carlo method to achieve a satisfactory accuracy.« less

Computing thermal Wigner densities with the phase integration method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Beutier, J.; Borgis, D.; Vuilleumier, R.

2014-08-28

We discuss how the Phase Integration Method (PIM), recently developed to compute symmetrized time correlation functions [M. Monteferrante, S. Bonella, and G. Ciccotti, Mol. Phys. 109, 3015 (2011)], can be adapted to sampling/generating the thermal Wigner density, a key ingredient, for example, in many approximate schemes for simulating quantum time dependent properties. PIM combines a path integral representation of the density with a cumulant expansion to represent the Wigner function in a form calculable via existing Monte Carlo algorithms for sampling noisy probability densities. The method is able to capture highly non-classical effects such as correlation among the momenta andmore » coordinates parts of the density, or correlations among the momenta themselves. By using alternatives to cumulants, it can also indicate the presence of negative parts of the Wigner density. Both properties are demonstrated by comparing PIM results to those of reference quantum calculations on a set of model problems.« less

Fluctuations of Wigner-type random matrices associated with symmetric spaces of class DIII and CI

NASA Astrophysics Data System (ADS)

Stolz, Michael

2018-02-01

Wigner-type randomizations of the tangent spaces of classical symmetric spaces can be thought of as ordinary Wigner matrices on which additional symmetries have been imposed. In particular, they fall within the scope of a framework, due to Schenker and Schulz-Baldes, for the study of fluctuations of Wigner matrices with additional dependencies among their entries. In this contribution, we complement the results of these authors by explicit calculations of the asymptotic covariances for symmetry classes DIII and CI and thus obtain explicit CLTs for these classes. On the technical level, the present work is an exercise in controlling the cumulative effect of systematically occurring sign factors in an involved sum of products by setting up a suitable combinatorial model for the summands. This aspect may be of independent interest. Research supported by Deutsche Forschungsgemeinschaft (DFG) via SFB 878.

Computing thermal Wigner densities with the phase integration method.

PubMed

Beutier, J; Borgis, D; Vuilleumier, R; Bonella, S

2014-08-28

We discuss how the Phase Integration Method (PIM), recently developed to compute symmetrized time correlation functions [M. Monteferrante, S. Bonella, and G. Ciccotti, Mol. Phys. 109, 3015 (2011)], can be adapted to sampling/generating the thermal Wigner density, a key ingredient, for example, in many approximate schemes for simulating quantum time dependent properties. PIM combines a path integral representation of the density with a cumulant expansion to represent the Wigner function in a form calculable via existing Monte Carlo algorithms for sampling noisy probability densities. The method is able to capture highly non-classical effects such as correlation among the momenta and coordinates parts of the density, or correlations among the momenta themselves. By using alternatives to cumulants, it can also indicate the presence of negative parts of the Wigner density. Both properties are demonstrated by comparing PIM results to those of reference quantum calculations on a set of model problems.

Closed-form solution for the Wigner phase-space distribution function for diffuse reflection and small-angle scattering in a random medium.

PubMed

Yura, H T; Thrane, L; Andersen, P E

2000-12-01

Within the paraxial approximation, a closed-form solution for the Wigner phase-space distribution function is derived for diffuse reflection and small-angle scattering in a random medium. This solution is based on the extended Huygens-Fresnel principle for the optical field, which is widely used in studies of wave propagation through random media. The results are general in that they apply to both an arbitrary small-angle volume scattering function, and arbitrary (real) ABCD optical systems. Furthermore, they are valid in both the single- and multiple-scattering regimes. Some general features of the Wigner phase-space distribution function are discussed, and analytic results are obtained for various types of scattering functions in the asymptotic limit s > 1, where s is the optical depth. In particular, explicit results are presented for optical coherence tomography (OCT) systems. On this basis, a novel way of creating OCT images based on measurements of the momentum width of the Wigner phase-space distribution is suggested, and the advantage over conventional OCT images is discussed. Because all previous published studies regarding the Wigner function are carried out in the transmission geometry, it is important to note that the extended Huygens-Fresnel principle and the ABCD matrix formalism may be used successfully to describe this geometry (within the paraxial approximation). Therefore for completeness we present in an appendix the general closed-form solution for the Wigner phase-space distribution function in ABCD paraxial optical systems for direct propagation through random media, and in a second appendix absorption effects are included.

Quantum Statistics of the Toda Oscillator in the Wigner Function Formalism

NASA Astrophysics Data System (ADS)

Vojta, Günter; Vojta, Matthias

Classical and quantum mechanical Toda systems (Toda molecules, Toda lattices, Toda quantum fields) recently found growing interest as nonlinear systems showing solitons and chaos. In this paper the statistical thermodynamics of a system of quantum mechanical Toda oscillators characterized by a potential energy V(q) = Vo cos h q is treated within the Wigner function formalism (phase space formalism of quantum statistics). The partition function is given as a Wigner- Kirkwood series expansion in terms of powers of h2 (semiclassical expansion). The partition function and all thermodynamic functions are written, with considerable exactness, as simple closed expressions containing only the modified Hankel functions Ko and K1 of the purely imaginary argument i with = Vo/kT.Translated AbstractQuantenstatistik des Toda-Oszillators im Formalismus der Wigner-FunktionKlassische und quantenmechanische Toda-Systeme (Toda-Moleküle, Toda-Gitter, Toda-Quantenfelder) haben als nichtlineare Systeme mit Solitonen und Chaos in jüngster Zeit zunehmend an Interesse gewonnen. Wir untersuchen die statistische Thermodynamik eines Systems quantenmechanischer Toda-Oszillatoren, die durch eine potentielle Energie der Form V(q) = Vo cos h q charakterisiert sind, im Formalismus der Wigner-Funktion (Phasenraum-Formalismus der Quantenstatistik). Die Zustandssumme wird als Wigner-Kirkwood-Reihe nach Potenzen von h2 (semiklassische Entwicklung) dargestellt, und aus ihr werden die thermodynamischen Funktionen berechnet. Sämtliche Funktionen sind durch einfache geschlossene Formeln allein mit den modifizierten Hankel-Funktionen Ko und K1 des rein imaginären Arguments i mit = Vo/kT mit großer Genauigkeit darzustellen.

A theoretical evaluation of aluminum gel propellant two-phase flow losses on vehicle performance

NASA Technical Reports Server (NTRS)

Mueller, Donn C.; Turns, Stephen R.

1993-01-01

A one-dimensional model of a hydrocarbon/Al/O2(gaseous) fueled rocket combustion chamber was developed to study secondary atomization effects on propellant combustion. This chamber model was coupled with a two dimensional, two-phase flow nozzle code to estimate the two-phase flow losses associated with solid combustion products. Results indicate that moderate secondary atomization significantly reduces propellant burnout distance and Al2O3 particle size; however, secondary atomization provides only moderate decreases in two-phase flow induced I(sub sp) losses. Despite these two-phase flow losses, a simple mission study indicates that aluminum gel propellants may permit a greater maximum payload than the hydrocarbon/O2 bi-propellant combination for a vehicle of fixed propellant volume. Secondary atomization was also found to reduce radiation losses from the solid combustion products to the chamber walls, primarily through reductions in propellant burnout distance.

The study of the Boltzmann equation of solid-gas two-phase flow with three-dimensional BGK model

NASA Astrophysics Data System (ADS)

Liu, Chang-jiang; Pang, Song; Xu, Qiang; He, Ling; Yang, Shao-peng; Qing, Yun-jie

2018-06-01

The motion of many solid-gas two-phase flows can be described by the Boltzmann equation. In order to simplify the Boltzmann equation, the convective-diffusion term is reserved and the collision term is replaced by the three-dimensional Bharnagar-Gross-Krook (BGK) model. Then the simplified Boltzmann equation is solved by homotopy perturbation method (HPM), and its approximate analytical solution is obtained. Through the analyzing, it is proved that the analytical solution satisfies all the constraint conditions, and its formation is in accord with the formation of the solution that is obtained by traditional Chapman-Enskog method, and the solving process of HPM is much more simple and convenient. This preliminarily shows the effectiveness and rapidness of HPM to solve the Boltzmann equation. The results obtained herein provide some theoretical basis for the further study of dynamic model of solid-gas two-phase flows, such as the sturzstrom of high-speed distant landslide caused by microseism and the sand storm caused by strong breeze.

Two-Dimensional Fullerene Assembly from an Exfoliated van der Waals Template.

PubMed

Lee, Kihong; Choi, Bonnie; Plante, Ilan Jen-La; Paley, Maria V; Zhong, Xinjue; Crowther, Andrew C; Owen, Jonathan S; Zhu, Xiaoyang; Roy, Xavier

2018-05-22

Two-dimensional (2D) materials are commonly prepared by exfoliating bulk layered van der Waals crystals. The creation of synthetic 2D materials from bottom-up methods is an important challenge as their structural flexibility will enable chemists to tune the materials properties. A 2D material was assembled using C 60 as a polymerizable monomer. The C 60 building blocks are first assembled into a layered solid using a molecular cluster as structure director. The resulting hierarchical crystal is used as a template to polymerize its C 60 monolayers, which can be exfoliated down to 2D crystalline nanosheets. Derived from the parent template, the 2D structure is composed of a layer of inorganic cluster, sandwiched between two monolayers of polymerized C 60 . The nanosheets can be transferred onto solid substrates and depolymerized by heating. Electronic absorption spectroscopy reveals an optical gap of 0.25 eV, narrower than that of the bulk parent crystalline solid. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

The autowave modes of solid phase polymerization of metal-containing monomers in two- and three-dimensional fiberglass-filled matrices

NASA Astrophysics Data System (ADS)

Barelko, V. V.; Pomogailo, A. D.; Dzhardimalieva, G. I.; Evstratova, S. I.; Rozenberg, A. S.; Uflyand, I. E.

1999-06-01

The phenomenon of autowave (frontal) solid phase polymerization of metal-containing monomers based on metal-acrylamide complexes is considered. The comparison of the features of autowave processes realized in both the single-component matrices of the monomer and the matrices filled by the fiberglass materials is performed. The unstable regimes of the polymerization wave as well as the conditions for the stabilization of the flat front in the filled matrices are described. The peculiarities of the frontal regimes in the three- and two-dimensional media are studied. Some possibilities for using of autowave polymerization in the fabrication of the polymer-fiberglass composites and composition prepregs are discussed.

Two-dimensional melting of colloids with long-range attractive interactions.

PubMed

Du, Di; Doxastakis, Manolis; Hilou, Elaa; Biswal, Sibani Lisa

2017-02-22

The solid-liquid melting transition in a two-dimensional (2-D) attractive colloidal system is visualized using superparamagnetic colloids that interact through a long-range isotropic attractive interaction potential, which is induced using a high-frequency rotating magnetic field. Various experiments, supported by Monte Carlo simulations, are carried out over a range of interaction potentials and densities to determine structure factors, Lindermann parameters, and translational and orientational order parameters. The system shows a first-order solid-liquid melting transition. Simulations and experiments suggest that dislocations and disclinations simultaneously unbind during melting. This is in direct contrast with reports of 2-D melting of paramagnetic particles that interact with a repulsive interaction potential.

Optimum Distribution of Metal Particles in the Solid-Propellant Charge in the Approximation of a One-Dimensional Flow Field in a Cylindrical Channel

NASA Astrophysics Data System (ADS)

Min'kov, L. L.; Shrager, É. R.

2015-03-01

A study has been made of ways of optimum distribution of particles of dispersed metal in the solid-propellant charge with a cylindrical central channel, which is firmly fastened to the case. The efficiency of combustion of this metal has been analyzed. Consideration has been given to the influence of the dynamic nonequilibrium of two-phase flow on the optimum distribution of metal particles in the indicated charge in the approximation of one-dimensionality of the flow field.

Wigner Functions for the Bateman System on Noncommutative Phase Space

NASA Astrophysics Data System (ADS)

Heng, Tai-Hua; Lin, Bing-Sheng; Jing, Si-Cong

2010-09-01

We study an important dissipation system, i.e. the Bateman model on noncommutative phase space. Using the method of deformation quantization, we calculate the Exp functions, and then derive the Wigner functions and the corresponding energy spectra.

Wigner Distribution for Angle Coordinates in Quantum Mechanics.

ERIC Educational Resources Information Center

Mukunda, N.

1979-01-01

Shows how to extend Wigner distribution functions, and Weyl correspondence between quantum and classical variables, from the usual kind of canonically conjugate position and momentum operators to the case of an angle and angular momentum operator pair. (Author/GA)

Non-local correlations via Wigner-Yanase skew information in two SC-qubit having mutual interaction under phase decoherence

NASA Astrophysics Data System (ADS)

Mohamed, Abdel-Baset A.

2017-10-01

An analytical solution of the master equation that describes a superconducting cavity containing two coupled superconducting charge qubits is obtained. Quantum-mechanical correlations based on Wigner-Yanase skew information, as local quantum uncertainty and uncertainty-induced quantum non-locality, are compared to the concurrence under the effects of the phase decoherence. Local quantum uncertainty exhibits sudden changes during its time evolution and revival process. Sudden death and sudden birth occur only for entanglement, depending on the initial state of the two coupled charge qubits, while the correlations of skew information does not vanish. The quantum correlations of skew information are found to be sensitive to the dephasing rate, the photons number in the cavity, the interaction strength between the two qubits, and the qubit distribution angle of the initial state. With a proper initial state, the stationary correlation of the skew information has a non-zero stationary value for a long time interval under the phase decoherence, that it may be useful in quantum information and computation processes.

Two-dimensional heat flow analysis applied to heat sterilization of ponderosa pine and Douglas-fir square timbers

Treesearch

William T. Simpson

2004-01-01

Equations for a two-dimensional finite difference heat flow analysis were developed and applied to ponderosa pine and Douglas-fir square timbers to calculate the time required to heat the center of the squares to target temperature. The squares were solid piled, which made their surfaces inaccessible to the heating air, and thus surface temperatures failed to attain...

A two-dimensional finite-difference solution for the temperature distribution in a radial gas turbine guide vane blade

NASA Technical Reports Server (NTRS)

Hosny, W. M.; Tabakoff, W.

1975-01-01

A two-dimensional finite difference numerical technique is presented to determine the temperature distribution in a solid blade of a radial guide vane. A computer program is written in Fortran IV for IBM 370/165 computer. The computer results obtained from these programs have a similar behavior and trend as those obtained by experimental results.

Mechanical properties of water-assembled graphene oxide Langmuir monolayers: Guiding controlled transfer

DOE PAGES

Harrison, Katharine L.; Biedermann, Laura B.; Zavadil, Kevin R.

2015-08-24

Liquid-phase transfer of graphene oxide (GO) and reduced graphene oxide (RGO) monolayers is investigated from the perspective of the mechanical properties of these films. Monolayers are assembled in a Langmuir–Blodgett trough, and oscillatory barrier measurements are used to characterize the resulting compressive and shear moduli as a function of surface pressure. GO monolayers are shown to develop a significant shear modulus (10–25 mN/m) at relevant surface pressures while RGO monolayers do not. The existence of a shear modulus indicates that GO is acting as a two-dimensional solid driven by strong interaction between the individual GO sheets. The absence of suchmore » behavior in RGO is attributed to the decrease in oxygen moieties on the sheet basal plane, permitting RGO sheets to slide across one another with minimum energy dissipation. Knowledge of this two-dimensional solid behavior is exploited to successfully transfer large-area, continuous GO films to hydrophobic Au substrates. The key to successful transfer is the use of shallow-angle dipping designed to minimize tensile stress present during the insertion or extraction of the substrate. A shallow dip angle on hydrophobic Au does not impart a beneficial effect for RGO monolayers, as these monolayers do not behave as two-dimensional solids and do not remain coherent during the transfer process. As a result, we hypothesize that this observed correlation between monolayer mechanical properties and continuous film transfer success is more universally applicable across substrate hydrophobicities and could be exploited to control the transfer of films composed of two-dimensional materials.« less

Synthesising topological links

DOE PAGES

Baas, Nils A.; Seeman, Nadrian C.; Stacey, Andrew

2014-10-14

In this paper, we discuss the chemical synthesis of topological links, in particular higher order links which have the Brunnian property (namely that removal of any one component unlinks the entire system). Finally, we suggest how to obtain both two dimensional and three dimensional objects (surfaces and solids, respectively) which also have this Brunnian property.

Cold spray nozzle mach number limitation

NASA Astrophysics Data System (ADS)

Jodoin, B.

2002-12-01

The classic one-dimensional isentropic flow approach is used along with a two-dimensional axisymmetric numerical model to show that the exit Mach number of a cold spray nozzle should be limited due to two factors. To show this, the two-dimensional model is validated with experimental data. Although both models show that the stagnation temperature is an important limiting factor, the one-dimensional approach fails to show how important the shock-particle interactions are at limiting the nozzle Mach number. It is concluded that for an air nozzle spraying solid powder particles, the nozzle Mach number should be set between 1.5 and 3 to limit the negative effects of the high stagnation temperature and of the shock-particle interactions.

Zooming in on AdS3/CFT2 near a BPS bound

NASA Astrophysics Data System (ADS)

Hartong, Jelle; Lei, Yang; Obers, Niels; Oling, Gerben

2018-05-01

Any ( d + 1)-dimensional CFT with a U(1) flavor symmetry, a BPS bound and an exactly marginal coupling admits a decoupling limit in which one zooms in on the spectrum close to the bound. This limit is an Inönü-Wigner contraction of so(2 , d+1)⊕ u(1) that leads to a relativistic algebra with a scaling generator but no conformal generators. In 2D CFTs, Lorentz boosts are abelian and by adding a second u(1) we find a contraction of two copies of sl(2, ℝ) ⊕ u(1) to two copies of P 2 c , the 2-dimensional centrally extended Poincaré algebra. We show that the bulk is described by a novel non-Lorentzian geometry that we refer to as pseudo-Newton-Cartan geometry. Both the Chern-Simons action on sl(2, ℝ) ⊕ u(1) and the entire phase space of asymptotically AdS3 spacetimes are well-behaved in the corresponding limit if we fix the radial component for the u(1) connection. With this choice, the resulting Newton-Cartan foliation structure is now associated not with time, but with the emerging holographic direction. Since the leaves of this foliation do not mix, the emergence of the holographic direction is much simpler than in AdS3 holography. Furthermore, we show that the asymptotic symmetry algebra of the limit theory consists of a left- and a right-moving warped Virasoro algebra.

Short-stack modeling of degradation in solid oxide fuel cells. Part I. Contact degradation

NASA Astrophysics Data System (ADS)

Gazzarri, J. I.; Kesler, O.

As the first part of a two paper series, we present a two-dimensional impedance model of a working solid oxide fuel cell (SOFC) to study the effect of contact degradation on the impedance spectrum for the purpose of non-invasive diagnosis. The two dimensional modeled geometry includes the ribbed interconnect, and is adequate to represent co- and counter-flow configurations. Simulated degradation modes include: cathode delamination, interconnect oxidation, and interconnect-cathode detachment. The simulations show differences in the way each degradation mode impacts the impedance spectrum shape, suggesting that identification is possible. In Part II, we present a sensitivity analysis of the results to input parameter variability that reveals strengths and limitations of the method, as well as describing possible interactions between input parameters and concurrent degradation modes.

Phase pupil functions for focal-depth enhancement derived from a Wigner distribution function.

PubMed

Zalvidea, D; Sicre, E E

1998-06-10

A method for obtaining phase-retardation functions, which give rise to an increase of the image focal depth, is proposed. To this end, the Wigner distribution function corresponding to a specific aperture that has an associated small depth of focus in image space is conveniently sheared in the phase-space domain to generate a new Wigner distribution function. From this new function a more uniform on-axis image irradiance can be accomplished. This approach is illustrated by comparison of the imaging performance of both the derived phase function and a previously reported logarithmic phase distribution.

Classical Wigner method with an effective quantum force: application to reaction rates.

PubMed

Poulsen, Jens Aage; Li, Huaqing; Nyman, Gunnar

2009-07-14

We construct an effective "quantum force" to be used in the classical molecular dynamics part of the classical Wigner method when determining correlation functions. The quantum force is obtained by estimating the most important short time separation of the Feynman paths that enter into the expression for the correlation function. The evaluation of the force is then as easy as classical potential energy evaluations. The ideas are tested on three reaction rate problems. The resulting transmission coefficients are in much better agreement with accurate results than transmission coefficients from the ordinary classical Wigner method.

Wigner's "Polanyian" Epistemology and the Measurement Problem: The Wigner-Polanyi Dialog on Tacit Knowledge

NASA Astrophysics Data System (ADS)

Jha, Stefania

2011-09-01

I analyze the long dialog that Eugene Wigner (1902-1995) and Michael Polanyi (1891-1976) carried out on Polanyi's concept of tacit knowledge and its meaning for the measurement problem in quantum physics, focusing in particular on their ten-year correspondence between 1961 and 1971 on these subjects and the related mind-body problem. They differed in their interpretations, epistemologies, and ontologies, and consequently never resolved their differences on the measurement and mind-body problems. Nonetheless, their long dialog is significant and opens up avenues for exploring these problems further.

On the Wigner law in dilute random matrices

NASA Astrophysics Data System (ADS)

Khorunzhy, A.; Rodgers, G. J.

1998-12-01

We consider ensembles of N × N symmetric matrices whose entries are weakly dependent random variables. We show that random dilution can change the limiting eigenvalue distribution of such matrices. We prove that under general and natural conditions the normalised eigenvalue counting function coincides with the semicircle (Wigner) distribution in the limit N → ∞. This can be explained by the observation that dilution (or more generally, random modulation) eliminates the weak dependence (or correlations) between random matrix entries. It also supports our earlier conjecture that the Wigner distribution is stable to random dilution and modulation.

Wigner expansions for partition functions of nonrelativistic and relativistic oscillator systems

NASA Technical Reports Server (NTRS)

Zylka, Christian; Vojta, Guenter

1993-01-01

The equilibrium quantum statistics of various anharmonic oscillator systems including relativistic systems is considered within the Wigner phase space formalism. For this purpose the Wigner series expansion for the partition function is generalized to include relativistic corrections. The new series for partition functions and all thermodynamic potentials yield quantum corrections in terms of powers of h(sup 2) and relativistic corrections given by Kelvin functions (modified Hankel functions) K(sub nu)(mc(sup 2)/kT). As applications, the symmetric Toda oscillator, isotonic and singular anharmonic oscillators, and hindered rotators, i.e. oscillators with cosine potential, are addressed.

Equilibration in the time-dependent Hartree-Fock approach probed with the Wigner distribution function

DOE Office of Scientific and Technical Information (OSTI.GOV)

Loebl, N.; Maruhn, J. A.; Reinhard, P.-G.

2011-09-15

By calculating the Wigner distribution function in the reaction plane, we are able to probe the phase-space behavior in the time-dependent Hartree-Fock scheme during a heavy-ion collision in a consistent framework. Various expectation values of operators are calculated by evaluating the corresponding integrals over the Wigner function. In this approach, it is straightforward to define and analyze quantities even locally. We compare the Wigner distribution function with the smoothed Husimi distribution function. Different reaction scenarios are presented by analyzing central and noncentral {sup 16}O +{sup 16}O and {sup 96}Zr +{sup 132}Sn collisions. Although we observe strong dissipation in the timemore » evolution of global observables, there is no evidence for complete equilibration in the local analysis of the Wigner function. Because the initial phase-space volumes of the fragments barely merge and mean values of the observables are conserved in fusion reactions over thousands of fm/c, we conclude that the time-dependent Hartree-Fock method provides a good description of the early stage of a heavy-ion collision but does not provide a mechanism to change the phase-space structure in a dramatic way necessary to obtain complete equilibration.« less

Exact-exchange spin-density functional theory of Wigner localization and phase transitions in quantum rings

NASA Astrophysics Data System (ADS)

Arnold, Thorsten; Siegmund, Marc; Pankratov, Oleg

2011-08-01

We apply exact-exchange spin-density functional theory in the Krieger-Li-Iafrate approximation to interacting electrons in quantum rings of different widths. The rings are threaded by a magnetic flux that induces a persistent current. A weak space and spin symmetry breaking potential is introduced to allow for localized solutions. As the electron-electron interaction strength described by the dimensionless parameter rS is increased, we observe—at a fixed spin magnetic moment—the subsequent transition of both spin sub-systems from the Fermi liquid to the Wigner crystal state. A dramatic signature of Wigner crystallization is that the persistent current drops sharply with increasing rS. We observe simultaneously the emergence of pronounced oscillations in the spin-resolved densities and in the electron localization functions indicating a spatial electron localization showing ferrimagnetic order after both spin sub-systems have undergone the Wigner crystallization. The critical rSc at the transition point is substantially smaller than in a fully spin-polarized system and decreases further with decreasing ring width. Relaxing the constraint of a fixed spin magnetic moment, we find that on increasing rS the stable phase changes from an unpolarized Fermi liquid to an antiferromagnetic Wigner crystal and finally to a fully polarized Fermi liquid.

Exact-exchange spin-density functional theory of Wigner localization and phase transitions in quantum rings.

PubMed

Arnold, Thorsten; Siegmund, Marc; Pankratov, Oleg

2011-08-24

We apply exact-exchange spin-density functional theory in the Krieger-Li-Iafrate approximation to interacting electrons in quantum rings of different widths. The rings are threaded by a magnetic flux that induces a persistent current. A weak space and spin symmetry breaking potential is introduced to allow for localized solutions. As the electron-electron interaction strength described by the dimensionless parameter r(S) is increased, we observe-at a fixed spin magnetic moment-the subsequent transition of both spin sub-systems from the Fermi liquid to the Wigner crystal state. A dramatic signature of Wigner crystallization is that the persistent current drops sharply with increasing r(S). We observe simultaneously the emergence of pronounced oscillations in the spin-resolved densities and in the electron localization functions indicating a spatial electron localization showing ferrimagnetic order after both spin sub-systems have undergone the Wigner crystallization. The critical r(S)(c) at the transition point is substantially smaller than in a fully spin-polarized system and decreases further with decreasing ring width. Relaxing the constraint of a fixed spin magnetic moment, we find that on increasing r(S) the stable phase changes from an unpolarized Fermi liquid to an antiferromagnetic Wigner crystal and finally to a fully polarized Fermi liquid. © 2011 IOP Publishing Ltd

Poles of the Zagreb analysis partial-wave T matrices

NASA Astrophysics Data System (ADS)

Batinić, M.; Ceci, S.; Švarc, A.; Zauner, B.

2010-09-01

The Zagreb analysis partial-wave T matrices included in the Review of Particle Physics [by the Particle Data Group (PDG)] contain Breit-Wigner parameters only. As the advantages of pole over Breit-Wigner parameters in quantifying scattering matrix resonant states are becoming indisputable, we supplement the original solution with the pole parameters. Because of an already reported numeric error in the S11 analytic continuation [Batinić , Phys. Rev. CPRVCAN0556-281310.1103/PhysRevC.57.1004 57, 1004(E) (1997); arXiv:nucl-th/9703023], we declare the old BATINIC 95 solution, presently included by the PDG, invalid. Instead, we offer two new solutions: (A) corrected BATINIC 95 and (B) a new solution with an improved S11 πN elastic input. We endorse solution (B).

Stock network stability in times of crisis

NASA Astrophysics Data System (ADS)

Heiberger, Raphael H.

2014-01-01

Despite many efforts crises on financial markets are in large part still scientific black-boxes. In this paper, we use a winner-take-all approach to construct a longitudinal network of S&P 500 companies and their correlations between 2000 and 2012. A comparison to complex ecosystems is drawn, especially whether the May-Wigner theorem can describe real-world economic phenomena. The results confirm the utility of the May-Wigner theorem as a stability indicator for the US stock market, since its development matches with the two major crises of this period, the dot-com bubble and, particularly, the financial crisis. In those times of financial turmoil, the stock network changes its composition, but unlike ecological systems it tightens and the disassortative structure of prosperous markets transforms into a more centralized topology.

The Wonderful Gift of Mathematics

ERIC Educational Resources Information Center

Norton, Anderson

2015-01-01

This theoretical analysis addresses "the unreasonable effectiveness of mathematics in the natural sciences" (Wigner, 1960). For example, how is it that ellipses--constructed by Greek geometers nearly two millennia before Kepler used them--provide such precise models for describing planetary motion? Historical models of gravity and…

Two-dimensional nuclear magnetic resonance of quadrupolar systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Shuanhu

1997-09-01

This dissertation describes two-dimensional nuclear magnetic resonance theory and experiments which have been developed to study quadruples in the solid state. The technique of multiple-quantum magic-angle spinning (MQMAS) is extensively reviewed and expanded upon in this thesis. Specifically, MQMAS is first compared with another technique, dynamic-angle spinning (DAS). The similarity between the two techniques allows us to extend much of the DAS work to the MQMAS case. Application of MQMAS to a series of aluminum containing materials is then presented. The superior resolution enhancement through MQMAS is exploited to detect the five- and six-coordinated aluminum in many aluminosilicate glasses. Combiningmore » the MQMAS method with other experiments, such as HETCOR, greatly expands the possibility of the use of MQMAS to study a large range of problems and is demonstrated in Chapter 5. Finally, the technique switching-angle spinning (SAS) is applied to quadrupolar nuclei to fully characterize a quadrupolar spin system in which all of the 8 NMR parameters are accurately determined. This dissertation is meant to demonstrate that with the combination of two-dimensional NMR concepts and new advanced spinning technologies, a series of multiple-dimensional NMR techniques can be designed to allow a detailed study of quadrupolar nuclei in the solid state.« less

FLEXWAL: A computer program for predicting the wall modifications for two-dimensional, solid, adaptive-wall tunnels

NASA Technical Reports Server (NTRS)

Everhart, J. L.

1983-01-01

A program called FLEXWAL for calculating wall modifications for solid, adaptive-wall wind tunnels is presented. The method used is the iterative technique of NASA TP-2081 and is applicable to subsonic and transonic test conditions. The program usage, program listing, and a sample case are given.

Symplectic evolution of Wigner functions in Markovian open systems.

PubMed

Brodier, O; Almeida, A M Ozorio de

2004-01-01

The Wigner function is known to evolve classically under the exclusive action of a quadratic Hamiltonian. If the system also interacts with the environment through Lindblad operators that are complex linear functions of position and momentum, then the general evolution is the convolution of a non-Hamiltonian classical propagation of the Wigner function with a phase space Gaussian that broadens in time. We analyze the consequences of this in the three generic cases of elliptic, hyperbolic, and parabolic Hamiltonians. The Wigner function always becomes positive in a definite time, which does not depend on the initial pure state. We observe the influence of classical dynamics and dissipation upon this threshold. We also derive an exact formula for the evolving linear entropy as the average of a narrowing Gaussian taken over a probability distribution that depends only on the initial state. This leads to a long time asymptotic formula for the growth of linear entropy. We finally discuss the possibility of recovering the initial state.

Self-consistent phonon theory of the crystallization and elasticity of attractive hard spheres.

PubMed

Shin, Homin; Schweizer, Kenneth S

2013-02-28

We propose an Einstein-solid, self-consistent phonon theory for the crystal phase of hard spheres that interact via short-range attractions. The approach is first tested against the known behavior of hard spheres, and then applied to homogeneous particles that interact via short-range square well attractions and the Baxter adhesive hard sphere model. Given the crystal symmetry, packing fraction, and strength and range of attractive interactions, an effective harmonic potential experienced by a particle confined to its Wigner-Seitz cell and corresponding mean square vibrational amplitude are self-consistently calculated. The crystal free energy is then computed and, using separate information about the fluid phase free energy, phase diagrams constructed, including a first-order solid-solid phase transition and its associated critical point. The simple theory qualitatively captures all the many distinctive features of the phase diagram (critical and triple point, crystal-fluid re-entrancy, low-density coexistence curve) as a function of attraction range, and overall is in good semi-quantitative agreement with simulation. Knowledge of the particle localization length allows the crystal shear modulus to be estimated based on elementary ideas. Excellent predictions are obtained for the hard sphere crystal. Expanded and condensed face-centered cubic crystals are found to have qualitatively different elastic responses to varying attraction strength or temperature. As temperature increases, the expanded entropic solid stiffens, while the energy-controlled, fully-bonded dense solid softens.

Inorganic nanotubes and fullerene-like nanoparticles.

PubMed

Tenne, R

2006-11-01

Although graphite, with its anisotropic two-dimensional lattice, is the stable form of carbon under ambient conditions, on nanometre length scales it forms zero- and one-dimensional structures, namely fullerenes and nanotubes, respectively. This virtue is not limited to carbon and, in recent years, fullerene-like structures and nanotubes have been made from numerous compounds with layered two-dimensional structures. Furthermore, crystalline and polycrystalline nanotubes of pure elements and compounds with quasi-isotropic (three-dimensional) unit cells have also been synthesized, usually by making use of solid templates. These findings open up vast opportunities for the synthesis and study of new kinds of nanostructures with properties that may differ significantly from the corresponding bulk materials. Various potential applications have been proposed for the inorganic nanotubes and the fullerene-like phases. Fullerene-like nanoparticles have been shown to exhibit excellent solid lubrication behaviour, suggesting many applications in, for example, the automotive and aerospace industries, home appliances, and recently for medical technology. Various other potential applications, in catalysis, rechargeable batteries, drug delivery, solar cells and electronics have also been proposed.

Inorganic nanotubes and fullerene-like nanoparticles

NASA Astrophysics Data System (ADS)

Tenne, R.

2006-11-01

Although graphite, with its anisotropic two-dimensional lattice, is the stable form of carbon under ambient conditions, on nanometre length scales it forms zero- and one-dimensional structures, namely fullerenes and nanotubes, respectively. This virtue is not limited to carbon and, in recent years, fullerene-like structures and nanotubes have been made from numerous compounds with layered two-dimensional structures. Furthermore, crystalline and polycrystalline nanotubes of pure elements and compounds with quasi-isotropic (three-dimensional) unit cells have also been synthesized, usually by making use of solid templates. These findings open up vast opportunities for the synthesis and study of new kinds of nanostructures with properties that may differ significantly from the corresponding bulk materials. Various potential applications have been proposed for the inorganic nanotubes and the fullerene-like phases. Fullerene-like nanoparticles have been shown to exhibit excellent solid lubrication behaviour, suggesting many applications in, for example, the automotive and aerospace industries, home appliances, and recently for medical technology. Various other potential applications, in catalysis, rechargeable batteries, drug delivery, solar cells and electronics have also been proposed.

The autowave modes of solid phase polymerization of metal-containing monomers in two- and three-dimensional fiberglass-filled matrices.

PubMed

Barelko, V. V.; Pomogailo, A. D.; Dzhardimalieva, G. I.; Evstratova, S. I.; Rozenberg, A. S.; Uflyand, I. E.

1999-06-01

The phenomenon of autowave (frontal) solid phase polymerization of metal-containing monomers based on metal-acrylamide complexes is considered. The comparison of the features of autowave processes realized in both the single-component matrices of the monomer and the matrices filled by the fiberglass materials is performed. The unstable regimes of the polymerization wave as well as the conditions for the stabilization of the flat front in the filled matrices are described. The peculiarities of the frontal regimes in the three- and two-dimensional media are studied. Some possibilities for using of autowave polymerization in the fabrication of the polymer-fiberglass composites and composition prepregs are discussed. (c) 1999 American Institute of Physics.

A study of complex scaling transformation using the Wigner representation of wavefunctions.

PubMed

Kaprálová-Ždánská, Petra Ruth

2011-05-28

The complex scaling operator exp(-θ ̂x̂p/ℏ), being a foundation of the complex scaling method for resonances, is studied in the Wigner phase-space representation. It is shown that the complex scaling operator behaves similarly to the squeezing operator, rotating and amplifying Wigner quasi-probability distributions of the respective wavefunctions. It is disclosed that the distorting effect of the complex scaling transformation is correlated with increased numerical errors of computed resonance energies and widths. The behavior of the numerical error is demonstrated for a computation of CO(2+) vibronic resonances. © 2011 American Institute of Physics

Phase-space analysis of charged and optical beam transport: Wigner rotation angle

NASA Technical Reports Server (NTRS)

Dattoli, G.; Torre, Amalia

1994-01-01

The possibility of using the phase space formalism to establish a correspondence between the dynamical behavior of squeezed states and optical or charged beams, propagating through linear systems, has received a great deal of attention during the last years. In this connection, it has been indicated how optical experiments may be conceived to measure the Wigner rotation angle. In this paper we address the topic within the context of the paraxial propagation of optical or charged beams and suggest a possible experiment for measuring the Wigner angle using an electron beam passing through quadrupoles and drift sections. The analogous optical system is also discussed.

Coherent mode decomposition using mixed Wigner functions of Hermite-Gaussian beams.

PubMed

Tanaka, Takashi

2017-04-15

A new method of coherent mode decomposition (CMD) is proposed that is based on a Wigner-function representation of Hermite-Gaussian beams. In contrast to the well-known method using the cross spectral density (CSD), it directly determines the mode functions and their weights without solving the eigenvalue problem. This facilitates the CMD of partially coherent light whose Wigner functions (and thus CSDs) are not separable, in which case the conventional CMD requires solving an eigenvalue problem with a large matrix and thus is numerically formidable. An example is shown regarding the CMD of synchrotron radiation, one of the most important applications of the proposed method.

Wigner Function Reconstruction in Levitated Optomechanics

NASA Astrophysics Data System (ADS)

Rashid, Muddassar; Toroš, Marko; Ulbricht, Hendrik

2017-10-01

We demonstrate the reconstruction of theWigner function from marginal distributions of the motion of a single trapped particle using homodyne detection. We show that it is possible to generate quantum states of levitated optomechanical systems even under the efect of continuous measurement by the trapping laser light. We describe the opto-mechanical coupling for the case of the particle trapped by a free-space focused laser beam, explicitly for the case without an optical cavity. We use the scheme to reconstruct the Wigner function of experimental data in perfect agreement with the expected Gaussian distribution of a thermal state of motion. This opens a route for quantum state preparation in levitated optomechanics.

Generalized Kubo formulas for the transport properties of incommensurate 2D atomic heterostructures

NASA Astrophysics Data System (ADS)

Cancès, Eric; Cazeaux, Paul; Luskin, Mitchell

2017-06-01

We give an exact formulation for the transport coefficients of incommensurate two-dimensional atomic multilayer systems in the tight-binding approximation. This formulation is based upon the C* algebra framework introduced by Bellissard and collaborators [Coherent and Dissipative Transport in Aperiodic Solids, Lecture Notes in Physics (Springer, 2003), Vol. 597, pp. 413-486 and J. Math. Phys. 35(10), 5373-5451 (1994)] to study aperiodic solids (disordered crystals, quasicrystals, and amorphous materials), notably in the presence of magnetic fields (quantum Hall effect). We also present numerical approximations and test our methods on a one-dimensional incommensurate bilayer system.

Numerical Fluid Dynamics.

DTIC Science & Technology

1983-01-01

COROLLARY. Similar bodies held in uniform streams of two incompressible viscous fluids with the same orientation must have the same drag coefficient at...Prandtl’s concept [A8, p. 59] was that the flow field around a streamlined body "splits up into two regions: 1. Surrounding the surface of the solid body ...them in ’source panels’ on the 6surface of the body . As in the two -dimensional case, it may be convenient to assume the solid to be at rest, and immersed

Infinite number of solvable generalizations of XY-chain, with cluster state, and with central charge c = m/2

NASA Astrophysics Data System (ADS)

Minami, Kazuhiko

2017-12-01

An infinite number of spin chains are solved and it is derived that the ground-state phase transitions belong to the universality classes with central charge c = m / 2, where m is an integer. The models are diagonalized by automatically obtained transformations, many of which are different from the Jordan-Wigner transformation. The free energies, correlation functions, string order parameters, exponents, central charges, and the phase diagram are obtained. Most of the examples consist of the stabilizers of the cluster state. A unified structure of the one-dimensional XY and cluster-type spin chains is revealed, and other series of solvable models can be obtained through this formula.

Zero- and two-dimensional hybrid carbon phosphors for high colorimetric purity white light-emission.

PubMed

Ding, Yamei; Chang, Qing; Xiu, Fei; Chen, Yingying; Liu, Zhengdong; Ban, Chaoyi; Cheng, Shuai; Liu, Juqing; Huang, Wei

2018-03-01

Carbon nanomaterials are promising phosphors for white light emission. A facile single-step synthesis method has been developed to prepare zero- and two-dimensional hybrid carbon phosphors for the first time. Zero-dimensional carbon dots (C-dots) emit bright blue luminescence under 365 nm UV light and two-dimensional nanoplates improve the dispersity and film forming ability of C-dots. As a proof-of-concept application, the as-prepared hybrid carbon phosphors emit bright white luminescence in the solid state, and the phosphor-coated blue LEDs exhibit high colorimetric purity white light-emission with a color coordinate of (0.3308, 0.3312), potentially enabling the successful application of white emitting phosphors in the LED field.

Mathematics as an Instigator of Scientific Revolutions

ERIC Educational Resources Information Center

Brush, Stephen G.

2015-01-01

In a famous 1960 paper, Wigner discussed "The Unreasonable Effectiveness of Mathematics in the Natural Sciences." I suggest that the effectiveness of mathematics in producing successful new theories and surprising discoveries is even more unreasonable than Wigner claimed. In this paper, I present several historical case studies to…

Eugene Wigner - A Gedanken Pioneer of the Second Quantum Revolution

NASA Astrophysics Data System (ADS)

Zeilinger, Anton

2014-09-01

Eugene Wigner pointed out very interesting consequences of quantum physics in elegant gedanken experiments. As a result of technical progress, these gedanken experiments have become real experiments and contribute to the development of novel concepts in quantum information science, often called the second quantum revolution.

Near-field scanning magneto-optical spectroscopy of Wigner molecules

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mintairov, A. M., E-mail: amintair@nd.edu; Rouvimov, S.; Ioffe Physical-Technical Institute of the Russian Academy of Sciences, Saint Petersburg, 194021

We study the emission spectra of single self-organized InP/GaInP QDs (size 100-220 nm) using high-spatial-resolution, low-temperature (5 K) near-field scanning optical microscope (NSOM) operating at magnetic field strength B=0-10 T. The dots contain up to twenty electrons and represent natural Wigner molecules (WM). We observed vibronic-type shake-up structure in single electron QDs manifesting formation of two electron (2e) WM in photo-excited state. We found that relative intensities of the shake-up components described well by vibronic Frank-Condon factors giving for dots having parabolic confinement energy ħω{sub 0}=1.2-4 meV molecule bond lengths 40-140 nm. We used measurements of magnetic-field-induced shifts to distinguishmore » emission of 2e-WM and singly charged exciton (trion). We also observed magnetic-field-induced molecular-droplet transition for two electron dot, emitting through doubly charge exciton (tetron) at zero magnetic field.« less

Nonclassical properties and teleportation in the two-mode photon-added displaced squeezed states

NASA Astrophysics Data System (ADS)

Hoai, Nguyen Thi Xuan; Duc, Truong Minh

2016-01-01

In this paper, we study the nonclassical properties and find out the effect of photon addition on these properties as well as the process of teleportation in the two-mode photon-added displaced squeezed (TMPADS) states. We derive the analytic expressions of the Wigner function, the photon number distribution and the intermode photon antibunching for these states. We show that photon addition operation not only makes the Wigner function become negative but also leads to increase the degree of antibunching. The peak of the photon number distribution becomes flatter and shifts to the greater number of photons by adding photons to both modes simultaneously. Furthermore, it is proved that the degree of intermodal entanglement becomes bigger and bigger through increasing the number of photons added to both modes. As expected, when using these states as an entanglement resource to teleport a state, the average fidelity of teleportation process is also improved by increasing the number of added photons.

Investigation of mechanical properties and deformation behavior of single-crystal Al-Cu core-shell nanowire generated using non-equilibrium molecular dynamics simulation

NASA Astrophysics Data System (ADS)

Sarkar, Jit

2018-06-01

Molecular dynamics (MD) simulation studies were carried out to generate a cylindrical single-crystal Al-Cu core-shell nanowire and its mechanical properties like yield strength and Young's modulus were evaluated in comparison to a solid aluminum nanowire and hollow copper nanowire which combines to constitute the core-shell structure respectively. The deformation behavior due to changes in the number of Wigner-Seitz defects and dislocations during the entire tensile deformation process was thoroughly studied for the Al-Cu core-shell nanowire. The single-crystal Al-Cu core-shell nanowire shows much higher yield strength and Young's modulus in comparison to the solid aluminum core and hollow copper shell nanowire due to tangling of dislocations caused by lattice mismatch between aluminum and copper. Thus, the Al-Cu core-shell nanowire can be reinforced in different bulk matrix to develop new type of light-weight nanocomposite materials with greatly enhanced material properties.

Communication: Wigner functions in action-angle variables, Bohr-Sommerfeld quantization, the Heisenberg correspondence principle, and a symmetrical quasi-classical approach to the full electronic density matrix

DOE PAGES

Miller, William H.; Cotton, Stephen J.

2016-08-28

It is pointed out that the classical phase space distribution in action-angle (a-a) variables obtained from a Wigner function depends on how the calculation is carried out: if one computes the standard Wigner function in Cartesian variables (p, x), and then replaces p and x by their expressions in terms of a-a variables, one obtains a different result than if the Wigner function is computed directly in terms of the a-a variables. Furthermore, the latter procedure gives a result more consistent with classical and semiclassical theory - e.g., by incorporating the Bohr-Sommerfeld quantization condition (quantum states defined by integer valuesmore » of the action variable) as well as the Heisenberg correspondence principle for matrix elements of an operator between such states - and has also been shown to be more accurate when applied to electronically non-adiabatic applications as implemented within the recently developed symmetrical quasi-classical (SQC) Meyer-Miller (MM) approach. Moreover, use of the Wigner function (obtained directly) in a-a variables shows how our standard SQC/MM approach can be used to obtain off-diagonal elements of the electronic density matrix by processing in a different way the same set of trajectories already used (in the SQC/MM methodology) to obtain the diagonal elements.« less

Communication: Wigner functions in action-angle variables, Bohr-Sommerfeld quantization, the Heisenberg correspondence principle, and a symmetrical quasi-classical approach to the full electronic density matrix.

PubMed

Miller, William H; Cotton, Stephen J

2016-08-28

It is pointed out that the classical phase space distribution in action-angle (a-a) variables obtained from a Wigner function depends on how the calculation is carried out: if one computes the standard Wigner function in Cartesian variables (p, x), and then replaces p and x by their expressions in terms of a-a variables, one obtains a different result than if the Wigner function is computed directly in terms of the a-a variables. Furthermore, the latter procedure gives a result more consistent with classical and semiclassical theory-e.g., by incorporating the Bohr-Sommerfeld quantization condition (quantum states defined by integer values of the action variable) as well as the Heisenberg correspondence principle for matrix elements of an operator between such states-and has also been shown to be more accurate when applied to electronically non-adiabatic applications as implemented within the recently developed symmetrical quasi-classical (SQC) Meyer-Miller (MM) approach. Moreover, use of the Wigner function (obtained directly) in a-a variables shows how our standard SQC/MM approach can be used to obtain off-diagonal elements of the electronic density matrix by processing in a different way the same set of trajectories already used (in the SQC/MM methodology) to obtain the diagonal elements.

Three-dimensional protonic conductivity in porous organic cage solids.

PubMed

Liu, Ming; Chen, Linjiang; Lewis, Scott; Chong, Samantha Y; Little, Marc A; Hasell, Tom; Aldous, Iain M; Brown, Craig M; Smith, Martin W; Morrison, Carole A; Hardwick, Laurence J; Cooper, Andrew I

2016-09-13

Proton conduction is a fundamental process in biology and in devices such as proton exchange membrane fuel cells. To maximize proton conduction, three-dimensional conduction pathways are preferred over one-dimensional pathways, which prevent conduction in two dimensions. Many crystalline porous solids to date show one-dimensional proton conduction. Here we report porous molecular cages with proton conductivities (up to 10(-3) S cm(-1) at high relative humidity) that compete with extended metal-organic frameworks. The structure of the organic cage imposes a conduction pathway that is necessarily three-dimensional. The cage molecules also promote proton transfer by confining the water molecules while being sufficiently flexible to allow hydrogen bond reorganization. The proton conduction is explained at the molecular level through a combination of proton conductivity measurements, crystallography, molecular simulations and quasi-elastic neutron scattering. These results provide a starting point for high-temperature, anhydrous proton conductors through inclusion of guests other than water in the cage pores.

Three-dimensional protonic conductivity in porous organic cage solids

NASA Astrophysics Data System (ADS)

Liu, Ming; Chen, Linjiang; Lewis, Scott; Chong, Samantha Y.; Little, Marc A.; Hasell, Tom; Aldous, Iain M.; Brown, Craig M.; Smith, Martin W.; Morrison, Carole A.; Hardwick, Laurence J.; Cooper, Andrew I.

2016-09-01

Proton conduction is a fundamental process in biology and in devices such as proton exchange membrane fuel cells. To maximize proton conduction, three-dimensional conduction pathways are preferred over one-dimensional pathways, which prevent conduction in two dimensions. Many crystalline porous solids to date show one-dimensional proton conduction. Here we report porous molecular cages with proton conductivities (up to 10-3 S cm-1 at high relative humidity) that compete with extended metal-organic frameworks. The structure of the organic cage imposes a conduction pathway that is necessarily three-dimensional. The cage molecules also promote proton transfer by confining the water molecules while being sufficiently flexible to allow hydrogen bond reorganization. The proton conduction is explained at the molecular level through a combination of proton conductivity measurements, crystallography, molecular simulations and quasi-elastic neutron scattering. These results provide a starting point for high-temperature, anhydrous proton conductors through inclusion of guests other than water in the cage pores.

Scaling between Wind Tunnels-Results Accuracy in Two-Dimensional Testing

NASA Astrophysics Data System (ADS)

Rasuo, Bosko

The establishment of exact two-dimensional flow conditions in wind tunnels is a very difficult problem. This has been evident for wind tunnels of all types and scales. In this paper, the principal factors that influence the accuracy of two-dimensional wind tunnel test results are analyzed. The influences of the Reynolds number, Mach number and wall interference with reference to solid and flow blockage (blockage of wake) as well as the influence of side-wall boundary layer control are analyzed. Interesting results are brought to light regarding the Reynolds number effects of the test model versus the Reynolds number effects of the facility in subsonic and transonic flow.

Multiphase flow in geometrically simple fracture intersections

USGS Publications Warehouse

Basagaoglu, H.; Meakin, P.; Green, C.T.; Mathew, M.; ,

2006-01-01

A two-dimensional lattice Boltzmann (LB) model with fluid-fluid and solid-fluid interaction potentials was used to study gravity-driven flow in geometrically simple fracture intersections. Simulated scenarios included fluid dripping from a fracture aperture, two-phase flow through intersecting fractures and thin-film flow on smooth and undulating solid surfaces. Qualitative comparisons with recently published experimental findings indicate that for these scenarios the LB model captured the underlying physics reasonably well.

Temperature field determination in slabs, circular plates and spheres with saw tooth heat generating sources

NASA Astrophysics Data System (ADS)

Diestra Cruz, Heberth Alexander

The Green's functions integral technique is used to determine the conduction heat transfer temperature field in flat plates, circular plates, and solid spheres with saw tooth heat generating sources. In all cases the boundary temperature is specified (Dirichlet's condition) and the thermal conductivity is constant. The method of images is used to find the Green's function in infinite solids, semi-infinite solids, infinite quadrants, circular plates, and solid spheres. The saw tooth heat generation source has been modeled using Dirac delta function and Heaviside step function. The use of Green's functions allows obtain the temperature distribution in the form of an integral that avoids the convergence problems of infinite series. For the infinite solid and the sphere, the temperature distribution is three-dimensional and in the cases of semi-infinite solid, infinite quadrant and circular plate the distribution is two-dimensional. The method used in this work is superior to other methods because it obtains elegant analytical or quasi-analytical solutions to complex heat conduction problems with less computational effort and more accuracy than the use of fully numerical methods.

Boundary condition computational procedures for inviscid, supersonic steady flow field calculations

NASA Technical Reports Server (NTRS)

Abbett, M. J.

1971-01-01

Results are given of a comparative study of numerical procedures for computing solid wall boundary points in supersonic inviscid flow calculatons. Twenty five different calculation procedures were tested on two sample problems: a simple expansion wave and a simple compression (two-dimensional steady flow). A simple calculation procedure was developed. The merits and shortcomings of the various procedures are discussed, along with complications for three-dimensional and time-dependent flows.

Signal Processing Applications Of Wigner-Ville Analysis

NASA Astrophysics Data System (ADS)

Whitehouse, H. J.; Boashash, B.

1986-04-01

The Wigner-Ville distribution (WVD), a form of time-frequency analysis, is shown to be useful in the analysis of a variety of non-stationary signals both deterministic and stochastic. The properties of the WVD are reviewed and alternative methods of calculating the WVD are discussed. Applications are presented.

Machinery Monitoring and Diagnostics Using Pseudo Wigner-Ville Distribution and Backpropagation Neural Network

DTIC Science & Technology

1993-09-01

frequency, which when used as an input to an artificial neural network will aide in the detection of location and severity of machinery faults...Research is presented where the union of an artificial neural network , utilizing the highly successful backpropagation paradigm, and the pseudo wigner

Wood composites

Treesearch

Lars Berglund; Roger M. Rowell

2005-01-01

A composite can be defined as two or more elements held together by a matrix. By this definition, what we call “solid wood” is a composite. Solid wood is a three-dimensional composite composed of cellulose, hemicelluloses and lignin (with smaller amounts of inorganics and extractives), held together by a lignin matrix. The advantages of developing wood composites are (...

Semiclassical geometry of integrable systems

NASA Astrophysics Data System (ADS)

Reshetikhin, Nicolai

2018-04-01

The main result of this paper is a formula for the scalar product of semiclassical eigenvectors of two integrable systems on the same symplectic manifold. An important application of this formula is the Ponzano–Regge type of asymptotic of Racah–Wigner coefficients. Dedicated to the memory of P P Kulish.

Nonclassical thermal-state superpositions: Analytical evolution law and decoherence behavior

NASA Astrophysics Data System (ADS)

Meng, Xiang-guo; Goan, Hsi-Sheng; Wang, Ji-suo; Zhang, Ran

2018-03-01

Employing the integration technique within normal products of bosonic operators, we present normal product representations of thermal-state superpositions and investigate their nonclassical features, such as quadrature squeezing, sub-Poissonian distribution, and partial negativity of the Wigner function. We also analytically and numerically investigate their evolution law and decoherence characteristics in an amplitude-decay model via the variations of the probability distributions and the negative volumes of Wigner functions in phase space. The results indicate that the evolution formulas of two thermal component states for amplitude decay can be viewed as the same integral form as a displaced thermal state ρ(V , d) , but governed by the combined action of photon loss and thermal noise. In addition, the larger values of the displacement d and noise V lead to faster decoherence for thermal-state superpositions.

Development of Three-Dimensional Object Completion in Infancy

ERIC Educational Resources Information Center

Soska, Kasey C.; Johnson, Scott P.

2008-01-01

Three-dimensional (3D) object completion was investigated by habituating 4- and 6-month-old infants (n = 24 total) with a computer-generated wedge stimulus that pivoted 15[degrees], providing only a limited view. Two displays, rotating 360[degrees], were then shown: a complete, solid volume and an incomplete, hollow form composed only of the sides…

Children's Schemes for Anticipating the Validity of Nets for Solids

ERIC Educational Resources Information Center

Wright, Vince; Smith, Ken

2017-01-01

There is growing acknowledgement of the importance of spatial abilities to student achievement across a broad range of domains and disciplines. Nets are one way to connect three-dimensional shapes and their two-dimensional representations and are a common focus of geometry curricula. Thirty-four students at year 6 (upper primary school) were…

Two-dimensional time-resolved X-ray diffraction study of liquid/solid fraction and solid particle size in Fe-C binary system with an electrostatic levitator furnace

NASA Astrophysics Data System (ADS)

Yonemura, M.; Okada, J.; Watanabe, Y.; Ishikawa, T.; Nanao, S.; Shobu, T.; Toyokawa, H.

2013-03-01

Liquid state provides functions such as matter transport or a reaction field and plays an important role in manufacturing processes such as refining, forging or welding. However, experimental procedures are significantly difficult for an observation of solidification process of iron and iron-based alloys in order to identify rapid transformations subjected to fast temperature evolution. Therefore, in order to study the solidification in iron and iron-based alloys, we considered a combination of high energy X-ray diffraction measurements and an electrostatic levitation method (ESL). In order to analyze the liquid/solid fraction, the solidification of melted spherical specimens was measured at a time resolution of 0.1 seconds during rapid cooling using the two-dimensional time-resolved X-ray diffraction. Furthermore, the observation of particle sizes and phase identification was performed on a trial basis using X-ray small angle scattering with X-ray diffraction.

Children's schemes for anticipating the validity of nets for solids

NASA Astrophysics Data System (ADS)

Wright, Vince; Smith, Ken

2017-09-01

There is growing acknowledgement of the importance of spatial abilities to student achievement across a broad range of domains and disciplines. Nets are one way to connect three-dimensional shapes and their two-dimensional representations and are a common focus of geometry curricula. Thirty-four students at year 6 (upper primary school) were interviewed on two occasions about their anticipation of whether or not given nets for the cube- and square-based pyramid would fold to form the target solid. Vergnaud's ( Journal of Mathematical Behavior, 17(2), 167-181, 1998, Human Development, 52, 83-94, 2009) four characteristics of schemes were used as a theoretical lens to analyse the data. Successful schemes depended on the interaction of operational invariants, such as strategic choice of the base, rules for action, particularly rotation of shapes, and anticipations of composites of polygons in the net forming arrangements of faces in the solid. Inferences were rare. These data suggest that students need teacher support to make inferences, in order to create transferable schemes.

The Kirillov picture for the Wigner particle

NASA Astrophysics Data System (ADS)

Gracia-Bondía, J. M.; Lizzi, F.; Várilly, J. C.; Vitale, P.

2018-06-01

We discuss the Kirillov method for massless Wigner particles, usually (mis)named ‘continuous spin’ or ‘infinite spin’ particles. These appear in Wigner’s classification of the unitary representations of the Poincaré group, labelled by elements of the enveloping algebra of the Poincaré Lie algebra. Now, the coadjoint orbit procedure introduced by Kirillov is a prelude to quantization. Here we exhibit for those particles the classical Casimir functions on phase space, in parallel to quantum representation theory. A good set of position coordinates are identified on the coadjoint orbits of the Wigner particles; the stabilizer subgroups and the symplectic structures of these orbits are also described. In memory of E C G Sudarshan.

Time-frequency representation of a highly nonstationary signal via the modified Wigner distribution

NASA Technical Reports Server (NTRS)

Zoladz, T. F.; Jones, J. H.; Jong, J.

1992-01-01

A new signal analysis technique called the modified Wigner distribution (MWD) is presented. The new signal processing tool has been very successful in determining time frequency representations of highly non-stationary multicomponent signals in both simulations and trials involving actual Space Shuttle Main Engine (SSME) high frequency data. The MWD departs from the classic Wigner distribution (WD) in that it effectively eliminates the cross coupling among positive frequency components in a multiple component signal. This attribute of the MWD, which prevents the generation of 'phantom' spectral peaks, will undoubtedly increase the utility of the WD for real world signal analysis applications which more often than not involve multicomponent signals.

Kinetics of Hydrogen Abstraction and Addition Reactions of 3-Hexene by ȮH Radicals.

PubMed

Yang, Feiyu; Deng, Fuquan; Pan, Youshun; Zhang, Yingjia; Tang, Chenglong; Huang, Zuohua

2017-03-09

Rate coefficients of H atom abstraction and H atom addition reactions of 3-hexene by the hydroxyl radicals were determined using both conventional transition-state theory and canonical variational transition-state theory, with the potential energy surface (PES) evaluated at the CCSD(T)/CBS//BHandHLYP/6-311G(d,p) level and quantum mechanical effect corrected by the compounded methods including one-dimensional Wigner method, multidimensional zero-curvature tunneling method, and small-curvature tunneling method. Results reveal that accounting for approximate 70% of the overall H atom abstractions occur in the allylic site via both direct and indirect channels. The indirect channel containing two van der Waals prereactive complexes exhibits two times larger rate coefficient relative to the direct one. The OH addition reaction also contains two van der Waals complexes, and its submerged barrier results in a negative temperature coefficient behavior at low temperatures. In contrast, The OH addition pathway dominates only at temperatures below 450 K whereas the H atom abstraction reactions dominate overwhelmingly at temperature over 1000 K. All of the rate coefficients calculated with an uncertainty of a factor of 5 were fitted in a quasi-Arrhenius formula. Analyses on the PES, minimum reaction path and activation free Gibbs energy were also performed in this study.

Topology-Scaling Identification of Layered Solids and Stable Exfoliated 2D Materials.

PubMed

Ashton, Michael; Paul, Joshua; Sinnott, Susan B; Hennig, Richard G

2017-03-10

The Materials Project crystal structure database has been searched for materials possessing layered motifs in their crystal structures using a topology-scaling algorithm. The algorithm identifies and measures the sizes of bonded atomic clusters in a structure's unit cell, and determines their scaling with cell size. The search yielded 826 stable layered materials that are considered as candidates for the formation of two-dimensional monolayers via exfoliation. Density-functional theory was used to calculate the exfoliation energy of each material and 680 monolayers emerge with exfoliation energies below those of already-existent two-dimensional materials. The crystal structures of these two-dimensional materials provide templates for future theoretical searches of stable two-dimensional materials. The optimized structures and other calculated data for all 826 monolayers are provided at our database (https://materialsweb.org).

Effect of heat transfer of melt/solid interface shape and solute segregation in Edge-Defined Film-Fed growth - Finite element analysis

NASA Technical Reports Server (NTRS)

Ettouney, H. M.; Brown, R. A.

1982-01-01

The effects of the heat transfer environment in Edge-Defined Film-Fed Growth on melt-solid interface shape and lateral dopant segregation are studied by finite-element analysis of two-dimensional models for heat and mass transfer. Heat transfer configurations are studied that correspond to the uniform surroundings assumed in previous models and to lowand high-speed growth systems. The maximum growth rate for a silicon sheet is calculated and the range of validity of one-dimensional heat transfer models is established. The lateral segregation that results from curvature of the solidification interface is calculated for two solutes, boron and aluminum. In this way, heat transfer is linked directly to the uniformity of the product crystal.

Biological control of aragonite formation in stony corals

NASA Astrophysics Data System (ADS)

Von Euw, Stanislas; Zhang, Qihong; Manichev, Viacheslav; Murali, Nagarajan; Gross, Juliane; Feldman, Leonard C.; Gustafsson, Torgny; Flach, Carol; Mendelsohn, Richard; Falkowski, Paul G.

2017-06-01

Little is known about how stony corals build their calcareous skeletons. There are two prevailing hypotheses: that it is a physicochemically dominated process and that it is a biologically mediated one. Using a combination of ultrahigh-resolution three-dimensional imaging and two-dimensional solid-state nuclear magnetic resonance (NMR) spectroscopy, we show that mineral deposition is biologically driven. Randomly arranged, amorphous nanoparticles are initially deposited in microenvironments enriched in organic material; they then aggregate and form ordered aragonitic structures through crystal growth by particle attachment. Our NMR results are consistent with heterogeneous nucleation of the solid mineral phase driven by coral acid-rich proteins. Such a mechanism suggests that stony corals may be able to sustain calcification even under lower pH conditions that do not favor the inorganic precipitation of aragonite.

Fresnel representation of the Wigner function: an operational approach.

PubMed

Lougovski, P; Solano, E; Zhang, Z M; Walther, H; Mack, H; Schleich, W P

2003-07-04

We present an operational definition of the Wigner function. Our method relies on the Fresnel transform of measured Rabi oscillations and applies to motional states of trapped atoms as well as to field states in cavities. We illustrate this technique using data from recent experiments in ion traps [Phys. Rev. Lett. 76, 1796 (1996)

Mean field limit for bosons with compact kernels interactions by Wigner measures transportation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liard, Quentin, E-mail: quentin.liard@univ-rennes1.fr; Pawilowski, Boris, E-mail: boris.pawilowski@univ-rennes1.fr

2014-09-15

We consider a class of many-body Hamiltonians composed of a free (kinetic) part and a multi-particle (potential) interaction with a compactness assumption on the latter part. We investigate the mean field limit of such quantum systems following the Wigner measures approach. We prove in particular the propagation of these measures along the flow of a nonlinear (Hartree) field equation. This enhances and complements some previous results of the same type shown in Z. Ammari and F. Nier and Fröhlich et al. [“Mean field limit for bosons and propagation of Wigner measures,” J. Math. Phys. 50(4), 042107 (2009); Z. Ammari andmore » F. Nier and Fröhlich et al., “Mean field propagation of Wigner measures and BBGKY hierarchies for general bosonic states,” J. Math. Pures Appl. 95(6), 585–626 (2011); Z. Ammari and F. Nier and Fröhlich et al., “Mean-field- and classical limit of many-body Schrödinger dynamics for bosons,” Commun. Math. Phys. 271(3), 681–697 (2007)].« less

Dynamics of the Wigner crystal of composite particles

NASA Astrophysics Data System (ADS)

Shi, Junren; Ji, Wencheng

2018-03-01

Conventional wisdom has long held that a composite particle behaves just like an ordinary Newtonian particle. In this paper, we derive the effective dynamics of a type-I Wigner crystal of composite particles directly from its microscopic wave function. It indicates that the composite particles are subjected to a Berry curvature in the momentum space as well as an emergent dissipationless viscosity. While the dissipationless viscosity is the Chern-Simons field counterpart for the Wigner crystal, the Berry curvature is a feature not presented in the conventional composite fermion theory. Hence, contrary to general belief, composite particles follow the more general Sundaram-Niu dynamics instead of the ordinary Newtonian one. We show that the presence of the Berry curvature is an inevitable feature for a dynamics conforming to the dipole picture of composite particles and Kohn's theorem. Based on the dynamics, we determine the dispersions of magnetophonon excitations numerically. We find an emergent magnetoroton mode which signifies the composite-particle nature of the Wigner crystal. It occurs at frequencies much lower than the magnetic cyclotron frequency and has a vanishing oscillator strength in the long-wavelength limit.

Computing Wigner distributions and time correlation functions using the quantum thermal bath method: application to proton transfer spectroscopy.

PubMed

Basire, Marie; Borgis, Daniel; Vuilleumier, Rodolphe

2013-08-14

Langevin dynamics coupled to a quantum thermal bath (QTB) allows for the inclusion of vibrational quantum effects in molecular dynamics simulations at virtually no additional computer cost. We investigate here the ability of the QTB method to reproduce the quantum Wigner distribution of a variety of model potentials, designed to assess the performances and limits of the method. We further compute the infrared spectrum of a multidimensional model of proton transfer in the gas phase and in solution, using classical trajectories sampled initially from the Wigner distribution. It is shown that for this type of system involving large anharmonicities and strong nonlinear coupling to the environment, the quantum thermal bath is able to sample the Wigner distribution satisfactorily and to account for both zero point energy and tunneling effects. It leads to quantum time correlation functions having the correct short-time behavior, and the correct associated spectral frequencies, but that are slightly too overdamped. This is attributed to the classical propagation approximation rather than the generation of the quantized initial conditions themselves.

The use of a selective saturation pulse to suppress t1 noise in two-dimensional 1H fast magic angle spinning solid-state NMR spectroscopy

NASA Astrophysics Data System (ADS)

Robertson, Aiden J.; Pandey, Manoj Kumar; Marsh, Andrew; Nishiyama, Yusuke; Brown, Steven P.

2015-11-01

A selective saturation pulse at fast magic angle spinning (MAS) frequencies (60+ kHz) suppresses t1 noise in the indirect dimension of two-dimensional 1H MAS NMR spectra. The method is applied to a synthetic nucleoside with an intense methyl 1H signal due to triisopropylsilyl (TIPS) protecting groups. Enhanced performance in terms of suppressing the methyl signal while minimising the loss of signal intensity of nearby resonances of interest relies on reducing spin diffusion - this is quantified by comparing two-dimensional 1H NOESY-like spin diffusion spectra recorded at 30-70 kHz MAS. For a saturation pulse centred at the methyl resonance, the effect of changing the nutation frequency at different MAS frequencies as well as the effect of changing the pulse duration is investigated. By applying a pulse of duration 30 ms and nutation frequency 725 Hz at 70 kHz MAS, a good compromise of significant suppression of the methyl resonance combined with the signal intensity of resonances greater than 5 ppm away from the methyl resonance being largely unaffected is achieved. The effectiveness of using a selective saturation pulse is demonstrated for both homonuclear 1H-1H double quantum (DQ)/single quantum (SQ) MAS and 14N-1H heteronuclear multiple quantum coherence (HMQC) two-dimensional solid-state NMR experiments.

Interacton-driven phenomena and Wigner transition in two-dimensional systems

NASA Astrophysics Data System (ADS)

Knighton, Talbot

The formation of a quantum Wigner Cyrstal (WC) is one of the most anticipated predictions of electron-electron interaction. This is expected to occur in zero magnetic field when the Coulomb energy EC dominates over the Fermi energy EF (at a ratio rs ≡ EC/ EF ˜ 37) for temperatures T << EF / kB. The extremely low T and ultra dilute carrier concentrations necessary to meet these requirements are difficult to achieve. Alternatively, a perpendicular magnetic B-field can be used to quench the kinetic energy. As B increases, various energies compete to produce the ground state. High purity systems with large interaction rs >1 tend to exhibit reentrant insulating phases (RIP) between the integer and fractional Hall states. These are suspected to be a form of WC, but the evidence is not yet conclusive. We use transport measurements to identify a conduction threshold in the RIP at filling factor nu = 0.37 (close to the 1/3 state) that is several orders of magnitude larger than the pinning observed in many other systems. We analyze the temperature and electric E-field dependence of this insulating phase and find them to be consistent with a second-order phase transition to WC. The measurements are performed on dilute holes p = 4 x 1010 cm-2 of mobility mu = 1/perho ˜ 2.5 x 106 cm 2/Vs in 20 nm GaAs/AlGaAs quantum square wells. We also discuss various other projects related to the study of topological states and strongly interacting charges: direct testing of the bulk conduction in a developing quantum Hall state using a corbino-disk-like geometry (or "anti-Hall bar"); preliminary results for ultra dilute charges in undoped heterojunction insulated gated field effect transistors; quantum capacitance measurement of the density of states across the vanadium dioxide metal insulator transition; progress towards a scanning capacitance measurement using the tip of an atomic force microscope; and graphene devices for optical detection.

Two-dimensional freezing criteria for crystallizing colloidal monolayers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang Ziren; Han Yilong; Alsayed, Ahmed M.

Video microscopy was employed to explore crystallization of colloidal monolayers composed of diameter-tunable microgel spheres. Two-dimensional (2D) colloidal liquids were frozen homogenously into polycrystalline solids, and four 2D criteria for freezing were experimentally tested in thermal systems for the first time: the Hansen-Verlet freezing rule, the Loewen-Palberg-Simon dynamical freezing criterion, and two other rules based, respectively, on the split shoulder of the radial distribution function and on the distribution of the shape factor of Voronoi polygons. Importantly, these freezing criteria, usually applied in the context of single crystals, were demonstrated to apply to the formation of polycrystalline solids. At themore » freezing point, we also observed a peak in the fluctuations of the orientational order parameter and a percolation transition associated with caged particles. Speculation about these percolated clusters of caged particles casts light on solidification mechanisms and dynamic heterogeneity in freezing.« less

Multicellular tumor spheroids as an in vivo-like tumor model for three-dimensional imaging of chemotherapeutic and nano material cellular penetration.

PubMed

Ma, Hui-li; Jiang, Qiao; Han, Siyuan; Wu, Yan; Cui Tomshine, Jin; Wang, Dongliang; Gan, Yaling; Zou, Guozhang; Liang, Xing-Jie

2012-01-01

We present a flexible and highly reproducible method using three-dimensional (3D) multicellular tumor spheroids to quantify chemotherapeutic and nanoparticle penetration properties in vitro. We generated HeLa cell-derived spheroids using the liquid overlay method. To properly characterize HeLa spheroids, scanning electron microscopy, transmission electron microscopy, and multiphoton microscopy were used to obtain high-resolution 3D images of HeLa spheroids. Next, pairing high-resolution optical characterization techniques with flow cytometry, we quantitatively compared the penetration of doxorubicin, quantum dots, and synthetic micelles into 3D HeLa spheroid versus HeLa cells grown in a traditional two-dimensional culturing system. Our data revealed that 3D cultured HeLa cells acquired several clinically relevant morphologic and cellular characteristics (such as resistance to chemotherapeutics) often found in human solid tumors. These characteristic, however, could not be captured using conventional two-dimensional cell culture techniques. This study demonstrated the remarkable versatility of HeLa spheroid 3D imaging. In addition, our results revealed the capability of HeLa spheroids to function as a screening tool for nanoparticles or synthetic micelles that, due to their inherent size, charge, and hydrophobicity, can penetrate into solid tumors and act as delivery vehicles for chemotherapeutics. The development of this image-based, reproducible, and quantifiable in vitro HeLa spheroid screening tool will greatly aid future exploration of chemotherapeutics and nanoparticle delivery into solid tumors.

Translational vibrations between chains of hydrogen-bonded molecules in solid-state aspirin form I

NASA Astrophysics Data System (ADS)

Takahashi, Masae; Ishikawa, Yoichi

2013-06-01

We perform dispersion-corrected first-principles calculations, and far-infrared (terahertz) spectroscopic experiments at 4 K, to examine translational vibrations between chains of hydrogen-bonded molecules in solid-state aspirin form I. The calculated frequencies and relative intensities reproduce the observed spectrum to accuracy of 11 cm-1 or less. The stronger one of the two peaks assigned to the translational mode includes the stretching vibration of the weak hydrogen bond between the acetyl groups of a neighboring one-dimensional chain. The calculation of aspirin form II performed for comparison gives the stretching vibration of the weak hydrogen bond in one-dimensional chain.

Continuous spin representations from group contraction

NASA Astrophysics Data System (ADS)

Khan, Abu M.; Ramond, Pierre

2005-05-01

We consider how the continuous spin representation (CSR) of the Poincaré group in four dimensions can be generated by dimensional reduction. The analysis uses the front-form little group in five dimensions, which must yield the Euclidean group E(2), the little group of the CSR. We consider two cases, one is the single spin massless representation of the Poincaré group in five dimensions, the other is the infinite component Majorana equation, which describes an infinite tower of massive states in five dimensions. In the first case, the double singular limit j, R →∞, with j /R fixed, where R is the Kaluza-Klein radius of the fifth dimension, and j is the spin of the particle in five dimensions, yields the CSR in four dimensions. It amounts to the Inönü-Wigner contraction, with the inverse Kaluza-Klein radius as contraction parameter. In the second case, the CSR appears only by taking a triple singular limit, where an internal coordinate of the Majorana theory goes to infinity, while leaving its ratio to the Kaluza-Klein radius fixed.

A spectral analysis of the domain decomposed Monte Carlo method for linear systems

DOE PAGES

Slattery, Stuart R.; Evans, Thomas M.; Wilson, Paul P. H.

2015-09-08

The domain decomposed behavior of the adjoint Neumann-Ulam Monte Carlo method for solving linear systems is analyzed using the spectral properties of the linear oper- ator. Relationships for the average length of the adjoint random walks, a measure of convergence speed and serial performance, are made with respect to the eigenvalues of the linear operator. In addition, relationships for the effective optical thickness of a domain in the decomposition are presented based on the spectral analysis and diffusion theory. Using the effective optical thickness, the Wigner rational approxi- mation and the mean chord approximation are applied to estimate the leakagemore » frac- tion of random walks from a domain in the decomposition as a measure of parallel performance and potential communication costs. The one-speed, two-dimensional neutron diffusion equation is used as a model problem in numerical experiments to test the models for symmetric operators with spectral qualities similar to light water reactor problems. We find, in general, the derived approximations show good agreement with random walk lengths and leakage fractions computed by the numerical experiments.« less

Simultaneous measurement of in-plane and out-of-plane displacement derivatives using dual-wavelength digital holographic interferometry.

PubMed

Rajshekhar, Gannavarpu; Gorthi, Sai Siva; Rastogi, Pramod

2011-12-01

The paper introduces a method for simultaneously measuring the in-plane and out-of-plane displacement derivatives of a deformed object in digital holographic interferometry. In the proposed method, lasers of different wavelengths are used to simultaneously illuminate the object along various directions such that a unique wavelength is used for a given direction. The holograms formed by multiple reference-object beam pairs of different wavelengths are recorded by a 3-color CCD camera with red, green, and blue channels. Each channel stores the hologram related to the corresponding wavelength and hence for the specific direction. The complex reconstructed interference field is obtained for each wavelength by numerical reconstruction and digital processing of the recorded holograms before and after deformation. Subsequently, the phase derivative is estimated for a given wavelength using two-dimensional pseudo Wigner-Ville distribution and the in-plane and out-of-plane components are obtained from the estimated phase derivatives using the sensitivity vectors of the optical configuration. © 2011 Optical Society of America

Calculation of nanodrop profile from fluid density distribution.

PubMed

Berim, Gersh O; Ruckenstein, Eli

2016-05-01

Two approaches are examined, which can be used to determine the drop profile from the fluid density distributions (FDDs) obtained on the basis of microscopic theories. For simplicity, only two-dimensional (cylindrical, or axisymmetrical) distributions are examined and it is assumed that the fluid is either in contact with a smooth solid or separated from the smooth solid by a lubricating liquid film. The first approach is based on the sharp-kink interface approximation in which the density of the liquid inside and the density of the vapor outside the drop are constant with the exception of the surface layer of the drop where the density is different from the above ones. In this case, the drop profile was calculated by minimizing the total potential energy of the system. The second approach is based on a nonuniform FDD obtained either by the density functional theory or molecular dynamics simulations. To determine the drop profile from such an FDD, which does not contain sharp interfaces, three procedures can be used. In the first two procedures, P1 and P2, the one-dimensional FDDs along straight lines which are parallel to the surface of the solid are extracted from the two-dimensional FDD. Each of those one-dimensional FDDs has a vapor-liquid interface at which the fluid density changes from vapor-like to liquid-like values. Procedure P1 uses the locations of the equimolar dividing surfaces for the one-dimensional FDDs as points of the drop profile. Procedure P2 is based on the assumption that the fluid density is constant on the surface of the drop, that density being selected either arbitrarily or as a fluid density at the location of the equimolar dividing surface for one of the one-dimensional FDDs employed in procedure P1. In the third procedure, P3, which is suggested for the first time in this paper, the one-dimensional FDDs are taken along the straight lines passing through a selected point inside the drop (radial line). Then, the drop profile is calculated like in procedure P1. It is shown, that procedure P3 provides a drop profile which is more reasonable than the other ones. Relationship of the discussed procedures to those used in image analysis is briefly discussed. Copyright © 2016 Elsevier B.V. All rights reserved.

Spectral decomposition of seismic data with reassigned smoothed pseudo Wigner-Ville distribution

NASA Astrophysics Data System (ADS)

Wu, Xiaoyang; Liu, Tianyou

2009-07-01

Seismic signals are nonstationary mainly due to absorption and attenuation of seismic energy in strata. Referring to spectral decomposition of seismic data, the conventional method using short-time Fourier transform (STFT) limits temporal and spectral resolution by a predefined window length. Continuous-wavelet transform (CWT) uses dilation and translation of a wavelet to produce a time-scale map. However, the wavelets utilized should be orthogonal in order to obtain a satisfactory resolution. The less applied, Wigner-Ville distribution (WVD) being superior in energy distribution concentration, is confronted with cross-terms interference (CTI) when signals are multi-component. In order to reduce the impact of CTI, Cohen class uses kernel function as low-pass filter. Nevertheless it also weakens energy concentration of auto-terms. In this paper, we employ smoothed pseudo Wigner-Ville distribution (SPWVD) with Gauss kernel function to reduce CTI in time and frequency domain, then reassign values of SPWVD (called reassigned SPWVD) according to the center of gravity of the considering energy region so that distribution concentration is maintained simultaneously. We conduct the method above on a multi-component synthetic seismic record and compare with STFT and CWT spectra. Two field examples reveal that RSPWVD potentially can be applied to detect low-frequency shadows caused by hydrocarbons and to delineate the space distribution of abnormal geological body more precisely.

electromagnetics, eddy current, computer codes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gartling, David

TORO Version 4 is designed for finite element analysis of steady, transient and time-harmonic, multi-dimensional, quasi-static problems in electromagnetics. The code allows simulation of electrostatic fields, steady current flows, magnetostatics and eddy current problems in plane or axisymmetric, two-dimensional geometries. TORO is easily coupled to heat conduction and solid mechanics codes to allow multi-physics simulations to be performed.

Quasi-two-dimensional complex plasma containing spherical particles and their binary agglomerates.

PubMed

Chaudhuri, M; Semenov, I; Nosenko, V; Thomas, H M

2016-05-01

A unique type of quasi-two-dimensional complex plasma system was observed which consisted of monodisperse microspheres and their binary agglomerations (dimers). The particles and their dimers levitated in a plasma sheath at slightly different heights and formed two distinct sublayers. The system did not crystallize and may be characterized as a disordered solid. The dimers were identified based on their characteristic appearance in defocused images, i.e., rotating interference fringe patterns. The in-plane and interplane particle separations exhibit nonmonotonic dependence on the discharge pressure.

A two-dimensional layered Cd(II) coordination polymer with a three-dimensional supramolecular architecture incorporating mixed multidentate N- and O-donor ligands.

PubMed

Huang, Qiu-Ying; Su, Ming-Yang; Meng, Xiang-Ru

2015-06-01

The combination of N-heterocyclic and multicarboxylate ligands is a good choice for the construction of metal-organic frameworks. In the title coordination polymer, poly[bis{μ2-1-[(1H-benzimidazol-2-yl)methyl]-1H-tetrazole-κ(2)N(3):N(4)}(μ4-butanedioato-κ(4)O(1):O(1'):O(4):O(4'))(μ2-butanedioato-κ(2)O(1):O(4))dicadmium], [Cd(C4H4O4)(C9H8N6)]n, each Cd(II) ion exhibits an irregular octahedral CdO4N2 coordination geometry and is coordinated by four O atoms from three carboxylate groups of three succinate (butanedioate) ligands and two N atoms from two 1-[(1H-benzimidazol-2-yl)methyl]-1H-tetrazole (bimt) ligands. Cd(II) ions are connected by two kinds of crystallographically independent succinate ligands to generate a two-dimensional layered structure with bimt ligands located on each side of the layer. Adjacent layers are further connected by hydrogen bonding, leading to a three-dimensional supramolecular architecture in the solid state. Thermogravimetric analysis of the title polymer shows that it is stable up to 529 K and then loses weight from 529 to 918 K, corresponding to the decomposition of the bimt ligands and succinate groups. The polymer exhibits a strong fluorescence emission in the solid state at room temperature.

Applicability, Indispensability, and Underdetermination: Puzzling over Wigner's "Unreasonable Effectiveness of Mathematics"

ERIC Educational Resources Information Center

Gelfert, Axel

2014-01-01

In his influential 1960 paper "The Unreasonable Effectiveness of Mathematics in the Natural Sciences", Eugene P. Wigner raises the question of why something that was developed without concern for empirical facts--mathematics--should turn out to be so powerful in explaining facts about the natural world. Recent philosophy of science has…

An Overview Of Wideband Signal Analysis Techniques

NASA Astrophysics Data System (ADS)

Speiser, Jeffrey M.; Whitehouse, Harper J.

1989-11-01

This paper provides a unifying perspective for several narowband and wideband signal processing techniques. It considers narrowband ambiguity functions and Wigner-Ville distibutions, together with the wideband ambiguity function and several proposed approaches to a wideband version of the Wigner-Ville distribution (WVD). A unifying perspective is provided by the methodology of unitary representations and ray representations of transformation groups.

Elementary Analysis of the Special Relativistic Combination of Velocities, Wigner Rotation and Thomas Precession

ERIC Educational Resources Information Center

O'Donnell, Kane; Visser, Matt

2011-01-01

The purpose of this paper is to provide an elementary introduction to the qualitative and quantitative results of velocity combination in special relativity, including the Wigner rotation and Thomas precession. We utilize only the most familiar tools of special relativity, in arguments presented at three differing levels: (1) utterly elementary,…

Entanglement and Wigner Function Negativity of Multimode Non-Gaussian States

NASA Astrophysics Data System (ADS)

Walschaers, Mattia; Fabre, Claude; Parigi, Valentina; Treps, Nicolas

2017-11-01

Non-Gaussian operations are essential to exploit the quantum advantages in optical continuous variable quantum information protocols. We focus on mode-selective photon addition and subtraction as experimentally promising processes to create multimode non-Gaussian states. Our approach is based on correlation functions, as is common in quantum statistical mechanics and condensed matter physics, mixed with quantum optics tools. We formulate an analytical expression of the Wigner function after the subtraction or addition of a single photon, for arbitrarily many modes. It is used to demonstrate entanglement properties specific to non-Gaussian states and also leads to a practical and elegant condition for Wigner function negativity. Finally, we analyze the potential of photon addition and subtraction for an experimentally generated multimode Gaussian state.

Entanglement Potential Versus Negativity of Wigner Function for SUP-Operated Quantum States

NASA Astrophysics Data System (ADS)

Chatterjee, Arpita

2018-02-01

We construct a distinct category of nonclassical quantum states by applying a superposition of products (SUP) of field annihilation (\\hat {a}) and creation (\\hat {a}^{\\dagger }) operators of the type (s\\hat {a}\\hat {a}^{\\dagger }+t\\hat {a}^{\\dagger }\\hat {a}), with s2+t2=1, upon thermal and even coherent states. We allow these SUP operated states to undergo a decoherence process and then describe the nonclassical features of the resulted field by using the entanglement potential (EP) and the negativity of the Wigner distribution function. Our analysis reveals that both the measures are reduced in the linear loss process. The partial negativity of the Wigner function disappears when losses exceed 50% but EP exists always.

Entanglement and Wigner Function Negativity of Multimode Non-Gaussian States.

PubMed

Walschaers, Mattia; Fabre, Claude; Parigi, Valentina; Treps, Nicolas

2017-11-03

Non-Gaussian operations are essential to exploit the quantum advantages in optical continuous variable quantum information protocols. We focus on mode-selective photon addition and subtraction as experimentally promising processes to create multimode non-Gaussian states. Our approach is based on correlation functions, as is common in quantum statistical mechanics and condensed matter physics, mixed with quantum optics tools. We formulate an analytical expression of the Wigner function after the subtraction or addition of a single photon, for arbitrarily many modes. It is used to demonstrate entanglement properties specific to non-Gaussian states and also leads to a practical and elegant condition for Wigner function negativity. Finally, we analyze the potential of photon addition and subtraction for an experimentally generated multimode Gaussian state.

Two-window heterodyne methods to characterize light fields

NASA Astrophysics Data System (ADS)

Reil, Frank

In this dissertation, I develop a novel Two-Window heterodyne technique for measuring the time-resolved Wigner function of light fields, which allows their complete characterization. A Wigner function is a quasi-probability density that describes the transverse position and transverse momentum of a light field and is Fourier-transform related to its mutual coherence function. It obeys rigorous transport equations and therefore provides an ideal way to characterize a light field and its propagation through various media. I first present the experimental setup of our Two-Window technique, which is based on a heterodyne scheme involving two phase-coupled Local Oscillator beams we call the Dual-LO. The Dual-LO consists of a focused beam ('SLO') which sets the spatial resolution, and a collimated beam ('BLO') which sets the momental resolution. The resolution in transverse position and transverse momentum can be adjusted individually by the size of the SLO and BLO, which enables a measurement resolution surpassing the uncertainty principle associated with Fourier-transform pairs which limits the resolution when just a single LO is used. We first use our technique to determine the beam size, transverse coherence length and radius of curvature of a Gaussian-Schell beam, as well as its longitudinal characteristics, which are related to its optical spectrum. We then examine Enhanced Backscattering at various path-lengths in the turbid medium. For the first time ever, we demonstrate the phase-conjugating properties of a turbid medium by observing the change in sign of the radius of curvature for a non-collimated field incident on the medium. We also perform time-resolved measurements in the transmission regime. In tenuous media we observe two peaks in phase-space confined by a hyperbola which are due to low-order scattering. Their distance depends on the chosen path-delay. Some coherence and even spatial properties of the incident field are preserved in those peaks as measurements with our Two-Window technique show. Various other applications are presented in less detail, such as the Wigner function of the field inside a speckle produced by a piece of glass containing air bubbles.

Freezing Transition Studies Through Constrained Cell Model Simulation

NASA Astrophysics Data System (ADS)

Nayhouse, Michael; Kwon, Joseph Sang-Il; Heng, Vincent R.; Amlani, Ankur M.; Orkoulas, G.

2014-10-01

In the present work, a simulation method based on cell models is used to deduce the fluid-solid transition of a system of particles that interact via a pair potential, , which is of the form with . The simulations are implemented under constant-pressure conditions on a generalized version of the constrained cell model. The constrained cell model is constructed by dividing the volume into Wigner-Seitz cells and confining each particle in a single cell. This model is a special case of a more general cell model which is formed by introducing an additional field variable that controls the number of particles per cell and, thus, the relative stability of the solid against the fluid phase. High field values force configurations with one particle per cell and thus favor the solid phase. Fluid-solid coexistence on the isotherm that corresponds to a reduced temperature of 2 is determined from constant-pressure simulations of the generalized cell model using tempering and histogram reweighting techniques. The entire fluid-solid phase boundary is determined through a thermodynamic integration technique based on histogram reweighting, using the previous coexistence point as a reference point. The vapor-liquid phase diagram is obtained from constant-pressure simulations of the unconstrained system using tempering and histogram reweighting. The phase diagram of the system is found to contain a stable critical point and a triple point. The phase diagram of the corresponding constrained cell model is also found to contain both a stable critical point and a triple point.

Entanglement complexity in quantum many-body dynamics, thermalization, and localization

NASA Astrophysics Data System (ADS)

Yang, Zhi-Cheng; Hamma, Alioscia; Giampaolo, Salvatore M.; Mucciolo, Eduardo R.; Chamon, Claudio

2017-07-01

Entanglement is usually quantified by von Neumann entropy, but its properties are much more complex than what can be expressed with a single number. We show that the three distinct dynamical phases known as thermalization, Anderson localization, and many-body localization are marked by different patterns of the spectrum of the reduced density matrix for a state evolved after a quantum quench. While the entanglement spectrum displays Poisson statistics for the case of Anderson localization, it displays universal Wigner-Dyson statistics for both the cases of many-body localization and thermalization, albeit the universal distribution is asymptotically reached within very different time scales in these two cases. We further show that the complexity of entanglement, revealed by the possibility of disentangling the state through a Metropolis-like algorithm, is signaled by whether the entanglement spectrum level spacing is Poisson or Wigner-Dyson distributed.

First observation of the Λ(1405) line shape in electroproduction

NASA Astrophysics Data System (ADS)

Lu, H. Y.; Schumacher, R. A.; Adhikari, K. P.; Adikaram, D.; Aghasyan, M.; Amaryan, M. J.; Pereira, S. Anefalos; Ball, J.; Battaglieri, M.; Batourine, V.; Bedlinskiy, I.; Biselli, A. S.; Boiarinov, S.; Briscoe, W. J.; Brooks, W. K.; Burkert, V. D.; Carman, D. S.; Celentano, A.; Chandavar, S.; Cole, P. L.; Collins, P.; Contalbrigo, M.; Cortes, O.; Crede, V.; D'Angelo, A.; Dashyan, N.; De Vita, R.; De Sanctis, E.; Deur, A.; Djalali, C.; Doughty, D.; Dupre, R.; Egiyan, H.; Alaoui, A. El; Fassi, L. El; Eugenio, P.; Fedotov, G.; Fegan, S.; Fleming, J. A.; Gabrielyan, M.; Gevorgyan, N.; Gilfoyle, G. P.; Giovanetti, K. L.; Girod, F. X.; Goetz, J. T.; Gohn, W.; Golovatch, E.; Gothe, R. W.; Griffioen, K. A.; Guidal, M.; Guo, L.; Hafidi, K.; Hakobyan, H.; Harrison, N.; Heddle, D.; Hicks, K.; Ho, D.; Holtrop, M.; Hyde, C. E.; Ilieva, Y.; Ireland, D. G.; Ishkhanov, B. S.; Isupov, E. L.; Jo, H. S.; Joo, K.; Keller, D.; Khandaker, M.; Kim, W.; Klein, A.; Klein, F. J.; Koirala, S.; Kubarovsky, A.; Kubarovsky, V.; Kuleshov, S. V.; Lewis, S.; Livingston, K.; MacGregor, I. J. D.; Martinez, D.; Mayer, M.; McKinnon, B.; Meyer, C. A.; Mineeva, T.; Mirazita, M.; Mokeev, V.; Montgomery, R. A.; Moriya, K.; Moutarde, H.; Munevar, E.; Camacho, C. Munoz; Nadel-Turonski, P.; Nepali, C. S.; Niccolai, S.; Niculescu, G.; Niculescu, I.; Osipenko, M.; Ostrovidov, A. I.; Pappalardo, L. L.; Paremuzyan, R.; Park, K.; Park, S.; Pasyuk, E.; Peng, P.; Phelps, E.; Phillips, J. J.; Pisano, S.; Pogorelko, O.; Pozdniakov, S.; Price, J. W.; Procureur, S.; Prok, Y.; Protopopescu, D.; Puckett, A. J. R.; Raue, B. A.; Rimal, D.; Ripani, M.; Rosner, G.; Rossi, P.; Sabatié, F.; Saini, M. S.; Salgado, C.; Schott, D.; Seder, E.; Seraydaryan, H.; Sharabian, Y. G.; Smith, G. D.; Sober, D. I.; Sokhan, D.; Stepanyan, S. S.; Stoler, P.; Strauch, S.; Taiuti, M.; Tang, W.; Tian, Ye; Tkachenko, S.; Torayev, B.; Vernarsky, B.; Voskanyan, H.; Voutier, E.; Walford, N. K.; Weygand, D. P.; Wood, M. H.; Zachariou, N.; Zana, L.; Zhang, J.; Zhao, Z. W.

2013-10-01

We report the first observation of the line shape of the Λ(1405) from electroproduction, and show that it is not a simple Breit-Wigner resonance. Electroproduction of K+Λ(1405) off the proton was studied by using data from CLAS at Jefferson Lab in the range 1.0

Bivariate- distribution for transition matrix elements in Breit-Wigner to Gaussian domains of interacting particle systems.

PubMed

Kota, V K B; Chavda, N D; Sahu, R

2006-04-01

Interacting many-particle systems with a mean-field one-body part plus a chaos generating random two-body interaction having strength lambda exhibit Poisson to Gaussian orthogonal ensemble and Breit-Wigner (BW) to Gaussian transitions in level fluctuations and strength functions with transition points marked by lambda = lambda c and lambda = lambda F, respectively; lambda F > lambda c. For these systems a theory for the matrix elements of one-body transition operators is available, as valid in the Gaussian domain, with lambda > lambda F, in terms of orbital occupation numbers, level densities, and an integral involving a bivariate Gaussian in the initial and final energies. Here we show that, using a bivariate-t distribution, the theory extends below from the Gaussian regime to the BW regime up to lambda = lambda c. This is well tested in numerical calculations for 6 spinless fermions in 12 single-particle states.

Use of the Wigner representation in scattering problems

NASA Technical Reports Server (NTRS)

Bemler, E. A.

1975-01-01

The basic equations of quantum scattering were translated into the Wigner representation, putting quantum mechanics in the form of a stochastic process in phase space, with real valued probability distributions and source functions. The interpretative picture associated with this representation is developed and stressed and results used in applications published elsewhere are derived. The form of the integral equation for scattering as well as its multiple scattering expansion in this representation are derived. Quantum corrections to classical propagators are briefly discussed. The basic approximation used in the Monte-Carlo method is derived in a fashion which allows for future refinement and which includes bound state production. Finally, as a simple illustration of some of the formalism, scattering is treated by a bound two body problem. Simple expressions for single and double scattering contributions to total and differential cross-sections as well as for all necessary shadow corrections are obtained.

ππ P-wave resonant scattering from lattice QCD

NASA Astrophysics Data System (ADS)

Paul, Srijit; Alexandrou, Constantia; Leskovec, Luka; Meinel, Stefan; Negele, John W.; Petschlies, Marcus; Pochinsky, Andrew; Rendon Suzuki, Jesus Gumaro; Syritsyn, Sergey

2018-03-01

We present a high-statistics analysis of the ρ resonance in ππ scattering, using 2 + 1 flavors of clover fermions at a pion mass of approximately 320 MeV and a lattice size of approximately 3:6 fm. The computation of the two-point functions are carried out using combinations of forward, sequential, and stochastic propagators. For the extraction of the ρ-resonance parameters, we compare different fit methods and demonstrate their consistency. For the ππ scattering phase shift, we consider different Breit-Wigner parametrizations and also investigate possible nonresonant contributions. We find that the minimal Breit-Wigner model is suffcient to describe our data, and obtain amρ = 0:4609(16)stat(14)sys and gρππ = 5:69(13)stat(16)sys. In our comparison with other lattice QCD results, we consider the dimensionless ratios amρ/amN and amπ/amN to avoid scale setting ambiguities.

Wave-front singularities for two-dimensional anisotropic elastic waves.

NASA Technical Reports Server (NTRS)

Payton, R. G.

1972-01-01

Wavefront singularities for the displacement functions, associated with the radiation of linear elastic waves from a point source embedded in a finitely strained two-dimensional elastic solid, are examined in detail. It is found that generally the singularities are of order d to the -1/2 power, where d measures distance away from the front. However, in certain exceptional cases singularities of order d to the -n power, where n = 1/4, 2/3, 3/4, may be encountered.

Finite-amplitude strain waves in laser-excited plates.

PubMed

Mirzade, F Kh

2008-07-09

The governing equations for two-dimensional finite-amplitude longitudinal strain waves in isotropic laser-excited solid plates are derived. Geometric and weak material nonlinearities are included, and the interaction of longitudinal displacements with the field of concentration of non-equilibrium laser-generated atomic defects is taken into account. An asymptotic approach is used to show that the equations are reducible to the Kadomtsev-Petviashvili-Burgers nonlinear evolution equation for a longitudinal self-consistent strain field. It is shown that two-dimensional shock waves can propagate in plates.

Nanophase diagram of binary eutectic Au-Ge nanoalloys for vapor-liquid-solid semiconductor nanowires growth

NASA Astrophysics Data System (ADS)

Lu, Haiming; Meng, Xiangkang

2015-06-01

Although the vapor-liquid-solid growth of semiconductor nanowire is a non-equilibrium process, the equilibrium phase diagram of binary alloy provides important guidance on the growth conditions, such as the temperature and the equilibrium composition of the alloy. Given the small dimensions of the alloy seeds and the nanowires, the known phase diagram of bulk binary alloy cannot be expected to accurately predict the behavior of the nanowire growth. Here, we developed a unified model to describe the size- and dimensionality-dependent equilibrium phase diagram of Au-Ge binary eutectic nanoalloys based on the size-dependent cohesive energy model. It is found that the liquidus curves reduce and shift leftward with decreasing size and dimensionality. Moreover, the effects of size and dimensionality on the eutectic composition are small and negligible when both components in binary eutectic alloys have the same dimensionality. However, when two components have different dimensionality (e.g. Au nanoparticle-Ge nanowire usually used in the semiconductor nanowires growth), the eutectic composition reduces with decreasing size.

Electron tunneling in nanoscale electrodes for battery applications

NASA Astrophysics Data System (ADS)

Yamada, Hidenori; Narayanan, Rajaram; Bandaru, Prabhakar R.

2018-03-01

It is shown that the electrical current that may be obtained from a nanoscale electrochemical system is sensitive to the dimensionality of the electrode and the density of states (DOS). Considering the DOS of lower dimensional systems, such as two-dimensional graphene, one-dimensional nanotubes, or zero-dimensional quantum dots, yields a distinct variation of the current-voltage characteristics. Such aspects go beyond conventional Arrhenius theory based kinetics which are often used in experimental interpretation. The obtained insights may be adapted to other devices, such as solid-state batteries. It is also indicated that electron transport in such devices may be considered through electron tunneling.

Calcium Coordination Solids for pH-Triggered Release of Olsalazine

DOE Office of Scientific and Technical Information (OSTI.GOV)

Levine, Dana J.; Gonzalez, Miguel I.; Legendre, Christina M.

Here, calcium coordination solids were synthesized and evaluated for delivery of olsalazine (H 4olz), an anti-inflammatory compound used for treatment of ulcerative colitis. The materials include one-dimensional Ca(H 2olz)•4H 2O chains, two-dimensional Ca(H 2olz)•2H 2O sheets, and a three-dimensional metal-organic framework Ca(H 2olz)•2DMF (DMF= N,N-dimethylformamide). The framework undergoes structural changes in response to solvent, forming a dense Ca(H 2olz) phase when exposed to aqueous HCl. The compounds Ca(H 2olz)•xH 2O (x=0, 2, 4) were each pressed into pellets and exposed to simulated gastrointestinal fluids to mimic the passage of a pill from the acidic stomach to the pH-neutral intestines. Allmore » three calcium materials exhibited a delayed release of olsalazine relative to Na 2(H 2olz), the commercial formulation, illustrating how formulation of a drug within an extended coordination solid can serve to tune its solubility and performance.« less

Calcium Coordination Solids for pH-Triggered Release of Olsalazine

DOE PAGES

Levine, Dana J.; Gonzalez, Miguel I.; Legendre, Christina M.; ...

2017-09-12

Here, calcium coordination solids were synthesized and evaluated for delivery of olsalazine (H 4olz), an anti-inflammatory compound used for treatment of ulcerative colitis. The materials include one-dimensional Ca(H 2olz)•4H 2O chains, two-dimensional Ca(H 2olz)•2H 2O sheets, and a three-dimensional metal-organic framework Ca(H 2olz)•2DMF (DMF= N,N-dimethylformamide). The framework undergoes structural changes in response to solvent, forming a dense Ca(H 2olz) phase when exposed to aqueous HCl. The compounds Ca(H 2olz)•xH 2O (x=0, 2, 4) were each pressed into pellets and exposed to simulated gastrointestinal fluids to mimic the passage of a pill from the acidic stomach to the pH-neutral intestines. Allmore » three calcium materials exhibited a delayed release of olsalazine relative to Na 2(H 2olz), the commercial formulation, illustrating how formulation of a drug within an extended coordination solid can serve to tune its solubility and performance.« less

Biological control of aragonite formation in stony corals.

PubMed

Von Euw, Stanislas; Zhang, Qihong; Manichev, Viacheslav; Murali, Nagarajan; Gross, Juliane; Feldman, Leonard C; Gustafsson, Torgny; Flach, Carol; Mendelsohn, Richard; Falkowski, Paul G

2017-06-02

Little is known about how stony corals build their calcareous skeletons. There are two prevailing hypotheses: that it is a physicochemically dominated process and that it is a biologically mediated one. Using a combination of ultrahigh-resolution three - dimensional imaging and two-dimensional solid-state nuclear magnetic resonance (NMR) spectroscopy, we show that mineral deposition is biologically driven. Randomly arranged, amorphous nanoparticles are initially deposited in microenvironments enriched in organic material; they then aggregate and form ordered aragonitic structures through crystal growth by particle attachment. Our NMR results are consistent with heterogeneous nucleation of the solid mineral phase driven by coral acid-rich proteins. Such a mechanism suggests that stony corals may be able to sustain calcification even under lower pH conditions that do not favor the inorganic precipitation of aragonite. Copyright © 2017, American Association for the Advancement of Science.

Phase diagram of a symmetric electron–hole bilayer system: a variational Monte Carlo study

NASA Astrophysics Data System (ADS)

Sharma, Rajesh O.; Saini, L. K.; Prasad Bahuguna, Bhagwati

2018-05-01

We study the phase diagram of a symmetric electron–hole bilayer system at absolute zero temperature and in zero magnetic field within the quantum Monte Carlo approach. In particular, we conduct variational Monte Carlo simulations for various phases, i.e. the paramagnetic fluid phase, the ferromagnetic fluid phase, the anti-ferromagnetic Wigner crystal phase, the ferromagnetic Wigner crystal phase and the excitonic phase, to estimate the ground-state energy at different values of in-layer density and inter-layer spacing. Slater–Jastrow style trial wave functions, with single-particle orbitals appropriate for different phases, are used to construct the phase diagram in the (r s , d) plane by finding the relative stability of trial wave functions. At very small layer separations, we find that the fluid phases are stable, with the paramagnetic fluid phase being particularly stable at and the ferromagnetic fluid phase being particularly stable at . As the layer spacing increases, we first find that there is a phase transition from the ferromagnetic fluid phase to the ferromagnetic Wigner crystal phase when d reaches 0.4 a.u. at r s   =  20, and before there is a return to the ferromagnetic fluid phase when d approaches 1 a.u. However, for r s   <  20 and a.u., the excitonic phase is found to be stable. We do not find that the anti-ferromagnetic Wigner crystal is stable over the considered range of r s and d. We also find that as r s increases, the critical layer separations for Wigner crystallization increase.

A Proposal for Research on Complex Media, Imagining and Uncertainty Quantification

DTIC Science & Technology

2013-11-26

demonstration that the Green’s function for wave propagation in an ergodic cavity can be recovered exactly by cross correlation of signals at two points...the continuation of a project in which we have developed autofocus methods based on a phase space formulation ( Wigner transform) of the array data and

New Layered Materials and Functional Nanoelectronic Devices

NASA Astrophysics Data System (ADS)

Yu, Jaeeun

This thesis introduces functional nanomaterials including superatoms and carbon nanotubes (CNTs) for new layered solids and molecular devices. Chapters 1-3 present how we incorporate superatoms into two-dimensional (2D) materials. Chapter 1 describes a new and simple approach to dope transition metal dichalcogenides (TMDCs) using the superatom Co6Se8(PEt3)6 as the electron dopant. Doping is an effective method to modulate the electrical properties of materials, and we demonstrate an electron-rich cluster can be used as a tunable and controllable surface dopant for semiconducting TMDCs via charge transfer. As a demonstration of the concept, we make a p-n junction by patterning on specific areas of TMDC films. Chapter 2 and Chapter 3 introduce new 2D materials by molecular design of superatoms. Traditional atomic van der Waals materials such as graphene, hexagonal boron-nitride, and TMDCs have received widespread attention due to the wealth of unusual physical and chemical behaviors that arise when charges, spins, and vibrations are confined to a plane. Though not as widespread as their atomic counterparts, molecule-based layered solids offer significant benefits; their structural flexibility will enable the development of materials with tunable properties. Chapter 2 describes a layered van der Waals solid self-assembled from a structure-directing building block and C60 fullerene. The resulting crystalline solid contains a corrugated monolayer of neutral fullerenes and can be mechanically exfoliated. Chapter 3 describes a new method to functionalize electroactive superatoms with groups that can direct their assembly into covalent and non-covalent multi-dimensional frameworks. We synthesized Co6Se8[PEt2(4-C6H4COOH)]6 and found that it forms two types of crystalline assemblies with Zn(NO3)2, one is a three-dimensional solid and the other consists of stacked layers of two-dimensional sheets. The dimensionality is controlled by subtle changes in reaction conditions. CNT-based field-effect transistor (FETs), in which a single molecule spans an oxidatively cut gap in the CNT, provide a versatile, ground-state platform with well-defined electrical contacts. For statistical studies of a variety of small molecule bridges, Chapter 4 presents a novel fabrication method to produce hundreds of FETs on one single carbon nanotube. A large number of devices allows us to study the stability and uniformity of CNT FET properties. Moreover, the new platform also enables a quantitative analysis of molecular devices. In particular, we used CNT FETs for studying DNA-mediated charge transport. DNA conductance was measured by connecting DNA molecules of varying lengths to lithographically cut CNT FETs.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Walton, Mark A.

Quantum mechanics in phase space (or deformation quantization) appears to fail as an autonomous quantum method when infinite potential walls are present. The stationary physical Wigner functions do not satisfy the normal eigen equations, the *-eigen equations, unless an ad hoc boundary potential is added [N.C. Dias, J.N. Prata, J. Math. Phys. 43 (2002) 4602 (quant-ph/0012140)]. Alternatively, they satisfy a different, higher-order, '*-eigen-* equation', locally, i.e. away from the walls [S. Kryukov, M.A. Walton, Ann. Phys. 317 (2005) 474 (quant-ph/0412007)]. Here we show that this substitute equation can be written in a very simple form, even in the presence ofmore » an additional, arbitrary, but regular potential. The more general applicability of the *-eigen-* equation is then demonstrated. First, using an idea from [D.B. Fairlie, C.A. Manogue, J. Phys. A 24 (1991) 3807], we extend it to a dynamical equation describing time evolution. We then show that also for general contact interactions, the *-eigen-* equation is satisfied locally. Specifically, we treat the most general possible (Robin) boundary conditions at an infinite wall, general one-dimensional point interactions, and a finite potential jump. Finally, we examine a smooth potential, that has simple but different expressions for x positive and negative. We find that the *-eigen-* equation is again satisfied locally. It seems, therefore, that the *-eigen-* equation is generally relevant to the matching of Wigner functions; it can be solved piece-wise and its solutions then matched.« less

Holographic particle size extraction by using Wigner-Ville distribution

NASA Astrophysics Data System (ADS)

Chuamchaitrakool, Porntip; Widjaja, Joewono; Yoshimura, Hiroyuki

2014-06-01

A new method for measuring object size from in-line holograms by using Wigner-Ville distribution (WVD) is proposed. The proposed method has advantages over conventional numerical reconstruction in that it is free from iterative process and it can extract the object size and position with only single computation of the WVD. Experimental verification of the proposed method is presented.

Determination of Breit-Wigner features of the S{sub 11}(1535), S{sub 11}(1650), and P{sub 11}(1710) nucleon resonances

DOE Office of Scientific and Technical Information (OSTI.GOV)

Balandina, E. V., E-mail: lena@kiraton.sinp.msu.ru; Leikin, E. M.; Yudin, N. P.

2008-01-15

Basic Breit-Wigner features of the S{sub 11}(1535), S{sub 11}(1650), and P{sub 11}(1710) nucleon resonances are evaluated in a model-independent way on the basis of the results obtained previously from a partial-wave analysis of eta-meson photoproduction on protons.

A WENO-solver combined with adaptive momentum discretization for the Wigner transport equation and its application to resonant tunneling diodes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dorda, Antonius, E-mail: dorda@tugraz.at; Schürrer, Ferdinand, E-mail: ferdinand.schuerrer@tugraz.at

2015-03-01

We present a novel numerical scheme for the deterministic solution of the Wigner transport equation, especially suited to deal with situations in which strong quantum effects are present. The unique feature of the algorithm is the expansion of the Wigner function in local basis functions, similar to finite element or finite volume methods. This procedure yields a discretization of the pseudo-differential operator that conserves the particle density on arbitrarily chosen grids. The high flexibility in refining the grid spacing together with the weighted essentially non-oscillatory (WENO) scheme for the advection term allows for an accurate and well-resolved simulation of themore » phase space dynamics. A resonant tunneling diode is considered as test case and a detailed convergence study is given by comparing the results to a non-equilibrium Green's functions calculation. The impact of the considered domain size and of the grid spacing is analyzed. The obtained convergence of the results towards a quasi-exact agreement of the steady state Wigner and Green's functions computations demonstrates the accuracy of the scheme, as well as the high flexibility to adjust to different physical situations.« less

Quantum computation and analysis of Wigner and Husimi functions: toward a quantum image treatment.

PubMed

Terraneo, M; Georgeot, B; Shepelyansky, D L

2005-06-01

We study the efficiency of quantum algorithms which aim at obtaining phase-space distribution functions of quantum systems. Wigner and Husimi functions are considered. Different quantum algorithms are envisioned to build these functions, and compared with the classical computation. Different procedures to extract more efficiently information from the final wave function of these algorithms are studied, including coarse-grained measurements, amplitude amplification, and measure of wavelet-transformed wave function. The algorithms are analyzed and numerically tested on a complex quantum system showing different behavior depending on parameters: namely, the kicked rotator. The results for the Wigner function show in particular that the use of the quantum wavelet transform gives a polynomial gain over classical computation. For the Husimi distribution, the gain is much larger than for the Wigner function and is larger with the help of amplitude amplification and wavelet transforms. We discuss the generalization of these results to the simulation of other quantum systems. We also apply the same set of techniques to the analysis of real images. The results show that the use of the quantum wavelet transform allows one to lower dramatically the number of measurements needed, but at the cost of a large loss of information.

A WENO-solver combined with adaptive momentum discretization for the Wigner transport equation and its application to resonant tunneling diodes

PubMed Central

Dorda, Antonius; Schürrer, Ferdinand

2015-01-01

We present a novel numerical scheme for the deterministic solution of the Wigner transport equation, especially suited to deal with situations in which strong quantum effects are present. The unique feature of the algorithm is the expansion of the Wigner function in local basis functions, similar to finite element or finite volume methods. This procedure yields a discretization of the pseudo-differential operator that conserves the particle density on arbitrarily chosen grids. The high flexibility in refining the grid spacing together with the weighted essentially non-oscillatory (WENO) scheme for the advection term allows for an accurate and well-resolved simulation of the phase space dynamics. A resonant tunneling diode is considered as test case and a detailed convergence study is given by comparing the results to a non-equilibrium Green's functions calculation. The impact of the considered domain size and of the grid spacing is analyzed. The obtained convergence of the results towards a quasi-exact agreement of the steady state Wigner and Green's functions computations demonstrates the accuracy of the scheme, as well as the high flexibility to adjust to different physical situations. PMID:25892748

A WENO-solver combined with adaptive momentum discretization for the Wigner transport equation and its application to resonant tunneling diodes.

PubMed

Dorda, Antonius; Schürrer, Ferdinand

2015-03-01

We present a novel numerical scheme for the deterministic solution of the Wigner transport equation, especially suited to deal with situations in which strong quantum effects are present. The unique feature of the algorithm is the expansion of the Wigner function in local basis functions, similar to finite element or finite volume methods. This procedure yields a discretization of the pseudo-differential operator that conserves the particle density on arbitrarily chosen grids. The high flexibility in refining the grid spacing together with the weighted essentially non-oscillatory (WENO) scheme for the advection term allows for an accurate and well-resolved simulation of the phase space dynamics. A resonant tunneling diode is considered as test case and a detailed convergence study is given by comparing the results to a non-equilibrium Green's functions calculation. The impact of the considered domain size and of the grid spacing is analyzed. The obtained convergence of the results towards a quasi-exact agreement of the steady state Wigner and Green's functions computations demonstrates the accuracy of the scheme, as well as the high flexibility to adjust to different physical situations.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Miller, William H., E-mail: millerwh@berkeley.edu; Cotton, Stephen J., E-mail: StephenJCotton47@gmail.com

It is pointed out that the classical phase space distribution in action-angle (a-a) variables obtained from a Wigner function depends on how the calculation is carried out: if one computes the standard Wigner function in Cartesian variables (p, x), and then replaces p and x by their expressions in terms of a-a variables, one obtains a different result than if the Wigner function is computed directly in terms of the a-a variables. Furthermore, the latter procedure gives a result more consistent with classical and semiclassical theory—e.g., by incorporating the Bohr-Sommerfeld quantization condition (quantum states defined by integer values of themore » action variable) as well as the Heisenberg correspondence principle for matrix elements of an operator between such states—and has also been shown to be more accurate when applied to electronically non-adiabatic applications as implemented within the recently developed symmetrical quasi-classical (SQC) Meyer-Miller (MM) approach. Moreover, use of the Wigner function (obtained directly) in a-a variables shows how our standard SQC/MM approach can be used to obtain off-diagonal elements of the electronic density matrix by processing in a different way the same set of trajectories already used (in the SQC/MM methodology) to obtain the diagonal elements.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Miller, William H.; Cotton, Stephen J.

It is pointed out that the classical phase space distribution in action-angle (a-a) variables obtained from a Wigner function depends on how the calculation is carried out: if one computes the standard Wigner function in Cartesian variables (p, x), and then replaces p and x by their expressions in terms of a-a variables, one obtains a different result than if the Wigner function is computed directly in terms of the a-a variables. Furthermore, the latter procedure gives a result more consistent with classical and semiclassical theory - e.g., by incorporating the Bohr-Sommerfeld quantization condition (quantum states defined by integer valuesmore » of the action variable) as well as the Heisenberg correspondence principle for matrix elements of an operator between such states - and has also been shown to be more accurate when applied to electronically non-adiabatic applications as implemented within the recently developed symmetrical quasi-classical (SQC) Meyer-Miller (MM) approach. Moreover, use of the Wigner function (obtained directly) in a-a variables shows how our standard SQC/MM approach can be used to obtain off-diagonal elements of the electronic density matrix by processing in a different way the same set of trajectories already used (in the SQC/MM methodology) to obtain the diagonal elements.« less

Defects in a nonlinear pseudo one-dimensional solid

NASA Astrophysics Data System (ADS)

Blanchet, Graciela B.; Fincher, C. R., Jr.

1985-03-01

These infrared studies of acetanilide together with the existence of two equivalent structures for the hydrogen-bonded chain suggest the possibility of a topological defect state rather than a Davydov soliton as suggested previously. Acetanilide is an example of a class of one-dimensional materials where solitons are a consequence of a twofold degenerate structure and the nonlinear dynamics of the hydrogen-bonded network.

Quantum corrections of the truncated Wigner approximation applied to an exciton transport model.

PubMed

Ivanov, Anton; Breuer, Heinz-Peter

2017-04-01

We modify the path integral representation of exciton transport in open quantum systems such that an exact description of the quantum fluctuations around the classical evolution of the system is possible. As a consequence, the time evolution of the system observables is obtained by calculating the average of a stochastic difference equation which is weighted with a product of pseudoprobability density functions. From the exact equation of motion one can clearly identify the terms that are also present if we apply the truncated Wigner approximation. This description of the problem is used as a basis for the derivation of a new approximation, whose validity goes beyond the truncated Wigner approximation. To demonstrate this we apply the formalism to a donor-acceptor transport model.

Time Evolution of the Wigner Operator as a Quasi-density Operator in Amplitude Dessipative Channel

NASA Astrophysics Data System (ADS)

Yu, Zhisong; Ren, Guihua; Yu, Ziyang; Wei, Chenhuinan; Fan, Hongyi

2018-06-01

For developing quantum mechanics theory in phase space, we explore how the Wigner operator {Δ } (α ,α ^{\\ast } )≡ {1}/{π } :e^{-2(α ^{\\ast } -α ^{\\dag })(α -α )}:, when viewed as a quasi-density operator correponding to the Wigner quasiprobability distribution, evolves in a damping channel. with the damping constant κ. We derive that it evolves into 1/T + 1:\\exp 2/T + 1[-(α^{\\ast} e^{-κ t}-a^{\\dag} )(α e^{-κ t}-a)]: where T ≡ 1 - e - 2 κ t . This in turn helps to directly obtain the final state ρ( t) out of the dessipative channel from the initial classical function corresponding to initial ρ(0). Throught the work, the method of integration within ordered product (IWOP) of operators is employed.

Shape and Symmetry Determine Two-Dimensional Melting Transitions of Hard Regular Polygons

NASA Astrophysics Data System (ADS)

Anderson, Joshua A.; Antonaglia, James; Millan, Jaime A.; Engel, Michael; Glotzer, Sharon C.

2017-04-01

The melting transition of two-dimensional systems is a fundamental problem in condensed matter and statistical physics that has advanced significantly through the application of computational resources and algorithms. Two-dimensional systems present the opportunity for novel phases and phase transition scenarios not observed in 3D systems, but these phases depend sensitively on the system and, thus, predicting how any given 2D system will behave remains a challenge. Here, we report a comprehensive simulation study of the phase behavior near the melting transition of all hard regular polygons with 3 ≤n ≤14 vertices using massively parallel Monte Carlo simulations of up to 1 ×106 particles. By investigating this family of shapes, we show that the melting transition depends upon both particle shape and symmetry considerations, which together can predict which of three different melting scenarios will occur for a given n . We show that systems of polygons with as few as seven edges behave like hard disks; they melt continuously from a solid to a hexatic fluid and then undergo a first-order transition from the hexatic phase to the isotropic fluid phase. We show that this behavior, which holds for all 7 ≤n ≤14 , arises from weak entropic forces among the particles. Strong directional entropic forces align polygons with fewer than seven edges and impose local order in the fluid. These forces can enhance or suppress the discontinuous character of the transition depending on whether the local order in the fluid is compatible with the local order in the solid. As a result, systems of triangles, squares, and hexagons exhibit a Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) predicted continuous transition between isotropic fluid and triatic, tetratic, and hexatic phases, respectively, and a continuous transition from the appropriate x -atic to the solid. In particular, we find that systems of hexagons display continuous two-step KTHNY melting. In contrast, due to symmetry incompatibility between the ordered fluid and solid, systems of pentagons and plane-filling fourfold pentilles display a one-step first-order melting of the solid to the isotropic fluid with no intermediate phase.

Three-particle correlation functions of quasi-two-dimensional one-component and binary colloid suspensions.

PubMed

Ho, Hau My; Lin, Binhua; Rice, Stuart A

2006-11-14

We report the results of experimental determinations of the triplet correlation functions of quasi-two-dimensional one-component and binary colloid suspensions in which the colloid-colloid interaction is short ranged. The suspensions studied range in density from modestly dilute to solid. The triplet correlation function of the one-component colloid system reveals extensive ordering deep in the liquid phase. At the same density the ordering of the larger diameter component in a binary colloid system is greatly diminished by a very small amount of the smaller diameter component. The possible utilization of information contained in the triplet correlation function in the theory of melting of a quasi-two-dimensional system is briefly discussed.

Three-dimensional control of crystal growth using magnetic fields

NASA Astrophysics Data System (ADS)

Dulikravich, George S.; Ahuja, Vineet; Lee, Seungsoo

1993-07-01

Two coupled systems of partial differential equations governing three-dimensional laminar viscous flow undergoing solidification or melting under the influence of arbitrarily oriented externally applied magnetic fields have been formulated. The model accounts for arbitrary temperature dependence of physical properties including latent heat release, effects of Joule heating, magnetic field forces, and mushy region existence. On the basis of this model a numerical algorithm has been developed and implemented using central differencing on a curvilinear boundary-conforming grid and Runge-Kutta explicit time-stepping. The numerical results clearly demonstrate possibilities for active and practically instantaneous control of melt/solid interface shape, the solidification/melting front propagation speed, and the amount and location of solid accrued.

The use of a selective saturation pulse to suppress t1 noise in two-dimensional (1)H fast magic angle spinning solid-state NMR spectroscopy.

PubMed

Robertson, Aiden J; Pandey, Manoj Kumar; Marsh, Andrew; Nishiyama, Yusuke; Brown, Steven P

2015-11-01

A selective saturation pulse at fast magic angle spinning (MAS) frequencies (60+kHz) suppresses t1 noise in the indirect dimension of two-dimensional (1)H MAS NMR spectra. The method is applied to a synthetic nucleoside with an intense methyl (1)H signal due to triisopropylsilyl (TIPS) protecting groups. Enhanced performance in terms of suppressing the methyl signal while minimising the loss of signal intensity of nearby resonances of interest relies on reducing spin diffusion--this is quantified by comparing two-dimensional (1)H NOESY-like spin diffusion spectra recorded at 30-70 kHz MAS. For a saturation pulse centred at the methyl resonance, the effect of changing the nutation frequency at different MAS frequencies as well as the effect of changing the pulse duration is investigated. By applying a pulse of duration 30 ms and nutation frequency 725 Hz at 70 kHz MAS, a good compromise of significant suppression of the methyl resonance combined with the signal intensity of resonances greater than 5 ppm away from the methyl resonance being largely unaffected is achieved. The effectiveness of using a selective saturation pulse is demonstrated for both homonuclear (1)H-(1)H double quantum (DQ)/single quantum (SQ) MAS and (14)N-(1)H heteronuclear multiple quantum coherence (HMQC) two-dimensional solid-state NMR experiments. Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.

Self-assembly of graphene ribbons by spontaneous self-tearing and peeling from a substrate

NASA Astrophysics Data System (ADS)

Annett, James; Cross, Graham L. W.

2016-07-01

Graphene and related two-dimensional materials have shown unusual and exceptional mechanical properties, with similarities to origami-like paper folding and kirigami-like cutting demonstrated. For paper analogues, a critical difference between macroscopic sheets and a two-dimensional solid is the molecular scale of the thin dimension of the latter, allowing the thermal activation of considerable out-of-plane motion. So far thermal activity has been shown to produce local wrinkles in a free graphene sheet that help in theoretically understanding its stability, for example, and give rise to unexpected long-range bending stiffness. Here we show that thermal activation can have a more marked effect on the behaviour of two-dimensional solids, leading to spontaneous and self-driven sliding, tearing and peeling from a substrate on scales approaching the macroscopic. We demonstrate that scalable nanoimprint-style contact techniques can nucleate and direct the parallel self-assembly of graphene ribbons of controlled shape in ambient conditions. We interpret our observations through a simple fracture-mechanics model that shows how thermodynamic forces drive the formation of the graphene-graphene interface in lieu of substrate contact with sufficient strength to peel and tear multilayer graphene sheets. Our results show how weak physical surface forces can be harnessed and focused by simple folded configurations of graphene to tear the strongest covalent bond. This effect may hold promise for the patterning and mechanical actuating of devices based on two-dimensional materials.

Foreword

NASA Astrophysics Data System (ADS)

Brazovskii, Serguei; Monceau, Pierre; Kirova, Natacha

2005-12-01

The International Workshop on ELECTRONIC CRYSTALS, ECRYS-2005, was the fourth in the series of such meetings held in France: following ECRYS-93 in Carry-le-Rouet, ECRYS-99, in La Colle-surLoup, and ECRYS-02 in Saint-Flour. The Workshop brought together nearly 100 researchers, chemists and physicists, from 11 countries; it was hosted by the Institut d'Études Scientifiques of the CNRS, at Cargèse, Corsica, France. The Workshop was supported by the European Physical Society, the Office of Naval Research Global of US, the Department of Mathematics and Physics of the CNRS, France. ECRYS Workshops are intended to provide a cross-link between various communities engaged in parallel studies of static and dynamic properties of superstructures formed by electrons and vortices. Representatives of such electronic crystals are charge and spin density waves in low dimensional materials, Wigner crystals of electrons in bulks, at 2D interfaces and in wires, stripe phases in conducting oxides including the family of high Tc superconductors, various forms of charge order in organic quasi 1D one- and two-dimensional materials, charged colloidal crystals. ECRYS Workshops consider also related systems like vortex lattices in superconductors, domain walls in magnetic and ferroelectric materials. While microscopic physical mechanisms are diverse and specific to each system, the general phenomena are quite universal: a depinning above a threshold, collective transport properties due to the sliding phenomena, non-stationary and memory effects, glassy properties due to numerous metastable states, aging dynamics and rejuvenation phenomena, etc. In recent years, much of experimental progress has been achieved in fields covered by ECRYS Workshops with the use of advanced techniques: focused ion beam and reactive ion etching for fabrication of CDW submicronic devices, atomic resolution in UHV STM, point contact spectroscopy, electron photoemission, microbeam diffraction, coherent X-ray diffraction, pulse laser light excitation, etc. The present proceedings highlight the state-of-art in this field. The topics discussed at the Workshop were related to microscopic mechanisms and quantum effects, charge ordering and charge disproportionation, ferroelectricity, collective effects in pinning and sliding, glassy behavior, tunneling, high magnetic fields and field induced density wave, two dimensional electron solids at heterojunctions, meso- and nanostructures of charge density wave materials. A short session was also devoted to charges in soft matter. Theoretical aspects ranged from the phenomenology of the collective sliding to microscopics of strongly correlated electrons. The discussion forum opened by the Workshop ECRYS-05, as well as the preceding ones, fills the need of an international meeting with a cross-disciplinary nature for a review of new developments and results in the field of spontaneous superstructures. The present ECRYS-05 Workshop Proceedings demonstrates, we believe, the lively research activity in this field and will serve as a useful reference document. We are grateful to all participants of the Workshop for their active contribution. Serguei Brazovskii, Pierre Monceau and Natacha Kirova

David Lee, Douglas Osheroff, Superfluidity, and Helium 3

Science.gov Websites

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Microstructure based model for sound absorption predictions of perforated closed-cell metallic foams.

PubMed

Chevillotte, Fabien; Perrot, Camille; Panneton, Raymond

2010-10-01

Closed-cell metallic foams are known for their rigidity, lightness, thermal conductivity as well as their low production cost compared to open-cell metallic foams. However, they are also poor sound absorbers. Similarly to a rigid solid, a method to enhance their sound absorption is to perforate them. This method has shown good preliminary results but has not yet been analyzed from a microstructure point of view. The objective of this work is to better understand how perforations interact with closed-cell foam microstructure and how it modifies the sound absorption of the foam. A simple two-dimensional microstructural model of the perforated closed-cell metallic foam is presented and numerically solved. A rough three-dimensional conversion of the two-dimensional results is proposed. The results obtained with the calculation method show that the perforated closed-cell foam behaves similarly to a perforated solid; however, its sound absorption is modulated by the foam microstructure, and most particularly by the diameters of both perforation and pore. A comparison with measurements demonstrates that the proposed calculation method yields realistic trends. Some design guides are also proposed.

Selective deposition of nanostructured ruthenium oxide using Tobacco mosaic virus for micro-supercapacitors in solid Nafion electrolyte

NASA Astrophysics Data System (ADS)

Gnerlich, Markus; Ben-Yoav, Hadar; Culver, James N.; Ketchum, Douglas R.; Ghodssi, Reza

2015-10-01

A three-dimensional micro-supercapacitor has been developed using a novel bottom-up assembly method combining genetically modified Tobacco mosaic virus (TMV-1Cys), photolithographically defined micropillars and selective deposition of ruthenium oxide on multi-metallic microelectrodes. The three-dimensional microelectrodes consist of a titanium nitride current collector with two functionalized areas: (1) gold coating on the active electrode area promotes TMV-1Cys adhesion, and (2) sacrificial nickel pads dissolve in ruthenium tetroxide plating solution to produce ruthenium oxide on all electrically connected areas. The microfabricated electrodes are arranged in an interdigitated pattern, and the capacitance per electrode has been measured as high as 203 mF cm-2 with solid Nafion electrolyte. The process integration of bio-templated ruthenium oxide with microfabricated electrodes and solid electrolyte is an important advance towards the energy storage needs of mass produced self-sufficient micro-devices.

Selective deposition of nanostructured ruthenium oxide using Tobacco mosaic virus for micro-supercapacitors in solid Nafion electrolyte

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gnerlich, Markus; Ben-Yoav, Hadar; Culver, James N.

A three-dimensional micro-supercapacitor has been developed using a novel bottom-up assembly method combining genetically modified Tobacco mosaic virus (TMV-1Cys), photolithographically defined micropillars and selective deposition of ruthenium oxide on multi-metallic microelectrodes. The three-dimensional microelectrodes consist of a titanium nitride current collector with two functionalized areas: (1) gold coating on the active electrode area promotes TMV-1Cys adhesion, and (2) sacrificial nickel pads dissolve in ruthenium tetroxide plating solution to produce ruthenium oxide on all electrically connected areas. The microfabricated electrodes are arranged in an interdigitated pattern, and the capacitance per electrode has been measured as high as 203 mF cm-2 withmore » solid Nafion electrolyte. The process integration of bio-templated ruthenium oxide with microfabricated electrodes and solid electrolyte is an important advance towards the energy storage needs of mass produced self-sufficient micro-devices.« less

Biofilm growth program and architecture revealed by single-cell live imaging

NASA Astrophysics Data System (ADS)

Yan, Jing; Sabass, Benedikt; Stone, Howard; Wingreen, Ned; Bassler, Bonnie

Biofilms are surface-associated bacterial communities. Little is known about biofilm structure at the level of individual cells. We image living, growing Vibrio cholerae biofilms from founder cells to ten thousand cells at single-cell resolution, and discover the forces underpinning the architectural evolution of the biofilm. Mutagenesis, matrix labeling, and simulations demonstrate that surface-adhesion-mediated compression causes V. cholerae biofilms to transition from a two-dimensional branched morphology to a dense, ordered three-dimensional cluster. We discover that directional proliferation of rod-shaped bacteria plays a dominant role in shaping the biofilm architecture, and this growth pattern is controlled by a single gene. Competition analyses reveal the advantages of the dense growth mode in providing the biofilm with superior mechanical properties. We will further present continuum theory to model the three-dimensional growth of biofilms at the solid-liquid interface as well as solid-air interface.

Engineering New Layered Solids from Exfoliated Inorganics: a Periodically Alternating Hydrotalcite – Montmorillonite Layered Hybrid

PubMed Central

Chalasani, Rajesh; Gupta, Amit; Vasudevan, Sukumaran

2013-01-01

Two-dimensional (2D) nanosheets obtained by exfoliating inorganic layered crystals have emerged as a new class of materials with unique attributes. One of the critical challenges is to develop robust and versatile methods for creating new nanostructures from these 2D-nanosheets. Here we report the delamination of layered materials that belonging to two different classes - the cationic clay, montmorillonite, and the anionic clay, hydrotalcite - by intercalation of appropriate ionic surfactants followed by dispersion in a non-polar solvent. The solids are delaminated to single layers of atomic thickness with the ionic surfactants remaining tethered to the inorganic and consequently the nanosheets are electrically neutral. We then show that when dispersions of the two solids are mixed the exfoliated sheets self-assemble as a new layered solid with periodically alternating hydrotalcite and montmorillonite layers. The procedure outlined here is easily extended to other layered solids for creating new superstructures from 2D-nanosheets by self-assembly. PMID:24336682

Phase equilibrium in argon films stabilized by homogeneous surfaces and thermodynamics of two-stage melting transition.

PubMed

Ustinov, E A

2014-02-21

Freezing of gases adsorbed on open surfaces (e.g., graphite) and in narrow pores is a widespread phenomenon which is a subject of a large number of publications. Modeling of the gas/liquid-solid transition is usually accomplished with a molecular simulation technique. However, quantitative analysis of the gas/liquid-solid coexistence and thermodynamic properties of the solid layer still encounters serious difficulties. This is mainly due to the effect of simulation box size on the lattice constant. Since the lattice constant is a function of loading and temperature, once the ordering transition has occurred, the simulation box size must be corrected in the course of simulation according to the Gibbs-Duhem equation. A significant problem is also associated with accurate prediction of the two-dimensional liquid-solid coexistence because of a small difference in densities of coexisting phases. The aim of this study is thermodynamic analysis of the two-dimensional phase coexistence in systems involving crystal-like free of defects layers in narrow slit pores. A special attention was paid to the determination of triple point temperatures. It is shown that intrinsic properties of argon monolayer adsorbed on the graphite surface are similar to those of isolated monolayer accommodated in the slit pore having width of two argon collision diameters. Analysis of the latter system is shown to be clearer and less time-consuming than the former one, which has allowed for explanation of the experimentally observed two-stage melting transition of argon monolayer on graphite without invoking the periodic surface potential modulation and orientational transition.

Phase equilibrium in argon films stabilized by homogeneous surfaces and thermodynamics of two-stage melting transition

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ustinov, E. A., E-mail: eustinov@mail.wplus.net

Freezing of gases adsorbed on open surfaces (e.g., graphite) and in narrow pores is a widespread phenomenon which is a subject of a large number of publications. Modeling of the gas/liquid–solid transition is usually accomplished with a molecular simulation technique. However, quantitative analysis of the gas/liquid–solid coexistence and thermodynamic properties of the solid layer still encounters serious difficulties. This is mainly due to the effect of simulation box size on the lattice constant. Since the lattice constant is a function of loading and temperature, once the ordering transition has occurred, the simulation box size must be corrected in the coursemore » of simulation according to the Gibbs–Duhem equation. A significant problem is also associated with accurate prediction of the two-dimensional liquid–solid coexistence because of a small difference in densities of coexisting phases. The aim of this study is thermodynamic analysis of the two-dimensional phase coexistence in systems involving crystal-like free of defects layers in narrow slit pores. A special attention was paid to the determination of triple point temperatures. It is shown that intrinsic properties of argon monolayer adsorbed on the graphite surface are similar to those of isolated monolayer accommodated in the slit pore having width of two argon collision diameters. Analysis of the latter system is shown to be clearer and less time-consuming than the former one, which has allowed for explanation of the experimentally observed two-stage melting transition of argon monolayer on graphite without invoking the periodic surface potential modulation and orientational transition.« less

Thomas precession, Wigner rotations and gauge transformations

NASA Technical Reports Server (NTRS)

Han, D.; Kim, Y. S.; Son, D.

1987-01-01

The exact Lorentz kinematics of the Thomas precession is discussed in terms of Wigner's O(3)-like little group which describes rotations in the Lorentz frame in which the particle is at rest. A Lorentz-covariant form for the Thomas factor is derived. It is shown that this factor is a Lorentz-boosted rotation matrix, which becomes a gauge transformation in the infinite-momentum or zero-mass limit.

Nanoscale solid-state cooling: a review.

PubMed

Ziabari, Amirkoushyar; Zebarjadi, Mona; Vashaee, Daryoosh; Shakouri, Ali

2016-09-01

The recent developments in nanoscale solid-state cooling are reviewed. This includes both theoretical and experimental studies of different physical concepts, as well as nanostructured material design and device configurations. We primarily focus on thermoelectric, thermionic and thermo-magnetic coolers. Particular emphasis is given to the concepts based on metal-semiconductor superlattices, graded materials, non-equilibrium thermoelectric devices, Thomson coolers, and photon assisted Peltier coolers as promising methods for efficient solid-state cooling. Thermomagnetic effects such as magneto-Peltier and Nernst-Ettingshausen cooling are briefly described and recent advances and future trends in these areas are reviewed. The ongoing progress in solid-state cooling concepts such as spin-calorimetrics, electrocalorics, non-equilibrium/nonlinear Peltier devices, superconducting junctions and two-dimensional materials are also elucidated and practical achievements are reviewed. We explain the thermoreflectance thermal imaging microscopy and the transient Harman method as two unique techniques developed for characterization of thermoelectric microrefrigerators. The future prospects for solid-state cooling are briefly summarized.

Directly and indirectly detected through-bond heteronuclear correlation solid-state NMR spectroscopy under fast MAS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mao, Kanmi; Pruski, Marek

Two-dimensional through-bond {sup 1}H({sup 13}C) solid-state NMR experiments utilizing fast magic angle spinning (MAS) and homonuclear multipulse {sup 1}H decoupling are presented. Remarkable efficiency of polarization transfer can be achieved at MAS rates exceeding 40 kHz, which is instrumental in these measurements. Schemes utilizing direct and indirect detection of heteronuclei are compared in terms of resolution and sensitivity. A simple procedure for optimization of {sup 1}H homonuclear decoupling sequences under these conditions is proposed. The capabilities of these techniques were confirmed on two naturally abundant solids, tripeptide N-formyl-l-methionyl-l-leucyl-l-phenylalanine (f-MLF-OH) and brown coal.

Directly and indirectly detected through-bond heteronuclear correlation solid-state NMR spectroscopy under fast MAS

NASA Astrophysics Data System (ADS)

Mao, Kanmi; Pruski, Marek

2009-12-01

Two-dimensional through-bond 1H{ 13C} solid-state NMR experiments utilizing fast magic angle spinning (MAS) and homonuclear multipulse 1H decoupling are presented. Remarkable efficiency of polarization transfer can be achieved at MAS rates exceeding 40 kHz, which is instrumental in these measurements. Schemes utilizing direct and indirect detection of heteronuclei are compared in terms of resolution and sensitivity. A simple procedure for optimization of 1H homonuclear decoupling sequences under these conditions is proposed. The capabilities of these techniques were confirmed on two naturally abundant solids, tripeptide N- formyl- L-methionyl- L-leucyl- L-phenylalanine (f-MLF-OH) and brown coal.

Improved modeling of two-dimensional transitions in dense phases on crystalline surfaces. Krypton–graphite system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ustinov, E. A., E-mail: eustinov@mail.wplus.net

This paper presents a refined technique to describe two-dimensional phase transitions in dense fluids adsorbed on a crystalline surface. Prediction of parameters of 2D liquid–solid equilibrium is known to be an extremely challenging problem, which is mainly due to a small difference in thermodynamic functions of coexisting phases and lack of accuracy of numerical experiments in case of their high density. This is a serious limitation of various attempts to circumvent this problem. To improve this situation, a new methodology based on the kinetic Monte Carlo method was applied. The methodology involves analysis of equilibrium gas–liquid and gas–solid systems undergoingmore » an external potential, which allows gradual shifting parameters of the phase coexistence. The interrelation of the chemical potential and tangential pressure for each system is then treated with the Gibbs–Duhem equation to obtain the point of intersection corresponding to the liquid/solid–solid equilibrium coexistence. The methodology is demonstrated on the krypton–graphite system below and above the 2D critical temperature. Using experimental data on the liquid–solid and the commensurate–incommensurate transitions in the krypton monolayer derived from adsorption isotherms, the Kr–graphite Lennard–Jones parameters have been corrected resulting in a higher periodic potential modulation.« less

Variable dimensionality in the uranium fluoride/2-methyl-piperazine system: Synthesis and structures of UFO-5, -6, and -7; Zero-, one-, and two-dimensional materials with unprecedented topologies

DOE Office of Scientific and Technical Information (OSTI.GOV)

Francis, R.J.; Halasyamani, P.S.; Bee, J.S.

Recently, low temperature (T < 300 C) hydrothermal reactions of inorganic precursors in the presence of organic cations have proven highly productive for the synthesis of novel solid-state materials. Interest in these materials is driven by the astonishingly diverse range of structures produced, as well as by their many potential materials chemistry applications. This report describes the high yield, phase pure hydrothermal syntheses of three new uranium fluoride phases with unprecedented structure types. Through the systematic control of the synthesis conditions the authors have successfully controlled the architecture and dimensionality of the phase formed and selectively synthesized novel zero-, one-,more » and two-dimensional materials.« less

Linearized semiclassical initial value time correlation functions with maximum entropy analytic continuation.

PubMed

Liu, Jian; Miller, William H

2008-09-28

The maximum entropy analytic continuation (MEAC) method is used to extend the range of accuracy of the linearized semiclassical initial value representation (LSC-IVR)/classical Wigner approximation for real time correlation functions. LSC-IVR provides a very effective "prior" for the MEAC procedure since it is very good for short times, exact for all time and temperature for harmonic potentials (even for correlation functions of nonlinear operators), and becomes exact in the classical high temperature limit. This combined MEAC+LSC/IVR approach is applied here to two highly nonlinear dynamical systems, a pure quartic potential in one dimensional and liquid para-hydrogen at two thermal state points (25 and 14 K under nearly zero external pressure). The former example shows the MEAC procedure to be a very significant enhancement of the LSC-IVR for correlation functions of both linear and nonlinear operators, and especially at low temperature where semiclassical approximations are least accurate. For liquid para-hydrogen, the LSC-IVR is seen already to be excellent at T=25 K, but the MEAC procedure produces a significant correction at the lower temperature (T=14 K). Comparisons are also made as to how the MEAC procedure is able to provide corrections for other trajectory-based dynamical approximations when used as priors.

Seismic signal time-frequency analysis based on multi-directional window using greedy strategy

NASA Astrophysics Data System (ADS)

Chen, Yingpin; Peng, Zhenming; Cheng, Zhuyuan; Tian, Lin

2017-08-01

Wigner-Ville distribution (WVD) is an important time-frequency analysis technology with a high energy distribution in seismic signal processing. However, it is interfered by many cross terms. To suppress the cross terms of the WVD and keep the concentration of its high energy distribution, an adaptive multi-directional filtering window in the ambiguity domain is proposed. This begins with the relationship of the Cohen distribution and the Gabor transform combining the greedy strategy and the rotational invariance property of the fractional Fourier transform in order to propose the multi-directional window, which extends the one-dimensional, one directional, optimal window function of the optimal fractional Gabor transform (OFrGT) to a two-dimensional, multi-directional window in the ambiguity domain. In this way, the multi-directional window matches the main auto terms of the WVD more precisely. Using the greedy strategy, the proposed window takes into account the optimal and other suboptimal directions, which also solves the problem of the OFrGT, called the local concentration phenomenon, when encountering a multi-component signal. Experiments on different types of both the signal models and the real seismic signals reveal that the proposed window can overcome the drawbacks of the WVD and the OFrGT mentioned above. Finally, the proposed method is applied to a seismic signal's spectral decomposition. The results show that the proposed method can explore the space distribution of a reservoir more precisely.

Pressure Oscillations and Structural Vibrations in Space Shuttle RSRM and ETM-3 Motors

NASA Technical Reports Server (NTRS)

Mason, D. R.; Morstadt, R. A.; Cannon, S. M.; Gross, E. G.; Nielsen, D. B.

2004-01-01

The complex interactions between internal motor pressure oscillations resulting from vortex shedding, the motor's internal acoustic modes, and the motor's structural vibration modes were assessed for the Space Shuttle four-segment booster Reusable Solid Rocket Motor and for the five-segment engineering test motor ETM-3. Two approaches were applied 1) a predictive procedure based on numerically solving modal representations of a solid rocket motor s acoustic equations of motion and 2) a computational fluid dynamics two-dimensional axi-symmetric large eddy simulation at discrete motor burn times.

Dimensional Effects on the Charge Density Waves in Ultrathin Films of TiSe 2

DOE PAGES

Chen, P.; Chan, Y. -H.; Wong, M. -H.; ...

2016-09-20

Charge density wave (CDW) formation in solids is a critical phenomenon involving the collective reorganization of the electrons and atoms in the system into a wave structure, and it is expected to be sensitive to the geometric constraint of the system at the nanoscale. Here, we study the CDW transition in TiSe 2, a quasi-two-dimensional layered material, to determine the effects of quantum confinement and changing dimensions in films ranging from a single layer to multilayers. Of key interest is the characteristic length scale for the transformation from a two-dimensional case to the three-dimensional limit. Angle-resolved photoemission (ARPES) measurements ofmore » films with thicknesses up to six layers reveal substantial variations in the energy structure of discrete quantum well states; however, the temperature-dependent band-gap renormalization converges at just three layers. The results indicate a layer-dependent mixture of two transition temperatures and a very-short-range CDW interaction within a three-dimensional framework.« less

The resistance of an n-dimensional tetrahedron

NASA Astrophysics Data System (ADS)

Griffiths, Martin

2013-01-01

We consider here a problem that is suitable for introducing high-school students to the notion of generalizing shapes and solids to n dimensions. In particular, we calculate the effective resistance between any two vertices of an n-dimensional tetrahedron whose edges are each 1-Ω resistors. This leads, in a natural way, to more demanding problems, and indeed ideas for more advanced work in this area are also suggested.

Phase diagram of a symmetric electron-hole bilayer system: a variational Monte Carlo study.

PubMed

Sharma, Rajesh O; Saini, L K; Bahuguna, Bhagwati Prasad

2018-05-10

We study the phase diagram of a symmetric electron-hole bilayer system at absolute zero temperature and in zero magnetic field within the quantum Monte Carlo approach. In particular, we conduct variational Monte Carlo simulations for various phases, i.e. the paramagnetic fluid phase, the ferromagnetic fluid phase, the anti-ferromagnetic Wigner crystal phase, the ferromagnetic Wigner crystal phase and the excitonic phase, to estimate the ground-state energy at different values of in-layer density and inter-layer spacing. Slater-Jastrow style trial wave functions, with single-particle orbitals appropriate for different phases, are used to construct the phase diagram in the (r s , d) plane by finding the relative stability of trial wave functions. At very small layer separations, we find that the fluid phases are stable, with the paramagnetic fluid phase being particularly stable at [Formula: see text] and the ferromagnetic fluid phase being particularly stable at [Formula: see text]. As the layer spacing increases, we first find that there is a phase transition from the ferromagnetic fluid phase to the ferromagnetic Wigner crystal phase when d reaches 0.4 a.u. at r s   =  20, and before there is a return to the ferromagnetic fluid phase when d approaches 1 a.u. However, for r s   <  20 and [Formula: see text] a.u., the excitonic phase is found to be stable. We do not find that the anti-ferromagnetic Wigner crystal is stable over the considered range of r s and d. We also find that as r s increases, the critical layer separations for Wigner crystallization increase.

Numerical investigation for design and critical performance evaluation of a horizontal axis hydrokinetic turbine

NASA Astrophysics Data System (ADS)

Subhra Mukherji, Suchi; Banerjee, Arindam

2010-11-01

We will discuss findings from our numerical investigation on the hydrodynamic performance of horizontal axis hydrokinetic turbines (HAHkT) under different turbine geometries and flow conditions. Hydrokinetic turbines are a class of zero-head hydropower systems which utilizes kinetic energy of flowing water to drive a generator. However, such turbines very often suffer from low efficiency which is primarily controlled by tip-speed ratio, solidity, angle of attack and number of blades. A detailed CFD study was performed using two-dimensional and three dimensional numerical models to examine the effect of each of these parameters on the performance of small HAHkTs having power capacities <= 10 kW. The two-dimensional numerical results provide an optimum angle of attack that maximizes the lift as well as lift to drag ratio yielding maximum power output. However three-dimensional numerical studies estimate optimum turbine solidity and blade numbers that produces maximum power coefficient at a given tip speed ratio. In addition, simulations were also performed to observe the axial velocity deficit at the turbine rotor downstream for different tip-speed ratios to obtain both qualitative and quantitative details about stall delay phenomena and the energy loss suffered by the turbine under ambient flow condition.

Imaging quasiperiodic electronic states in a synthetic Penrose tiling

NASA Astrophysics Data System (ADS)

Collins, Laura C.; Witte, Thomas G.; Silverman, Rochelle; Green, David B.; Gomes, Kenjiro K.

2017-06-01

Quasicrystals possess long-range order but lack the translational symmetry of crystalline solids. In solid state physics, periodicity is one of the fundamental properties that prescribes the electronic band structure in crystals. In the absence of periodicity and the presence of quasicrystalline order, the ways that electronic states change remain a mystery. Scanning tunnelling microscopy and atomic manipulation can be used to assemble a two-dimensional quasicrystalline structure mapped upon the Penrose tiling. Here, carbon monoxide molecules are arranged on the surface of Cu(111) one at a time to form the potential landscape that mimics the ionic potential of atoms in natural materials by constraining the electrons in the two-dimensional surface state of Cu(111). The real-space images reveal the presence of the quasiperiodic order in the electronic wave functions and the Fourier analysis of our results links the energy of the resonant states to the local vertex structure of the quasicrystal.

Imaging quasiperiodic electronic states in a synthetic Penrose tiling.

PubMed

Collins, Laura C; Witte, Thomas G; Silverman, Rochelle; Green, David B; Gomes, Kenjiro K

2017-06-22

Quasicrystals possess long-range order but lack the translational symmetry of crystalline solids. In solid state physics, periodicity is one of the fundamental properties that prescribes the electronic band structure in crystals. In the absence of periodicity and the presence of quasicrystalline order, the ways that electronic states change remain a mystery. Scanning tunnelling microscopy and atomic manipulation can be used to assemble a two-dimensional quasicrystalline structure mapped upon the Penrose tiling. Here, carbon monoxide molecules are arranged on the surface of Cu(111) one at a time to form the potential landscape that mimics the ionic potential of atoms in natural materials by constraining the electrons in the two-dimensional surface state of Cu(111). The real-space images reveal the presence of the quasiperiodic order in the electronic wave functions and the Fourier analysis of our results links the energy of the resonant states to the local vertex structure of the quasicrystal.

Exergy analysis of a solid oxide fuel cell micropowerplant

NASA Astrophysics Data System (ADS)

Hotz, Nico; Senn, Stephan M.; Poulikakos, Dimos

In this paper, an analytical model of a micro solid oxide fuel cell (SOFC) system fed by butane is introduced and analyzed in order to optimize its exergetic efficiency. The micro SOFC system is equipped with a partial oxidation (POX) reformer, a vaporizer, two pre-heaters, and a post-combustor. A one-dimensional (1D) polarization model of the SOFC is used to examine the effects of concentration overpotentials, activation overpotentials, and ohmic resistances on cell performance. This 1D polarization model is extended in this study to a two-dimensional (2D) fuel cell model considering convective mass and heat transport along the fuel cell channel and from the fuel cell to the environment. The influence of significant operational parameters on the exergetic efficiency of the micro SOFC system is discussed. The present study shows the importance of an exergy analysis of the fuel cell as part of an entire thermodynamic system (transportable micropowerplant) generating electric power.

Equation of State of the Two-Dimensional Hubbard Model

NASA Astrophysics Data System (ADS)

Cocchi, Eugenio; Miller, Luke A.; Drewes, Jan H.; Koschorreck, Marco; Pertot, Daniel; Brennecke, Ferdinand; Köhl, Michael

2016-04-01

The subtle interplay between kinetic energy, interactions, and dimensionality challenges our comprehension of strongly correlated physics observed, for example, in the solid state. In this quest, the Hubbard model has emerged as a conceptually simple, yet rich model describing such physics. Here we present an experimental determination of the equation of state of the repulsive two-dimensional Hubbard model over a broad range of interactions 0 ≲U /t ≲20 and temperatures, down to kBT /t =0.63 (2 ) using high-resolution imaging of ultracold fermionic atoms in optical lattices. We show density profiles, compressibilities, and double occupancies over the whole doping range, and, hence, our results constitute benchmarks for state-of-the-art theoretical approaches.

Laser Fabrication of Two-Dimensional Rotating-Lattice Single Crystal

DOE PAGES

Savytskii, Dmytro; Au-Yeung, Courtney; Dierolf, Volkmar; ...

2017-03-09

A rotating lattice single (RLS) crystal is a unique form of solid, which was fabricated recently as one-dimensional architecture in glass via solid state transformation induced by laser irradiation. In these objects, the lattice rotates gradually and predictably about an axis that lies in the plane of the crystal and is normal to the laser scanning direction. This paper reports on the fabrication of Sb 2S 3 two-dimensional (2D) RLS crystals on the surface of 16SbI 3-84Sb 2S 3 glass, as a model example: individual RLS crystal lines are joined together using "stitching" or "rastering" as two successful protocols. Themore » electron back scattered diffraction mapping and scanning Laue X-ray microdiffraction of the 2D RLS crystals show gradual rotation of lattice comprising of two components, one along the length of each line and another normal to this direction. The former component is determined by the rotation of the first line of the 2D pattern, but the relative contribution of the last component depends on the extent of overlap between two successive lines. By the appropriate choice of initial seed orientation and the direction of scanning, it is possible to control the lattice rotation, and even to reduce it down to 5 for a 50 × 50 μm 2 2D pattern of Sb 2S 3 crystal.« less

Extended Salecker-Wigner formula for optimal accuracy in reading a clock via a massive signal particle

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kudaka, Shoju; Matsumoto, Shuichi

2007-07-15

In order to acquire an extended Salecker-Wigner formula from which to derive the optimal accuracy in reading a clock with a massive particle as the signal, von Neumann's classical measurement is employed, by which simultaneously both position and momentum of the signal particle can be measured approximately. By an appropriate selection of wave function for the initial state of the composite system (a clock and a signal particle), the formula is derived accurately. Valid ranges of the running time of a clock with a given optimal accuracy are also given. The extended formula means that contrary to the Salecker-Wigner formulamore » there exists the possibility of a higher accuracy of time measurement, even if the mass of the clock is very small.« less

Functional Wigner representation of quantum dynamics of Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Opanchuk, B.; Drummond, P. D.

2013-04-01

We develop a method of simulating the full quantum field dynamics of multi-mode multi-component Bose-Einstein condensates in a trap. We use the truncated Wigner representation to obtain a probabilistic theory that can be sampled. This method produces c-number stochastic equations which may be solved using conventional stochastic methods. The technique is valid for large mode occupation numbers. We give a detailed derivation of methods of functional Wigner representation appropriate for quantum fields. Our approach describes spatial evolution of spinor components and properly accounts for nonlinear losses. Such techniques are applicable to calculating the leading quantum corrections, including effects such as quantum squeezing, entanglement, EPR correlations, and interactions with engineered nonlinear reservoirs. By using a consistent expansion in the inverse density, we are able to explain an inconsistency in the nonlinear loss equations found by earlier authors.

Quantum mechanics on phase space: The hydrogen atom and its Wigner functions

NASA Astrophysics Data System (ADS)

Campos, P.; Martins, M. G. R.; Fernandes, M. C. B.; Vianna, J. D. M.

2018-03-01

Symplectic quantum mechanics (SQM) considers a non-commutative algebra of functions on a phase space Γ and an associated Hilbert space HΓ, to construct a unitary representation for the Galilei group. From this unitary representation the Schrödinger equation is rewritten in phase space variables and the Wigner function can be derived without the use of the Liouville-von Neumann equation. In this article the Coulomb potential in three dimensions (3D) is resolved completely by using the phase space Schrödinger equation. The Kustaanheimo-Stiefel(KS) transformation is applied and the Coulomb and harmonic oscillator potentials are connected. In this context we determine the energy levels, the amplitude of probability in phase space and correspondent Wigner quasi-distribution functions of the 3D-hydrogen atom described by Schrödinger equation in phase space.

Rapid determination of six carcinogenic primary aromatic amines in mainstream cigarette smoke by two-dimensional online solid phase extraction combined with liquid chromatography tandem mass spectrometry.

PubMed

Bie, Zhenying; Lu, Wei; Zhu, You; Chen, Yusong; Ren, Hubo; Ji, Lishun

2017-01-27

A fully automated, rapid, and reliable method for simultaneous determination of six carcinogenic primary aromatic amines (AAs), including o-toluidine (o-TOL), 2, 6-dimethylaniline (2, 6-DMA), o-anisidine (o-ASD), 1-naphthylamine (1-ANP), 2-naphthylamine (2-ANP), and 4-aminobiphenyl (4-ABP), in mainstream cigarette smoke was established. The proposed method was based on two-dimensional online solid phase extraction combined with liquid chromatography tandem mass spectrometry (SPE/LC-MS/MS). The particulate phase of the mainstream cigarette smoke was collected on a Cambridge filter pad and pretreated via ultrasonic extraction with 2% formic acid (FA), while the gas phase was trapped by 2% FA without pretreatment for determination. The two-dimensional online SPE comprised of two cartridges with different absorption characteristics was applied for sample pretreatment. Analysis was performed by liquid chromatography coupled with tandem mass spectrometry (LC-MS/MS) under multiple reaction monitoring mode. Each sample required about 0.5h for solid phase extraction and analysis. The limit of detections (LODs) for six AAs ranged from 0.04 to 0.58ng/cig and recoveries were within 84.5%-122.9%. The relative standard deviations of intra- and inter-day tests for 3R4F reference cigarette were less than 6% and 7%, respectively, while no more than 7% and 8% separately for a type of Virginia cigarette. The proposed method enabled minimum sample pretreatment, full automation, and high throughput with high selectivity, sensitivity, and accuracy. As a part of the validation procedure, fifteen brands of cigarettes were tested by the designed method. Copyright © 2016 Elsevier B.V. All rights reserved.

Phase transition kinetics for a Bose Einstein condensate in a periodically driven band system

NASA Astrophysics Data System (ADS)

Michon, E.; Cabrera-Gutiérrez, C.; Fortun, A.; Berger, M.; Arnal, M.; Brunaud, V.; Billy, J.; Petitjean, C.; Schlagheck, P.; Guéry-Odelin, D.

2018-05-01

The dynamical transition of an atomic Bose–Einstein condensate from a spatially periodic state to a staggered state with alternating sign in its wavefunction is experimentally studied using a one-dimensional phase modulated optical lattice. We observe the crossover from quantum to thermal fluctuations as the triggering mechanism for the nucleation of staggered states. In good quantitative agreement with numerical simulations based on the truncated Wigner method, we experimentally investigate how the nucleation time varies with the renormalized tunneling rate, the atomic density, and the driving frequency. The effective inverted energy band in the driven lattice is identified as the key ingredient which explains the emergence of gap solitons as observed in numerics and the possibility to nucleate staggered states from interband excitations as reported experimentally.

Ray tracing the Wigner distribution function for optical simulations

NASA Astrophysics Data System (ADS)

Mout, Marco; Wick, Michael; Bociort, Florian; Petschulat, Joerg; Urbach, Paul

2018-01-01

We study a simulation method that uses the Wigner distribution function to incorporate wave optical effects in an established framework based on geometrical optics, i.e., a ray tracing engine. We use the method to calculate point spread functions and show that it is accurate for paraxial systems but produces unphysical results in the presence of aberrations. The cause of these anomalies is explained using an analytical model.

Moments of the Wigner function and Renyi entropies at freeze-out

NASA Astrophysics Data System (ADS)

Bialas, A.; Czyz, W.; Zalewski, K.

2006-03-01

The relation between Renyi entropies and moments of the Wigner function, representing the quantum mechanical description of the M-particle semi-inclusive distribution at freeze-out, is investigated. It is shown that in the limit of infinite volume of the system, the classical and quantum descriptions are equivalent. Finite volume corrections are derived and shown to be small for systems encountered in relativistic heavy ion collisions.

Coulomb Problem for Z > Zcr in Doped Graphene

NASA Astrophysics Data System (ADS)

Kuleshov, V. M.; Mur, V. D.; Fedotov, A. M.; Lozovik, Yu. E.

2017-12-01

The dynamics of charge carriers in doped graphene, i.e., graphene with a gap in the energy spectrum depending on the substrate, in the presence of a Coulomb impurity with charge Z is considered within the effective two-dimensional Dirac equation. The wave functions of carriers with conserved angular momentum J = M + 1/2 are determined for a Coulomb potential modified at small distances. This case, just as any two-dimensional physical system, admits both integer and half-integer quantization of the orbital angular momentum in plane, M = 0, ±1, ±2, …. For J = 0, ±1/2, ±1, critical values of the effective charge Z cr( J, n) are calculated for which a level with angular momentum J and radial quantum numbers n = 0 and n = 1 reaches the upper boundary of the valence band. For Z < Z cr ( J, n = 0), the energy of a level is presented as a function of charge Z for the lowest values of orbital angular momentum M, the level with J = 0 being the first to descend to the band edge. For Z > Z cr ( J, n = 0), scattering phases are calculated as a function of hole energy for several values of supercriticality, as well as the positions ɛ0 and widths γ of quasistationary states as a function of supercriticality. The values of ɛ0* and width γ* are pointed out for which quasidiscrete levels may show up as Breit-Wigner resonances in the scattering of holes by a supercritical impurity. Since the phases are real, the partial scattering matrix is unitary, so that the radial Dirac equation is consistent even for Z > Z cr. In this single-particle approximation, there is no spontaneous creation of electron-hole pairs, and the impurity charge cannot be screened by this mechanism.

Anderson transition in a three-dimensional kicked rotor

NASA Astrophysics Data System (ADS)

Wang, Jiao; García-García, Antonio M.

2009-03-01

We investigate Anderson localization in a three-dimensional (3D) kicked rotor. By a finite-size scaling analysis we identify a mobility edge for a certain value of the kicking strength k=kc . For k>kc dynamical localization does not occur, all eigenstates are delocalized and the spectral correlations are well described by Wigner-Dyson statistics. This can be understood by mapping the kicked rotor problem onto a 3D Anderson model (AM) where a band of metallic states exists for sufficiently weak disorder. Around the critical region k≈kc we carry out a detailed study of the level statistics and quantum diffusion. In agreement with the predictions of the one parameter scaling theory (OPT) and with previous numerical simulations, the number variance is linear, level repulsion is still observed, and quantum diffusion is anomalous with ⟨p2⟩∝t2/3 . We note that in the 3D kicked rotor the dynamics is not random but deterministic. In order to estimate the differences between these two situations we have studied a 3D kicked rotor in which the kinetic term of the associated evolution matrix is random. A detailed numerical comparison shows that the differences between the two cases are relatively small. However in the deterministic case only a small set of irrational periods was used. A qualitative analysis of a much larger set suggests that deviations between the random and the deterministic kicked rotor can be important for certain choices of periods. Heuristically it is expected that localization effects will be weaker in a nonrandom potential since destructive interference will be less effective to arrest quantum diffusion. However we have found that certain choices of irrational periods enhance Anderson localization effects.

Spectral and entropic characterizations of Wigner functions: applications to model vibrational systems.

PubMed

Luzanov, A V

2008-09-07

The Wigner function for the pure quantum states is used as an integral kernel of the non-Hermitian operator K, to which the standard singular value decomposition (SVD) is applied. It provides a set of the squared singular values treated as probabilities of the individual phase-space processes, the latter being described by eigenfunctions of KK(+) (for coordinate variables) and K(+)K (for momentum variables). Such a SVD representation is employed to obviate the well-known difficulties in the definition of the phase-space entropy measures in terms of the Wigner function that usually allows negative values. In particular, the new measures of nonclassicality are constructed in the form that automatically satisfies additivity for systems composed of noninteracting parts. Furthermore, the emphasis is given on the geometrical interpretation of the full entropy measure as the effective phase-space volume in the Wigner picture of quantum mechanics. The approach is exemplified by considering some generic vibrational systems. Specifically, for eigenstates of the harmonic oscillator and a superposition of coherent states, the singular value spectrum is evaluated analytically. Numerical computations are given for the nonlinear problems (the Morse and double well oscillators, and the Henon-Heiles system). We also discuss the difficulties in implementation of a similar technique for electronic problems.

Continuous-variable teleportation of a negative Wigner function

NASA Astrophysics Data System (ADS)

Mišta, Ladislav, Jr.; Filip, Radim; Furusawa, Akira

2010-07-01

Teleportation is a basic primitive for quantum communication and quantum computing. We address the problem of continuous-variable (unconditional and conditional) teleportation of a pure single-photon state and a mixed attenuated single-photon state generally in a nonunity-gain regime. Our figure of merit is the maximum negativity of the Wigner function, which demonstrates a highly nonclassical feature of the teleported state. We find that the negativity of the Wigner function of the single-photon state can be unconditionally teleported for an arbitrarily weak squeezed state used to create the entangled state shared in teleportation. In contrast, for the attenuated single-photon state there is a strict threshold squeezing one has to surpass to successfully teleport the negativity of its Wigner function. The conditional teleportation allows one to approach perfect transmission of the single photon for an arbitrarily low squeezing at a cost of decrease of the success rate. In contrast, for the attenuated single photon state, conditional teleportation cannot overcome the squeezing threshold of the unconditional teleportation and it approaches negativity of the input state only if the squeezing increases simultaneously. However, as soon as the threshold squeezing is surpassed, conditional teleportation still pronouncedly outperforms the unconditional one. The main consequences for quantum communication and quantum computing with continuous variables are discussed.

Continuous-variable teleportation of a negative Wigner function

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mista, Ladislav Jr.; Filip, Radim; Furusawa, Akira

2010-07-15

Teleportation is a basic primitive for quantum communication and quantum computing. We address the problem of continuous-variable (unconditional and conditional) teleportation of a pure single-photon state and a mixed attenuated single-photon state generally in a nonunity-gain regime. Our figure of merit is the maximum negativity of the Wigner function, which demonstrates a highly nonclassical feature of the teleported state. We find that the negativity of the Wigner function of the single-photon state can be unconditionally teleported for an arbitrarily weak squeezed state used to create the entangled state shared in teleportation. In contrast, for the attenuated single-photon state there ismore » a strict threshold squeezing one has to surpass to successfully teleport the negativity of its Wigner function. The conditional teleportation allows one to approach perfect transmission of the single photon for an arbitrarily low squeezing at a cost of decrease of the success rate. In contrast, for the attenuated single photon state, conditional teleportation cannot overcome the squeezing threshold of the unconditional teleportation and it approaches negativity of the input state only if the squeezing increases simultaneously. However, as soon as the threshold squeezing is surpassed, conditional teleportation still pronouncedly outperforms the unconditional one. The main consequences for quantum communication and quantum computing with continuous variables are discussed.« less

Entanglement with negative Wigner function of three thousand atoms heralded by one photon

NASA Astrophysics Data System (ADS)

McConnell, Robert; Zhang, Hao; Hu, Jiazhong; Ćuk, Senka; Vuletić, Vladan

2016-06-01

Quantum-mechanically correlated (entangled) states of many particles are of interest in quantum information, quantum computing and quantum metrology. Metrologically useful entangled states of large atomic ensembles have been experimentally realized [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], but these states display Gaussian spin distribution functions with a non-negative Wigner function. Non-Gaussian entangled states have been produced in small ensembles of ions [11, 12], and very recently in large atomic ensembles [13, 14, 15]. Here, we generate entanglement in a large atomic ensemble via the interaction with a very weak laser pulse; remarkably, the detection of a single photon prepares several thousand atoms in an entangled state. We reconstruct a negative-valued Wigner function, an important hallmark of nonclassicality, and verify an entanglement depth (minimum number of mutually entangled atoms) of 2910 ± 190 out of 3100 atoms. Attaining such a negative Wigner function and the mutual entanglement of virtually all atoms is unprecedented for an ensemble containing more than a few particles. While the achieved purity of the state is slightly below the threshold for entanglement-induced metrological gain, further technical improvement should allow the generation of states that surpass this threshold, and of more complex Schrödinger cat states for quantum metrology and information processing.

Pinning mode of integer quantum Hall Wigner crystal of skyrmions

NASA Astrophysics Data System (ADS)

Zhu, Han; Sambandamurthy, G.; Chen, Y. P.; Jiang, P.-H.; Engel, L. W.; Tsui, D. C.; Pfeiffer, L. N.; West, K. W.

2009-03-01

Just away from integer Landau level (LL) filling factors ν, the dilute quasi-particles/holes at the partially filled LL form an integer-quantum-Hall Wigner crystal, which exhibits microwave pinning mode resonances [1]. Due to electron-electron interaction, it was predicted that the elementary excitation around ν= 1 is not a single spin flip, but a larger-scale spin texture, known as a skyrmion [2]. We have compared the pinning mode resonances [1] of integer quantum Hall Wigner crystals formed in the partly filled LL just away from ν= 1 and ν= 2, in the presence of an in-plane magnetic field. As an in-plane field is applied, the peak frequencies of the resonances near ν= 1 increase, while the peak frequencies below ν= 2 show neligible dependence on in-plane field. We interpret this observation as due to a skyrmion crystal phase around ν= 1 and a single-hole Wigner crystal phase below ν= 2. The in-plane field increases the Zeeman gap and causes shrinking of the skyrmion size toward single spin flips. [1] Yong P. Chen et al., Phys. Rev. Lett. 91, 016801 (2003). [2] S. L. Sondhi et al., Phys. Rev. B 47, 16 419 (1993); L. Brey et al., Phys. Rev. Lett. 75, 2562 (1995).

Thermal stability and structural characterization of organic/inorganic hybrid nonlinear optical material containing a two-dimensional chromophore.

PubMed

Chang, Po-Hsun; Tsai, Hsieh-Chih; Chen, Yu-Ren; Chen, Jian-Yu; Hsiue, Ging-Ho

2008-10-21

In this study, two nonlinear optic hybrid materials with different dimensional alkoxysilane dyes were prepared and characterized. One NLO silane (Cz2PhSO 2OH- TES), a two-dimensional structure based on carbazole, had a larger rotational volume than the other (DR19-TES). Second harmonic ( d 33) analysis verified there is an optimum heating process for the best poling efficiency. The maximum d 33 value of NLO hybrid film containing Cz2PhSO 2OH was obtained for 10.7 pm/V after precuring at 150 degrees C for 3 h and poling at 210 degrees C for 60 min. The solid-state (29)Si NMR spectrum shows that the main factor influencing poling efficiency and thermal stability was cross-linking degree of NLO silane, but not that of TMOS. In particular, the two-dimensional sol-gel system has a greater dynamic and temporary stability than the one-dimensional system due to Cz2PhSO 2OH-TES requiring a larger volume to rotate in the hybrid matrix after cross-linking.

Probing hydrogen bond networks in half-sandwich Ru(II) building blocks by a combined 1H DQ CRAMPS solid-state NMR, XRPD, and DFT approach.

PubMed

Chierotti, Michele R; Gobetto, Roberto; Nervi, Carlo; Bacchi, Alessia; Pelagatti, Paolo; Colombo, Valentina; Sironi, Angelo

2014-01-06

The hydrogen bond network of three polymorphs (1α, 1β, and 1γ) and one solvate form (1·H2O) arising from the hydration-dehydration process of the Ru(II) complex [(p-cymene)Ru(κN-INA)Cl2] (where INA is isonicotinic acid), has been ascertained by means of one-dimensional (1D) and two-dimensional (2D) double quantum (1)H CRAMPS (Combined Rotation and Multiple Pulses Sequences) and (13)C CPMAS solid-state NMR experiments. The resolution improvement provided by homonuclear decoupling pulse sequences, with respect to fast MAS experiments, has been highlighted. The solid-state structure of 1γ has been fully characterized by combining X-ray powder diffraction (XRPD), solid-state NMR, and periodic plane-wave first-principles calculations. None of the forms show the expected supramolecular cyclic dimerization of the carboxylic functions of INA, because of the presence of Cl atoms as strong hydrogen bond (HB) acceptors. The hydration-dehydration process of the complex has been discussed in terms of structure and HB rearrangements.

Resonant tunneling of 1-dimensional electrons across an array of 3-dimensionally confined potential wells

NASA Astrophysics Data System (ADS)

Allee, D. R.; Chou, S. Y.; Harris, J. S.; Pease, R. F. W.

A lateral resonant tunneling field effect transistor has been fabricated with a gate electrode in the form of a railway such that the two rails form a lateral double barrier potential at the GaAs/AlGaAs interface. The ties confine the electrons in the third dimension forming an array of potential boxes or three dimensionally confined potential wells. The width of the ties and rails is 50nm; the spacings between the ties and between the two rails are 230nm and 150nm respectively. The ties are 750nm long and extend beyond the the two rails forming one dimensional wires on either side. Conductance oscillations are observed in the drain current at 4.2K as the gate voltage is scanned. Comparison with devices with a solid gate, and with a monorail gate with ties fabricated on the same wafer suggest that these conductance oscillations are electron resonant tunneling from one dimensional wires through the quasi-bound states of the three dimensionally confined potential wells. Comparison with a device with a two rail gate without ties (previously published) indicates that additional confinement due to the ties enhances the strength of the conductance oscillations.

Numerical Model of Flame Spread Over Solids in Microgravity: A Supplementary Tool for Designing a Space Experiment

NASA Technical Reports Server (NTRS)

Shih, Hsin-Yi; Tien, James S.; Ferkul, Paul (Technical Monitor)

2001-01-01

The recently developed numerical model of concurrent-flow flame spread over thin solids has been used as a simulation tool to help the designs of a space experiment. The two-dimensional and three-dimensional, steady form of the compressible Navier-Stokes equations with chemical reactions are solved. With the coupled multi-dimensional solver of the radiative heat transfer, the model is capable of answering a number of questions regarding the experiment concept and the hardware designs. In this paper, the capabilities of the numerical model are demonstrated by providing the guidance for several experimental designing issues. The test matrix and operating conditions of the experiment are estimated through the modeling results. The three-dimensional calculations are made to simulate the flame-spreading experiment with realistic hardware configuration. The computed detailed flame structures provide the insight to the data collection. In addition, the heating load and the requirements of the product exhaust cleanup for the flow tunnel are estimated with the model. We anticipate that using this simulation tool will enable a more efficient and successful space experiment to be conducted.

Metallic hydrogen

NASA Astrophysics Data System (ADS)

Silvera, Isaac F.; Dias, Ranga

2018-06-01

Hydrogen is the simplest and most abundant element in the Universe. There are two pathways for creating metallic hydrogen under high pressures. Over 80 years ago Wigner and Huntington predicted that if solid molecular hydrogen was sufficiently compressed in the T  =  0 K limit, molecules would dissociate to form atomic metallic hydrogen (MH). We have observed this transition at a pressure of 4.95 megabars. MH in this form has probably never existed on Earth or in the Universe; it may be a room temperature superconductor and is predicted to be metastable. If metastable it will have an important technological impact. Liquid metallic hydrogen can also be produced at intermediate pressures and high temperatures and is believed to make up ~90% of the planet Jupiter. We have observed this liquid–liquid transition, also known as the plasma phase transition, at pressures of ~1–2 megabar and temperatures ~1000–2000 K. However, in this paper we shall focus on the Wigner–Huntington transition. We shall discuss the methods used to observe metallic hydrogen at extreme conditions of static pressure in the laboratory, extending our understanding of the phase diagram of the simplest atom in the periodic table.

X-Ray Reflectometry of DMPS Monolayers on a Water Substrate

NASA Astrophysics Data System (ADS)

Tikhonov, A. M.; Asadchikov, V. E.; Volkov, Yu. O.; Roshchin, B. S.; Ermakov, Yu. A.

2017-12-01

The molecular structure of dimyristoyl phosphatidylserine (DMPS) monolayers on a water substrate in different phase states has been investigated by X-ray reflectometry with a photon energy of 8 keV. According to the experimental data, the transition from a two-dimensional expanded liquid state to a solid gel state (liquid crystal) accompanied by the ordering of the hydrocarbon tails C14H27 of the DMPS molecule occurs in the monolayer as the surface pressure rises. The monolayer thickness is 20 ± 3 and 28 ± 2 Å in the liquid and solid phases, respectively, with the deflection angle of the molecular tail axis from the normal to the surface in the gel phase being 26° ± 8°. At least a twofold decrease in the degree of hydration of the polar lipid groups also occurs under two-dimensional monolayer compression. The reflectometry data have been analyzed using two approaches: under the assumption about the presence of two layers with different electron densities in the monolayer and without any assumptions about the transverse surface structure. Both approaches demonstrate satisfactory agreement between themselves in describing the experimental results.

Solid stress and elastic energy as measures of tumour mechanopathology

PubMed Central

Nia, Hadi T.; Liu, Hao; Seano, Giorgio; Datta, Meenal; Jones, Dennis; Rahbari, Nuh; Incio, Joao; Chauhan, Vikash P.; Jung, Keehoon; Martin, John D.; Askoxylakis, Vasileios; Padera, Timothy P.; Fukumura, Dai; Boucher, Yves; Hornicek, Francis J.; Grodzinsky, Alan J.; Baish, James W.; Munn, Lance L.

2017-01-01

Solid stress and tissue stiffness affect tumour growth, invasion, metastasis and treatment. Unlike stiffness, which can be precisely mapped in tumours, the measurement of solid stresses is challenging. Here, we show that two-dimensional spatial mappings of solid stress and the resulting elastic energy in excised or in situ tumours with arbitrary shapes and wide size ranges can be obtained via three distinct and quantitative techniques that rely on the measurement of tissue displacement after disruption of the confining structures. Application of these methods in models of primary tumours and metastasis revealed that: (i) solid stress depends on both cancer cells and their microenvironment; (ii) solid stress increases with tumour size; and (iii) mechanical confinement by the surrounding tissue significantly contributes to intratumoural solid stress. Further study of the genesis and consequences of solid stress, facilitated by the engineering principles presented here, may lead to significant discoveries and new therapies. PMID:28966873

Solid phase microextraction-comprehensive two-dimensional gas chromatography-time-of-flight mass spectrometry for the analysis of honey volatiles.

PubMed

Cajka, Tomás; Hajslová, Jana; Cochran, Jack; Holadová, Katerina; Klimánková, Eva

2007-03-01

Head-space solid phase microextration (SPME), followed by comprehensive two-dimensional gas chromatography-time-of-flight mass spectrometry (GCxGC-TOFMS), has been implemented for the analysis of honey volatiles, with emphasis on the optimal selection of SPME fibre and the first- and second-dimension GC capillaries. From seven SPME fibres investigated, a divinylbenzene/Carboxen/polydimethylsiloxane (DVB/CAR/PDMS) 50/30 microm fibre provided the best sorption capacity and the broadest range of volatiles extracted from the headspace of a mixed honey sample. A combination of DB-5ms x SUPELCOWAX 10 columns enabled the best resolution of sample components compared to the other two tested column configurations. Employing this powerful analytical strategy led to the identification of 164 volatile compounds present in a honey mixture during a 19-min GC run. Combination of this simple and inexpensive SPME-based sampling/concentration technique with the advanced separation/identification approach represented by GCxGC-TOFMS allows a rapid and comprehensive examination of the honey volatiles profile. In this way, the laboratory sample throughput can be increased significantly and, at the same time, the risk of erroneous identification, which cannot be avoided in one-dimensional GC separation, is minimised.

Lax-Wendroff and TVD finite volume methods for unidimensional thermomechanical numerical simulations of impacts on elastic-plastic solids

NASA Astrophysics Data System (ADS)

Heuzé, Thomas

2017-10-01

We present in this work two finite volume methods for the simulation of unidimensional impact problems, both for bars and plane waves, on elastic-plastic solid media within the small strain framework. First, an extension of Lax-Wendroff to elastic-plastic constitutive models with linear and nonlinear hardenings is presented. Second, a high order TVD method based on flux-difference splitting [1] and Superbee flux limiter [2] is coupled with an approximate elastic-plastic Riemann solver for nonlinear hardenings, and follows that of Fogarty [3] for linear ones. Thermomechanical coupling is accounted for through dissipation heating and thermal softening, and adiabatic conditions are assumed. This paper essentially focuses on one-dimensional problems since analytical solutions exist or can easily be developed. Accordingly, these two numerical methods are compared to analytical solutions and to the explicit finite element method on test cases involving discontinuous and continuous solutions. This allows to study in more details their respective performance during the loading, unloading and reloading stages. Particular emphasis is also paid to the accuracy of the computed plastic strains, some differences being found according to the numerical method used. Lax-Wendoff two-dimensional discretization of a one-dimensional problem is also appended at the end to demonstrate the extensibility of such numerical scheme to multidimensional problems.

High performance Solid Rocket Motor (SRM) submerged nozzle/combustion cavity flowfield assessment

NASA Technical Reports Server (NTRS)

Freeman, J. A.; Chan, J. S.; Murph, J. E.; Xiques, K. E.

1987-01-01

Two and three dimensional internal flowfield solutions for critical points in the Space Shuttle solid rocket booster burn time were developed using the Lockheed Huntsville GIM/PAID Navier-Stokes solvers. These perfect gas, viscous solutions for the high performance motor characterize the flow in the aft segment and nozzle of the booster. Two dimensional axisymmetric solutions were developed at t = 20 and t = 85 sec motor burn times. The t = 85 sec solution indicates that the aft segment forward inhibitor stub produces vortices with are shed and convected downwards. A three dimensional 3.5 deg gimbaled nozzle flowfield solution was developed for the aft segment and nozzle at t = 9 sec motor burn time. This perfect gas, viscous analysis, provided a steady state solution for the core region and the flow through the nozzle, but indicated that unsteady flow exists in the region under the nozzle nose and near the flexible boot and nozzle/case joint. The flow in the nozzle/case joint region is characterized by low magnitude pressure waves which travel in the circumferential direction. From the two and three dimensional flowfield calculations presented it can be concluded that there is no evidence from these results that steady state gas dynamics is the primary mechanism resulting in the nozzle pocketing erosion experienced on SRM nozzles 8A or 17B. The steady state flowfield results indicate pocketing erosion is not directly initiated by a steady state gas dynamics phenomenon.

Construction of high-dimensional universal quantum logic gates using a Λ system coupled with a whispering-gallery-mode microresonator.

PubMed

He, Ling Yan; Wang, Tie-Jun; Wang, Chuan

2016-07-11

High-dimensional quantum system provides a higher capacity of quantum channel, which exhibits potential applications in quantum information processing. However, high-dimensional universal quantum logic gates is difficult to achieve directly with only high-dimensional interaction between two quantum systems and requires a large number of two-dimensional gates to build even a small high-dimensional quantum circuits. In this paper, we propose a scheme to implement a general controlled-flip (CF) gate where the high-dimensional single photon serve as the target qudit and stationary qubits work as the control logic qudit, by employing a three-level Λ-type system coupled with a whispering-gallery-mode microresonator. In our scheme, the required number of interaction times between the photon and solid state system reduce greatly compared with the traditional method which decomposes the high-dimensional Hilbert space into 2-dimensional quantum space, and it is on a shorter temporal scale for the experimental realization. Moreover, we discuss the performance and feasibility of our hybrid CF gate, concluding that it can be easily extended to a 2n-dimensional case and it is feasible with current technology.

Ladar imaging detection of salient map based on PWVD and Rényi entropy

NASA Astrophysics Data System (ADS)

Xu, Yuannan; Zhao, Yuan; Deng, Rong; Dong, Yanbing

2013-10-01

Spatial-frequency information of a given image can be extracted by associating the grey-level spatial data with one of the well-known spatial/spatial-frequency distributions. The Wigner-Ville distribution (WVD) has a good characteristic that the images can be represented in spatial/spatial-frequency domains. For intensity and range images of ladar, through the pseudo Wigner-Ville distribution (PWVD) using one or two dimension window, the statistical property of Rényi entropy is studied. We also analyzed the change of Rényi entropy's statistical property in the ladar intensity and range images when the man-made objects appear. From this foundation, a novel method for generating saliency map based on PWVD and Rényi entropy is proposed. After that, target detection is completed when the saliency map is segmented using a simple and convenient threshold method. For the ladar intensity and range images, experimental results show the proposed method can effectively detect the military vehicles from complex earth background with low false alarm.

A novel joint timing/frequency synchronization scheme based on Radon-Wigner transform of LFM signals in CO-OFDM systems

NASA Astrophysics Data System (ADS)

Liu, Jianfei; Wei, Ying; Zeng, Xiangye; Lu, Jia; Zhang, Shuangxi; Wang, Mengjun

2018-03-01

A joint timing and frequency synchronization method has been proposed for coherent optical orthogonal frequency-division multiplexing (CO-OFDM) system in this paper. The timing offset (TO), integer frequency offset (FO) and the fractional FO can be realized by only one training symbol, which consists of two linear frequency modulation (LFM) signals with opposite chirp rates. By detecting the peak of LFM signals after Radon-Wigner transform (RWT), the TO and the integer FO can be estimated at the same time, moreover, the fractional FO can be acquired correspondingly through the self-correlation characteristic of the same training symbol. Simulation results show that the proposed method can give a more accurate TO estimation than the existing methods, especially at poor OSNR conditions; for the FO estimation, both the fractional and the integer FO can be estimated through the proposed training symbol with no extra overhead, a more accurate estimation and a large FO estimation range of [ - 5 GHz, 5GHz] can be acquired.

A new class of ensemble conserving algorithms for approximate quantum dynamics: Theoretical formulation and model problems.

PubMed

Smith, Kyle K G; Poulsen, Jens Aage; Nyman, Gunnar; Rossky, Peter J

2015-06-28

We develop two classes of quasi-classical dynamics that are shown to conserve the initial quantum ensemble when used in combination with the Feynman-Kleinert approximation of the density operator. These dynamics are used to improve the Feynman-Kleinert implementation of the classical Wigner approximation for the evaluation of quantum time correlation functions known as Feynman-Kleinert linearized path-integral. As shown, both classes of dynamics are able to recover the exact classical and high temperature limits of the quantum time correlation function, while a subset is able to recover the exact harmonic limit. A comparison of the approximate quantum time correlation functions obtained from both classes of dynamics is made with the exact results for the challenging model problems of the quartic and double-well potentials. It is found that these dynamics provide a great improvement over the classical Wigner approximation, in which purely classical dynamics are used. In a special case, our first method becomes identical to centroid molecular dynamics.

First Observation of the {Lambda}(1405) Line Shape in Electroproduction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lu, Haiyun; Schumacher, Reinhard A.

2013-10-01

We report the first observation of the line shape of the {Lambda}(1405) from electroproduction, and show that it is not a simple Breit-Wigner resonance. Electroproduction of K{sup +}{Lambda}(1405) off the proton was studied by using data from CLAS at Jefferson Lab in the range 1.0

Time-frequency distributions for propulsion-system diagnostics

NASA Astrophysics Data System (ADS)

Griffin, Michael E.; Tulpule, Sharayu

1991-12-01

The Wigner distribution and its smoothed versions, i.e., Choi-Williams and Gaussian kernels, are evaluated for propulsion system diagnostics. The approach is intended for off-line kernel design by using the ambiguity domain to select the appropriate Gaussian kernel. The features produced by the Wigner distribution and its smoothed versions correlate remarkably well with documented failure indications. The selection of the kernel on the other hand is very subjective for our unstructured data.

Extracting Micro-Doppler Radar Signatures from Rotating Targets Using Fourier-Bessel Transform and Time-Frequency Analysis

DTIC Science & Technology

2014-10-16

Time-Frequency analysis, Short-Time Fourier Transform, Wigner Ville Distribution, Fourier Bessel Transform, Fractional Fourier Transform. I...INTRODUCTION Most widely used time-frequency transforms are short-time Fourier Transform (STFT) and Wigner Ville distribution (WVD). In STFT, time and...frequency resolutions are limited by the size of window function used in calculating STFT. For mono-component signals, WVD gives the best time and frequency

Functional Wigner representation of quantum dynamics of Bose-Einstein condensate

DOE Office of Scientific and Technical Information (OSTI.GOV)

Opanchuk, B.; Drummond, P. D.

2013-04-15

We develop a method of simulating the full quantum field dynamics of multi-mode multi-component Bose-Einstein condensates in a trap. We use the truncated Wigner representation to obtain a probabilistic theory that can be sampled. This method produces c-number stochastic equations which may be solved using conventional stochastic methods. The technique is valid for large mode occupation numbers. We give a detailed derivation of methods of functional Wigner representation appropriate for quantum fields. Our approach describes spatial evolution of spinor components and properly accounts for nonlinear losses. Such techniques are applicable to calculating the leading quantum corrections, including effects such asmore » quantum squeezing, entanglement, EPR correlations, and interactions with engineered nonlinear reservoirs. By using a consistent expansion in the inverse density, we are able to explain an inconsistency in the nonlinear loss equations found by earlier authors.« less

Wigner time delay in photodetachment of Tm-and in photoionization of Yb: A comparative study

NASA Astrophysics Data System (ADS)

Saha, Soumyajit; Jose, Jobin; Deshmukh, Pranawa; Dolmatov, Valeriy; Kheifets, Anatoli; Manson, Steven

2017-04-01

Preliminary studies of Wigner time delay in photodetachment spectra of negative ions have been reported. Photodetachment time delay for some dipole channels of Tm- and of Cl- were calculated using relativistic random phase approximation (RRPA). Comparisons between photodetachment time delay of Cl- and photoionization time delay of Ar were made. We investigate the photodetachment time delay for all three relativistically split nd -> ɛ f channels of Tm- and for nd -> ɛ f channels of Yb (isoelectronic to Tm-) using RRPA. We study the effect of the shape resonance, brought about by the centrifugal barrier potential, on photodetachment time delay. A negative ion is a good laboratory for studying the effects of shape resonances on time delay since the phase is unaffected by the Coulomb component. Wigner time delay in photodetachment of Tm- and in photoionization of Yb: A comparative study.

Tertiary instability of zonal flows within the Wigner-Moyal formulation of drift turbulence

NASA Astrophysics Data System (ADS)

Zhu, Hongxuan; Ruiz, D. E.; Dodin, I. Y.

2017-10-01

The stability of zonal flows (ZFs) is analyzed within the generalized-Hasegawa-Mima model. The necessary and sufficient condition for a ZF instability, which is also known as the tertiary instability, is identified. The qualitative physics behind the tertiary instability is explained using the recently developed Wigner-Moyal formulation and the corresponding wave kinetic equation (WKE) in the geometrical-optics (GO) limit. By analyzing the drifton phase space trajectories, we find that the corrections proposed in Ref. to the WKE are critical for capturing the spatial scales characteristic for the tertiary instability. That said, we also find that this instability itself cannot be adequately described within a GO formulation in principle. Using the Wigner-Moyal equations, which capture diffraction, we analytically derive the tertiary-instability growth rate and compare it with numerical simulations. The research was sponsored by the U.S. Department of Energy.

Hans Bethe's early life

NASA Astrophysics Data System (ADS)

Bernstein, Jeremy

2012-10-01

In 1937, two years after he moved to the US to escape Nazi persecution, the physicist Hans Bethe sent a letter to his mother in Germany. In it, he wrote, "I think I am about the leading theoretician in America. [Eugene] Wigner is certainly better and [Robert] Oppenheimer and [Edward] Teller probably just as good. But I do more and talk more and that counts too."

7 Å resolution in protein two-dimensional-crystal X-ray diffraction at Linac Coherent Light Source

PubMed Central

Pedrini, Bill; Tsai, Ching-Ju; Capitani, Guido; Padeste, Celestino; Hunter, Mark S.; Zatsepin, Nadia A.; Barty, Anton; Benner, W. Henry; Boutet, Sébastien; Feld, Geoffrey K.; Hau-Riege, Stefan P.; Kirian, Richard A.; Kupitz, Christopher; Messerschmitt, Marc; Ogren, John I.; Pardini, Tommaso; Segelke, Brent; Williams, Garth J.; Spence, John C. H.; Abela, Rafael; Coleman, Matthew; Evans, James E.; Schertler, Gebhard F. X.; Frank, Matthias; Li, Xiao-Dan

2014-01-01

Membrane proteins arranged as two-dimensional crystals in the lipid environment provide close-to-physiological structural information, which is essential for understanding the molecular mechanisms of protein function. Previously, X-ray diffraction from individual two-dimensional crystals did not represent a suitable investigational tool because of radiation damage. The recent availability of ultrashort pulses from X-ray free-electron lasers (XFELs) has now provided a means to outrun the damage. Here, we report on measurements performed at the Linac Coherent Light Source XFEL on bacteriorhodopsin two-dimensional crystals mounted on a solid support and kept at room temperature. By merging data from about a dozen single crystal diffraction images, we unambiguously identified the diffraction peaks to a resolution of 7 Å, thus improving the observable resolution with respect to that achievable from a single pattern alone. This indicates that a larger dataset will allow for reliable quantification of peak intensities, and in turn a corresponding increase in the resolution. The presented results pave the way for further XFEL studies on two-dimensional crystals, which may include pump–probe experiments at subpicosecond time resolution. PMID:24914166

Finite-volume application of high order ENO schemes to multi-dimensional boundary-value problems

NASA Technical Reports Server (NTRS)

Casper, Jay; Dorrepaal, J. Mark

1990-01-01

The finite volume approach in developing multi-dimensional, high-order accurate essentially non-oscillatory (ENO) schemes is considered. In particular, a two dimensional extension is proposed for the Euler equation of gas dynamics. This requires a spatial reconstruction operator that attains formal high order of accuracy in two dimensions by taking account of cross gradients. Given a set of cell averages in two spatial variables, polynomial interpolation of a two dimensional primitive function is employed in order to extract high-order pointwise values on cell interfaces. These points are appropriately chosen so that correspondingly high-order flux integrals are obtained through each interface by quadrature, at each point having calculated a flux contribution in an upwind fashion. The solution-in-the-small of Riemann's initial value problem (IVP) that is required for this pointwise flux computation is achieved using Roe's approximate Riemann solver. Issues to be considered in this two dimensional extension include the implementation of boundary conditions and application to general curvilinear coordinates. Results of numerical experiments are presented for qualitative and quantitative examination. These results contain the first successful application of ENO schemes to boundary value problems with solid walls.

Simulation of hydrodynamics using large eddy simulation-second-order moment model in circulating fluidized beds

NASA Astrophysics Data System (ADS)

Juhui, Chen; Yanjia, Tang; Dan, Li; Pengfei, Xu; Huilin, Lu

2013-07-01

Flow behavior of gas and particles is predicted by the large eddy simulation of gas-second order moment of solid model (LES-SOM model) in the simulation of flow behavior in CFB. This study shows that the simulated solid volume fractions along height using a two-dimensional model are in agreement with experiments. The velocity, volume fraction and second-order moments of particles are computed. The second-order moments of clusters are calculated. The solid volume fraction, velocity and second order moments are compared at the three different model constants.

The apparent size of three-dimensional objects and their silhouettes: a solid-superiority effect.

PubMed

Walker, J T; Walker, M J

1988-01-01

A solid object looks larger than its outline or silhouette under many viewing conditions. This solid-superiority effect may result from the assimilation or confusion of visual contours within the projection of a three-dimensional object on the picture plane. An aspect of the Müller-Lyer illusion may also play a role.

Measurement of the Equation of State of the Two-Dimensional Hubbard Model

NASA Astrophysics Data System (ADS)

Miller, Luke; Cocchi, Eugenio; Drewes, Jan; Koschorreck, Marco; Pertot, Daniel; Brennecke, Ferdinand; Koehl, Michael

2016-05-01

The subtle interplay between kinetic energy, interactions and dimensionality challenges our comprehension of strongly-correlated physics observed, for example, in the solid state. In this quest, the Hubbard model has emerged as a conceptually simple, yet rich model describing such physics. Here we present an experimental determination of the equation of state of the repulsive two-dimensional Hubbard model over a broad range of interactions, 0 <= U / t <= 20 , and temperatures, down to kB T / t = 0 . 63(2) using high-resolution imaging of ultracold fermionic atoms in optical lattices. We show density profiles, compressibilities and double occupancies over the whole doping range, and hence our results constitute benchmarks for state-of-the-art theoretical approaches.

Localized Ambient Solidity Separation Algorithm Based Computer User Segmentation.

PubMed

Sun, Xiao; Zhang, Tongda; Chai, Yueting; Liu, Yi

2015-01-01

Most of popular clustering methods typically have some strong assumptions of the dataset. For example, the k-means implicitly assumes that all clusters come from spherical Gaussian distributions which have different means but the same covariance. However, when dealing with datasets that have diverse distribution shapes or high dimensionality, these assumptions might not be valid anymore. In order to overcome this weakness, we proposed a new clustering algorithm named localized ambient solidity separation (LASS) algorithm, using a new isolation criterion called centroid distance. Compared with other density based isolation criteria, our proposed centroid distance isolation criterion addresses the problem caused by high dimensionality and varying density. The experiment on a designed two-dimensional benchmark dataset shows that our proposed LASS algorithm not only inherits the advantage of the original dissimilarity increments clustering method to separate naturally isolated clusters but also can identify the clusters which are adjacent, overlapping, and under background noise. Finally, we compared our LASS algorithm with the dissimilarity increments clustering method on a massive computer user dataset with over two million records that contains demographic and behaviors information. The results show that LASS algorithm works extremely well on this computer user dataset and can gain more knowledge from it.

Localized Ambient Solidity Separation Algorithm Based Computer User Segmentation

PubMed Central

Sun, Xiao; Zhang, Tongda; Chai, Yueting; Liu, Yi

2015-01-01

Most of popular clustering methods typically have some strong assumptions of the dataset. For example, the k-means implicitly assumes that all clusters come from spherical Gaussian distributions which have different means but the same covariance. However, when dealing with datasets that have diverse distribution shapes or high dimensionality, these assumptions might not be valid anymore. In order to overcome this weakness, we proposed a new clustering algorithm named localized ambient solidity separation (LASS) algorithm, using a new isolation criterion called centroid distance. Compared with other density based isolation criteria, our proposed centroid distance isolation criterion addresses the problem caused by high dimensionality and varying density. The experiment on a designed two-dimensional benchmark dataset shows that our proposed LASS algorithm not only inherits the advantage of the original dissimilarity increments clustering method to separate naturally isolated clusters but also can identify the clusters which are adjacent, overlapping, and under background noise. Finally, we compared our LASS algorithm with the dissimilarity increments clustering method on a massive computer user dataset with over two million records that contains demographic and behaviors information. The results show that LASS algorithm works extremely well on this computer user dataset and can gain more knowledge from it. PMID:26221133

Trapped-mode-induced Fano resonance and acoustical transparency in a one-dimensional solid-fluid phononic crystal

NASA Astrophysics Data System (ADS)

Quotane, Ilyasse; El Boudouti, El Houssaine; Djafari-Rouhani, Bahram

2018-01-01

We investigate theoretically and numerically the possibility of existence of Fano and acoustic-induced transparency (AIT) resonances in a simple though realistic one-dimensional acoustic structure made of solid-fluid layers inserted between two fluids. These resonances are obtained by combining appropriately the zeros of transmission (antiresonance) induced by the solid layers and the local resonances induced by the solid or combined solid-fluid layers with surface free boundary conditions. In particular, we show the possibility of trapped modes, also called bound states in continuum, which have recently found a high renewal interest. These modes appear as resonances with zero width in the transmission spectra as well as in the density of states (DOS). We consider three different structures: (i) a single solid layer inserted between two fluids. This simple structure shows the possibility of existence of trapped modes, which are discrete modes of the solid layer that lie in the continuum modes of the surrounding fluids. We give explicit analytical expressions of the dispersion relation of these eigenmodes of the solid layer which are found independent of the nature of the surrounding fluids. By slightly detuning the angle of incidence from that associated to the trapped mode, we get a well-defined Fano resonance characterized by an asymmetric Fano profile in the transmission spectra. (ii) The second structure consists of a solid-fluid-solid triple layer embedded between two fluids. This structure is found more appropriate to show both Fano and acoustic-induced transparency resonances. We provide detailed analytical expressions for the transmission and reflection coefficients that enable us to deduce a closed-form expression of the dispersion relation giving the trapped modes. Two situations can be distinguished in the triple-layer system: in the case of a symmetric structure (i.e., the same solid layers) we show, by detuning the incidence angle θ , the possibility of existence of Fano resonances that can be fitted following a Fano-type expression. The variation of the Fano parameter that describes the asymmetry of such resonances as well as their width versus θ is studied in detail. In the case of an asymmetric structure (i.e., different solid layers), we show the existence of an incidence angle that enables to squeeze a resonance between two transmission zeros induced by the two solid layers. This resonance behaves like an AIT resonance, its position and width depend on the nature of the fluid and solid layers as well as on the difference between the thicknesses of the solid layers. (iii) In the case of a periodic structure (phononic crystal), we show that trapped modes and Fano resonances give rise, respectively, to dispersionless flat bands with zero group velocity and nearly flat bands with negative or positive group velocities. The analytical results presented here are obtained by means of the Green's function method which enables to deduce in closed form: dispersion curves, transmission and reflection coefficients, DOS, as well as the displacement fields. The proposed solid-fluid layered structures should have important applications for designing acoustic mirrors and acoustic filters as well as supersonic and subsonic materials.

Numerical model of two-dimensional heterogeneous combustion in porous media under natural convection or forced filtration

NASA Astrophysics Data System (ADS)

Lutsenko, Nickolay A.

2018-03-01

A novel mathematical model and original numerical method for investigating the two-dimensional waves of heterogeneous combustion in porous media are proposed and described in detail. The mathematical model is constructed within the framework of the model of interacting interpenetrating continua and includes equations of state, continuity, momentum conservation and energy for solid and gas phases. Combustion, considered in the paper, is due to the exothermic reaction between fuel in the porous solid medium and oxidiser contained in the gas flowing through the porous object. The original numerical method is based on a combination of explicit and implicit finite-difference schemes. A distinctive feature of the proposed model is that the gas velocity at the open boundaries (inlet and outlet) of the porous object is unknown and has to be found from the solution of the problem, i.e. the flow rate of the gas regulates itself. This approach allows processes to be modelled not only under forced filtration, but also under free convection, when there is no forced gas input in porous objects, which is typical for many natural or anthropogenic disasters (burning of peatlands, coal dumps, landfills, grain elevators). Some two-dimensional time-dependent problems of heterogeneous combustion in porous objects have been solved using the proposed numerical method. It is shown that two-dimensional waves of heterogeneous combustion in porous media can propagate in two modes with different characteristics, as in the case of one-dimensional combustion, but the combustion front can move in a complex manner, and gas dynamics within the porous objects can be complicated. When natural convection takes place, self-sustaining combustion waves can go through the all parts of the object regardless of where an ignition zone was located, so the all combustible material in each part of the object is burned out, in contrast to forced filtration.

Avalanches in Strained Amorphous Solids: Does Inertia Destroy Critical Behavior?

NASA Astrophysics Data System (ADS)

Salerno, K. Michael; Maloney, Craig E.; Robbins, Mark O.

2012-09-01

Simulations are used to determine the effect of inertia on athermal shear of amorphous two-dimensional solids. In the quasistatic limit, shear occurs through a series of rapid avalanches. The distribution of avalanches is analyzed using finite-size scaling with thousands to millions of disks. Inertia takes the system to a new underdamped universality class rather than driving the system away from criticality as previously thought. Scaling exponents are determined for the underdamped and overdamped limits and a critical damping that separates the two regimes. Systems are in the overdamped universality class even when most vibrational modes are underdamped.

Nebula: reconstruction and visualization of scattering data in reciprocal space.

PubMed

Reiten, Andreas; Chernyshov, Dmitry; Mathiesen, Ragnvald H

2015-04-01

Two-dimensional solid-state X-ray detectors can now operate at considerable data throughput rates that allow full three-dimensional sampling of scattering data from extended volumes of reciprocal space within second to minute time-scales. For such experiments, simultaneous analysis and visualization allows for remeasurements and a more dynamic measurement strategy. A new software, Nebula , is presented. It efficiently reconstructs X-ray scattering data, generates three-dimensional reciprocal space data sets that can be visualized interactively, and aims to enable real-time processing in high-throughput measurements by employing parallel computing on commodity hardware.

Nebula: reconstruction and visualization of scattering data in reciprocal space

PubMed Central

Reiten, Andreas; Chernyshov, Dmitry; Mathiesen, Ragnvald H.

2015-01-01

Two-dimensional solid-state X-ray detectors can now operate at considerable data throughput rates that allow full three-dimensional sampling of scattering data from extended volumes of reciprocal space within second to minute time­scales. For such experiments, simultaneous analysis and visualization allows for remeasurements and a more dynamic measurement strategy. A new software, Nebula, is presented. It efficiently reconstructs X-ray scattering data, generates three-dimensional reciprocal space data sets that can be visualized interactively, and aims to enable real-time processing in high-throughput measurements by employing parallel computing on commodity hardware. PMID:25844083

Atomistics of vapour–liquid–solid nanowire growth

PubMed Central

Wang, Hailong; Zepeda-Ruiz, Luis A.; Gilmer, George H.; Upmanyu, Moneesh

2013-01-01

Vapour–liquid–solid route and its variants are routinely used for scalable synthesis of semiconducting nanowires, yet the fundamental growth processes remain unknown. Here we employ atomic-scale computations based on model potentials to study the stability and growth of gold-catalysed silicon nanowires. Equilibrium studies uncover segregation at the solid-like surface of the catalyst particle, a liquid AuSi droplet, and a silicon-rich droplet–nanowire interface enveloped by heterogeneous truncating facets. Supersaturation of the droplets leads to rapid one-dimensional growth on the truncating facets and much slower nucleation-controlled two-dimensional growth on the main facet. Surface diffusion is suppressed and the excess Si flux occurs through the droplet bulk which, together with the Si-rich interface and contact line, lowers the nucleation barrier on the main facet. The ensuing step flow is modified by Au diffusion away from the step edges. Our study highlights key interfacial characteristics for morphological and compositional control of semiconducting nanowire arrays. PMID:23752586

Uniform analytic approximation of Wigner rotation matrices

NASA Astrophysics Data System (ADS)

Hoffmann, Scott E.

2018-02-01

We derive the leading asymptotic approximation, for low angle θ, of the Wigner rotation matrix elements, dm1m2 j(θ ) , uniform in j, m1, and m2. The result is in terms of a Bessel function of integer order. We numerically investigate the error for a variety of cases and find that the approximation can be useful over a significant range of angles. This approximation has application in the partial wave analysis of wavepacket scattering.

A Wigner Monte Carlo approach to density functional theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sellier, J.M., E-mail: jeanmichel.sellier@gmail.com; Dimov, I.

2014-08-01

In order to simulate quantum N-body systems, stationary and time-dependent density functional theories rely on the capacity of calculating the single-electron wave-functions of a system from which one obtains the total electron density (Kohn–Sham systems). In this paper, we introduce the use of the Wigner Monte Carlo method in ab-initio calculations. This approach allows time-dependent simulations of chemical systems in the presence of reflective and absorbing boundary conditions. It also enables an intuitive comprehension of chemical systems in terms of the Wigner formalism based on the concept of phase-space. Finally, being based on a Monte Carlo method, it scales verymore » well on parallel machines paving the way towards the time-dependent simulation of very complex molecules. A validation is performed by studying the electron distribution of three different systems, a Lithium atom, a Boron atom and a hydrogenic molecule. For the sake of simplicity, we start from initial conditions not too far from equilibrium and show that the systems reach a stationary regime, as expected (despite no restriction is imposed in the choice of the initial conditions). We also show a good agreement with the standard density functional theory for the hydrogenic molecule. These results demonstrate that the combination of the Wigner Monte Carlo method and Kohn–Sham systems provides a reliable computational tool which could, eventually, be applied to more sophisticated problems.« less

Decoherence of odd compass states in the phase-sensitive amplifying/dissipating environment

NASA Astrophysics Data System (ADS)

Dodonov, V. V.; Valverde, C.; Souza, L. S.; Baseia, B.

2016-08-01

We study the evolution of odd compass states (specific superpositions of four coherent states), governed by the standard master equation with phase-sensitive amplifying/attenuating terms, in the presence of a Hamiltonian describing a parametric degenerate linear amplifier. Explicit expressions for the time-dependent Wigner function are obtained. The time of disappearance of the so called ;sub-Planck structures; is calculated using the negative value of the Wigner function at the origin of phase space. It is shown that this value rapidly decreases during a short ;conventional interference degradation time; (CIDT), which is inversely proportional to the size of quantum superposition, provided the anti-Hermitian terms in the master equation are of the same order (or stronger) as the Hermitian ones (governing the parametric amplification). The CIDT is compared with the final positivization time (FPT), when the Wigner function becomes positive. It appears that the FPT does not depend on the size of superpositions, moreover, it can be much bigger in the amplifying media than in the attenuating ones. Paradoxically, strengthening the Hamiltonian part results in decreasing the CIDT, so that the CIDT almost does not depend on the size of superpositions in the asymptotical case of very weak reservoir coupling. We also analyze the evolution of the Mandel factor, showing that for some sets of parameters this factor remains significantly negative, even when the Wigner function becomes positive.

Fast Magic-Angle Spinning Three-Dimensional NMR Experiment for Simultaneously Probing H-H and N-H Proximities in Solids.

PubMed

Reddy, G N Manjunatha; Malon, Michal; Marsh, Andrew; Nishiyama, Yusuke; Brown, Steven P

2016-12-06

A fast magic-angle spinning (MAS, 70 kHz) solid-state NMR experiment is presented that combines 1 H Double-Quantum (DQ) and 14 N- 1 H HMQC (Heteronuclear Multiple-Quantum Coherence) pulse-sequence elements, so as to simultaneously probe H-H and N-H proximities in molecular solids. The proposed experiment can be employed in both two-dimensional (2D) and three-dimensional (3D) versions: first, a 2D 14 N HMQC-filtered 1 H-DQ experiment provides specific DQ-SQ correlation peaks for proton pairs that are in close proximities to the nitrogen sites, thereby achieving spectral filtration. Second, a proton-detected three-dimensional (3D) 1 H(DQ)- 14 N(SQ)- 1 H(SQ) experiment correlates 1 H(DQ)- 1 H(SQ) chemical shifts with 14 N shifts such that longer range N···H-H correlations are observed between protons and nitrogen atoms with internuclear NH distances exceeding 3 Å. Both 2D and 3D versions of the proposed experiment are demonstrated for an amino acid hydrochloride salt, l-histidine·HCl·H 2 O, and a DNA nucleoside, guanosine·2H 2 O. In the latter case, the achieved spectral filtration ensures that DQ cross peaks are only observed for guanine NH and CH8 1 H resonances and not ribose and water 1 H resonances, thus providing insight into the changes in the solid-state structure of this hydrate that occur over time; significant changes are observed in the NH and NH 2 1 H chemical shifts as compared to the freshly recrystallized sample previously studied by Reddy et al., Cryst. Growth Des. 2015, 15, 5945.

Characterization of van der Waals type bimodal,- lambda,- meta- and spinodal phase transitions in liquid mixtures, solid suspensions and thin films.

PubMed

Rosenholm, Jarl B

2018-03-01

The perfect gas law is used as a reference when selecting state variables (P, V, T, n) needed to characterize ideal gases (vapors), liquids and solids. Van der Waals equation of state is used as a reference for models characterizing interactions in liquids, solids and their mixtures. Van der Waals loop introduces meta- and unstable states between the observed gas (vapor)-liquid P-V transitions at low T. These intermediate states are shown to appear also between liquid-liquid, liquid-solid and solid-solid phase transitions. First-order phase transitions are characterized by a sharp discontinuity of first-order partial derivatives (P, S, V) of Helmholtz and Gibbs free energies. Second-order partial derivatives (K T , B, C V , C P , E) consist of a static contribution relating to second-order phase transitions and a relaxation contribution representing the degree of first-order phase transitions. Bimodal (first-order) and spinodal (second-order) phase boundaries are used to separate stable phases from metastable and unstable phases. The boundaries are identified and quantified by partial derivatives of molar Gibbs free energy or chemical potentials with respect to P, S, V and composition (mole fractions). Molecules confined to spread Langmuir monolayers or adsorbed Gibbs monolayers are characterized by equation of state and adsorption isotherms relating to a two-dimensional van der Waals equation of state. The basic work of two-dimensional wetting (cohesion, adsorption, spreading, immersion), have to be adjusted by a horizontal surface pressure in the presence of adsorbed vapor layers. If the adsorption is extended to liquid films a vertical surface pressure (Π) may be added to account for the lateral interaction, thus restoring PV = ΠAh dependence of thin films. Van der Waals attraction, Coulomb repulsion and structural hydration forces contribute to the vertical surface pressure. A van der Waals type coexistence of ordered (dispersed) and disordered (aggregated) phases is shown to exist when liquid vapor is confined in capillaries (condensation-liquefaction-evaporation and flux). This pheno-menon can be experimentally illustrated with suspended nano-sized particles (flocculation-coagulation-peptisation of colloidal sols) being confined in sample holders of varying size. The self-assembled aggregates represent critical self-similar equilibrium structures corres-ponding to rate determining complexes in kinetics. Overall, a self-consistent thermodynamic framework is established for the characterization of two- and three-dimensional phase separations in one-, two- and three-component systems. Copyright © 2018 Elsevier B.V. All rights reserved.

Adsorption of hard spheres via the non-uniform Percus-Yevick equation

NASA Astrophysics Data System (ADS)

Sokołowski, S.

We study the adsorption of hard spheres on solids interacting according to potentials whose Boltzmann functions contain a δ-function. The nonuniform Percus-Yevick equation is solved by using the method introduced by Lado to study two dimensional fluids.

Polymer diffusion in the interphase between surface and solution.

PubMed

Weger, Lukas; Weidmann, Monika; Ali, Wael; Hildebrandt, Marcus; Gutmann, Jochen Stefan; Hoffmann-Jacobsen, Kerstin

2018-05-22

Total internal reflection fluorescence correlation spectroscopy (TIR-FCS) is applied to study the self-diffusion of polyethylene glycol solutions in the presence of weakly attractive interfaces. Glass coverslips modified with aminopropyl- and propyl-terminated silanes are used to study the influence of solid surfaces on polymer diffusion. A model of three phases of polymer diffusion allows to describe the experimental fluorescence autocorrelation functions. Besides the two-dimensional diffusion of adsorbed polymer on the substrate and three-dimensional free diffusion in bulk solution, a third diffusion time scale is observed with intermediate diffusion times. This retarded three-dimensional diffusion in solution is assigned to long range effects of solid surfaces on diffusional dynamics of polymers. The respective diffusion constants show Rouse scaling (D~N -1 ) indicating a screening of hydrodynamic interactions by the presence of the surface. Hence, the presented TIR-FCS method proves to be a valuable tool to investigate the effect of surfaces on polymer diffusion beyond the first adsorbed polymer layer on the 100 nm length scale.

Solid-state radar switchboard

NASA Astrophysics Data System (ADS)

Thiebaud, P.; Cross, D. C.

1980-07-01

A new solid-state radar switchboard equipped with 16 input ports which will output data to 16 displays is presented. Each of the ports will handle a single two-dimensional radar input, or three ports will accommodate a three-dimensional radar input. A video switch card of the switchboard is used to switch all signals, with the exception of the IFF-mode-control lines. Each card accepts inputs from up to 16 sources and can pass a signal with bandwidth greater than 20 MHz to the display assigned to that card. The synchro amplifier of current systems has been eliminated and in the new design each PPI receives radar data via a single coaxial cable. This significant reduction in cabling is achieved by adding a serial-to-parallel interface and a digital-to-synchro converter located at the PPI.

Co-assembly of Zn(SPh){sub 2} and organic linkers into helical and zig-zag polymer chains

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu Yi; Yu Lingmin; Loo, Say Chye Joachim

2012-07-15

Two novel one-dimensional coordination polymers, single helicate [Zn(SPh){sub 2}(TPyTA)(EG)]{sub n} (EG=ethylene glycol) (1) and zig-zag structure [Zn(SPh){sub 2}(BPyVB)]{sub n} (2), were synthesized under solvothermal conditions at 150 Degree-Sign C or room temperature by the co-assembly of Zn(SPh){sub 2} and organic linkers such as 2,4,6-tri(4-pyridyl)-1,3,5-triazine (TPyTA) and 1,3-bis(trans-4-pyridylvinyl)benzene (BPyVB). X-ray crystallography study reveals that both polymers 1 and 2 crystallize in space group P2{sub 1}/c of the monoclinic system. The solid-state UV-vis absorption spectra show that 1 and 2 have maxium absorption onsets at 400 nm and 420 nm, respectively. TGA analysis indicates that 1 and 2 are stable up tomore » 110 Degree-Sign C and 210 Degree-Sign C. - Graphical abstract: Two novel one-dimensional coordination polymers, single helicate [Zn(SPh){sub 2}(TPyTA)(EG)]{sub n} (1) and zig-zag structure [Zn(SPh){sub 2}(BPyVB)]{sub n} (2), were synthesized. Solid-state UV-vis absorptions show that 1 and 2 have maxium absorption onsets at 400 nm and 420 nm, respectively. TGA analysis indicates that 1 and 2 are stable up to 110 Degree-Sign C and 210 Degree-Sign C. Highlights: Black-Right-Pointing-Pointer Two novel one-dimensional coordination polymers have been synthesized. Black-Right-Pointing-Pointer TPyTA results in helical structures in 1 while BPyVB leads to zig-zag chains in 2. Black-Right-Pointing-Pointer Solid-state UV-vis absorption spectra and TGA analysis of the title polymers were studied.« less

Berezinskii-Kosterlitz-Thouless transition and two-dimensional melting

NASA Astrophysics Data System (ADS)

Ryzhov, V. N.; Tareyeva, E. E.; Fomin, Yu D.; Tsiok, E. N.

2017-12-01

The main aspects of the theory of phase transitions in two-dimensional degenerate systems (Berezinskii-Kosterlitz-Thouless, or BKT, transitions) are reviewed in detail, including the transition mechanism, the renormalization group as a tool for describing the transition, and how the transition scenario can possibly depend on the core energy of topological defects (in particular, in thin superconducting films). Various melting scenarios in two-dimensional systems are analyzed, and the current status of actual experiments and computer simulations in the field is examined. Whereas in three dimensions melting always occurs as a single first-order transition, in two dimensions, as shown by Halperin, Nelson, and Young, melting via two continuous BKT transitions with an intermediate hexatic phase characterized by quasi-long-range orientational order is possible. But there is also a possibility for a first-order phase transition to occur. Recently, one further melting scenario, different from that occurring in the Berezinskii-Kosterlitz-Thouless-Halperin-Nelson-Young theory, has been proposed, according to which a solid can melt in two stages: a continuous BKT-type solid-hexatic transition and then a first-order hexatic-phase-isotropic-liquid phase transition. Particular attention is given to the melting scenario as a function of the potential shape and to the random pinning effect on two-dimensional melting. In particular, it is shown that random pinning can alter the melting scenario fundamentally in the case of a first-order transition. Also considered is the melting of systems with potentials having a negative curvature in the repulsion region-potentials that are successfully used in describing the anomalous properties of water in two dimensions. This review is an extended version of the report “Old and new in the physics of phase transitions” presented at the scientific session of the Physical Sciences Division of the Russian Academy of Sciences on 21 December 2016 (see Phys. Usp. 60 948-957 (2017); Usp. Fiz. Nauk 187 1021 (2017)). (Editor’s note.)

Computer-intensive simulation of solid-state NMR experiments using SIMPSON.

PubMed

Tošner, Zdeněk; Andersen, Rasmus; Stevensson, Baltzar; Edén, Mattias; Nielsen, Niels Chr; Vosegaard, Thomas

2014-09-01

Conducting large-scale solid-state NMR simulations requires fast computer software potentially in combination with efficient computational resources to complete within a reasonable time frame. Such simulations may involve large spin systems, multiple-parameter fitting of experimental spectra, or multiple-pulse experiment design using parameter scan, non-linear optimization, or optimal control procedures. To efficiently accommodate such simulations, we here present an improved version of the widely distributed open-source SIMPSON NMR simulation software package adapted to contemporary high performance hardware setups. The software is optimized for fast performance on standard stand-alone computers, multi-core processors, and large clusters of identical nodes. We describe the novel features for fast computation including internal matrix manipulations, propagator setups and acquisition strategies. For efficient calculation of powder averages, we implemented interpolation method of Alderman, Solum, and Grant, as well as recently introduced fast Wigner transform interpolation technique. The potential of the optimal control toolbox is greatly enhanced by higher precision gradients in combination with the efficient optimization algorithm known as limited memory Broyden-Fletcher-Goldfarb-Shanno. In addition, advanced parallelization can be used in all types of calculations, providing significant time reductions. SIMPSON is thus reflecting current knowledge in the field of numerical simulations of solid-state NMR experiments. The efficiency and novel features are demonstrated on the representative simulations. Copyright © 2014 Elsevier Inc. All rights reserved.

A two dimensional interface element for coupling of independently modeled three dimensional finite element meshes and extensions to dynamic and non-linear regimes

NASA Technical Reports Server (NTRS)

Aminpour, Mohammad

1995-01-01

The work reported here pertains only to the first year of research for a three year proposal period. As a prelude to this two dimensional interface element, the one dimensional element was tested and errors were discovered in the code for built-up structures and curved interfaces. These errors were corrected and the benchmark Boeing composite crown panel was analyzed successfully. A study of various splines led to the conclusion that cubic B-splines best suit this interface element application. A least squares approach combined with cubic B-splines was constructed to make a smooth function from the noisy data obtained with random error in the coordinate data points of the Boeing crown panel analysis. Preliminary investigations for the formulation of discontinuous 2-D shell and 3-D solid elements were conducted.

Ion association at discretely-charged dielectric interfaces: Giant charge inversion

NASA Astrophysics Data System (ADS)

Wang, Zhi-Yong; Wu, Jianzhong

2017-07-01

Giant charge reversal has been identified for the first time by Monte Carlo simulation for a discretely charged surface in contact with a trivalent electrolyte solution. It takes place regardless of the surface charge density under study and the monovalent salt. In stark contrast to earlier predictions based on the 2-dimensional Wigner crystal model to describe strong correlation of counterions at the macroion surface, we find that giant charge reversal reflects an intricate interplay of ionic volume effects, electrostatic correlations, surface charge heterogeneity, and the dielectric response of the confined fluids. While the novel phenomenon is yet to be confirmed with experiment, the simulation results appear in excellent agreement with a wide range of existing observations in the subregime of charge inversion. Our findings may have far-reaching implications to understanding complex electrochemical phenomena entailing ionic fluids under dielectric confinements.

Wave dispersion and propagation in state-based peridynamics

NASA Astrophysics Data System (ADS)

Butt, Sahir N.; Timothy, Jithender J.; Meschke, Günther

2017-11-01

Peridynamics is a nonlocal continuum model which offers benefits over classical continuum models in cases, where discontinuities, such as cracks, are present in the deformation field. However, the nonlocal characteristics of peridynamics leads to a dispersive dynamic response of the medium. In this study we focus on the dispersion properties of a state-based linear peridynamic solid model and specifically investigate the role of the peridynamic horizon. We derive the dispersion relation for one, two and three dimensional cases and investigate the effect of horizon size, mesh size (lattice spacing) and the influence function on the dispersion properties. We show how the influence function can be used to minimize wave dispersion at a fixed lattice spacing and demonstrate it qualitatively by wave propagation analysis in one- and two-dimensional models of elastic solids. As a main contribution of this paper, we propose to associate peridynamic non-locality expressed by the horizon with a characteristic length scale related to the material microstructure. To this end, the dispersion curves obtained from peridynamics are compared with experimental data for two kinds of sandstone.

Role of cell deformability in the two-dimensional melting of biological tissues

NASA Astrophysics Data System (ADS)

Li, Yan-Wei; Ciamarra, Massimo Pica

2018-04-01

The size and shape of a large variety of polymeric particles, including biological cells, star polymers, dendrimes, and microgels, depend on the applied stresses as the particles are extremely soft. In high-density suspensions these particles deform as stressed by their neighbors, which implies that the interparticle interaction becomes of many-body type. Investigating a two-dimensional model of cell tissue, where the single particle shear modulus is related to the cell adhesion strength, here we show that the particle deformability affects the melting scenario. On increasing the temperature, stiff particles undergo a first-order solid/liquid transition, while soft ones undergo a continuous solid/hexatic transition followed by a discontinuous hexatic/liquid transition. At zero temperature the melting transition driven by the decrease of the adhesion strength occurs through two continuous transitions as in the Kosterlitz, Thouless, Halperin, Nelson, and Young scenario. Thus, there is a range of adhesion strength values where the hexatic phase is stable at zero temperature, which suggests that the intermediate phase of the epithelial-to-mesenchymal transition could be hexatic type.

Frequency Dynamics of the First Heart Sound

NASA Astrophysics Data System (ADS)

Wood, John Charles

Cardiac auscultation is a fundamental clinical tool but first heart sound origins and significance remain controversial. Previous clinical studies have implicated resonant vibrations of both the myocardium and the valves. Accordingly, the goals of this thesis were threefold, (1) to characterize the frequency dynamics of the first heart sound, (2) to determine the relative contribution of the myocardium and the valves in determining first heart sound frequency, and (3) to develop new tools for non-stationary signal analysis. A resonant origin for first heart sound generation was tested through two studies in an open-chest canine preparation. Heart sounds were recorded using ultralight acceleration transducers cemented directly to the epicardium. The first heart sound was observed to be non-stationary and multicomponent. The most dominant feature was a powerful, rapidly-rising frequency component that preceded mitral valve closure. Two broadband components were observed; the first coincided with mitral valve closure while the second significantly preceded aortic valve opening. The spatial frequency of left ventricular vibrations was both high and non-stationary which indicated that the left ventricle was not vibrating passively in response to intracardiac pressure fluctuations but suggested instead that the first heart sound is a propagating transient. In the second study, regional myocardial ischemia was induced by left coronary circumflex arterial occlusion. Acceleration transducers were placed on the ischemic and non-ischemic myocardium to determine whether ischemia produced local or global changes in first heart sound amplitude and frequency. The two zones exhibited disparate amplitude and frequency behavior indicating that the first heart sound is not a resonant phenomenon. To objectively quantify the presence and orientation of signal components, Radon transformation of the time -frequency plane was performed and found to have considerable potential for pattern classification. Radon transformation of the Wigner spectrum (Radon-Wigner transform) was derived to be equivalent to dechirping in the time and frequency domains. Based upon this representation, an analogy between time-frequency estimation and computed tomography was drawn. Cohen's class of time-frequency representations was subsequently shown to result from simple changes in reconstruction filtering parameters. Time-varying filtering, adaptive time-frequency transformation and linear signal synthesis were also performed from the Radon-Wigner representation.

Visualizing the shape of soft solid and fluid contacts between two surfaces

NASA Astrophysics Data System (ADS)

Pham, Jonathan; Schellenberger, Frank; Kappl, Michael; Vollmer, Doris; Butt, Hans-Jürgen

The soft contact between two surfaces is fundamentally interesting for soft materials and fluid mechanics and relevant for friction and wear. The deformation of soft solid interfaces has received much interest because it interestingly reveals similarities to fluid wetting. We present an experimental route towards visualizing the three-dimensional contact geometry of either liquid-solid (i.e., oil and glass) or solid-solid (i.e., elastomer and glass) interfaces using a home-built combination of confocal microscopy and atomic force microscopy. We monitor the shape of a fluid capillary bridge and the depth of indentation in 3D while simultaneously measuring the force. In agreement with theoretical predictions, the height of the capillary bridge depends on the interfacial tensions. By using a slowly evaporating solvent, we quantify the temporal evolution of the capillary bridge and visualized the influence of pinning points on its shape. The position dependence of the advancing and receding contact angle along the three-phase contact line, particle-liquid-air, is resolved. Extending our system, we explore the contact deformation of soft solids where elasticity, in addition to surface tension, becomes an important factor.

Phase-space quantum mechanics study of two identical particles in an external oscillatory potential

NASA Technical Reports Server (NTRS)

Nieto, Luis M.; Gadella, Manuel

1993-01-01

This simple example is used to show how the formalism of Moyal works when it is applied to systems of identical particles. The symmetric and antisymmetric Moyal propagators are evaluated for this case; from them, the correct energy levels of energy are obtained, as well as the Wigner functions for the symmetric and antisymmetric states of the two identical particle system. Finally, the solution of the Bloch equation is straightforwardly obtained from the expressions of the Moyal propagators.

Quantum Properties of the Superposition of Two Nearly Identical Coherent States

NASA Astrophysics Data System (ADS)

Othman, Anas; Yevick, David

2018-04-01

In this paper, we examine the properties of the state obtained when two nearly identical coherent states are superimposed. We found that this state exhibits many nonclassical properties such as sub-Poissonian statistics, squeezing and a partially negative Wigner function. These and other properties indicate that such states, here termed near coherent states, are significantly closer to coherent states more than the generalized Schrördinger cat states. We finally provide an experimental procedure for generating the near coherent states.

MODELING MULTICOMPONENT ORGANIC CHEMICAL TRANSPORT IN THREE-FLUID-PHASE POROUS MEDIA

EPA Science Inventory

A two dimensional finite-element model was developed to predict coupled transient flow and multicomponent transport of organic chemicals which can partition between NAPL, water, gas and solid phases in porous media under the assumption of local chemical equilibrium. as-phase pres...

MODELING MULTICOMPONENT ORGANIC CHEMICAL TRANSPORT IN THREE FLUID PHASE POROUS MEDIA

EPA Science Inventory

A two-dimensional finite-element model was developed to predict coupled transient flow and multicomponent transport of organic chemicals which can partition between nonaqueous phase liquid, water, gas and solid phases in porous media under the assumption of local chemical equilib...