Nonlinear stationary solutions of the Wigner and Wigner-Poisson equations

International Nuclear Information System (INIS)

Haas, F.; Shukla, P. K.

2008-01-01

Exact nonlinear stationary solutions of the one-dimensional Wigner and Wigner-Poisson equations in the terms of the Wigner functions that depend not only on the energy but also on position are presented. In this way, the Bernstein-Greene-Kruskal modes of the classical plasma are adapted for the quantum formalism in the phase space. The solutions are constructed for the case of a quartic oscillator potential, as well as for the self-consistent Wigner-Poisson case. Conditions for well-behaved physically meaningful equilibrium Wigner functions are discussed.

Topology of local atomic environments: implications for magnetism and superconductivity

International Nuclear Information System (INIS)

Bennett, L.H.; Watson, R.E.; Pearson, W.B.

1985-01-01

Wigner-Seitz cells have been constructed, as a function of atomic size, for a number of transition-metal alloys (SmCo 5 etc.) and a disclination network has been obtained from these. Magnetism in these alloys can be related to the disclination lines, much like the superexchange paths familiar in the magnetism of salts

Nonlinear stationary solutions of the Wigner and Wigner-Poisson equations

OpenAIRE

Haas, F.; Shukla, P. K.

2008-01-01

Exact nonlinear stationary solutions of the one-dimensional Wigner and Wigner-Poisson equations in the terms of the Wigner functions that depend not only on the energy but also on position are presented. In this way, the Bernstein-Greene-Kruskal modes of the classical plasma are adapted for the quantum formalism in the phase space. The solutions are constructed for the case of a quartic oscillator potential, as well as for the self-consistent Wigner-Poisson case. Conditions for well-behaved p...

Simplified polynomial representation of cross sections for reactor calculation

International Nuclear Information System (INIS)

Dias, A.M.; Sakai, M.

1985-01-01

It is shown a simplified representation of a cross section library generated by transport theory using the cell model of Wigner-Seitz for typical PWR fuel elements. The effect of burnup evolution through tables of reference cross sections and the effect of the variation of the reactor operation parameters considered by adjusted polynomials are presented. (M.C.K.) [pt

Density of the Breit--Wigner functions

International Nuclear Information System (INIS)

Perry, W.L.; Luning, C.D.

1975-01-01

It is shown, for certain sequences [lambda/sub i/] in the complex plane, that linear combinations of the Breit-Wigner functions [B/sub i/] approximate, in the mean square, any function in L 2 (0,infinity). Implications and numerical use of this result are discussed

Non-Equilibrium Liouville and Wigner Equations: Moment Methods and Long-Time Approximations

Directory of Open Access Journals (Sweden)

Ramon F. Álvarez-Estrada

2014-03-01

Full Text Available We treat the non-equilibrium evolution of an open one-particle statistical system, subject to a potential and to an external “heat bath” (hb with negligible dissipation. For the classical equilibrium Boltzmann distribution, Wc,eq, a non-equilibrium three-term hierarchy for moments fulfills Hermiticity, which allows one to justify an approximate long-time thermalization. That gives partial dynamical support to Boltzmann’s Wc,eq, out of the set of classical stationary distributions, Wc;st, also investigated here, for which neither Hermiticity nor that thermalization hold, in general. For closed classical many-particle systems without hb (by using Wc,eq, the long-time approximate thermalization for three-term hierarchies is justified and yields an approximate Lyapunov function and an arrow of time. The largest part of the work treats an open quantum one-particle system through the non-equilibrium Wigner function, W. Weq for a repulsive finite square well is reported. W’s (< 0 in various cases are assumed to be quasi-definite functionals regarding their dependences on momentum (q. That yields orthogonal polynomials, HQ,n(q, for Weq (and for stationary Wst, non-equilibrium moments, Wn, of W and hierarchies. For the first excited state of the harmonic oscillator, its stationary Wst is a quasi-definite functional, and the orthogonal polynomials and three-term hierarchy are studied. In general, the non-equilibrium quantum hierarchies (associated with Weq for the Wn’s are not three-term ones. As an illustration, we outline a non-equilibrium four-term hierarchy and its solution in terms of generalized operator continued fractions. Such structures also allow one to formulate long-time approximations, but make it more difficult to justify thermalization. For large thermal and de Broglie wavelengths, the dominant Weq and a non-equilibrium equation for W are reported: the non-equilibrium hierarchy could plausibly be a three-term one and possibly not

Eugene Wigner and nuclear energy: a reminiscence

International Nuclear Information System (INIS)

Weinberg, A.M.

1987-01-01

Dr. Weinberg reviews Wigner's contributions in each of the fields to which he contributed: designs for fast breeders and thermal breeders and some of the earliest calculations on water moderated cooling systems; Clinton Laboratories, 1946-47, The Materials Testing Reactor (MTR); gas-cooled reactors; the Nautilus; Savannah River Reactors, Project Hope; a chemical plant that would reprocess spent fuel at an affordable cost in a full-fledged breeder; reactor physics and general engineering; microscopic reactor theory; spherical harmonics method; correction to the sphericized cell calculation, the fast effect; macroscopic reactor theory; two-group theory; perturbation theory; control rod theory (statics); kinetics; pile oscillator; shielding; fission products; temperature effects; The Wigner-Wilkins Distribution; solid state physics; the Wigner Disease; neutron diffraction; and general energy policy. Eugene Wigner was one of the early contributors to the debate on the role of nuclear power

Flux flow of Abrikosov vortices in type-II superconductors

International Nuclear Information System (INIS)

Chen, J.L.; Yang, T.J.

1994-01-01

The theory of flux flow developed by Bardeen and Stephen (BS) is modified and extended to the high-field case. The Clem model and Wigner-Seitz circle-cell approximation for vortices are used in our approach. The distinct boundary of the normal core of a vortex in BS theory is removed and treated naturally. Several interesting results come out as a consequence. The Lorentz force is determined by the normal current rather than the supercurrent. But the supercurrent can sustain the magnetic-field distribution of flux quanta. From energy dissipation considerations, the Lorentz force is equal to viscosity force automatically without assumption as made in BS theory. An expression for the viscosity is also obtained

Dynamics of Gaussian Wigner functions derived from a time-dependent variational principle

Directory of Open Access Journals (Sweden)

Jens Aage Poulsen

2017-11-01

Full Text Available By using a time-dependent variational principle formulated for Wigner phase-space functions, we obtain the optimal time-evolution for two classes of Gaussian Wigner functions, namely those of either thawed real-valued or frozen but complex Gaussians. It is shown that tunneling effects are approximately included in both schemes.

Lattice Wigner equation

Science.gov (United States)

Solórzano, S.; Mendoza, M.; Succi, S.; Herrmann, H. J.

2018-01-01

We present a numerical scheme to solve the Wigner equation, based on a lattice discretization of momentum space. The moments of the Wigner function are recovered exactly, up to the desired order given by the number of discrete momenta retained in the discretization, which also determines the accuracy of the method. The Wigner equation is equipped with an additional collision operator, designed in such a way as to ensure numerical stability without affecting the evolution of the relevant moments of the Wigner function. The lattice Wigner scheme is validated for the case of quantum harmonic and anharmonic potentials, showing good agreement with theoretical results. It is further applied to the study of the transport properties of one- and two-dimensional open quantum systems with potential barriers. Finally, the computational viability of the scheme for the case of three-dimensional open systems is also illustrated.

Entropy and wigner functions

Science.gov (United States)

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.

Entropy and Wigner Functions

OpenAIRE

Manfredi, G.; Feix, M. R.

2002-01-01

The properties of an alternative definition of quantum entropy, based on Wigner functions, are discussed. Such 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

Wigner Functions on a Lattice

OpenAIRE

Takami, A.; Hashimoto, T.; Horibe, M.; Hayashi, A.

2000-01-01

The Wigner functions on the one dimensional lattice are studied. Contrary to the previous claim in literature, Wigner functions exist on the lattice with any number of sites, whether it is even or odd. There are infinitely many solutions satisfying the conditions which reasonable Wigner functions should respect. After presenting a heuristic method to obtain Wigner functions, we give the general form of the solutions. Quantum mechanical expectation values in terms of Wigner functions are also ...

Wigner distribution in optics

NARCIS (Netherlands)

Bastiaans, M.J.; Testorf, M.; Hennelly, B.; Ojeda-Castañeda, J.

2009-01-01

In 1932 Wigner introduced a distribution function in mechanics that permitted a description of mechanical phenomena in a phase space. Such a Wigner distribution was introduced in optics by Dolin and Walther in the sixties, to relate partial coherence to radiometry. A few years later, the Wigner

Positive Wigner functions render classical simulation of quantum computation efficient.

Science.gov (United States)

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.

Computing thermal Wigner densities with the phase integration method

International Nuclear Information System (INIS)

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

2014-01-01

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

Computing thermal Wigner densities with the phase integration method.

Science.gov (United States)

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.

Moments of the Wigner delay times

International Nuclear Information System (INIS)

Berkolaiko, Gregory; Kuipers, Jack

2010-01-01

The Wigner time delay is a measure of the time spent by a particle inside the scattering region of an open system. For chaotic systems, the statistics of the individual delay times (whose average is the Wigner time delay) are thought to be well described by random matrix theory. Here we present a semiclassical derivation showing the validity of random matrix results. In order to simplify the semiclassical treatment, we express the moments of the delay times in terms of correlation functions of scattering matrices at different energies. In the semiclassical approximation, the elements of the scattering matrix are given in terms of the classical scattering trajectories, requiring one to study correlations between sets of such trajectories. We describe the structure of correlated sets of trajectories and formulate the rules for their evaluation to the leading order in inverse channel number. This allows us to derive a polynomial equation satisfied by the generating function of the moments. Along with showing the agreement of our semiclassical results with the moments predicted by random matrix theory, we infer that the scattering matrix is unitary to all orders in the semiclassical approximation.

Modelling and theories of alloy phase behavior

International Nuclear Information System (INIS)

Watson, R.E.; Davenport, J.W.; Weinert, M.; Bennett, L.H.

1987-01-01

Many trends in alloy phase formation are readily understood in terms of physically plausible atomic parameters. This has led to the introduction of structural maps where two (or more) such atomic parameters are employed as the coordinates and well-defined regions are observed to be associated with particular crystalline phases. These coordinates sometimes involve the difference in atomic parameters and sometimes involve an average. An alternative approach to the emphasis on atomic parameters has been the consideration of how atoms are packed in some crystal structure and how this controls what the constituent atoms may be. Recently this has led to the utilization of Wigner-Seitz (sometimes called Voronoi or Dirichlet) constructs of the atomic cells in a crystal structure and to the observation that sometimes two crystals which are nominally considered to have the same crystal structure according to normal crystallographic designation should be considered to be different. The Wigner-Seitz cell constructs have also offered a framework for understanding trends in the magnetic and chemical properties of particular phases as well as making coordination between crystalline and glassy structures. Neither of the above approaches provides numerical estimates of quantities of thermodynamic interest such as heats of formation. Such heats are being calculated. 42 refs., 15 figs

Phase-space path-integral calculation of the Wigner function

International Nuclear Information System (INIS)

Samson, J H

2003-01-01

The Wigner function W(q, p) is formulated as a phase-space path integral, whereby its sign oscillations can be seen to follow from interference between the geometrical phases of the paths. The approach has similarities to the path-centroid method in the configuration-space path integral. Paths can be classified by the midpoint of their ends; short paths where the midpoint is close to (q, p) and which lie in regions of low energy (low P function of the Hamiltonian) will dominate, and the enclosed area will determine the sign of the Wigner function. As a demonstration, the method is applied to a sequence of density matrices interpolating between a Poissonian number distribution and a number state, each member of which can be represented exactly by a discretized path integral with a finite number of vertices. Saddle-point evaluation of these integrals recovers (up to a constant factor) the WKB approximation to the Wigner function of a number state

Wigner functions defined with Laplace transform kernels.

Science.gov (United States)

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

Wigner distribution function of circularly truncated light beams

NARCIS (Netherlands)

Bastiaans, M.J.; Nijhawan, O.P.; Gupta, A.K.; Musla, A.K.; Singh, Kehar

1998-01-01

Truncating a light beam is expressed as a convolution of its Wigner distribution function and the WDF of the truncating aperture. The WDF of a circular aperture is derived and an approximate expression - which is exact in the space and the spatial-frequency origin and whose integral over the spatial

Compressibility of air in fibrous materials

DEFF Research Database (Denmark)

Tarnow, Viggo

1996-01-01

The dynamic compressibility of air in fibrous materials has been computed for two assumed configurations of fibers which are close to the geometry of real fiber materials. Models with parallel cylinders placed in a regular square lattice and placed randomly are treated. For these models...... the compressibility is computed approximately from the diameter and mean distances between cylinders. This requires calculation of the air temperature, which is calculated for cylinders in a regular lattive by the Wigner-Seitz cell approximation. In the case of random placement, the calculation is done by a summation...... over thermal waves from all fibers, and by a self-consistent procedure. Figuren of the compressibility in the frequency range 10-100 000 Hz, are given for diameter of the cylinders of 6.8 µm, and mean distances between them from 50 to 110 µm, which corresponds to glass wool with a density of 40 to 16...

Voronoi Cell Patterns: Application of the size distribution to societal systems

Science.gov (United States)

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

2012-02-01

In studying the growth of islands on a surface subjected to a particle flux, we found it useful to characterize the distribution of the areas of associated Voronoi (proximity or Wigner-Seitz) cells in terms of the generalized Wigner surmiseootnotetextAP & TLE, PRL 99 (2007) 226102; PRL 104 (2010) 149602 and the gamma distributions. Here we show that the same concepts and distributions are useful in analyzing several problems arising in society.ootnotetextDLG et al., arXiv 1109.3994; RS, Ph.D. dissertation; RS et al., preprint We analyze the 1D problem of the distribution of gaps between parked cars, assuming that successive cars park in the middle of vacant spaces, and compare with published data. We study the formation of second-level administrative divisions, e.g. French arrondissements. We study the actual distribution of arrondissements and the Voronoi tessellation associated with the chief town in each. While generally applicable, there are subtleties in some cases. Lastly, we consider the pattern formed by Paris M'etro stations and show that near the central area, the associated Voronoi construction also has this sort of distribution.

Heat capacity of the neutron star inner crust within an extended nuclear statistical equilibrium model

Science.gov (United States)

Burrello, S.; Gulminelli, F.; Aymard, F.; Colonna, M.; Raduta, Ad. R.

2015-11-01

Background: Superfluidity in the crust is a key ingredient for the cooling properties of proto-neutron stars. Present theoretical calculations employ the quasiparticle mean-field Hartree-Fock-Bogoliubov theory with temperature-dependent occupation numbers for the quasiparticle states. Purpose: Finite temperature stellar matter is characterized by a whole distribution of different nuclear species. We want to assess the importance of this distribution on the calculation of heat capacity in the inner crust. Method: Following a recent work, the Wigner-Seitz cell is mapped into a model with cluster degrees of freedom. The finite temperature distribution is then given by a statistical collection of Wigner-Seitz cells. We additionally introduce pairing correlations in the local density BCS approximation both in the homogeneous unbound neutron component, and in the interface region between clusters and neutrons. Results: The heat capacity is calculated in the different baryonic density conditions corresponding to the inner crust, and in a temperature range varying from 100 KeV to 2 MeV. We show that accounting for the cluster distribution has a small effect at intermediate densities, but it considerably affects the heat capacity both close to the outer crust and close to the core. We additionally show that it is very important to consider the temperature evolution of the proton fraction for a quantitatively reliable estimation of the heat capacity. Conclusions: We present the first modelization of stellar matter containing at the same time a statistical distribution of clusters at finite temperature, and pairing correlations in the unbound neutron component. The effect of the nuclear distribution on the superfluid properties can be easily added in future calculations of the neutron star cooling curves. A strong influence of resonance population on the heat capacity at high temperature is observed, which deserves to be further studied within more microscopic calculations.

Pycnonuclear fusion rates. [In white dwarf and neutron stars

Energy Technology Data Exchange (ETDEWEB)

Schramm, S.; Koonin, S.E. (California Institute of Technology, Pasadena (USA))

1990-12-01

Pycnonuclear fusion processes in an ionic crystal at zero temperature are discussed. Rearrangement effects of the lattice during the fusion process are accounted for exactly in the screening potential by computing the relaxation of the surrounding nuclei. The dynamics of the rearranging ions also generates an increased effective mass that must be used in describing the tunneling of the fusing nuclei. The opposing effects of lattice polarization through enhanced screening and the effective mass results in pycnonuclear reaction rates that are several orders of magnitude smaller than those calculated in the Wigner-Seitz approximation and are roughly equal to those obtained in the static approximation that neglects polarization entirely. 12 refs.

Structure of neutron star crusts from new Skyrme effective interactions constrained by chiral effective field theory

Science.gov (United States)

Lim, Yeunhwan; Holt, Jeremy W.

2017-06-01

We investigate the structure of neutron star crusts, including the crust-core boundary, based on new Skyrme mean field models constrained by the bulk-matter equation of state from chiral effective field theory and the ground-state energies of doubly-magic nuclei. Nuclear pasta phases are studied using both the liquid drop model as well as the Thomas-Fermi approximation. We compare the energy per nucleon for each geometry (spherical nuclei, cylindrical nuclei, nuclear slabs, cylindrical holes, and spherical holes) to obtain the ground state phase as a function of density. We find that the size of the Wigner-Seitz cell depends strongly on the model parameters, especially the coefficients of the density gradient interaction terms. We employ also the thermodynamic instability method to check the validity of the numerical solutions based on energy comparisons.

The relationship between the Wigner-Weyl kinetic formalism and the complex geometrical optics method

OpenAIRE

Maj, Omar

2004-01-01

The relationship between two different asymptotic techniques developed in order to describe the propagation of waves beyond the standard geometrical optics approximation, namely, the Wigner-Weyl kinetic formalism and the complex geometrical optics method, is addressed. More specifically, a solution of the wave kinetic equation, relevant to the Wigner-Weyl formalism, is obtained which yields the same wavefield intensity as the complex geometrical optics method. Such a relationship is also disc...

Wigner distribution and fractional Fourier transform

NARCIS (Netherlands)

Alieva, T.; Bastiaans, M.J.

2001-01-01

The connection between the Wigner distribution and the squared modulus of the fractional Fourier transform - which are both well-known time-frequency representations of a signal - is established. In particular the Radon-Wigner transform is used, which relates projections of the Wigner distribution

Wigner distribution and fractional Fourier transform

NARCIS (Netherlands)

Alieva, T.; Bastiaans, M.J.; Boashash, B.

2003-01-01

We have described the relationship between the fractional Fourier transform and the Wigner distribution by using the Radon-Wigner transform, which is a set of projections of the Wigner distribution as well as a set of squared moduli of the fractional Fourier transform. We have introduced the concept

The Wigner phase-space description of collision processes

International Nuclear Information System (INIS)

Lee, H.W.

1984-01-01

The paper concerns the Wigner distribution function in collision theory. Wigner phase-space description of collision processes; some general consideration on Wigner trajectories; and examples of Wigner trajectories; are all discussed. (U.K.)

Disadvantage factors for square lattice cells using a collision probability method

International Nuclear Information System (INIS)

Raghav, H.P.

1976-01-01

The flux distribution in an infinite square lattice consisting of cylindrical fuel rods and moderator is calculated by using a collision probability method. Neutrons are assumed to be monoenergetic and the sources as well as scattering are assumed to be isotropic. Carlvik's method for the calculation of collision probability is used. The important features of the method are that the square boundary is treated exactly and the contribution of the surrounding cells is calculated explicitly. The method is programmed in a computer code CELLC. This carries out integration by Simpson's rule. The convergence and accuracy of CELLC is assessed by computing disadvantage factors for the well-known Thie lattices and comparing the results with Monte Carlo and other integral transport theory methods used elsewhere. It is demonstrated that it is not correct to apply the white boundary condition in the Wigner Seitz Cell for low pitch and low cross sections. (orig.) [de

The Wigner function in the relativistic quantum mechanics

Energy Technology Data Exchange (ETDEWEB)

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.

Application of Wigner-transformations in heavy ion reactions

International Nuclear Information System (INIS)

Esbensen, H.

1981-01-01

One of the main features of inelastic heavy ion reactions is the excitation of collective surface vibrations. It is discussed a model, based on Wigner transformations and classical dynamics, that gives a semiclassical description of the excitation of surface vibrations due to the Coulomb and nuclear interaction in heavy ion collisions. The treatment consists of three stages, viz. the preparation of classical initial conditions compatible with the quantal ground state of surface vibrations, the dynamical evolution of the system governed by Liouville's equation (i.e. classical mechanics) and finally the interpretation of final results after the interaction in terms of excitation probabilities, elastic and inelastic cross sections etc. The first and the last stage are exact and based on the Wigner transformations while the time evolution described by classical mechanics is an approximation. Application examples are given. (author)

Wigner functions of s waves

International Nuclear Information System (INIS)

Dahl, J. P.; Varro, S.; Wolf, A.; Schleich, W. P.

2007-01-01

We derive explicit expressions for the Wigner function of wave functions in D dimensions which depend on the hyperradius--that is, of s waves. They are based either on the position or the momentum representation of the s wave. The corresponding Wigner function depends on three variables: the absolute value of the D-dimensional position and momentum vectors and the angle between them. We illustrate these expressions by calculating and discussing the Wigner functions of an elementary s wave and the energy eigenfunction of a free particle

Wigner functions of s waves

DEFF Research Database (Denmark)

Dahl, Jens Peder; Varro, S.; Wolf, A.

2007-01-01

We derive explicit expressions for the Wigner function of wave functions in D dimensions which depend on the hyperradius-that is, of s waves. They are based either on the position or the momentum representation of the s wave. The corresponding Wigner function depends on three variables......: the absolute value of the D-dimensional position and momentum vectors and the angle between them. We illustrate these expressions by calculating and discussing the Wigner functions of an elementary s wave and the energy eigenfunction of a free particle....

Full charge-density calculation of the surface energy of metals

DEFF Research Database (Denmark)

Vitos, Levente; Kollár, J..; Skriver, Hans Lomholt

1994-01-01

of a spherically symmetrized charge density, while the Coulomb and exchange-correlation contributions are calculated by means of the complete, nonspherically symmetric charge density within nonoverlapping, space-filling Wigner-Seitz cells. The functional is used to assess the convergence and the accuracy......We have calculated the surface energy and the work function of the 4d metals by means of an energy functional based on a self-consistent, spherically symmetric atomic-sphere potential. In this approach the kinetic energy is calculated completely within the atomic-sphere approximation (ASA) by means...... of the linear-muffin-tin-orbitals (LMTO) method and the ASA in surface calculations. We find that the full charge-density functional improves the agreement with recent full-potential LMTO calculations to a level where the average deviation in surface energy over the 4d series is down to 10%....

Weyl-Wigner correspondence in two space dimensions

DEFF Research Database (Denmark)

Dahl, Jens Peder; Varro, S.; Wolf, A.

2007-01-01

We consider Wigner functions in two space dimensions. In particular, we focus on Wigner functions corresponding to energy eigenstates of a non-relativistic particle moving in two dimensions in the absence of a potential. With the help of the Weyl-Wigner correspondence we first transform...... the eigenvalue equations for energy and angular momentum into phase space. As a result we arrive at partial differential equations in phase space which determine the corresponding Wigner function. We then solve the resulting equations using appropriate coordinates....

The Wigner-Yanase entropy is not subadditive

DEFF Research Database (Denmark)

Hansen, Frank

2007-01-01

Wigner and Yanase introduced in 1963 the Wigner-Yanase entropy defined as minus the skew information of a state with respect to a conserved observable. They proved that the Wigner-Yanase entropy is a concave function in the state and conjectured that it is subadditive with respect...... to the aggregation of possibly interacting subsystems. While this turned out to be true for the quantum-mechanical entropy, we negate the conjecture for the Wigner-Yanase entropy by providing a counter example....

A model for the condensation of a dusty plasma

International Nuclear Information System (INIS)

Bellan, P.M.

2004-01-01

A model for the condensation of a dusty plasma is constructed by considering the spherical shielding layers surrounding a dust grain test particle. The collisionless region less than a collision mean free path from the test particle is shown to separate into three concentric layers, each having distinct physics. The method of matched asymptotic expansions is invoked at the interfaces between these layers and provides equations which determine the radii of the interfaces. Despite being much smaller than the Wigner-Seitz radius, the dust Debye length is found to be physically significant because it gives the scale length of a precipitous cut-off of the shielded electrostatic potential at the interface between the second and third layers. Condensation is predicted to occur when the ratio of this cut-off radius to the Wigner-Seitz radius exceeds unity and this prediction is shown to be in good agreement with experiments

The truncated Wigner method for Bose-condensed gases: limits of validity and applications

International Nuclear Information System (INIS)

Sinatra, Alice; Lobo, Carlos; Castin, Yvan

2002-01-01

We study the truncated Wigner method applied to a weakly interacting spinless Bose-condensed gas which is perturbed away from thermal equilibrium by a time-dependent external potential. The principle of the method is to generate an ensemble of classical fields ψ(r) which samples the Wigner quasi-distribution function of the initial thermal equilibrium density operator of the gas, and then to evolve each classical field with the Gross-Pitaevskii equation. In the first part of the paper we improve the sampling technique over our previous work (Sinatra et al 2000 J. Mod. Opt. 47 2629-44) and we test its accuracy against the exactly solvable model of the ideal Bose gas. In the second part of the paper we investigate the conditions of validity of the truncated Wigner method. For short evolution times it is known that the time-dependent Bogoliubov approximation is valid for almost pure condensates. The requirement that the truncated Wigner method reproduces the Bogoliubov prediction leads to the constraint that the number of field modes in the Wigner simulation must be smaller than the number of particles in the gas. For longer evolution times the nonlinear dynamics of the noncondensed modes of the field plays an important role. To demonstrate this we analyse the case of a three-dimensional spatially homogeneous Bose-condensed gas and we test the ability of the truncated Wigner method to correctly reproduce the Beliaev-Landau damping of an excitation of the condensate. We have identified the mechanism which limits the validity of the truncated Wigner method: the initial ensemble of classical fields, driven by the time-dependent Gross-Pitaevskii equation, thermalizes to a classical field distribution at a temperature T class which is larger than the initial temperature T of the quantum gas. When T class significantly exceeds T a spurious damping is observed in the Wigner simulation. This leads to the second validity condition for the truncated Wigner method, T class - T

Wigner Functions for Arbitrary Quantum Systems.

Science.gov (United States)

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.

Semiclassical propagation: Hilbert space vs. Wigner representation

Science.gov (United States)

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 phase-space description of collision processes

International Nuclear Information System (INIS)

Lee, H.; Scully, M.O.

1983-01-01

This year marks the 50th anniversary of the birth of the celebrated Wigner distribution function. Many advances made in various areas of science during the 50 year period can be attributed to the physical insights that the Wigner distribution function provides when applied to specific problems. In this paper the usefulness of the Wigner distribution function in collision theory is described

Symmetry, Wigner functions and particle reactions

International Nuclear Information System (INIS)

Chavlejshvili, M.P.

1994-01-01

We consider the great principle of physics - symmetry - and some ideas, connected with it, suggested by a great physicist Eugene Wigner. We will discuss the concept of symmetry and spin, study the problem of separation of kinematics and dynamics in particle reactions. Using Wigner rotation functions (reflecting symmetry properties) in helicity amplitude decomposition and crossing-symmetry between helicity amplitudes (which contains the same Wigner functions) we get convenient general formalism for description of reactions between particles with any masses and spins. We also consider some applications of the formalism. 17 refs., 1 tab

On the treatment of light-ion electronic stopping in dense matter

Energy Technology Data Exchange (ETDEWEB)

Schiwietz, G. (Hahn-Meitner-Inst. Berlin GmbH, Div., FD (Germany)); Grande, P.L. (Hahn-Meitner-Inst. Berlin GmbH, Div., FD (Germany))

1994-05-01

A review is given on single-electron mechanisms and the corresponding theoretical approaches describing the electronic energy-transfer processes of light ions in gases and solids. Special emphasis is given to a discussion on the connection between exact Bloch-wave treatments and free-atom approximations. In the case of solids, perturbation theory is applied to the stopping of low-energy ions in the alkaline metals Li and Na. These calculations include Bloch wavefunctions of the Wigner-Seitz type obtained from a Hartree-Fock-Slater calculation and allow for a prediction of the mean energy loss under channeling conditions. Results of the most widely used local-density approximation are compared to data of our more complete perturbative treatment. Comparison is also made with recent LCAO calculations. (orig.)

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

Energy Technology Data Exchange (ETDEWEB)

Shao, Sihong, E-mail: sihong@math.pku.edu.cn [LMAM and School of Mathematical Sciences, Peking University, Beijing 100871 (China); Sellier, Jean Michel, E-mail: jeanmichel.sellier@parallel.bas.bg [IICT, Bulgarian Academy of Sciences, Acad. G. Bonchev str. 25A, 1113 Sofia (Bulgaria)

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 of 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.

Wigner functions and density matrices in curved spaces as computational tools

International Nuclear Information System (INIS)

Habib, S.; Kandrup, H.E.

1989-01-01

This paper contrasts two alternative approaches to statistical quantum field theory in curved spacetimes, namely (1) a canonical Hamiltonian approach, in which the basic object is a density matrix ρ characterizing the noncovariant, but globally defined, modes of the field; and (2) a Wigner function approach, in which the basic object is a Wigner function f defined quasilocally from the Hadamard, or correlation, function G 1 (x 1 , x 2 ). The key object is to isolate on the conceptual biases underlying each of these approaches and then to assess their utility and limitations in effecting concerete calculations. The following questions are therefore addressed and largely answered. What sort of spacetimes (e.g., de Sitter or Friedmann-Robertson-Walker) are comparatively eas to consider? What sorts of objects (e.g., average fields or renormalized stress energies) are easy to compute approximately? What, if anything, can be computed exactly? What approximations are intrinsic to each approach or convenient as computational tools? What sorts of ''field entropies'' are natural to define? copyright 1989 Academic Press, Inc

On the applicability of deformed jellium model to the description of metal clusters

DEFF Research Database (Denmark)

Lyalin, Andrey G.; Matveentsev, Anton; Solov'yov, Ilia

2003-01-01

-density approximation deformed jellium model we have calculated the binding energies per atom, ionization potentials, deformation parameters and the optimized values of the Wigner-Seitz radii for neutral and singly charged sodium clusters with the number of atoms $N0$. These characteristics are compared...... shape deformations in the formation cluster properties and the quite reasonable level of applicability of the deformed jellium model.......This work is devoted to the elucidation the applicability of jellium model to the description of alkali cluster properties on the basis of comparison the jellium model results with those derived from experiment and within ab initio theoretical framework. On the basis of the Hartree-Fock and local...

Fractional-Fourier-domain weighted Wigner distribution

NARCIS (Netherlands)

Stankovic, L.; Alieva, T.; Bastiaans, M.J.

2001-01-01

A fractional-Fourier-domain realization of the weighted Wigner distribution (or S-method), producing auto-terms close to the ones in the Wigner distribution itself, but with reduced cross-terms, is presented. The computational cost of this fractional-domain realization is the same as the

Generalized Wigner functions in curved spaces: A new approach

International Nuclear Information System (INIS)

Kandrup, H.E.

1988-01-01

It is well known that, given a quantum field in Minkowski space, one can define Wigner functions f/sub W//sup N/(x 1 ,p 1 ,...,x/sub N/,p/sub N/) which (a) are convenient to analyze since, unlike the field itself, they are c-number quantities and (b) can be interpreted in a limited sense as ''quantum distribution functions.'' Recently, Winter and Calzetta, Habib and Hu have shown one way in which these flat-space Wigner functions can be generalized to a curved-space setting, deriving thereby approximate kinetic equations which make sense ''quasilocally'' for ''short-wavelength modes.'' This paper suggests a completely orthogonal approach for defining curved-space Wigner functions which generalizes instead an object such as the Fourier-transformed f/sub W/ 1 (k,p), which is effectively a two-point function viewed in terms of the ''natural'' creation and annihilation operators a/sup dagger/(p-(12k) and a(p+(12k). The approach suggested here lacks the precise phase-space interpretation implicit in the approach of Winter or Calzetta, Habib, and Hu, but it is useful in that (a) it is geared to handle any ''natural'' mode decomposition, so that (b) it can facilitate exact calculations at least in certain limits, such as for a source-free linear field in a static spacetime

Wigner's function and other distribution functions in mock phase spaces

International Nuclear Information System (INIS)

Balazs, N.L.; Jennings, B.K.

1983-06-01

This review deals with the methods of associating functions with quantum mechanical operators in such a manner that these functions should furnish conveniently semiclassical approximations. We present a unified treatment of methods and result which usually appear under the expressions Wigner's functions, Weyl's association, Kirkwood's expansion, Glauber's coherent state representation, etc.; we also construct some new associations. The mathematical paraphernalia are collected in the appendices

Wigner function and tomogram of the pair coherent state

International Nuclear Information System (INIS)

Meng, Xiang-Guo; Wang, Ji-Suo; Fan, Hong-Yi

2007-01-01

Using the entangled state representation of Wigner operator and the technique of integration within an ordered product (IWOP) of operators, the Wigner function of the pair coherent state is derived. The variations of the Wigner function with the parameters α and q in the ρ-γ phase space are discussed. The physical meaning of the Wigner function for the pair coherent state is given by virtue of its marginal distributions. The tomogram of the pair coherent state is calculated with the help of the Radon transform between the Wigner operator and the projection operator of the entangled state |η 1 ,η 2 ,τ 1 ,τ 2 >

A diffusion-theoretical method to calculate the neutron flux distribution in multisphere configurations

International Nuclear Information System (INIS)

Schuerrer, F.

1980-01-01

For characterizing heterogene configurations of pebble-bed reactors the fine structure of the flux distribution as well as the determination of the macroscopic neutronphysical quantities are of interest. When calculating system parameters of Wigner-Seitz-cells the usual codes for neutron spectra calculation always neglect the modulation of the neutron flux by the influence of neighbouring spheres. To judge the error arising from that procedure it is necessary to determinate the flux distribution in the surrounding of a spherical fuel element. In the present paper an approximation method to calculate the flux distribution in the two-sphere model is developed. This method is based on the exactly solvable problem of the flux determination of a point source of neutrons in an infinite medium, which contains a spherical perturbation zone eccentric to the point source. An iteration method allows by superposing secondary fields and alternately satisfying the conditions of continuity on the surface of each of the two fuel elements to advance to continually improving approximations. (orig.) 891 RW/orig. 892 CKA [de

Wigner functions for fermions in strong magnetic fields

Science.gov (United States)

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.

Wigner method dynamics in the interaction picture

DEFF Research Database (Denmark)

Møller, Klaus Braagaard; Dahl, Jens Peder; Henriksen, Niels Engholm

1994-01-01

that the dynamics of the interaction picture Wigner function is solved by running a swarm of trajectories in the classical interaction picture introduced previously in the literature. Solving the Wigner method dynamics of collision processes in the interaction picture ensures that the calculated transition......The possibility of introducing an interaction picture in the semiclassical Wigner method is investigated. This is done with an interaction Picture description of the density operator dynamics as starting point. We show that the dynamics of the density operator dynamics as starting point. We show...... probabilities are unambiguous even when the asymptotic potentials are anharmonic. An application of the interaction picture Wigner method to a Morse oscillator interacting with a laser field is presented. The calculated transition probabilities are in good agreement with results obtained by a numerical...

Wigner function for the generalized excited pair coherent state

International Nuclear Information System (INIS)

Meng Xiangguo; Wang Jisuo; Liang Baolong; Li Hongqi

2008-01-01

This paper introduces the generalized excited pair coherent state (GEPCS). Using the entangled state |η> representation of Wigner operator, it obtains the Wigner function for the GEPCS. In the ρ-γ phase space, the variations of the Wigner function distributions with the parameters q, α, k and l are discussed. The tomogram of the GEPCS is calculated with the help of the Radon transform between the Wigner operator and the projection operator of the entangled state |η 1 , η 2 , τ 1 , τ 2 >. The entangled states |η> and η 1 , η 2 , τ 1 , τ 2 > provide two good representative space for studying the Wigner functions and tomograms of various two-mode correlated quantum states

Hydrogen atom in phase space: the Wigner representation

International Nuclear Information System (INIS)

Praxmeyer, Ludmila; Mostowski, Jan; Wodkiewicz, Krzysztof

2006-01-01

The hydrogen atom is a fundamental exactly soluble system for which the Wigner function, being a quantum analogue of the joint probability distribution of position and momentum, is unknown. In this paper, we present an effective method of calculating the Wigner function, for all bound states of the nonrelativistic hydrogen atom. The formal similarity between the eigenfunctions of the nonrelativistic hydrogen atom in the momentum representation and the Klein-Gordon propagator has allowed the calculation of the Wigner function for an arbitrary bound state of the hydrogen atom, using a simple atomic integral as a generator. These Wigner functions for some low-lying states are depicted and discussed

Wigner function for the Dirac oscillator in spinor space

International Nuclear Information System (INIS)

Ma Kai; Wang Jianhua; Yuan Yi

2011-01-01

The Wigner function for the Dirac oscillator in spinor space is studied in this paper. Firstly, since the Dirac equation is described as a matrix equation in phase space, it is necessary to define the Wigner function as a matrix function in spinor space. Secondly, the matrix form of the Wigner function is proven to support the Dirac equation. Thirdly, by solving the Dirac equation, energy levels and the Wigner function for the Dirac oscillator in spinor space are obtained. (authors)

Discrete Wigner Function Reconstruction and Compressed Sensing

OpenAIRE

Zhang, Jia-Ning; Fang, Lei; Ge, Mo-Lin

2011-01-01

A new reconstruction method for Wigner function is reported for quantum tomography based on compressed sensing. By analogy with computed tomography, Wigner functions for some quantum states can be reconstructed with less measurements utilizing this compressed sensing based method.

Wigner functions on non-standard symplectic vector spaces

Science.gov (United States)

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.

Neutrino diffusion in the pasta phase matter within the Thomas-Fermi approach

Energy Technology Data Exchange (ETDEWEB)

Furtado, U.J.; Avancini, S.S. [Universidade Federal de Santa Catarina, Departamento de Fisica, CFM, CP. 476, Florianopolis - SC (Brazil); University of Coimbra, CFisUC, Department of Physics, Coimbra (Portugal); Marinelli, J.R.; Martarello, W. [Universidade Federal de Santa Catarina, Departamento de Fisica, CFM, CP. 476, Florianopolis - SC (Brazil); Providencia, C. [University of Coimbra, CFisUC, Department of Physics, Coimbra (Portugal)

2016-09-15

The behaviour and properties of neutrinos in non-uniform nuclear matter, surrounded by electrons and other neutrinos are studied in the protoneutron star early stage characterized by trapped neutrinos. The nuclear matter itself is modelled by a relativistic mean-field approach, and models with both constant couplings and density-dependent couplings are considered. The so-called nuclear pasta phases at sub-saturation densities, described using the Thomas-Fermi approximation and solved in a Wigner-Seitz cell, are included in the calculation. We obtain the neutrino total cross section and mean free path, taking into account scattering and absorption processes and we compare the final results obtained with different parametrizations. The solution for this problem is important for the understanding of neutrino diffusion in a newly born neutron star after a supernovae explosion. It is shown that the pasta phase will increase the neutrino mean free path by as much as an order of magnitude, therefore contributing for shorter emission time-scales. (orig.)

Neutrino diffusion in the pasta phase matter within the Thomas-Fermi approach

International Nuclear Information System (INIS)

Furtado, U.J.; Avancini, S.S.; Marinelli, J.R.; Martarello, W.; Providencia, C.

2016-01-01

The behaviour and properties of neutrinos in non-uniform nuclear matter, surrounded by electrons and other neutrinos are studied in the protoneutron star early stage characterized by trapped neutrinos. The nuclear matter itself is modelled by a relativistic mean-field approach, and models with both constant couplings and density-dependent couplings are considered. The so-called nuclear pasta phases at sub-saturation densities, described using the Thomas-Fermi approximation and solved in a Wigner-Seitz cell, are included in the calculation. We obtain the neutrino total cross section and mean free path, taking into account scattering and absorption processes and we compare the final results obtained with different parametrizations. The solution for this problem is important for the understanding of neutrino diffusion in a newly born neutron star after a supernovae explosion. It is shown that the pasta phase will increase the neutrino mean free path by as much as an order of magnitude, therefore contributing for shorter emission time-scales. (orig.)

Experiences with the quadratic Korringa-Kohn-Rostoker band theory method

International Nuclear Information System (INIS)

Faulkner, J.S.

1992-01-01

This paper reports on the Quadratic Korriga-Kohn-Rostoker method which is a fast band theory method in the sense that all eigenvalues for a given k are obtained from one matrix diagonalization, but it differs from other fast band theory methods in that it is derived entirely from multiple-scattering theory, without the introduction of a Rayleigh-Ritz variations step. In this theory, the atomic potentials are shifted by Δσ(r) with Δ equal to E-E 0 and σ(r) equal to one when r is inside the Wigner-Seitz cell and zero otherwise, and it turns out that the matrix of coefficients is an entire function of Δ. This matrix can be terminated to give a linear KKR, quadratic KKR, cubic KKR,..., or not terminated at all to give the pivoted multiple-scattering equations. Full potential are no harder to deal with than potentials with a shape approximation

Wigner distribution function for an oscillator

International Nuclear Information System (INIS)

Davies, R.W.; Davies, K.T.R.

1975-01-01

We present two new derivations of the Wigner distribution function for a simple harmonic oscillator Hamiltonian. Both methods are facilitated using a formula which expresses the Wigner function as a simple trace. The first method of derivation utilizes a modification of a theorem due to Messiah. An alternative procedure makes use of the coherent state representation of an oscillator. The Wigner distribution function gives a semiclassical joint probability for finding the system with given coordinates and momenta, and the joint probability is factorable for the special case of an oscillator. An important application of this result occurs in the theory of nuclear fission for calculating the probability distributions for the masses, kinetic energies, and vibrational energies of the fission fragments at infinite separation. (U.S.)

Radon-Wigner transform for optical field analysis

NARCIS (Netherlands)

Alieva, T.; Bastiaans, M.J.; Nijhawan, O.P.; Gupta, A.K.; Musla, A.K.; Singh, Kehar

1998-01-01

The Radon-Wigner transform, associated with the intensity distribution in the fractional Fourier transform system, is used for the analysis of complex structures of coherent as well as partially coherent optical fields. The application of the Radon-Wigner transform to the analysis of fractal fields

Absence of single critical dose for the amorphization of quartz under ion irradiation

Science.gov (United States)

Zhang, S.; Pakarinen, O. H.; Backholm, M.; Djurabekova, F.; Nordlund, K.; Keinonen, J.; Wang, T. S.

2018-01-01

In this work, we first simulated the amorphization of crystalline quartz under 50 keV 23 Na ion irradiation with classical molecular dynamics (MD). We then used binary collision approximation algorithms to simulate the Rutherford backscattering spectrometry in channeling conditions (RBS-C) from these irradiated MD cells, and compared the RBS-C spectra with experiments. The simulated RBS-C results show an agreement with experiments in the evolution of amorphization as a function of dose, showing what appears to be (by this measure) full amorphization at about 2.2 eVṡatom-1 . We also applied other analysis methods, such as angular structure factor, Wigner-Seitz, coordination analysis and topological analysis, to analyze the structural evolution of the irradiated MD cells. The results show that the atomic-level structure of the sample keeps evolving after the RBS signal has saturated, until the dose of about 5 eVṡatom-1 . The continued evolution of the SiO2 structure makes the definition of what is, on the atomic level, an amorphized quartz ambiguous.

Some properties of the smoothed Wigner function

International Nuclear Information System (INIS)

Soto, F.; Claverie, P.

1981-01-01

Recently it has been proposed a modification of the Wigner function which consists in smoothing it by convolution with a phase-space gaussian function; this smoothed Wigner function is non-negative if the gaussian parameters Δ and delta satisfy the condition Δdelta > h/2π. We analyze in this paper the predictions of this modified Wigner function for the harmonic oscillator, for anharmonic oscillator and finally for the hydrogen atom. We find agreement with experiment in the linear case, but for strongly nonlinear systems, such as the hydrogen atom, the results obtained are completely wrong. (orig.)

Wigner Function of Density Operator for Negative Binomial Distribution

International Nuclear Information System (INIS)

Xu Xinglei; Li Hongqi

2008-01-01

By using the technique of integration within an ordered product (IWOP) of operator we derive Wigner function of density operator for negative binomial distribution of radiation field in the mixed state case, then we derive the Wigner function of squeezed number state, which yields negative binomial distribution by virtue of the entangled state representation and the entangled Wigner operator

Pure state condition for the semi-classical Wigner function

International Nuclear Information System (INIS)

Ozorio de Almeida, A.M.

1982-01-01

The Wigner function W(p,q) is a symmetrized Fourier transform of the density matrix e(q 1 ,q 2 ), representing quantum-mechanical states or their statistical mixture in phase space. Identification of these two alternatives in the case of density matrices depends on the projection identity e 2 = e; its Wigner correspondence is the pure state condition. This criterion is applied to the Wigner functions botained from standard semiclassical wave functions, determining as pure states those whose classical invariant tori satisfy the generalized Bohr-Sommerfeld conditions. Superpositions of eigenstates are then examined and it is found that the Wigner function corresponding to Gaussian random wave functions are smoothed out in the manner of mixedstate Wigner functions. Attention is also given to the pure-state condition in the case where an angular coordinate is used. (orig.)

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

Science.gov (United States)

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

Wigner Functions and Quark Orbital Angular Momentum

OpenAIRE

Mukherjee, Asmita; Nair, Sreeraj; Ojha, Vikash Kumar

2014-01-01

Wigner distributions contain combined position and momentum space information of the quark distributions and are related to both generalized parton distributions (GPDs) and transverse momentum dependent parton distributions (TMDs). We report on a recent model calculation of the Wigner distributions for the quark and their relation to the orbital angular momentum.

New Interpretation of the Wigner Function

Science.gov (United States)

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.

Classical effective Hamiltonians, Wigner functions, and the sign problem

International Nuclear Information System (INIS)

Samson, J.H.

1995-01-01

In the functional-integral technique an auxiliary field, coupled to appropriate operators such as spins, linearizes the interaction term in a quantum many-body system. The partition function is then averaged over this time-dependent stochastic field. Quantum Monte Carlo methods evaluate this integral numerically, but suffer from the sign (or phase) problem: the integrand may not be positive definite (or not real). It is shown that, in certain cases that include the many-band Hubbard model and the Heisenberg model, the sign problem is inevitable on fundamental grounds. Here, Monte Carlo simulations generate a distribution of incompatible operators---a Wigner function---from which expectation values and correlation functions are to be calculated; in general no positive-definite distribution of this form exists. The distribution of time-averaged auxiliary fields is the convolution of this operator distribution with a Gaussian of variance proportional to temperature, and is interpreted as a Boltzmann distribution exp(-βV eff ) in classical configuration space. At high temperatures and large degeneracies this classical effective Hamiltonian V eff tends to the static approximation as a classical limit. In the low-temperature limit the field distribution becomes a Wigner function, the sign problem occurs, and V eff is complex. Interpretations of the distributions, and a criterion for their positivity, are discussed. The theory is illustrated by an exact evaluation of the Wigner function for spin s and the effective classical Hamiltonian for the spin-1/2 van der Waals model. The field distribution can be negative here, more noticeably if the number of spins is odd

Characteristic and Wigner function for number difference and operational phase

International Nuclear Information System (INIS)

Fan Hongyi; Hu Haipeng

2004-01-01

We introduce the characteristic function in the sense of number difference-operational phase, and we employ the correlated-amplitude-number-difference state representation to calculate it. It results in the form of the corresponding Wigner function and Wigner operator. The marginal distributions of the generalized Wigner function are briefly discussed

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

Science.gov (United States)

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.

Wigner functions from the two-dimensional wavelet group.

Science.gov (United States)

Ali, S T; Krasowska, A E; Murenzi, R

2000-12-01

Following a general procedure developed previously [Ann. Henri Poincaré 1, 685 (2000)], here we construct Wigner functions on a phase space related to the similitude group in two dimensions. Since the group space in this case is topologically homeomorphic to the phase space in question, the Wigner functions so constructed may also be considered as being functions on the group space itself. Previously the similitude group was used to construct wavelets for two-dimensional image analysis; we discuss here the connection between the wavelet transform and the Wigner function.

Wigner Functions and Quark Orbital Angular Momentum

Directory of Open Access Journals (Sweden)

Mukherjee Asmita

2015-01-01

Full Text Available Wigner distributions contain combined position and momentum space information of the quark distributions and are related to both generalized parton distributions (GPDs and transverse momentum dependent parton distributions (TMDs. We report on a recent model calculation of the Wigner distributions for the quark and their relation to the orbital angular momentum.

Wigner particle theory and local quantum physics

International Nuclear Information System (INIS)

Fassarella, Lucio; Schroer, Bert

2002-01-01

Wigner's irreducible positive energy representations of the Poincare group are often used to give additional justifications for the Lagrangian quantization formalism of standard QFT. Here we study another more recent aspect. We explain in this paper modular concepts by which we are able to construct the local operator algebras for all standard positive energy representations directly without going through field coordinations. In this way the artificial emphasis on Lagrangian field coordinates is avoided from the very beginning. These new concepts allow to treat also those cases of 'exceptional' Wigner representations associated with anyons and the famous Wigner spin tower which have remained inaccessible to Lagrangian quantization. Together with the d=1+1 factorizing models (whose modular construction has been studied previously), they form an interesting family of theories with a rich vacuum-polarization structure (but no on shell real particle creation) to which the modular methods can be applied for their explicit construction. We explain and illustrate the algebraic strategy of this construction. We also comment on possibilities of formulating the Wigner theory in a setting of a noncommutativity. (author)

Time evolution of the Wigner function in the entangled-state representation

International Nuclear Information System (INIS)

Fan Hongyi

2002-01-01

For quantum-mechanical entangled states we introduce the entangled Wigner operator in the entangled-state representation. We derive the time evolution equation of the entangled Wigner operator . The trace product rule for entangled Wigner functions is also obtained

Thermal Wigner Operator in Coherent Thermal State Representation and Its Application

Institute of Scientific and Technical Information of China (English)

FAN HongYi

2002-01-01

In the coherent thermal state representation we introduce thermal Wigner operator and find that it is"squeezed" under the thermal transformation. The thermal Wigner operator provides us with a new direct and neatapproach for deriving Wigner functions of thermal states.

Scars of the Wigner Function.

Science.gov (United States)

Toscano; de Aguiar MA; Ozorio De Almeida AM

2001-01-01

We propose a picture of Wigner function scars as a sequence of concentric rings along a two-dimensional surface inside a periodic orbit. This is verified for a two-dimensional plane that contains a classical hyperbolic orbit of a Hamiltonian system with 2 degrees of freedom. The stationary wave functions are the familiar mixture of scarred and random waves, but the spectral average of the Wigner functions in part of the plane is nearly that of a harmonic oscillator and individual states are also remarkably regular. These results are interpreted in terms of the semiclassical picture of chords and centers.

Linear ray and wave optics in phase space bridging ray and wave optics via the Wigner phase-space picture

CERN Document Server

Torre, Amalia

2005-01-01

Ray, wave and quantum concepts are central to diverse and seemingly incompatible models of light. Each model particularizes a specific ''manifestation'' of light, and then corresponds to adequate physical assumptions and formal approximations, whose domains of applicability are well-established. Accordingly each model comprises its own set of geometric and dynamic postulates with the pertinent mathematical means.At a basic level, the book is a complete introduction to the Wigner optics, which bridges between ray and wave optics, offering the optical phase space as the ambience and the Wigner f

Application of the Wigner distribution function in optics

NARCIS (Netherlands)

Bastiaans, M.J.; Mecklenbräuker, W.; Hlawatsch, F.

1997-01-01

This contribution presents a review of the Wigner distribution function and of some of its applications to optical problems. The Wigner distribution function describes a signal in space and (spatial) frequency simultaneously and can be considered as the local frequency spectrum of the signal.

Thermal Wigner Operator in Coherent Thermal State Representation and Its Application

Institute of Scientific and Technical Information of China (English)

FANHong－Yi

2002-01-01

In the coherent thermal state representation we introduce thermal Wigner operator and find that it is “squeezed” under the thermal transformation.The thermal Wigner operator provides us with a new direct and neat approach for deriving Wigner functions of thermal states.

Study of nuclear statics and dynamics using the Wigner transform

International Nuclear Information System (INIS)

Shlomo, S.

1983-01-01

The Wigner phase-space distribution function, given as the shifted Fourier transform of the density matrix, provides a framework for an exact reformulation of non-relativistic quantum mechanics in terms of classical concepts. The Wigner distribution function (WDF), f(r-vector, p-vector), is considered as a quantum mechanical generalization of the classical phase space distribution function. While basic observables, such as matter density and momentum density, are given by the same integrals over f(r-vector, p-vector) as in classical physics, f(r-vector, p-vector) differs from its classical analog by the fact that it can assume negative values in some regions. However, it is known that the WDF is a useful and convenient tool for the study of the static and the dynamical aspects of many-body quantum systems, and the equation of motion for f(r-vector, p-vector) serves as a starting point for semi-classical approximations. The aim of this talk is to present and discuss some recent results for static and dynamic properties of nuclei obtained by exact evaluation of the WDF

Wigner Function of Thermo-Invariant Coherent State

International Nuclear Information System (INIS)

Xue-Fen, Xu; Shi-Qun, Zhu

2008-01-01

By using the thermal Winger operator of thermo-field dynamics in the coherent thermal state |ξ) representation and the technique of integration within an ordered product of operators, the Wigner function of the thermo-invariant coherent state |z,ℵ> is derived. The nonclassical properties of state |z,ℵ> is discussed based on the negativity of the Wigner function. (general)

Relativistic Wigner functions

Directory of Open Access Journals (Sweden)

Bialynicki-Birula Iwo

2014-01-01

Full Text Available Original definition of the Wigner function can be extended in a natural manner to relativistic domain in the framework of quantum field theory. Three such generalizations are described. They cover the cases of the Dirac particles, the photon, and the full electromagnetic field.

Applications of Wigner transformations in heavy-ion reactions

International Nuclear Information System (INIS)

Esbensen, H.

1981-01-01

We discuss a model, based on Wigner transformations and classical dynamics, that gives a semiclassical description of the excitation of surface vibrations due to the Coulomb and nuclear interaction in heavy-ion collisions. The treatment will consist of three stages, viz. the preparation of classical initial conditions compatible with the quantal ground state of surface vibrations, the dynamical evolution of the system governed by Liouville's equation (i.e. classical mechanics) and finally the interpretation, of final results after the interaction in terms of excitation probabilities, elastic and inelastic cross-sections, etc. The first and the last stage are exact and based on the Wigher transformations, while the time evolution described by classical mechanics is an approximation. We shall later return to the question of the applicability of this approximation and give some illustrative examples. (orig./HSI)

Wigner particle theory and local quantum physics

Energy Technology Data Exchange (ETDEWEB)

Fassarella, Lucio; Schroer, Bert [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]. E-mail: fassarel@cbpf.br; schroer@cbpf.br

2002-01-01

Wigner's irreducible positive energy representations of the Poincare group are often used to give additional justifications for the Lagrangian quantization formalism of standard QFT. Here we study another more recent aspect. We explain in this paper modular concepts by which we are able to construct the local operator algebras for all standard positive energy representations directly without going through field coordinations. In this way the artificial emphasis on Lagrangian field coordinates is avoided from the very beginning. These new concepts allow to treat also those cases of 'exceptional' Wigner representations associated with anyons and the famous Wigner spin tower which have remained inaccessible to Lagrangian quantization. Together with the d=1+1 factorizing models (whose modular construction has been studied previously), they form an interesting family of theories with a rich vacuum-polarization structure (but no on shell real particle creation) to which the modular methods can be applied for their explicit construction. We explain and illustrate the algebraic strategy of this construction. We also comment on possibilities of formulating the Wigner theory in a setting of a noncommutativity. (author)

Quantum phase space points for Wigner functions in finite-dimensional spaces

OpenAIRE

Luis Aina, Alfredo

2004-01-01

We introduce quantum states associated with single phase space points in the Wigner formalism for finite-dimensional spaces. We consider both continuous and discrete Wigner functions. This analysis provides a procedure for a direct practical observation of the Wigner functions for states and transformations without inversion formulas.

Quantum phase space points for Wigner functions in finite-dimensional spaces

International Nuclear Information System (INIS)

Luis, Alfredo

2004-01-01

We introduce quantum states associated with single phase space points in the Wigner formalism for finite-dimensional spaces. We consider both continuous and discrete Wigner functions. This analysis provides a procedure for a direct practical observation of the Wigner functions for states and transformations without inversion formulas

On the Debye temperature in the Slack approximation for an estimation of the thermal conductivity of nonmetallic compounds

International Nuclear Information System (INIS)

Bruls, R.; Hintzen, H.T.; Metselaar, R.

2005-01-01

The value of the Debye temperature of the acoustic modes, as required in the application of Slack's approximation [G. A. Slack, Solid State Physics, edited by F. Seitz, D. Turnbull, and H. Ehrenreich, (Academic, New York, 1979), Vol. 34, pp. 1-71] for the thermal conductivity, is not always available. It is shown that for these cases, the value at the minimum of the curve of the Debye temperature versus the temperature obtained from specific-heat data, gives a good approximation

The Wigner distribution function for the one-dimensional parabose oscillator

International Nuclear Information System (INIS)

Jafarov, E; Lievens, S; Jeugt, J Van der

2008-01-01

In the beginning of the 1950s, Wigner introduced a fundamental deformation from the canonical quantum mechanical harmonic oscillator, which is nowadays sometimes called a Wigner quantum oscillator or a parabose oscillator. Also, in quantum mechanics the so-called Wigner distribution is considered to be the closest quantum analogue of the classical probability distribution over the phase space. In this paper, we consider which definition for such a distribution function could be used in the case of non-canonical quantum mechanics. We then explicitly compute two different expressions for this distribution function for the case of the parabose oscillator. Both expressions turn out to be multiple sums involving (generalized) Laguerre polynomials. Plots then show that the Wigner distribution function for the ground state of the parabose oscillator is similar in behaviour to the Wigner distribution function of the first excited state of the canonical quantum oscillator

Trace forms for the generalized Wigner functions

Energy Technology Data Exchange (ETDEWEB)

D`Ariano, G. M. [Pavia, Univ. (Italy). Dipt. di Fisica ``Alessandro Volta``; Sacchi, M. F. [Evanston, Univ. (United States). Dept. of Electrical and Computer Engineering]|[Evanston, Univ. (United States). Dept. of Physics and Astronomy

1997-06-01

They derive simple formulas connecting the generalized Wigner functions for s-ordering with the density matrix, and vice versa. These formulas proved very useful for quantum-mechanical applications, as, for example, for connecting master equations with Fokker-Plank equations, or for evaluating the quantum state from Monte Carlo simulations of Fokker-Plank equations, and finally for studying positivity of the generalized Wigner functions in the complex plane.

Trace forms for the generalized Wigner functions

International Nuclear Information System (INIS)

D'Ariano, G. M.; Sacchi, M. F.; Evanston, Univ.

1997-01-01

They derive simple formulas connecting the generalized Wigner functions for s-ordering with the density matrix, and vice versa. These formulas proved very useful for quantum-mechanical applications, as, for example, for connecting master equations with Fokker-Plank equations, or for evaluating the quantum state from Monte Carlo simulations of Fokker-Plank equations, and finally for studying positivity of the generalized Wigner functions in the complex plane

A new formulation for the problem of fuel cell homogenization

International Nuclear Information System (INIS)

Chao, Y.-A.; Martinez, A.S.

1982-01-01

A new homogenization method for reactor cells is described. This new method consists in eliminating the NR approximation for the fuel resonance and the Wigner approximation for the resonance escape probability; the background cross section is then redefined and the problem studied is reanalyzed. (E.G.) [pt

Wigner's Symmetry Representation Theorem

Indian Academy of Sciences (India)

Home; Journals; Resonance – Journal of Science Education; Volume 19; Issue 10. Wigner's Symmetry Representation Theorem: At the Heart of Quantum Field Theory! Aritra Kr Mukhopadhyay. General Article Volume 19 Issue 10 October 2014 pp 900-916 ...

Fractional Wigner Crystal in the Helical Luttinger Liquid.

Science.gov (United States)

Traverso Ziani, N; Crépin, F; Trauzettel, B

2015-11-13

The properties of the strongly interacting edge states of two dimensional topological insulators in the presence of two-particle backscattering are investigated. We find an anomalous behavior of the density-density correlation functions, which show oscillations that are neither of Friedel nor of Wigner type: they, instead, represent a Wigner crystal of fermions of fractional charge e/2, with e the electron charge. By studying the Fermi operator, we demonstrate that the state characterized by such fractional oscillations still bears the signatures of spin-momentum locking. Finally, we compare the spin-spin correlation functions and the density-density correlation functions to argue that the fractional Wigner crystal is characterized by a nontrivial spin texture.

Specification of optical components using Wigner distribution function

International Nuclear Information System (INIS)

Xu Jiancheng; Li Haibo; Xu Qiao; Chai Liqun; Fan Changjiang

2010-01-01

In order to characterize and specify small-scale local wavefront deformation of optical component, a method based on Wigner distribution function has been proposed, which can describe wavefront deformation in spatial and spatial frequency domain. The relationship between Wigner distribution function and power spectral density is analyzed and thus the specification of small-scale local wavefront deformation is obtained by Wigner distribution function. Simulation and experiment demonstrate the effectiveness of the proposed method. The proposed method can not only identify whether the optical component meets the requirement of inertial confinement fusion (ICF), but also determine t he location where small-scale wavefront deformation is unqualified. Thus it provides an effective guide to the revision of unqualified optical components. (authors)

Generalized Reduction Formula for Discrete Wigner Functions of Multiqubit Systems

Science.gov (United States)

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.

Geometrical approach to the discrete Wigner function in prime power dimensions

International Nuclear Information System (INIS)

Klimov, A B; Munoz, C; Romero, J L

2006-01-01

We analyse the Wigner function in prime power dimensions constructed on the basis of the discrete rotation and displacement operators labelled with elements of the underlying finite field. We separately discuss the case of odd and even characteristics and analyse the algebraic origin of the non-uniqueness of the representation of the Wigner function. Explicit expressions for the Wigner kernel are given in both cases

Transformation of covariant quark Wigner operator to noncovariant one

International Nuclear Information System (INIS)

Selikhov, A.V.

1989-01-01

The gauge in which covariant and noncovariant quark Wigner operators coincide has been found. In this gauge the representations of vector potential via field strength tensor is valid. The system of equations for the coefficients of covariant Wigner operator expansion in the basis γ-matrices algebra is obtained. 12 refs.; 3 figs

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

Science.gov (United States)

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.

Wigner Ville Distribution in Signal Processing, using Scilab Environment

Directory of Open Access Journals (Sweden)

Petru Chioncel

2011-01-01

Full Text Available The Wigner Ville distribution offers a visual display of quantitative information about the way a signal’s energy is distributed in both, time and frequency. Through that, this distribution embodies the fundamentally concepts of the Fourier and time-domain analysis. The energy of the signal is distributed so that specific frequencies are localized in time by the group delay time and at specifics instants in time the frequency is given by the instantaneous frequency. The net positive volum of the Wigner distribution is numerically equal to the signal’s total energy. The paper shows the application of the Wigner Ville distribution, in the field of signal processing, using Scilab environment.

Adaption of optical Fresnel transform to optical Wigner transform

International Nuclear Information System (INIS)

Lv Cuihong; Fan Hongyi

2010-01-01

Enlightened by the algorithmic isomorphism between the rotation of the Wigner distribution function (WDF) and the αth fractional Fourier transform, we show that the optical Fresnel transform performed on the input through an ABCD system makes the output naturally adapting to the associated Wigner transform, i.e. there exists algorithmic isomorphism between ABCD transformation of the WDF and the optical Fresnel transform. We prove this adaption in the context of operator language. Both the single-mode and the two-mode Fresnel operators as the image of classical Fresnel transform are introduced in our discussions, while the two-mode Wigner operator in the entangled state representation is introduced for fitting the two-mode Fresnel operator.

Measurement-induced decoherence and Gaussian smoothing of the Wigner distribution function

International Nuclear Information System (INIS)

Chun, Yong-Jin; Lee, Hai-Woong

2003-01-01

We study the problem of measurement-induced decoherence using the phase-space approach employing the Gaussian-smoothed Wigner distribution function. Our investigation is based on the notion that measurement-induced decoherence is represented by the transition from the Wigner distribution to the Gaussian-smoothed Wigner distribution with the widths of the smoothing function identified as measurement errors. We also compare the smoothed Wigner distribution with the corresponding distribution resulting from the classical analysis. The distributions we computed are the phase-space distributions for simple one-dimensional dynamical systems such as a particle in a square-well potential and a particle moving under the influence of a step potential, and the time-frequency distributions for high-harmonic radiation emitted from an atom irradiated by short, intense laser pulses

Rigorous solution to Bargmann-Wigner equation for integer spin

CERN Document Server

Huang Shi Zhong; Wu Ning; Zheng Zhi Peng

2002-01-01

A rigorous method is developed to solve the Bargamann-Wigner equation for arbitrary integer spin in coordinate representation in a step by step way. The Bargmann-Wigner equation is first transformed to a form easier to solve, the new equations are then solved rigorously in coordinate representation, and the wave functions in a closed form are thus derived

Nodal Structure of the Electronic Wigner Function

DEFF Research Database (Denmark)

Schmider, Hartmut; Dahl, Jens Peder

1996-01-01

On the example of several atomic and small molecular systems, the regular behavior of nodal patterns in the electronic one-particle reduced Wigner function is demonstrated. An expression found earlier relates the nodal pattern solely to the dot-product of the position and the momentum vector......, if both arguments are large. An argument analogous to the ``bond-oscillatory principle'' for momentum densities links the nuclear framework in a molecule to an additional oscillatory term in momenta parallel to bonds. It is shown that these are visible in the Wigner function in terms of characteristic...

The Wigner distribution function for the su(2) finite oscillator and Dyck paths

International Nuclear Information System (INIS)

Oste, Roy; Jeugt, Joris Van der

2014-01-01

Recently, a new definition for a Wigner distribution function for a one-dimensional finite quantum system, in which the position and momentum operators have a finite (multiplicity-free) spectrum, was developed. This distribution function is defined on discrete phase-space (a finite square grid), and can thus be referred to as the Wigner matrix. In the current paper, we compute this Wigner matrix (or rather, the pre-Wigner matrix, which is related to the Wigner matrix by a simple matrix multiplication) for the case of the su(2) finite oscillator. The first expression for the matrix elements involves sums over squares of Krawtchouk polynomials, and follows from standard techniques. We also manage to present a second solution, where the matrix elements are evaluations of Dyck polynomials. These Dyck polynomials are defined in terms of the well-known Dyck paths. This combinatorial expression of the pre-Wigner matrix elements turns out to be particularly simple. (paper)

Wigner distribution function of Hermite-cosine-Gaussian beams through an apertured optical system.

Science.gov (United States)

Sun, Dong; Zhao, Daomu

2005-08-01

By introducing the hard-aperture function into a finite sum of complex Gaussian functions, the approximate analytical expressions of the Wigner distribution function for Hermite-cosine-Gaussian beams passing through an apertured paraxial ABCD optical system are obtained. The analytical results are compared with the numerically integrated ones, and the absolute errors are also given. It is shown that the analytical results are proper and that the calculation speed for them is much faster than for the numerical results.

An introduction to applied quantum mechanics in the Wigner Monte Carlo formalism

International Nuclear Information System (INIS)

Sellier, J.M.; Nedjalkov, M.; Dimov, I.

2015-01-01

The Wigner formulation of quantum mechanics is a very intuitive approach which allows the comprehension and prediction of quantum mechanical phenomena in terms of quasi-distribution functions. In this review, our aim is to provide a detailed introduction to this theory along with a Monte Carlo method for the simulation of time-dependent quantum systems evolving in a phase-space. This work consists of three main parts. First, we introduce the Wigner formalism, then we discuss in detail the Wigner Monte Carlo method and, finally, we present practical applications. In particular, the Wigner model is first derived from the Schrödinger equation. Then a generalization of the formalism due to Moyal is provided, which allows to recover important mathematical properties of the model. Next, the Wigner equation is further generalized to the case of many-body quantum systems. Finally, a physical interpretation of the negative part of a quasi-distribution function is suggested. In the second part, the Wigner Monte Carlo method, based on the concept of signed (virtual) particles, is introduced in detail for the single-body problem. Two extensions of the Wigner Monte Carlo method to quantum many-body problems are introduced, in the frameworks of time-dependent density functional theory and ab-initio methods. Finally, in the third and last part of this paper, applications to single- and many-body problems are performed in the context of quantum physics and quantum chemistry, specifically focusing on the hydrogen, lithium and boron atoms, the H 2 molecule and a system of two identical Fermions. We conclude this work with a discussion on the still unexplored directions the Wigner Monte Carlo method could take in the next future

The Wigner distribution function applied to optical signals and systems

NARCIS (Netherlands)

Bastiaans, M.J.

1978-01-01

In this paper the Wigner distribution function has been introduced for optical signals and systems. The Wigner distribution function of an optical signal appears to be in close resemblance to the ray concept in geometrical optics. This resemblance reaches even farther: although derived from Fourier

Wigner functions and tomograms of the photon-depleted even and odd coherent states

International Nuclear Information System (INIS)

Wang Jisuo; Meng Xiangguo

2008-01-01

Using the coherent state representation of Wigner operator and the technique of integration within an ordered product (IWOP) of operators, this paper derives the Wigner functions for the photon-depleted even and odd coherent states (PDEOCSs). Moreover, in terms of the Wigner functions with respect to the complex parameter α the nonclassical properties of the PDEOCSs are discussed. The results show that the nonclassicality for the state |β, m) o (or |β, m) e ) is more pronounced when m is even (or odd). According to the marginal distributions of the Wigner functions, the physical meaning of the Wigner functions is given. Further, the tomograms of the PDEOCSs are calculated with the aid of newly introduced intermediate coordinate-momentum representation in quantum optics

Existence of the Wigner function with correct marginal distributions along tilted lines on a lattice

International Nuclear Information System (INIS)

Horibe, Minoru; Takami, Akiyoshi; Hashimoto, Takaaki; Hayashi, Akihisa

2002-01-01

For the Wigner function of a system in N-dimensional Hilbert space, we propose the condition, which ensures that the Wigner function has correct marginal distributions along tilted lines. Under this condition we get the Wigner function without ambiguity if N is odd. If N is even, the Wigner function does not exist

Thermo Wigner operator in thermo field dynamics: its introduction and application

International Nuclear Information System (INIS)

Fan Hongyi; Jiang Nianquan

2008-01-01

Because in thermo-field dynamics (TFD) the thermo-operator has a neat expression in the thermo-entangled state representation, we need to introduce the thermo-Wigner operator (THWO) in the same representation. We derive the THWO in a direct way, which brings much conveniece to calculating the Wigner functions of thermo states in TFD. We also discuss the condition for existence of a wavefunction corresponding to a given Wigner function in the context of TFD by using the explicit form of the THWO.

Wigner functions for angle and orbital angular momentum. Operators and dynamics

Energy Technology Data Exchange (ETDEWEB)

Kastrup, Hans A. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Gruppe Theorie

2017-02-15

Recently a paper on the construction of consistent Wigner functions for cylindrical phase spaces S{sup 1} x R, i.e. for the canonical pair angle and orbital angular momentum, was presented, main properties of those functions derived, discussed and their usefulness illustrated by examples. The present paper is a continuation which compares properties of the new Wigner functions for cylindrical phase spaces with those of the well-known Wigner functions on planar ones in more detail. Furthermore, the mutual (Weyl) correspondence between HIlbert space operators and their phase space functions is discussed. The * product formalism is shown to be completely implementable. In addition basic dynamical laws for Wigner and Moyal functions are derived as generalized Liouville and energy equations. They are very similar to those of the planar case, but also show characteristic differences.

Wigner functions for angle and orbital angular momentum. Operators and dynamics

International Nuclear Information System (INIS)

Kastrup, Hans A.

2017-02-01

Recently a paper on the construction of consistent Wigner functions for cylindrical phase spaces S"1 x R, i.e. for the canonical pair angle and orbital angular momentum, was presented, main properties of those functions derived, discussed and their usefulness illustrated by examples. The present paper is a continuation which compares properties of the new Wigner functions for cylindrical phase spaces with those of the well-known Wigner functions on planar ones in more detail. Furthermore, the mutual (Weyl) correspondence between HIlbert space operators and their phase space functions is discussed. The * product formalism is shown to be completely implementable. In addition basic dynamical laws for Wigner and Moyal functions are derived as generalized Liouville and energy equations. They are very similar to those of the planar case, but also show characteristic differences.

Measurement of complete and continuous Wigner functions for discrete atomic systems

Science.gov (United States)

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.

Wigner Function Reconstruction in Levitated Optomechanics

Science.gov (United States)

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.

Higher-order stochastic differential equations and the positive Wigner function

Science.gov (United States)

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.

Discrete Wigner Function Derivation of the Aaronson–Gottesman Tableau Algorithm

Directory of Open Access Journals (Sweden)

Lucas Kocia

2017-07-01

Full Text Available The Gottesman–Knill theorem established that stabilizer states and Clifford operations can be efficiently simulated classically. For qudits with odd dimension three and greater, stabilizer states and Clifford operations have been found to correspond to positive discrete Wigner functions and dynamics. We present a discrete Wigner function-based simulation algorithm for odd-d qudits that has the same time and space complexity as the Aaronson–Gottesman algorithm for qubits. We show that the efficiency of both algorithms is due to harmonic evolution in the symplectic structure of discrete phase space. The differences between the Wigner function algorithm for odd-d and the Aaronson–Gottesman algorithm for qubits are likely due only to the fact that the Weyl–Heisenberg group is not in S U ( d for d = 2 and that qubits exhibit state-independent contextuality. This may provide a guide for extending the discrete Wigner function approach to qubits.

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

International Nuclear Information System (INIS)

Przanowski, Maciej; Brzykcy, Przemysław; Tosiek, Jaromir

2014-01-01

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 ^ 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

An introduction to applied quantum mechanics in the Wigner Monte Carlo formalism

Energy Technology Data Exchange (ETDEWEB)

Sellier, J.M., E-mail: jeanmichel.sellier@parallel.bas.bg [IICT, Bulgarian Academy of Sciences, Acad. G. Bonchev str. 25A, 1113 Sofia (Bulgaria); Nedjalkov, M. [IICT, Bulgarian Academy of Sciences, Acad. G. Bonchev str. 25A, 1113 Sofia (Bulgaria); Institute for Microelectronics, TU Wien, Gußhausstraße 27-29/E360, 1040 Wien (Austria); Dimov, I. [IICT, Bulgarian Academy of Sciences, Acad. G. Bonchev str. 25A, 1113 Sofia (Bulgaria)

2015-05-12

The Wigner formulation of quantum mechanics is a very intuitive approach which allows the comprehension and prediction of quantum mechanical phenomena in terms of quasi-distribution functions. In this review, our aim is to provide a detailed introduction to this theory along with a Monte Carlo method for the simulation of time-dependent quantum systems evolving in a phase-space. This work consists of three main parts. First, we introduce the Wigner formalism, then we discuss in detail the Wigner Monte Carlo method and, finally, we present practical applications. In particular, the Wigner model is first derived from the Schrödinger equation. Then a generalization of the formalism due to Moyal is provided, which allows to recover important mathematical properties of the model. Next, the Wigner equation is further generalized to the case of many-body quantum systems. Finally, a physical interpretation of the negative part of a quasi-distribution function is suggested. In the second part, the Wigner Monte Carlo method, based on the concept of signed (virtual) particles, is introduced in detail for the single-body problem. Two extensions of the Wigner Monte Carlo method to quantum many-body problems are introduced, in the frameworks of time-dependent density functional theory and ab-initio methods. Finally, in the third and last part of this paper, applications to single- and many-body problems are performed in the context of quantum physics and quantum chemistry, specifically focusing on the hydrogen, lithium and boron atoms, the H{sub 2} molecule and a system of two identical Fermions. We conclude this work with a discussion on the still unexplored directions the Wigner Monte Carlo method could take in the next future.

Wigner function and Schroedinger equation in phase-space representation

International Nuclear Information System (INIS)

Chruscinski, Dariusz; Mlodawski, Krzysztof

2005-01-01

We discuss a family of quasidistributions (s-ordered Wigner functions of Agarwal and Wolf [Phys. Rev. D 2, 2161 (1970); Phys. Rev. D 2, 2187 (1970); Phys. Rev. D 2, 2206 (1970)]) and its connection to the so-called phase space representation of the Schroedinger equation. It turns out that although Wigner functions satisfy the Schroedinger equation in phase space, they have a completely different interpretation

Wigner-Eisenbud-Smith photoionization time delay due to autoioinization resonances

Science.gov (United States)

Deshmukh, P. C.; Kumar, A.; Varma, H. R.; Banerjee, S.; Manson, Steven T.; Dolmatov, V. K.; Kheifets, A. S.

2018-03-01

An empirical ansatz for the complex photoionization amplitude and Wigner-Eisenbud-Smith time delay in the vicinity of a Fano autoionization resonance are proposed to evaluate and interpret the time delay in the resonant region. The utility of this expression is evaluated in comparison with accurate numerical calculations employing the ab initio relativistic random phase approximation and relativistic multichannel quantum defect theory. The indisputably good qualitative agreement (and semiquantitative agreement) between corresponding results of the proposed model and results produced by the ab initio theories proves the usability of the model. In addition, the phenomenology of the time delay in the vicinity of multichannel autoionizing resonances is detailed.

About the functions of the Wigner distribution for the q-deformed harmonic oscillator model

International Nuclear Information System (INIS)

Atakishiev, N.M.; Nagiev, S.M.; Djafarov, E.I.; Imanov, R.M.

2005-01-01

Full text : A q-deformed model of the linear harmonic oscillator in the Wigner phase-space is studied. It was derived an explicit expression for the Wigner probability distribution function, as well as the Wigner distribution function of a thermodynamic equilibrium for this model

Accessing the quark orbital angular momentum with Wigner distributions

Energy Technology Data Exchange (ETDEWEB)

Lorce, Cedric [IPNO, Universite Paris-Sud, CNRS/IN2P3, 91406 Orsay, France and LPT, Universite Paris-Sud, CNRS, 91406 Orsay (France); Pasquini, Barbara [Dipartimento di Fisica, Universita degli Studi di Pavia, Pavia, Italy and Istituto Nazionale di Fisica Nucleare, Sezione di Pavia, Pavia (Italy)

2013-04-15

The quark orbital angular momentum (OAM) has been recognized as an important piece of the proton spin puzzle. A lot of effort has been invested in trying to extract it quantitatively from the generalized parton distributions (GPDs) and the transverse-momentum dependent parton distributions (TMDs), which are accessed in high-energy processes and provide three-dimensional pictures of the nucleon. Recently, we have shown that it is more natural to access the quark OAM from the phase-space or Wigner distributions. We discuss the concept of Wigner distributions in the context of quantum field theory and show how they are related to the GPDs and the TMDs. We summarize the different definitions discussed in the literature for the quark OAM and show how they can in principle be extracted from the Wigner distributions.

Accessing the quark orbital angular momentum with Wigner distributions

International Nuclear Information System (INIS)

Lorcé, Cédric; Pasquini, Barbara

2013-01-01

The quark orbital angular momentum (OAM) has been recognized as an important piece of the proton spin puzzle. A lot of effort has been invested in trying to extract it quantitatively from the generalized parton distributions (GPDs) and the transverse-momentum dependent parton distributions (TMDs), which are accessed in high-energy processes and provide three-dimensional pictures of the nucleon. Recently, we have shown that it is more natural to access the quark OAM from the phase-space or Wigner distributions. We discuss the concept of Wigner distributions in the context of quantum field theory and show how they are related to the GPDs and the TMDs. We summarize the different definitions discussed in the literature for the quark OAM and show how they can in principle be extracted from the Wigner distributions.

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

International Nuclear Information System (INIS)

Bovino, F. A.; Colla, A. M.; Castagnoli, G.; Castelletto, S.; Degiovanni, I. P.; Rastello, M. L.

2003-01-01

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

Understanding squeezing of quantum states with the Wigner function

Science.gov (United States)

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.

Proof of a conjecture on the supports of Wigner distributions

NARCIS (Netherlands)

Janssen, A.J.E.M.

1998-01-01

In this note we prove that the Wigner distribution of an f ¿ L2(Rn) cannot be supported by a set of finite measure in R2n unless f = 0. We prove a corresponding statement for cross-ambiguity functions. As a strengthening of the conjecture we show that for an f ¿ L2(Rn) its Wigner distribution has a

Wigner function and the probability representation of quantum states

Directory of Open Access Journals (Sweden)

Man’ko Margarita A.

2014-01-01

Full Text Available The relation of theWigner function with the fair probability distribution called tomographic distribution or quantum tomogram associated with the quantum state is reviewed. The connection of the tomographic picture of quantum mechanics with the integral Radon transform of the Wigner quasidistribution is discussed. The Wigner–Moyal equation for the Wigner function is presented in the form of kinetic equation for the tomographic probability distribution both in quantum mechanics and in the classical limit of the Liouville equation. The calculation of moments of physical observables in terms of integrals with the state tomographic probability distributions is constructed having a standard form of averaging in the probability theory. New uncertainty relations for the position and momentum are written in terms of optical tomograms suitable for directexperimental check. Some recent experiments on checking the uncertainty relations including the entropic uncertainty relations are discussed.

A Wigner quasi-distribution function for charged particles in classical electromagnetic fields

International Nuclear Information System (INIS)

Levanda, M.; Fleurov, V.

2001-01-01

A gauge-invariant Wigner quasi-distribution function for charged particles in classical electromagnetic fields is derived in a rigorous way. Its relation to the axial gauge is discussed, as well as the relation between the kinetic and canonical momenta in the Wigner representation. Gauge-invariant quantum analogs of Hamilton-Jacobi and Boltzmann kinetic equations are formulated for arbitrary classical electromagnetic fields in terms of the 'slashed' derivatives and momenta, introduced for this purpose. The kinetic meaning of these slashed quantities is discussed. We introduce gauge-invariant conditional moments and use them to derive a kinetic momentum continuity equation. This equation provides us with a hydrodynamic representation for quantum transport processes and a definition of the 'collision force'. The hydrodynamic equation is applied for the rotation part of the electron motion. The theory is illustrated by its application in three examples: Wigner quasi-distribution function and equations for an electron in a magnetic field and harmonic potential; Wigner quasi-distribution function for a charged particle in periodic systems using the kq representation; two Wigner quasi-distribution functions for heavy-mass polaron in an electric field

The Kirillov picture for the Wigner particle

Science.gov (United States)

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.

A new class of ensemble conserving algorithms for approximate quantum dynamics: Theoretical formulation and model problems

International Nuclear Information System (INIS)

Smith, Kyle K. G.; Poulsen, Jens Aage; Nyman, Gunnar; Rossky, Peter J.

2015-01-01

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

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

Science.gov (United States)

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.

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

Science.gov (United States)

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.

On the Wigner law in dilute random matrices

Science.gov (United States)

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.

Adsorption of volatile metals on metal surfaces and the possibilities of its application in nuclear chemistry

International Nuclear Information System (INIS)

Eichler, B.; Huebener, S.; Rossbach, H.

1985-08-01

Using an empiric model partial molar enthalpies of adsorption of the rare earth metals at zero coverage have been calculated for the adsorbent metals Ti, Fe, Ni, Cu, Zr, Nb, Mo, Rh, Pd, Ag, Ta, W, Re, Ir, Pt, Au as well as Al, Si, Zn, Ge, Cd, and Pb. The electron densities at the boundary of the Wigner-Seitz cells in the rare earth metals, necessary for the calculations, have been derived from the crystal entropies. In some cases the magnetic entropy was considered too. The calculated enthalpies of adsorption are compared with experimental data taken from the literature. The valence state of adsorbed europium and ytterbium is discussed in relation to the nature of the adsorbent metal. (author)

A SAS2H/KENO-V Methodology for 3D Full Core depletion analysis

International Nuclear Information System (INIS)

Milosevic, M.; Greenspan, E.; Vujic, J.; Petrovic, B.

2003-04-01

This paper describes the use of a SAS2H/KENO-V methodology for 3D full core depletion analysis and illustrates its capabilities by applying it to burnup analysis of the IRIS core benchmarks. This new SAS2H/KENO-V sequence combines a 3D Monte Carlo full core calculation of node power distribution and a 1D Wigner-Seitz equivalent cell transport method for independent depletion calculation of each of the nodes. This approach reduces by more than an order of magnitude the time required for getting comparable results using the MOCUP code system. The SAS2H/KENO-V results for the asymmetric IRIS core benchmark are in good agreement with the results of the ALPHA/PHOENIX/ANC code system. (author)

Wigner representation in scattering problems

International Nuclear Information System (INIS)

Remler, E.A.

1975-01-01

The basic equations of quantum scattering are translated into the Wigner representation. This puts quantum mechanics in the form of a stochastic process in phase space. Instead of complex valued wavefunctions and transition matrices, one now works with real-valued probability distributions and source functions, objects more responsive to physical intuition. Aside from writing out certain necessary basic expressions, the main purpose is to develop and stress the interpretive picture associated with this representation and to derive results used in applications published elsewhere. The quasiclassical guise assumed by the formalism lends itself particularly to approximations of complex multiparticle scattering problems is laid. The foundation for a systematic application of statistical approximations to such problems. The form of the integral equation for scattering as well as its mulitple scattering expansion in this representation are derived. Since this formalism remains unchanged upon taking the classical limit, these results also constitute a general treatment of classical multiparticle collision theory. Quantum corrections to classical propogators are discussed briefly. The basic approximation used in the Monte Carlo method is derived in a fashion that allows for future refinement and includes bound state production. The close connection that must exist between inclusive production of a bound state and of its constituents is brought out in an especially graphic way by this formalism. In particular one can see how comparisons between such cross sections yield direct physical insight into relevant production mechanisms. A simple illustration of scattering by a bound two-body system is treated. Simple expressions for single- and double-scattering contributions to total and differential cross sections, as well as for all necessary shadow corrections thereto, are obtained and compared to previous results of Glauber and Goldberger

Symplectic evolution of Wigner functions in Markovian open systems.

Science.gov (United States)

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.

The Wigner distribution function and Hamilton's characteristics of a geometric-optical system

NARCIS (Netherlands)

Bastiaans, M.J.

1979-01-01

Four system functions have been defined for an optical system; each of these functions describes the system completely in terms of Fourier optics. From the system functions the Wigner distribution function of an optical system has been defined; although derived from Fourier optics, this Wigner

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

Science.gov (United States)

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.

Interpretation of the Wigner transform

International Nuclear Information System (INIS)

Casas, M.; Krivine, H.; Martorell, J.

1990-01-01

In quantum mechanics it is not possible to define a probability for finding a particle at position r with momentum p. Nevertheless there is a function introduced by Wigner, which retains many significant features of the classical probability distribution. Using simple one dimensional models we try to understand the very involved structure of this function

On the nodal structure of atomic and molecular Wigner functions

International Nuclear Information System (INIS)

Dahl, J.P.; Schmider, H.

1996-01-01

In previous work on the phase-space representation of quantum mechanics, we have presented detailed pictures of the electronic one-particle reduced Wigner function for atoms and small molecules. In this communication, we focus upon the nodal structure of the function. On the basis of the simplest systems, we present an expression which relates the oscillatory decay of the Wigner function solely to the dot product of the position and momentum vector, if both arguments are large. We then demonstrate the regular behavior of nodal patterns for the larger systems. For the molecular systems, an argument analogous to the open-quotes bond-oscillatory principleclose quotes for momentum densities links the nuclear framework to an additional oscillatory term in momenta parallel to bonds. It is shown that these are visible in the Wigner function in terms of characteristic nodes

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

International Nuclear Information System (INIS)

Jiang, Haiyan; Lu, Tiao; Cai, Wei

2014-01-01

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 at 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

Wigner-like crystallization of Anderson-localized electron systems with low electron densities

CERN Document Server

Slutskin, A A; Pepper, M

2002-01-01

We consider an electron system under conditions of strong Anderson localization, taking into account interelectron long-range Coulomb repulsion. We establish that at sufficiently low electron densities and sufficiently low temperatures the Coulomb electron interaction brings about ordering of the Anderson-localized electrons into a structure that is close to an ideal (Wigner) crystal lattice, provided the dimension of the system is > 1. This Anderson-Wigner glass (AWG) is a new macroscopic electron state that, on the one hand, is beyond the conventional Fermi glass concept, and on the other hand, qualitatively differs from the known 'plain' Wigner glass (inherent in self-localized electron systems) in that the random slight electron displacements from the ideal crystal sites essentially depend on the electron density. With increasing electron density the AWG is found to turn into the plain Wigner glass or Fermi glass, depending on the width of the random spread of the electron levels. It is shown that the res...

Comment on ‘Wigner function for a particle in an infinite lattice’

International Nuclear Information System (INIS)

Bizarro, João P S

2013-01-01

It is pointed out that in a recent paper (2012 New J. Phys. 14 103009) in which a Wigner function for a particle in an infinite lattice (a system described by an unbounded discrete coordinate and its conjugate angle-like momentum) has been introduced, no reference is made to previous, pioneering work on discrete Wigner distributions (more precisely, on the rotational Wigner function for a system described by a rotation angle and its unbounded discrete-conjugate angular momentum). Not only has the problem addressed in essence been solved for a long time (the discrete coordinate and angle-like conjugate momentum are the perfect dual of the rotation angle and discrete-conjugate angular momentum), but the solution advanced only in some distorted manner obeys two of the fundamental properties of a Wigner distribution (that, when integrated over one period of the momentum variable, it should yield the correct marginal distribution on the discrete position variable, and that it should be invariant with respect to translation). (comment)

Dynamics of the Wigner crystal of composite particles

Science.gov (United States)

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.

The Wigner distribution function for squeezed vacuum superposed state

International Nuclear Information System (INIS)

Zayed, E.M.E.; Daoud, A.S.; AL-Laithy, M.A.; Naseem, E.N.

2005-01-01

In this paper, we construct the Wigner distribution function for a single-mode squeezed vacuum mixed-state which is a superposition of the squeezed vacuum state. This state is defined as a P-representation for the density operator. The obtained Wigner function depends, beside the phase-space variables, on the mean number of photons occupied by the coherent state of the mode. This mean number relates to the mean free path through a given relation, which enables us to measure this number experimentally by measuring the mean free path

The Collected Works of Eugene Paul Wigner the Scientific Papers

CERN Document Server

Wigner, Eugene Paul

1993-01-01

Eugene Wigner is one of the few giants of 20th-century physics His early work helped to shape quantum mechanics, he laid the foundations of nuclear physics and nuclear engineering, and he contributed significantly to solid-state physics His philosophical and political writings are widely known All his works will be reprinted in Eugene Paul Wigner's Collected Workstogether with descriptive annotations by outstanding scientists The present volume begins with a short biographical sketch followed by Wigner's papers on group theory, an extremely powerful tool he created for theoretical quantum physics They are presented in two parts The first, annotated by B Judd, covers applications to atomic and molecular spectra, term structure, time reversal and spin In the second, G Mackey introduces to the reader the mathematical papers, many of which are outstanding contributions to the theory of unitary representations of groups, including the famous paper on the Lorentz group

A non-negative Wigner-type distribution

International Nuclear Information System (INIS)

Cartwright, N.D.

1976-01-01

The Wigner function, which is commonly used as a joint distribution for non-commuting observables, is shown to be non-negative in all quantum states when smoothed with a gaussian whose variances are greater than or equal to those of the minimum uncertainty wave packet. (Auth.)

Quantum Statistics of the Toda Oscillator in the Wigner Function Formalism

Science.gov (United States)

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.

Discrete Wigner functions and quantum computation

International Nuclear Information System (INIS)

Galvao, E.

2005-01-01

Full text: Gibbons et al. have recently defined a class of discrete Wigner functions W to represent quantum states in a finite Hilbert space dimension d. I characterize the set C d of states having non-negative W simultaneously in all definitions of W in this class. I then argue that states in this set behave classically in a well-defined computational sense. I show that one-qubit states in C 2 do not provide for universal computation in a recent model proposed by Bravyi and Kitaev [quant-ph/0403025]. More generally, I show that the only pure states in C d are stabilizer states, which have an efficient description using the stabilizer formalism. This result shows that two different notions of 'classical' states coincide: states with non-negative Wigner functions are those which have an efficient description. This suggests that negativity of W may be necessary for exponential speed-up in pure-state quantum computation. (author)

Friedel oscillations from the Wigner-Kirkwood distribution in half infinite matter

International Nuclear Information System (INIS)

Durand, M.; Schuck, P.; Vinas, X.

1985-01-01

The Wigner-Kirkwood expansion is derived in complete analogy to the low temperature expansion of the Fermi function showing that the Planck's constant and T play analogous roles in both cases. In detail however the Wigner distribution close to a surface is quite different from a Fermi function and we showed for instance that the Planck's constant expansion can account for the surface oscillations of the distribution

Nuclear Statistical Equilibrium for compact stars: modelling the nuclear energy functional

International Nuclear Information System (INIS)

Aymard, Francois

2015-01-01

and beyond. At densities above two-three times saturation, other degrees of freedom are expected to appear, which potentially lead to other consistency problems but this issue will not be treated in this thesis. The thesis is divided into three parts. In part I, we present the Nuclear Statistical Equilibrium model based on the grand canonical statistics and non-relativistic Skyrme interactions. Results at β-equilibrium are shown and the importance of the clusters distribution as well as a realistic treatment for the free energy model is discussed. Part II investigates the functional behavior of the baryonic energy in the Wigner-Seitz cell within the Extended-Thomas-Fermi approximation. In particular, both bulk and surface in-medium effects are studied, and their dependence on cluster size and asymmetry as well as gas densities and asymmetry is investigated. A preliminary result of in-medium surface effects is presented within some approximations in the case of β-equilibrated matter. In part III, we develop approximations in order to obtain a reliable analytical expression of the mass formula, directly linked to the functional form and parameters of the Skyrme interaction. In this part, we mainly focus on nuclei in vacuum, and analyse the different binding energy components in terms of bulk and surface properties, as well as isovector and isoscalar properties. (author)

Stochastic Nuclear Reaction Theory: Breit-Wigner nuclear noise

International Nuclear Information System (INIS)

de Saussure, G.; Perez, R.B.

1988-01-01

The purpose of this paper is the application of various statistical tests for the detection of the intermediate structure, which lies immersed in the Breit-Wigner ''noise'' arising from the superposition of many compound nucleus resonances. To this end, neutron capture cross sections are constructed by Monte-Carlo simulations of the compound nucleus, hence providing the ''noise'' component. In a second step intermediate structure is added to the Breit-Wigner noise. The performance of the statistical tests in detecting the intermediate structure is evaluated using mocked-up neutron cross sections as the statistical samples. Afterwards, the statistical tests are applied to actual nuclear cross section data. 10 refs., 1 fig., 2 tabs

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

Science.gov (United States)

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.

Entrainment in the inner crust of a neutron star

International Nuclear Information System (INIS)

Chamel, N.

2004-01-01

The inner crust of a neutron star, which is composed of a solid Coulomb lattice of nuclei immersed in a neutron super-fluid, is studied from both a macroscopic and a microscopic level. In the first part, we develop a non-relativistic but 4-dimensionally covariant formulation of the hydrodynamics of a perfect fluid mixture based on a variational principle. This formalism is applied to the description of neutron star crust as 2-fluid model, a neutron super-fluid and a plasma of nuclei and electrons coupled via non dissipative entrainment effects, whose microscopic evaluation is studied in a second part. Applying mean field methods beyond the Wigner-Seitz approximation, the Bragg scattering of dripped neutrons upon crustal nuclei lead to a 'mesoscopic' effective neutron mass, which unlike the 'microscopic' effective mass, takes very large values compared to the bare mass in the middle layers of the crust. (author)

Mean-field approximation for spacing distribution functions in classical systems

Science.gov (United States)

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.

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

International Nuclear Information System (INIS)

Gosson, Maurice A. de; Gosson, Serge M. de

2012-01-01

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. -- Highlights: ► Application of the cross-Wigner transform to a redefinition of the weak value of a quantum observable. ► Phase space approach to weak values, associated with a complex probability distribution. ► Opens perspectives for the study of retrodiction.

A second stage homogenization method

International Nuclear Information System (INIS)

Makai, M.

1981-01-01

A second homogenization is needed before the diffusion calculation of the core of large reactors. Such a second stage homogenization is outlined here. Our starting point is the Floquet theorem for it states that the diffusion equation for a periodic core always has a particular solution of the form esup(j)sup(B)sup(x) u (x). It is pointed out that the perturbation series expansion of function u can be derived by solving eigenvalue problems and the eigenvalues serve to define homogenized cross sections. With the help of these eigenvalues a homogenized diffusion equation can be derived the solution of which is cos Bx, the macroflux. It is shown that the flux can be expressed as a series of buckling. The leading term in this series is the well known Wigner-Seitz formula. Finally three examples are given: periodic absorption, a cell with an absorber pin in the cell centre, and a cell of three regions. (orig.)

Tunneling of an energy eigenstate through a parabolic barrier viewed from Wigner phase space

DEFF Research Database (Denmark)

Heim, D.M.; Schleich, W.P.; Alsing, P.M.

2013-01-01

We analyze the tunneling of a particle through a repulsive potential resulting from an inverted harmonic oscillator in the quantum mechanical phase space described by the Wigner function. In particular, we solve the partial differential equations in phase space determining the Wigner function...... of an energy eigenstate of the inverted oscillator. The reflection or transmission coefficients R or T are then given by the total weight of all classical phase-space trajectories corresponding to energies below, or above the top of the barrier given by the Wigner function....

Wigner distribution, partial coherence, and phase-space optics

NARCIS (Netherlands)

Bastiaans, M.J.

2009-01-01

The Wigner distribution is presented as a perfect means to treat partially coherent optical signals and their propagation through first-order optical systems from a radiometric and phase-space optical perspective

Wigner-like crystallization of Anderson-localized electron systems with low electron densities

International Nuclear Information System (INIS)

Slutskin, A.A.; Kovtun, H.A.; Pepper, M.

2002-01-01

We consider an electron system under conditions of strong Anderson localization, taking into account interelectron long-range Coulomb repulsion. We establish that at sufficiently low electron densities and sufficiently low temperatures the Coulomb electron interaction brings about ordering of the Anderson-localized electrons into a structure that is close to an ideal (Wigner) crystal lattice, provided the dimension of the system is > 1. This Anderson-Wigner glass (AWG) is a new macroscopic electron state that, on the one hand, is beyond the conventional Fermi glass concept, and on the other hand, qualitatively differs from the known 'plain' Wigner glass (inherent in self-localized electron systems) in that the random slight electron displacements from the ideal crystal sites essentially depend on the electron density. With increasing electron density the AWG is found to turn into the plain Wigner glass or Fermi glass, depending on the width of the random spread of the electron levels. It is shown that the residual disorder of the AWG is characterized by a multi-valley ground-state degeneracy akin to that in a spin glass. Some general features of the AWG are discussed, and a new conduction mechanism of a creep type is predicted

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

Science.gov (United States)

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

Qualities of Wigner function and its applications to one-dimensional infinite potential and one-dimensional harmonic oscillator

International Nuclear Information System (INIS)

Xu Hao; Shi Tianjun

2011-01-01

In this article,the qualities of Wigner function and the corresponding stationary perturbation theory are introduced and applied to one-dimensional infinite potential well and one-dimensional harmonic oscillator, and then the particular Wigner function of one-dimensional infinite potential well is specified and a special constriction effect in its pure state Wigner function is discovered, to which,simultaneously, a detailed and reasonable explanation is elaborated from the perspective of uncertainty principle. Ultimately, the amendment of Wigner function and energy of one-dimensional infinite potential well and one-dimensional harmonic oscillator under perturbation are calculated according to stationary phase space perturbation theory. (authors)

Commuting periodic operators and the periodic Wigner function

International Nuclear Information System (INIS)

Zak, J

2004-01-01

Commuting periodic operators (CPO) depending on the coordinate x-hat and the momentum p-hat operators are defined. The CPO are functions of the two basic commuting operators exp(i x-hat 2π/a) and exp(i/h p-hat a), with a being an arbitrary constant. A periodic Wigner function (PWF) w(x, p) is defined and it is shown that it is applicable in a normal expectation value calculation to the CPO, as done in the original Wigner paper. Moreover, this PWF is non-negative everywhere, and it can therefore be interpreted as an actual probability distribution. The PWF w(x, p) is shown to be given as an expectation value of the periodic Dirac delta function in the phase plane. (letter to the editor)

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

Science.gov (United States)

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.

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

Science.gov (United States)

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.

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

Science.gov (United States)

2014-03-27

WIGNER DISTRIBUTION FUNCTIONS AS A TOOL FOR STUDYING GAS PHASE ALKALI METAL PLUS NOBLE GAS COLLISIONS THESIS Keith A. Wyman, Second Lieutenant, USAF...the U.S. Government and is not subject to copyright protection in the United States. AFIT-ENP-14-M-39 WIGNER DISTRIBUTION FUNCTIONS AS A TOOL FOR...APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED AFIT-ENP-14-M-39 WIGNER DISTRIBUTION FUNCTIONS AS A TOOL FOR STUDYING GAS PHASE ALKALI METAL PLUS

On the probability density interpretation of smoothed Wigner functions

International Nuclear Information System (INIS)

De Aguiar, M.A.M.; Ozorio de Almeida, A.M.

1990-01-01

It has been conjectured that the averages of the Wigner function over phase space volumes, larger than those of minimum uncertainty, are always positive. This is true for Gaussian averaging, so that the Husimi distribution is positive. However, we provide a specific counterexample for the averaging with a discontinuous hat function. The analysis of the specific system of a one-dimensional particle in a box also elucidates the respective advantages of the Wigner and the Husimi functions for the study of the semiclassical limit. The falsification of the averaging conjecture is shown not to depend on the discontinuities of the hat function, by considering the latter as the limit of a sequence of analytic functions. (author)

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

Science.gov (United States)

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.

The universal Racah-Wigner symbol for Uq(osp(1|2))

International Nuclear Information System (INIS)

Pawelkiewicz, Michal; Schomerus, Volker; Suchanek, Paulina; Wroclaw Univ.

2013-10-01

We propose a new and elegant formula for the Racah-Wigner symbol of self-dual continuous series of representations of U q (osp(1 vertical stroke 2)). It describes the entire fusing matrix for both NS and R sector of N=1 supersymmetric Liouville field theory. In the NS sector, our formula is related to an expression derived in an earlier paper (L. Hadaz, M. Pawelkiewicz, and V. Schomerus, arXiv:1305.4596[hep-th]). Through analytic continuation in the spin variables, our universal expression reproduces known formulas for the Racah-Wigner coefficients of finite dimensional representations.

Study of the Wigner function at the device boundaries in one-dimensional single- and double-barrier structures

International Nuclear Information System (INIS)

Savio, Andrea; Poncet, Alain

2011-01-01

In this work, we compute the Wigner distribution function on one-dimensional devices from wave functions generated by solving the Schroedinger equation. Our goal is to investigate certain issues that we encountered in implementing Wigner transport equation solvers, such as the large discrepancies observed between the boundary conditions and the solution in the neighborhood of the boundaries. By evaluating the Wigner function without solving the Wigner transport equation, we intend to ensure that the actual boundary conditions are consistent with those commonly applied in literature. We study both single- and double-barrier unbiased structures. We use simple potential profiles, so that we can compute the wave functions analytically for better accuracy. We vary a number of structure geometry, material, meshing, and numerical parameters, among which are the contact length, the barrier height, the number of incident wave functions, and the numerical precision used for the computations, and we observe how the Wigner function at the device boundaries is affected. For the double-barrier structures, we look at the density matrix function and we study a model for the device transmission spectrum which helps explain the lobelike artifacts that we observe on the Wigner function.

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

Science.gov (United States)

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.

Comment on "Wigner phase-space distribution function for the hydrogen atom"

DEFF Research Database (Denmark)

Dahl, Jens Peder; Springborg, Michael

1999-01-01

We object to the proposal that the mapping of the three-dimensional hydrogen atom into a four-dimensional harmonic oscillator can be readily used to determine the Wigner phase-space distribution function for the hydrogen atom. [S1050-2947(99)07005-5].......We object to the proposal that the mapping of the three-dimensional hydrogen atom into a four-dimensional harmonic oscillator can be readily used to determine the Wigner phase-space distribution function for the hydrogen atom. [S1050-2947(99)07005-5]....

Equivalence between contextuality and negativity of the Wigner function for qudits

Science.gov (United States)

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.

Entanglement versus negative domains of Wigner functions

DEFF Research Database (Denmark)

Dahl, Jens Peder; Mack, H.; Wolf, A.

2006-01-01

We show that s waves, that is wave functions that only depend on a hyperradius, are entangled if and only if the corresponding Wigner functions exhibit negative domains. We illustrate this feature using a special class of s waves which allows us to perform the calculations analytically. This class...

Wess-Zumino term for the AdS superstring and generalized Inoenue-Wigner contraction

International Nuclear Information System (INIS)

Hatsuda, Machiko; Sakaguchi, Makoto

2003-01-01

We examine a Wess-Zumino term, written in a form of bilinear in superinvariant currents, for a superstring in anti-de Sitter (AdS) space, and derive a procedure for obtaining the correct flat limit. The standard Inoenue-Wigner contraction does not give the correct flat limit but, rather, gives zero. This erroneous result originates from the fact that the fermionic metric of the super-Poincare group is degenerate. We propose a generalization of the Inoenue-Wigner contraction from which a 'nondegenerate' super-Poincare group is derived from the super-AdS group. For this reason, this contraction gives the correct flat limit of this Wess-Zumino term. We also discuss the M-algebra obtained using this generalized Inoenue-Wigner contraction from osp(1|32). (author)

Wigner Function:from Ensemble Average of Density Operator to Its One Matrix Element in Entangled Pure States

Institute of Scientific and Technical Information of China (English)

FAN Hong-Yi

2002-01-01

We show that the Wigner function W = Tr(△ρ) (an ensemble average of the density operator ρ, △ is theWigner operator) can be expressed as a matrix element of ρ in the entangled pure states. In doing so, converting fromquantum master equations to time-evolution equation of the Wigner functions seems direct and concise. The entangledstates are defined in the enlarged Fock space with a fictitious freedom.

Band-Structure of Thallium by the LMTO Method

DEFF Research Database (Denmark)

Holtham, P. M.; Jan, J. P.; Skriver, Hans Lomholt

1977-01-01

by an energy gap. The 6d and 7s bands were found to be far above the Fermi level and the 5d states were found to be far below it. Fermi surface properties and the electronic specific heat are computed and compared with experiment. The joint density of states has also been computed and is in reasonable...... and p bands for the HCP structure. Energy bands have been evaluated both with and without spin-orbit coupling which is particularly large in thallium. Energy bands close to the Fermi level were found to be mainly 6p like in character. The 6s states lay below the 6p bands and were separated from them......The relativistic band structure of thallium has been calculated using the linear muffin-tin orbital (LMTO) method. The positions and extents of the bands were found to follow the Wigner-Seitz rule approximately, and the origin of the dispersion of the bands was established from the canonical s...

Subcritical nuclear assembly

Energy Technology Data Exchange (ETDEWEB)

Vega C, H. R., E-mail: fermineutron@yahoo.com [Universidad Autonoma de Zacatecas, Unidad Academica de Estudios Nucleares, Cipres No. 10, Fracc. La Penuela, 98068 Zacatecas (Mexico)

2014-08-15

A Subcritical Nuclear Assembly is a device where the nuclear-fission chain reaction is initiated and maintained using an external neutron source. It is a valuable educational and research tool where in a safe way many reactor parameters can be measured. Here, we have used the Wigner-Seitz method in the six-factor formula to calculate the effective multiplication factor of a subcritical nuclear reactor Nuclear Chicago model 9000. This reactor has approximately 2500 kg of natural uranium heterogeneously distributed in slugs. The reactor uses a {sup 239}PuBe neutron source that is located in the center of an hexagonal array. Using Monte Carlo methods, with the MCNP5 code, a three-dimensional model of the subcritical reactor was designed to estimate the effective multiplication factor, the neutron spectra, the total and thermal neutron fluences along the radial and axial axis. With the neutron spectra in two locations outside the reactor the ambient dose equivalent were estimated. (Author)

Subcritical nuclear assembly

International Nuclear Information System (INIS)

Vega C, H. R.

2014-08-01

A Subcritical Nuclear Assembly is a device where the nuclear-fission chain reaction is initiated and maintained using an external neutron source. It is a valuable educational and research tool where in a safe way many reactor parameters can be measured. Here, we have used the Wigner-Seitz method in the six-factor formula to calculate the effective multiplication factor of a subcritical nuclear reactor Nuclear Chicago model 9000. This reactor has approximately 2500 kg of natural uranium heterogeneously distributed in slugs. The reactor uses a 239 PuBe neutron source that is located in the center of an hexagonal array. Using Monte Carlo methods, with the MCNP5 code, a three-dimensional model of the subcritical reactor was designed to estimate the effective multiplication factor, the neutron spectra, the total and thermal neutron fluences along the radial and axial axis. With the neutron spectra in two locations outside the reactor the ambient dose equivalent were estimated. (Author)

Generalised Wigner surmise for (2 X 2) random matrices

International Nuclear Information System (INIS)

Chau Huu-Tai, P.; Van Isacker, P.; Smirnova, N.A.

2001-01-01

We present new analytical results concerning the spectral distributions for (2 x 2) random real symmetric matrices which generalize the Wigner surmise. The study of the statistical properties of spectra of realistic many-body Hamiltonians requires consideration of a random matrix ensemble whose elements are not independent or whose distribution is not invariant under orthogonal transformation of a chosen basis. In this letter we have concentrated on the properties of (2 x 2) real symmetric matrices whose elements are independent Gaussian variables with zero means but do not belong to the GOE. We have derived the distribution of eigenvalues for such a matrix, the nearest-neighbour spacing distribution which generalizes the Wigner surmise and we have calculated some important moments. (authors)

Mixed-space formalism for the dielectric response in periodic systems

International Nuclear Information System (INIS)

Blase, X.; Rubio, A.; Louie, S.G.; Cohen, M.L.

1995-01-01

We present a useful formalism for the calculation of the polarizability and dielectric response of periodic systems. Our approach is to introduce intermediate ''mixed-space'' functions with the full translational periodicity of the lattice. This is a considerable advantage over existing real-space methods since the decay length of a response function [such as ε(r,r'|ω)] can be significantly larger than the Wigner-Seitz cell radius. Further, we show that, in supercell calculations, these mixed-space functions decay as fast as the corresponding real-space quantities within one supercell, so that the present scheme can be combined with usual real-space cutoff techniques. The advantage of the present method compared to a standard reciprocal space approach is exemplified for the case of bulk silicon and for the case of a Si surface in a slab geometry

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

Science.gov (United States)

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.

Wigner-Kirkwood expansion of the phase-space density for half infinite nuclear matter

International Nuclear Information System (INIS)

Durand, M.; Schuck, P.

1987-01-01

The phase space distribution of half infinite nuclear matter is expanded in a ℎ-series analogous to the low temperature expansion of the Fermi function. Besides the usual Wigner-Kirkwood expansion, oscillatory terms are derived. In the case of a Woods-Saxon potential, a smallness parameter is defined, which determines the convergence of the series and explains the very rapid convergence of the Wigner-Kirkwood expansion for average (nuclear) binding energies

An elementary aspect of the Weyl-Wigner representation

DEFF Research Database (Denmark)

Dahl, Jens Peder; Schleich, W.P.

2003-01-01

It is an elementary aspect of the Weyl-Wigner representation of quantum mechanics that the dynamical phase-space function corresponding to the square of a quantum-mechanical operator is, in general, different from the square of the function representing the operator itself. We call attention...

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

Science.gov (United States)

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 expansions for partition functions of nonrelativistic and relativistic oscillator systems

Science.gov (United States)

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.

Wigner measure and semiclassical limits of nonlinear Schrödinger equations

CERN Document Server

Zhang, Ping

2008-01-01

This book is based on a course entitled "Wigner measures and semiclassical limits of nonlinear Schrödinger equations," which the author taught at the Courant Institute of Mathematical Sciences at New York University in the spring of 2007. The author's main purpose is to apply the theory of semiclassical pseudodifferential operators to the study of various high-frequency limits of equations from quantum mechanics. In particular, the focus of attention is on Wigner measure and recent progress on how to use it as a tool to study various problems arising from semiclassical limits of Schrödinger-ty

Wigner functions for a class of semi-direct product groups

International Nuclear Information System (INIS)

Krasowska, Anna E; Ali, S Twareque

2003-01-01

Following a general method proposed earlier, we construct here Wigner functions defined on coadjoint orbits of a class of semidirect product groups. The groups in question are such that their unitary duals consist purely of representations from the discrete series and each unitary irreducible representation is associated with a coadjoint orbit. The set of all coadjoint orbits (hence UIRs) is finite and their union is dense in the dual of the Lie algebra. The simple structure of the groups and the orbits enables us to compute the various quantities appearing in the definition of the Wigner function explicitly. A large number of examples, with potential use in image analysis, is worked out

Wigner's function and other distribution functions in mock phase space

International Nuclear Information System (INIS)

Balazs, N.L.

1984-01-01

This review deals with the methods of associating functions with quantum mechanical operators in such a manner that these functions should furnish conveniently semiclassical approximations. We present a unified treatment of methods and results which usually appear under expressions such as Wigner's function. Weyl's association, Kirkwood's expansion, Glauber's coherent state representation, etc.; we also construct some new associations. Section 1 gives the motivation by discussing the Thomas-Fermi theory of an atom with this end in view. Section 2 introduce new operators which resemble Dirac delta functions with operator arguments, the operators being the momenta and coordinates. Reasons are given as to why this should be useful. Next we introduce the notion of an operator basis, and discuss the possibility and usefulness of writing an operator as a linear combination of the basis operators. The coefficients in the linear combination are c-numbers and the c-numbers are associated with the operator (in that particularly basis). The delta function type operators introduced before can be used as a basis for the dynamical operators, and the c-numbers obtained in this manner turn out to be the c-number functions used by Wigner, Weyl, Krikwood, Glauber, etc. New bases and associations can now be invented at will. One such new basis is presented and discussed. The reason and motivations for choosing different bases is then explained. The copious and seemingly random mathematical relations between these functions are then nothing else but the relations between the expansion coefficients engendered by the relations between bases. These are shown and discussed in this light. A brief discussion is then given to possible transformation of the p, q labels. Section 3 gives examples of how the semiclassical expansions are generated for these functions and exhibits their equivalence. The mathematical paraphernalia are collected in the appendices. (orig.)

Pinning mode of integer quantum Hall Wigner crystal of skyrmions

Science.gov (United States)

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).

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

International Nuclear Information System (INIS)

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

2011-01-01

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 16 O + 16 O and 96 Zr + 132 Sn collisions. Although we observe strong dissipation in the time 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.

The Wigner representation of classical mechanics, quantization and classical limit

Energy Technology Data Exchange (ETDEWEB)

Bolivar, A.O. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)

2001-08-01

Starting from the Liouvillian formulation of classical physics it is possible by means of a Fourier transform to introduce the Wigner representation and to derive an operator structure to classical mechanisms. The importance of this new representation lies on the fact that it turns out to be suitable route to establish a general method of quantization directly from the equations of motion without alluding to the existence of Hamiltonian and Lagrangian functions. Following this approach we quantize only the motion of a Browian particle with non-linear friction in the Markovian approximation - the thermal bath may be quantum or classical -, thus when the bath is classically described we obtain a master equation which reduces to Caldeira-Legget equation for the linear friction case, and when the reservoir is quantum we get an equation reducing to the one found by Caldeira et al. By neglecting the environmental influence we show that the system can be approximately described by equations of motion in terms of wave function, such as the Schrodinger-Langevin equation and equations of the Caldirola-Kanai type. Finally to make the present study self-consistent we evaluate the classical limit of these dynamical equations employing a new classical limiting method h/2{pi} {yields} 0. (author)

The Wigner representation of classical mechanics, quantization and classical limit

International Nuclear Information System (INIS)

Bolivar, A.O.

2001-08-01

Starting from the Liouvillian formulation of classical physics it is possible by means of a Fourier transform to introduce the Wigner representation and to derive an operator structure to classical mechanisms. The importance of this new representation lies on the fact that it turns out to be suitable route to establish a general method of quantization directly from the equations of motion without alluding to the existence of Hamiltonian and Lagrangian functions. Following this approach we quantize only the motion of a Browian particle with non-linear friction in the Markovian approximation - the thermal bath may be quantum or classical -, thus when the bath is classically described we obtain a master equation which reduces to Caldeira-Legget equation for the linear friction case, and when the reservoir is quantum we get an equation reducing to the one found by Caldeira et al. By neglecting the environmental influence we show that the system can be approximately described by equations of motion in terms of wave function, such as the Schrodinger-Langevin equation and equations of the Caldirola-Kanai type. Finally to make the present study self-consistent we evaluate the classical limit of these dynamical equations employing a new classical limiting method h/2π → 0. (author)

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

Science.gov (United States)

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.

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

Science.gov (United States)

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.

Wigner higher-order spectra: definition, properties, computation and application to transient signal analysis

OpenAIRE

Rodríguez Fonollosa, Javier; Nikias, Chrysostomos L.

1993-01-01

The Wigner higher order moment spectra (WHOS) are defined as extensions of the Wigner-Ville distribution (WD) to higher order moment spectra domains. A general class of time-frequency higher order moment spectra is also defined in terms of arbitrary higher order moments of the signal as generalizations of the Cohen’s general class of time-frequency representations. The properties of the general class of time-frequency higher order moment spectra can be related to the properties...

A Quantum Version of Wigner's Transition State Theory

NARCIS (Netherlands)

Schubert, R.; Waalkens, H.; Wiggins, S.

A quantum version of a recent realization of Wigner's transition state theory in phase space is presented. The theory developed builds on a quantum normal form which locally decouples the quantum dynamics near the transition state to any desired order in (h) over bar. This leads to an explicit

On the hydrogen atom via Wigner-Heisenberg algebra

International Nuclear Information System (INIS)

Rodrigues, R. de Lima . Unidade Academica de Educacao.

2008-01-01

We extend the usual Kustaanheimo-Stiefel 4D → 3D mapping to study and discuss a constrained super-Wigner oscillator in four dimensions. We show that the physical hydrogen atom is the system that emerges in the bosonic sector of the mapped super 3D system. (author)

Evidence of Wigner rotation phenomena in the beam splitting experiment at the LCLS

International Nuclear Information System (INIS)

Geloni, Gianluca; Kocharyan, Vitali; Saldin, Evgeni

2016-07-01

A result from particle tracking states that, after a microbunched electron beam is kicked, its trajectory changes while the orientation of the microbunching wavefront remains as before. Experiments at the LCLS showed that radiation in the kicked direction is produced practically without suppression. This could be explained if the orientation of the microbunching wavefront is readjusted along the kicked direction. In previous papers we showed that when the evolution of the electron beam modulation is treated according to relativistic kinematics, the orientation of the microbunching wavefront in the ultrarelativistic asymptotic is always perpendicular to the electron beam velocity. There we refrained from using advanced theoretical concepts to explain or analyze the wavefront rotation. For example, we only hinted to the relation of this phenomenon with the concept of Wigner rotation. This more abstract view of wavefront rotation underlines its elementary nature. The Wigner rotation is known as a fundamental effect in elementary particle physics. The composition of non collinear boosts does not result in a simple boost but, rather, in a Lorentz transformation involving a boost and a rotation, the Wigner rotation. Here we show that during the LCLS experiments, a Wigner rotation was actually directly recorded for the first time with a ultrarelativistic, macroscopic object: an ultrarelativistic electron bunch in an XFEL modulated at nm-scale of the size of about 10 microns. Here we point out the role of Wigner rotation in the analysis and interpretation of experiments with ultrarelativistic, microbunched electron beams in FELs. After the beam splitting experiment at the LCLS it became clear that, in the ultrarelativistic asymptotic, the projection of the microbunching wave vector onto the beam velocity is a Lorentz invariant, similar to the helicity in particle physics.

Evidence of Wigner rotation phenomena in the beam splitting experiment at the LCLS

Energy Technology Data Exchange (ETDEWEB)

Geloni, Gianluca [European XFEL GmbH, Hamburg (Germany); Kocharyan, Vitali; Saldin, Evgeni [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)

2016-07-15

A result from particle tracking states that, after a microbunched electron beam is kicked, its trajectory changes while the orientation of the microbunching wavefront remains as before. Experiments at the LCLS showed that radiation in the kicked direction is produced practically without suppression. This could be explained if the orientation of the microbunching wavefront is readjusted along the kicked direction. In previous papers we showed that when the evolution of the electron beam modulation is treated according to relativistic kinematics, the orientation of the microbunching wavefront in the ultrarelativistic asymptotic is always perpendicular to the electron beam velocity. There we refrained from using advanced theoretical concepts to explain or analyze the wavefront rotation. For example, we only hinted to the relation of this phenomenon with the concept of Wigner rotation. This more abstract view of wavefront rotation underlines its elementary nature. The Wigner rotation is known as a fundamental effect in elementary particle physics. The composition of non collinear boosts does not result in a simple boost but, rather, in a Lorentz transformation involving a boost and a rotation, the Wigner rotation. Here we show that during the LCLS experiments, a Wigner rotation was actually directly recorded for the first time with a ultrarelativistic, macroscopic object: an ultrarelativistic electron bunch in an XFEL modulated at nm-scale of the size of about 10 microns. Here we point out the role of Wigner rotation in the analysis and interpretation of experiments with ultrarelativistic, microbunched electron beams in FELs. After the beam splitting experiment at the LCLS it became clear that, in the ultrarelativistic asymptotic, the projection of the microbunching wave vector onto the beam velocity is a Lorentz invariant, similar to the helicity in particle physics.

A generalized Wigner function on the space of irreducible representations of the Weyl-Heisenberg group and its transformation properties

International Nuclear Information System (INIS)

Ibort, A; Man'ko, V I; Marmo, G; Simoni, A; Ventriglia, F

2009-01-01

A natural extension of the Wigner function to the space of irreducible unitary representations of the Weyl-Heisenberg group is discussed. The action of the automorphisms group of the Weyl-Heisenberg group onto Wigner functions and their generalizations and onto symplectic tomograms is elucidated. Some examples of physical systems are considered to illustrate some aspects of the characterization of the Wigner functions as solutions of differential equations

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

Science.gov (United States)

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.

Entanglement and Wigner Function Negativity of Multimode Non-Gaussian States

Science.gov (United States)

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.

Numerical methods for characterization of synchrotron radiation based on the Wigner function method

Directory of Open Access Journals (Sweden)

Takashi Tanaka

2014-06-01

Full Text Available Numerical characterization of synchrotron radiation based on the Wigner function method is explored in order to accurately evaluate the light source performance. A number of numerical methods to compute the Wigner functions for typical synchrotron radiation sources such as bending magnets, undulators and wigglers, are presented, which significantly improve the computation efficiency and reduce the total computation time. As a practical example of the numerical characterization, optimization of betatron functions to maximize the brilliance of undulator radiation is discussed.

Vacancies in quantal Wigner crystals near melting

International Nuclear Information System (INIS)

Barraza, N.; Colletti, L.; Tosi, M.P.

1999-04-01

We estimate the formation energy of lattice vacancies in quantal Wigner crystals of charged particles near their melting point at zero temperature, in terms of the crystalline Lindemann parameter and of the static dielectric function of the fluid phase near freezing. For both 3D and 2D crystals of electrons our results suggest the presence of vacancies in the ground state at the melting density. (author)

A Wigner-based ray-tracing method for imaging simulations

NARCIS (Netherlands)

Mout, B.M.; Wick, M.; Bociort, F.; Urbach, H.P.

2015-01-01

The Wigner Distribution Function (WDF) forms an alternative representation of the optical field. It can be a valuable tool for understanding and classifying optical systems. Furthermore, it possesses properties that make it suitable for optical simulations: both the intensity and the angular

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

Science.gov (United States)

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

Mapping the Wigner distribution function of the Morse oscillator onto a semiclassical distribution function

International Nuclear Information System (INIS)

Bund, G W; Tijero, M C

2004-01-01

The mapping of the Wigner distribution function (WDF) for a given bound state onto a semiclassical distribution function (SDF) satisfying the Liouville equation introduced previously by us is applied to the ground state of the Morse oscillator. The purpose of the present work is to obtain values of the potential parameters represented by the number of levels in the case of the Morse oscillator, for which the SDF becomes a faithful approximation of the corresponding WDF. We find that for a Morse oscillator with one level only, the agreement between the WDF and the mapped SDF is very poor but for a Morse oscillator of ten levels it becomes satisfactory. We also discuss the limit ℎ → 0 for fixed potential parameters

Continuous multipartite entangled state in Wigner representation and violation of the Zukowski-Brukner inequality

International Nuclear Information System (INIS)

Wu Chunfeng; Chen Jingling; Oh, C.H.; Kwek, L.C.; Xue Kang

2005-01-01

We construct an explicit Wigner function for the N-mode squeezed state. Based on a previous observation that the Wigner function describes correlations in the joint measurement of the phase-space displaced parity operator, we investigate the nonlocality of the multipartite entangled state by the violation of the Zukowski-Brukner N-qubit Bell inequality. We find that quantum predictions for such a squeezed state violate these inequalities by an amount that grows with the number N

Ordering of ''ladder'' operators, the Wigner function for number and phase, and the enlarged Hilbert space

International Nuclear Information System (INIS)

Luks, A.; Perinova, V.

1993-01-01

A suitable ordering of phase exponential operators has been compared with the antinormal ordering of the annihilation and creation operators of a single mode optical field. The extended Wigner function for number and phase in the enlarged Hilbert space has been used for the derivation of the Wigner function for number and phase in the original Hilbert space. (orig.)

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

Science.gov (United States)

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.

Wigner Functions for the Bateman System on Noncommutative Phase Space

Science.gov (United States)

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 Functions for the Bateman System on Noncommutative Phase Space

International Nuclear Information System (INIS)

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

2010-01-01

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

Schwinger pair production in space- and time-dependent electric fields: Relating the Wigner formalism to quantum kinetic theory

International Nuclear Information System (INIS)

Hebenstreit, F.; Alkofer, R.; Gies, H.

2010-01-01

The nonperturbative electron-positron pair production (Schwinger effect) is considered for space- and time-dependent electric fields E-vector(x-vector,t). Based on the Dirac-Heisenberg-Wigner formalism, we derive a system of partial differential equations of infinite order for the 16 irreducible components of the Wigner function. In the limit of spatially homogeneous fields the Vlasov equation of quantum kinetic theory is rediscovered. It is shown that the quantum kinetic formalism can be exactly solved in the case of a constant electric field E(t)=E 0 and the Sauter-type electric field E(t)=E 0 sech 2 (t/τ). These analytic solutions translate into corresponding expressions within the Dirac-Heisenberg-Wigner formalism and allow to discuss the effect of higher derivatives. We observe that spatial field variations typically exert a strong influence on the components of the Wigner function for large momenta or for late times.

Functional Wigner representation of quantum dynamics of Bose-Einstein condensate

Energy Technology Data Exchange (ETDEWEB)

Opanchuk, B.; Drummond, P. D. [Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, Hawthorn VIC 3122 (Australia)

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 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.

Measurement of the Wigner function via atomic beam deflection in the Raman-Nath regime

Energy Technology Data Exchange (ETDEWEB)

Khosa, Ashfaq H [Center for Quantum Physics, COMSATS Institute of Information Technology, Islamabad (Pakistan); Zubairy, M Suhail [Center for Quantum Physics, COMSATS Institute of Information Technology, Islamabad (Pakistan)

2006-12-28

A method for the reconstruction of photon statistics and even the Wigner function of a quantized cavity field state is proposed. The method is based on the measurement of momentum distribution of two-level atoms in the Raman-Nath regime. Both the cases of resonant and off-resonant atom-field interaction are considered. The Wigner function is reconstructed by displacing the photon statistics of the cavity field. This reconstruction method is straightforward and does not need much mathematical manipulation of experimental data.

Sympathetic Wigner-function tomography of a dark trapped ion

DEFF Research Database (Denmark)

Mirkhalaf, Safoura; Mølmer, Klaus

2012-01-01

A protocol is provided to reconstruct the Wigner function for the motional state of a trapped ion via fluorescence detection on another ion in the same trap. This “sympathetic tomography” of a dark ion without optical transitions suitable for state measurements is based on the mapping of its...

Ray tracing the Wigner distribution function for optical simulations

NARCIS (Netherlands)

Mout, B.M.; Wick, Michael; Bociort, F.; 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

Relativistic electron Wigner crystal formation in a cavity for electron acceleration

CERN Document Server

Thomas, Johannes; Pukhov, Alexander

2014-01-01

It is known that a gas of electrons in a uniform neutralizing background can crystallize and form a lattice if the electron density is less than a critical value. This crystallization may have two- or three-dimensional structure. Since the wake field potential in the highly-nonlinear-broken-wave regime (bubble regime) has the form of a cavity where the background electrons are evacuated from and only the positively charged ions remain, it is suited for crystallization of trapped and accelerated electron bunch. However, in this case, the crystal is moving relativistically and shows new three-dimensional structures that we call relativistic Wigner crystals. We analyze these structures using a relativistic Hamiltonian approach. We also check for stability and phase transitions of the relativistic Wigner crystals.

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

International Nuclear Information System (INIS)

Liard, Quentin; Pawilowski, Boris

2014-01-01

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 and 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)

On the path integral representation of the Wigner function and the Barker–Murray ansatz

International Nuclear Information System (INIS)

Sels, Dries; Brosens, Fons; Magnus, Wim

2012-01-01

The propagator of the Wigner function is constructed from the Wigner–Liouville equation as a phase space path integral over a new effective Lagrangian. In contrast to a paper by Barker and Murray (1983) , we show that the path integral can in general not be written as a linear superposition of classical phase space trajectories over a family of non-local forces. Instead, we adopt a saddle point expansion to show that the semiclassical Wigner function is a linear superposition of classical solutions for a different set of non-local time dependent forces. As shown by a simple example the specific form of the path integral makes the formulation ideal for Monte Carlo simulation. -- Highlights: ► We derive the quantum mechanical propagator of the Wigner function in the path integral representation. ► We show that the Barker–Murray ansatz is incomplete, explain the error and provide an alternative. ► An example of a Monte Carlo simulation of the semiclassical path integral is included.

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

Science.gov (United States)

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.

Wigner functions for evanescent waves.

Science.gov (United States)

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

2012-09-01

We propose phase space distributions, based on an extension of the Wigner distribution function, to describe fields of any state of coherence that contain evanescent components emitted into a half-space. The evanescent components of the field are described in an optical phase space of spatial position and complex-valued angle. Behavior of these distributions upon propagation is also considered, where the rapid decay of the evanescent components is associated with the exponential decay of the associated phase space distributions. To demonstrate the structure and behavior of these distributions, we consider the fields generated from total internal reflection of a Gaussian Schell-model beam at a planar interface.

Jordan-Wigner fermionization and the theory of low-dimensional quantum spin models

International Nuclear Information System (INIS)

Derzhko, O.

2007-01-01

The idea of mapping quantum spin lattice model onto fermionic lattice model goes back to Jordan and Wigner (1928) who transformed s = 1/2 operators which commute at different lattice sites into fermionic operators. Later on the Jordan-Wigner transformation was used for mapping one-dimensional s = 1/2 isotropic XY (XX) model onto an exactly solvable tight-binding model of spinless fermions (Lieb, Schultz and Mattis, 1961). Since that times the Jordan-Wigner transformation is known as a powerful tool in the condensed matter theory especially in the theory of low-dimensional quantum spin systems. The aim of these lectures is to review the applications of the Jordan-Wigner fermionization technique for calculating dynamic properties of low-dimensional quantum spin models. The dynamic quantities (such as dynamic structure factors or dynamic susceptibilities) are observable directly or indirectly in various experiments. The frequency and wave-vector dependence of the dynamic quantities yields valuable information about the magnetic structure of materials. Owing to a tremendous recent progress in synthesizing low-dimensional magnetic materials detailed comparisons of theoretical results with direct experimental observation are becoming possible. The lectures are organized as follows. After a brief introduction of the Jordan-Wigner transformation for one-dimensional spin one half systems and some of its extensions for higher dimensions and higher spin values we focus on the dynamic properties of several low-dimensional quantum spin models. We start from a famous s = 1/2 XX chain. As a first step we recall well-known results for dynamics of the z-spin-component fluctuation operator and then turn to dynamics of the dimer and trimer fluctuation operators. The dynamics of the trimer fluctuations involves both the two fermion (one particle and one hole) and the four-fermion (two particles and two holes) excitations. We discuss some properties of the two-fermion and four

Errors due to the cylindrical cell approximation in lattice calculations

Energy Technology Data Exchange (ETDEWEB)

Newmarch, D A [Reactor Development Division, Atomic Energy Establishment, Winfrith, Dorchester, Dorset (United Kingdom)

1960-06-15

It is shown that serious errors in fine structure calculations may arise through the use of the cylindrical cell approximation together with transport theory methods. The effect of this approximation is to overestimate the ratio of the flux in the moderator to the flux in the fuel. It is demonstrated that the use of the cylindrical cell approximation gives a flux in the moderator which is considerably higher than in the fuel, even when the cell dimensions in units of mean free path tend to zero; whereas, for the case of real cells (e.g. square or hexagonal), the flux ratio must tend to unity. It is also shown that, for cylindrical cells of any size, the ratio of the flux in the moderator to flux in the fuel tends to infinity as the total neutron cross section in the moderator tends to zero; whereas the ratio remains finite for real cells. (author)

Real-time generation of the Wigner distribution of complex functions using phase conjugation in photorefractive materials.

Science.gov (United States)

Sun, P C; Fainman, Y

1990-09-01

An optical processor for real-time generation of the Wigner distribution of complex amplitude functions is introduced. The phase conjugation of the input signal is accomplished by a highly efficient self-pumped phase conjugator based on a 45 degrees -cut barium titanate photorefractive crystal. Experimental results on the real-time generation of Wigner distribution slices for complex amplitude two-dimensional optical functions are presented and discussed.

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

Science.gov (United States)

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.

Discrete Wigner function and quantum-state tomography

Science.gov (United States)

Leonhardt, Ulf

1996-05-01

The theory of discrete Wigner functions and of discrete quantum-state tomography [U. Leonhardt, Phys. Rev. Lett. 74, 4101 (1995)] is studied in more detail guided by the picture of precession tomography. Odd- and even-dimensional systems (angular momenta and spins, bosons, and fermions) are considered separately. Relations between simple number theory and the quantum mechanics of finite-dimensional systems are pointed out. In particular, the multicomplementarity of the precession states distinguishes prime dimensions from composite ones.

Asymptotics of Wigner 3nj-symbols with small and large angular momenta: an elementary method

International Nuclear Information System (INIS)

Bonzom, Valentin; Fleury, Pierre

2012-01-01

Yu and Littlejohn recently studied in (2011 Phys. Rev. A 83 052114 (arXiv:1104.1499)) some asymptotics of Wigner symbols with some small and large angular momenta. They found that in this regime the essential information is captured by the geometry of a tetrahedron, and gave new formulae for 9j-, 12j- and 15j-symbols. We present here an alternative derivation which leads to a simpler formula, based on the use of the Ponzano–Regge formula for the relevant tetrahedron. The approach is generalized to Wigner 3nj-symbols with some large and small angular momenta, where more than one tetrahedron are needed, leading to new asymptotics for Wigner 3nj-symbols. As an illustration, we present 15j-symbols with one, two and four small angular momenta, and give an alternative formula to Yu’s recent 15j-symbol with three small spins. (paper)

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

Energy Technology Data Exchange (ETDEWEB)

Chowdhury, S. Hasibul Hassan, E-mail: shhchowdhury@gmail.com [Chern Institute of Mathematics, Nankai University, Tianjin 300071 (China); Department of Mathematics and Statistics, Concordia University, Montréal, Québec H3G 1M8 (Canada); Ali, S. Twareque, E-mail: twareque.ali@concordia.ca [Department of Mathematics and Statistics, Concordia University, Montréal, Québec H3G 1M8 (Canada)

2015-12-15

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 those of momentum not commuting, the position operators not commuting and finally, the case of standard quantum mechanics, obeying the canonical commutation relations only.

Spectral and entropic characterizations of Wigner functions: applications to model vibrational systems.

Science.gov (United States)

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.

Jauch-Piron system of imprimitivities for phonons. II. The Wigner function formalism

Science.gov (United States)

Banach, Zbigniew; Piekarski, Sławomir

1993-01-01

In 1932 Wigner defined and described a quantum mechanical phase space distribution function for a system composed of many identical particles of positive mass. This function has the property that it can be used to calculate a class of quantum mechanical averages in the same manner as the classical phase space distribution function is used to calculate classical averages. Considering the harmonic vibrations of a system of n atoms bound to one another by elastic forces and treating them as a gas of indistinguishable Bose particles, phonons, the primary objective of this paper is to show under which circumstances the Wigner formalism for classical particles can be extended to cover also the phonon case. Since the phonons are either strongly or weakly localizable particles (as described in a companion paper), the program of the present approach consists in applying the Jauch-Piron quantum description of localization in (discrete) space to the phonon system and then in deducing from such a treatment the explicit expression for the phonon analogue of the Wigner distribution function. The characteristic new features of the “phase-space” picture for phonons (as compared with the situation in ordinary theory) are pointed out. The generalization of the method to the case of relativistic particles is straightforward.

Low-frequency electromagnetic field in a Wigner crystal

OpenAIRE

Stupka, Anton

2016-01-01

Long-wave low-frequency oscillations are described in a Wigner crystal by generalization of the reverse continuum model for the case of electronic lattice. The internal self-consistent long-wave electromagnetic field is used to describe the collective motions in the system. The eigenvectors and eigenvalues of the obtained system of equations are derived. The velocities of longitudinal and transversal sound waves are found.

Fresnel representation of the Wigner function: an operational approach.

Science.gov (United States)

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)

Real-time dynamics of matrix quantum mechanics beyond the classical approximation

Science.gov (United States)

Buividovich, Pavel; Hanada, Masanori; Schäfer, Andreas

2018-03-01

We describe a numerical method which allows to go beyond the classical approximation for the real-time dynamics of many-body systems by approximating the many-body Wigner function by the most general Gaussian function with time-dependent mean and dispersion. On a simple example of a classically chaotic system with two degrees of freedom we demonstrate that this Gaussian state approximation is accurate for significantly smaller field strengths and longer times than the classical one. Applying this approximation to matrix quantum mechanics, we demonstrate that the quantum Lyapunov exponents are in general smaller than their classical counterparts, and even seem to vanish below some temperature. This behavior resembles the finite-temperature phase transition which was found for this system in Monte-Carlo simulations, and ensures that the system does not violate the Maldacena-Shenker-Stanford bound λL < 2πT, which inevitably happens for classical dynamics at sufficiently small temperatures.

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

Science.gov (United States)

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.

Q-boson interferometry and generalized Wigner function

International Nuclear Information System (INIS)

Zhang, Q.H.; Padula, Sandra S.

2004-01-01

Bose-Einstein correlations of two identically charged Q bosons are derived considering these particles to be confined in finite volumes. Boundary effects on single Q-boson spectrum are also studied. We illustrate the effects on the spectrum and on the two-Q-boson correlation function by means of two toy models. We also derive a generalized expression for the Wigner function depending on the deformation parameter Q, which is reduced to its original functional form in the limit of Q→1

Wigner distribution function and its application to first-order optics

NARCIS (Netherlands)

Bastiaans, M.J.

1979-01-01

The Wigner distribution function of optical signals and systems has been introduced. The concept of such functions is not restricted to deterministic signals, but can be applied to partially coherent light as well. Although derived from Fourier optics, the description of signals and systems by means

Evidence of two-stage melting of Wigner solids

Science.gov (United States)

Knighton, Talbot; Wu, Zhe; Huang, Jian; Serafin, Alessandro; Xia, J. S.; Pfeiffer, L. N.; West, K. W.

2018-02-01

Ultralow carrier concentrations of two-dimensional holes down to p =1 ×109cm-2 are realized. Remarkable insulating states are found below a critical density of pc=4 ×109cm-2 or rs≈40 . Sensitive dc V-I measurement as a function of temperature and electric field reveals a two-stage phase transition supporting the melting of a Wigner solid as a two-stage first-order transition.

Spin-orbit-enhanced Wigner localization in quantum dots

DEFF Research Database (Denmark)

Cavalli, Andrea; Malet, F.; Cremon, J. C.

2011-01-01

We investigate quantum dots with Rashba spin-orbit coupling in the strongly-correlated regime. We show that the presence of the Rashba interaction enhances the Wigner localization in these systems, making it achievable for higher densities than those at which it is observed in Rashba-free quantum...... dots. Recurring shapes in the pair distribution functions of the yrast spectrum, which might be associated with rotational and vibrational modes, are also reported....

Quantum kinetic field theory in curved spacetime: Covariant Wigner function and Liouville-Vlasov equations

International Nuclear Information System (INIS)

Calzetta, E.; Habib, S.; Hu, B.L.

1988-01-01

We consider quantum fields in an external potential and show how, by using the Fourier transform on propagators, one can obtain the mass-shell constraint conditions and the Liouville-Vlasov equation for the Wigner distribution function. We then consider the Hadamard function G 1 (x 1 ,x 2 ) of a real, free, scalar field in curved space. We postulate a form for the Fourier transform F/sup (//sup Q//sup )/(X,k) of the propagator with respect to the difference variable x = x 1 -x 2 on a Riemann normal coordinate centered at Q. We show that F/sup (//sup Q//sup )/ is the result of applying a certain Q-dependent operator on a covariant Wigner function F. We derive from the wave equations for G 1 a covariant equation for the distribution function and show its consistency. We seek solutions to the set of Liouville-Vlasov equations for the vacuum and nonvacuum cases up to the third adiabatic order. Finally we apply this method to calculate the Hadamard function in the Einstein universe. We show that the covariant Wigner function can incorporate certain relevant global properties of the background spacetime. Covariant Wigner functions and Liouville-Vlasov equations are also derived for free fermions in curved spacetime. The method presented here can serve as a basis for constructing quantum kinetic theories in curved spacetime or for near-uniform systems under quasiequilibrium conditions. It can also be useful to the development of a transport theory of quantum fields for the investigation of grand unification and post-Planckian quantum processes in the early Universe

State operator, constants of the motion, and Wigner functions: The two-dimensional isotropic harmonic oscillator

DEFF Research Database (Denmark)

Dahl, Jens Peder; Schleich, W. P.

2009-01-01

For a closed quantum system the state operator must be a function of the Hamiltonian. When the state is degenerate, additional constants of the motion enter the play. But although it is the Weyl transform of the state operator, the Wigner function is not necessarily a function of the Weyl...... transforms of the constants of the motion. We derive conditions for which this is actually the case. The Wigner functions of the energy eigenstates of a two-dimensional isotropic harmonic oscillator serve as an important illustration....

Eugene P. Wigner – in the light of unexpected events

Directory of Open Access Journals (Sweden)

Koblinger L.

2014-01-01

Full Text Available 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.

The universal Racah-Wigner symbol for U{sub q}(osp(1 vertical stroke 2))

Energy Technology Data Exchange (ETDEWEB)

Pawelkiewicz, Michal; Schomerus, Volker [DESY Hamburg (Germany). Theory Group; Suchanek, Paulina [DESY Hamburg (Germany). Theory Group; Wroclaw Univ. (Poland). Inst. for Theoretical Physics

2013-10-15

We propose a new and elegant formula for the Racah-Wigner symbol of self-dual continuous series of representations of U{sub q}(osp(1 vertical stroke 2)). It describes the entire fusing matrix for both NS and R sector of N=1 supersymmetric Liouville field theory. In the NS sector, our formula is related to an expression derived in an earlier paper (L. Hadaz, M. Pawelkiewicz, and V. Schomerus, arXiv:1305.4596[hep-th]). Through analytic continuation in the spin variables, our universal expression reproduces known formulas for the Racah-Wigner coefficients of finite dimensional representations.

From GCM energy kernels to Weyl-Wigner Hamiltonians: a particular mapping

International Nuclear Information System (INIS)

Galetti, D.

1984-01-01

A particular mapping is established which directly connects GCM energy kernels to Weyl-Wigner Hamiltonians, under the assumption of gaussian overlap kernel. As an application of this mapping scheme the collective Hamiltonians for some giant resonances are derived. (Author) [pt

Time-Frequency (Wigner Analysis of Linear and Nonlinear Pulse Propagation in Optical Fibers

Directory of Open Access Journals (Sweden)

José Azaña

2005-06-01

Full Text Available Time-frequency analysis, and, in particular, Wigner analysis, is applied to the study of picosecond pulse propagation through optical fibers in both the linear and nonlinear regimes. The effects of first- and second-order group velocity dispersion (GVD and self-phase modulation (SPM are first analyzed separately. The phenomena resulting from the interplay between GVD and SPM in fibers (e.g., soliton formation or optical wave breaking are also investigated in detail. Wigner analysis is demonstrated to be an extremely powerful tool for investigating pulse propagation dynamics in nonlinear dispersive systems (e.g., optical fibers, providing a clearer and deeper insight into the physical phenomena that determine the behavior of these systems.

Wigner representation for experiments on quantum cryptography using two-photon polarization entanglement produced in parametric down-conversion

International Nuclear Information System (INIS)

Casado, A; Guerra, S; Placido, J

2008-01-01

In this paper, the theory of parametric down-conversion in the Wigner representation is applied to Ekert's quantum cryptography protocol. We analyse the relation between two-photon entanglement and (non-secure) quantum key distribution within the Wigner framework in the Heisenberg picture. Experiments using two-qubit polarization entanglement generated in nonlinear crystals are analysed in this formalism, along with the effects of eavesdropping attacks in the case of projective measurements

Impacts of generalized uncertainty principle on black hole thermodynamics and Salecker-Wigner inequalities

International Nuclear Information System (INIS)

Tawfik, A.

2013-01-01

We investigate the impacts of Generalized Uncertainty Principle (GUP) proposed by some approaches to quantum gravity such as String Theory and Doubly Special Relativity on black hole thermodynamics and Salecker-Wigner inequalities. Utilizing Heisenberg uncertainty principle, the Hawking temperature, Bekenstein entropy, specific heat, emission rate and decay time are calculated. As the evaporation entirely eats up the black hole mass, the specific heat vanishes and the temperature approaches infinity with an infinite radiation rate. It is found that the GUP approach prevents the black hole from the entire evaporation. It implies the existence of remnants at which the specific heat vanishes. The same role is played by the Heisenberg uncertainty principle in constructing the hydrogen atom. We discuss how the linear GUP approach solves the entire-evaporation-problem. Furthermore, the black hole lifetime can be estimated using another approach; the Salecker-Wigner inequalities. Assuming that the quantum position uncertainty is limited to the minimum wavelength of measuring signal, Wigner second inequality can be obtained. If the spread of quantum clock is limited to some minimum value, then the modified black hole lifetime can be deduced. Based on linear GUP approach, the resulting lifetime difference depends on black hole relative mass and the difference between black hole mass with and without GUP is not negligible

SLP - A single level Breit-Wigner cross-section generating programme

International Nuclear Information System (INIS)

Doherty, G.

1965-06-01

Unbroadened cross-sections are calculated from a single level Breit-Wigner approximation which allows for resonance-potential interference but not resonance-resonance interference. Doppler broadening, and instrumental resolution broadening for thin samples, are optionally performed by successive numerical convolutions. An energy point selection and discard system enables the cross-section over a specified energy range to be represented to a required degree of accuracy using the minimum number of energy points. An energy grid prepared by the user can be incorporated in the calculation but the programme will usually be more efficient if only the end points of the energy range of interest are specified by the user and the intermediate energy points left to the programme to organise. The capacity of the programme varies with the energy range and type of resonance (narrow or broad). About fifty resonances may be sufficient to generate an energy grid of 4000 energy points, which is the maximum allowable energy vector. The programme is written in KDF9 EGTRAN (a FORTRAN dialect); output is printed and may be copied on cards, and intermediate results are stored on magnetic disc. (author)

Semiclassical propagator of the Wigner function.

Science.gov (United States)

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.

Wigner tomography of multispin quantum states

Science.gov (United States)

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.

The Wigner semi-circle law in quantum electro dynamics

International Nuclear Information System (INIS)

Accardi, L.; Nagoya Univ.; Lu, Y.G.; Nagoya Univ.

1996-01-01

In the present paper, the basic ideas of the stochastic limit of quantum theory are applied to quantum electro-dynamics. This naturally leads to the study of a new type of quantum stochastic calculus on a Hilbert module. Our main result is that in the weak coupling limit of a system composed of a free particle (electron, atom,..) interacting, via the minimal coupling, with the quantum electromagnetic field, a new type of quantum noise arises, living on a Hilbert module rather than a Hilbert space. Moreover we prove that the vacuum distribution of the limiting field operator is not Gaussian, as usual, but a nonlinear deformation of the Wigner semi-circle law. A third new object arising from the present theory, is the so-called interacting Fock space. A kind of Fock space in which the n quanta, in the n-particle space, are not independent, but interact. The origin of all these new features is that we do not introduce the dipole approximation, but we keep the exponential response term, coupling the electron to the quantum electromagnetic field. This produces a nonlinear interaction among all the modes of the limit master field (quantum noise) whose explicit expression, that we find, can be considered as a nonlinear generalization of the Fermi golden rule. (orig.)

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

Science.gov (United States)

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

Wigner representation for experiments on quantum cryptography using two-photon polarization entanglement produced in parametric down-conversion

Energy Technology Data Exchange (ETDEWEB)

Casado, A [Departamento de Fisica Aplicada III, Escuela Superior de Ingenieros, Universidad de Sevilla, 41092 Sevilla (Spain); Guerra, S [Centro Asociado de la Universidad Nacional de Educacion a Distancia de Las Palmas de Gran Canaria (Spain); Placido, J [Departamento de Fisica, Universidad de Las Palmas de Gran Canaria (Spain)], E-mail: acasado@us.es

2008-02-28

In this paper, the theory of parametric down-conversion in the Wigner representation is applied to Ekert's quantum cryptography protocol. We analyse the relation between two-photon entanglement and (non-secure) quantum key distribution within the Wigner framework in the Heisenberg picture. Experiments using two-qubit polarization entanglement generated in nonlinear crystals are analysed in this formalism, along with the effects of eavesdropping attacks in the case of projective measurements.

Description of nuclear collective motion by Wigner function moments

International Nuclear Information System (INIS)

Balbutsev, E.B.

1996-01-01

The method is presented in which the collective motion is described by the dynamic equations for the nuclear integral characteristics. The 'macroscopic' dynamics is formulated starting from the equations of the microscopic theory. This is done by taking the phase space moments of the Wigner function equation. The theory is applied to the description of collective excitations with multipolarities up to λ=5. (author)

Time-dependent Wigner distribution function employed in coherent Schroedinger cat states: |Ψ(t))=N-1/2(|α)+eiφ|-α))

International Nuclear Information System (INIS)

Choi, Jeong Ryeol; Yeon, Kyu Hwang

2008-01-01

The Wigner distribution function for the time-dependent quadratic Hamiltonian system in the coherent Schroedinger cat state is investigated. The type of state we consider is a superposition of two coherent states, which are by an angle of π out of phase with each other. The exact Wigner distribution function of the system is evaluated under a particular choice of phase, δ c,q . Our development is employed for two special cases, namely, the Caldirola-Kanai oscillator and the frequency stable damped harmonic oscillator. On the basis of the diverse values of the Wigner distribution function that were plotted, we analyze the nonclassical behavior of the systems.

Wigner functions for the pair angle and orbital angular momentum. Possible applications in quantum information theories

International Nuclear Information System (INIS)

Kastrup, H.A.

2017-01-01

The framework of Wigner functions for the canonical pair angle and orbital angular momentum, derived and analyzed in 2 recent papers [H. A. Kastrup, Phys. Rev. A 94, 062113(2016) and Phys. Rev. A 95, 052111(2017)], is applied to elementary concepts of quantum information like qubits and 2-qubits, e.g., entangled EPR/Bell states etc. Properties of the associated Wigner functions are discussed and illustrated. The results may be useful for quantum information experiments with orbital angular momenta of light beams or electron beams.

Wigner functions for the pair angle and orbital angular momentum. Possible applications in quantum information theories

Energy Technology Data Exchange (ETDEWEB)

Kastrup, H.A. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group

2017-10-17

The framework of Wigner functions for the canonical pair angle and orbital angular momentum, derived and analyzed in 2 recent papers [H. A. Kastrup, Phys. Rev. A 94, 062113(2016) and Phys. Rev. A 95, 052111(2017)], is applied to elementary concepts of quantum information like qubits and 2-qubits, e.g., entangled EPR/Bell states etc. Properties of the associated Wigner functions are discussed and illustrated. The results may be useful for quantum information experiments with orbital angular momenta of light beams or electron beams.

Quantum mechanics on phase space: The hydrogen atom and its Wigner functions

Science.gov (United States)

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.

Magnetic moment, vorticity-spin coupling and parity-odd conductivity of chiral fermions in 4-dimensional Wigner functions

Energy Technology Data Exchange (ETDEWEB)

Gao, Jian-hua [Shandong Provincial Key Laboratory of Optical Astronomy and Solar-Terrestrial Environment, Institute of Space Sciences, Shandong University, Weihai, Shandong 264209 (China); Wang, Qun, E-mail: qunwang@ustc.edu.cn [Interdisciplinary Center for Theoretical Study and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026 (China); Physics Department, Brookhaven National Laboratory, Upton, NY 11973-5000 (United States)

2015-10-07

We demonstrate the emergence of the magnetic moment and spin-vorticity coupling of chiral fermions in 4-dimensional Wigner functions. In linear response theory with space–time varying electromagnetic fields, the parity-odd part of the electric conductivity can also be derived which reproduces results of the one-loop and the hard-thermal or hard-dense loop. All these properties show that the 4-dimensional Wigner functions capture comprehensive aspects of physics for chiral fermions in electromagnetic fields.

Wigner's dynamical transition state theory in phase space : classical and quantum

NARCIS (Netherlands)

Waalkens, Holger; Schubert, Roman; Wiggins, Stephen

We develop Wigner's approach to a dynamical transition state theory in phase space in both the classical and quantum mechanical settings. The key to our development is the construction of a normal form for describing the dynamics in the neighbourhood of a specific type of saddle point that governs

Eugene Wigner – A Gedanken Pioneer of the Second Quantum Revolution

Directory of Open Access Journals (Sweden)

Zeilinger Anton

2014-01-01

Full Text Available 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.

Ray tracing the Wigner distribution function for optical simulations

Science.gov (United States)

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.

Semiclassical analysis of the Wigner 12j symbol with one small angular momentum

International Nuclear Information System (INIS)

Yu Liang

2011-01-01

We derive an asymptotic formula for the Wigner 12j symbol, in the limit of one small and 11 large angular momenta. There are two kinds of asymptotic formulas for the 12j symbol with one small angular momentum. We present the first kind of formula in this paper. Our derivation relies on the techniques developed in the semiclassical analysis of the Wigner 9j symbol [L. Yu and R. G. Littlejohn, Phys. Rev. A 83, 052114 (2011)], where we used a gauge-invariant form of the multicomponent WKB wave functions to derive asymptotic formulas for the 9j symbol with small and large angular momenta. When applying the same technique to the 12j symbol in this paper, we find that the spinor is diagonalized in the direction of an intermediate angular momentum. In addition, we find that the geometry of the derived asymptotic formula for the 12j symbol is expressed in terms of the vector diagram for a 9j symbol. This illustrates a general geometric connection between asymptotic limits of the various 3nj symbols. This work contributes an asymptotic formula for the 12j symbol to the quantum theory of angular momentum, and serves as a basis for finding asymptotic formulas for the Wigner 15j symbol with two small angular momenta.

Magnetic moment, vorticity-spin coupling and parity-odd conductivity of chiral fermions in 4-dimensional Wigner functions

Directory of Open Access Journals (Sweden)

Jian-hua Gao

2015-10-01

Full Text Available We demonstrate the emergence of the magnetic moment and spin-vorticity coupling of chiral fermions in 4-dimensional Wigner functions. In linear response theory with space–time varying electromagnetic fields, the parity-odd part of the electric conductivity can also be derived which reproduces results of the one-loop and the hard-thermal or hard-dense loop. All these properties show that the 4-dimensional Wigner functions capture comprehensive aspects of physics for chiral fermions in electromagnetic fields.

Quantum computation and analysis of Wigner and Husimi functions: toward a quantum image treatment.

Science.gov (United States)

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.

Universality for 1d Random Band Matrices: Sigma-Model Approximation

Science.gov (United States)

Shcherbina, Mariya; Shcherbina, Tatyana

2018-02-01

The paper continues the development of the rigorous supersymmetric transfer matrix approach to the random band matrices started in (J Stat Phys 164:1233-1260, 2016; Commun Math Phys 351:1009-1044, 2017). We consider random Hermitian block band matrices consisting of W× W random Gaussian blocks (parametrized by j,k \\in Λ =[1,n]^d\\cap Z^d ) with a fixed entry's variance J_{jk}=δ _{j,k}W^{-1}+β Δ _{j,k}W^{-2} , β >0 in each block. Taking the limit W→ ∞ with fixed n and β , we derive the sigma-model approximation of the second correlation function similar to Efetov's one. Then, considering the limit β , n→ ∞, we prove that in the dimension d=1 the behaviour of the sigma-model approximation in the bulk of the spectrum, as β ≫ n , is determined by the classical Wigner-Dyson statistics.

Negative Differential Resistance and Astability of the Wigner Solid

OpenAIRE

Csathy, G. A.; Tsui, D. C.; Pfeiffer, L. N.; West, K. W.

2005-01-01

We report an unusual breakdown of the magnetically induced Wigner solid in an exceptional two-dimensional electron gas. The current-voltage characteristic is found to be hysteretic in the voltage biased setup and has a region of negative differential resistance in the current biased setup. When the sample is current biased in the region of negative differential resistance, the voltage on and the current through the sample develop spontaneous narrow band oscillations.

New experimental method to study the collective modes in exotic nuclei; influence of the superfluidity on the cooling time of a neutron star; Nouvelle methode experimentale dediee a l'etude des modes collectifs dans les noyaux exotiques; influence de la superfluidite sur le temps de refroidissement d'une etoile a neutrons

Energy Technology Data Exchange (ETDEWEB)

Monrozeau, Ch

2007-07-15

Giant monopole (GMR) and quadrupole (GQR) resonances have been measured in the {sup 56}Ni using inelastic scattering of 50 A.MeV deuteron at the Grand Accelerateur National d'Ions Lourds facility. This is the first experimental observation of isoscalar collective modes in a short-lived nucleus. The secondary beam was impinged on the active target Maya filled with a pure deuterium gas. Recoiling deuterons were detected in Maya and in a wall of nine silicon detectors. The GMR and GQR are centered at 19.3(0.5) and 16.2(0.5) MeV, respectively. Corresponding angular distributions were extracted from 3 to 7 degrees in the centre of mass frame. DWBA analysis based on RPA transition densities yields the percentage of the energy weighted sum rule exhausted: 136(27) % for the GMR et 76(13) % for the GQR. A finite temperature Hartree-Fock-Bogoliubov model was implemented to describe the 10 Wigner-Seitz cells which compose the inner crust of neutron stars and to microscopically calculate their specific heat. Calculations are performed with two contact pairing forces chosen to simulate the pairing properties of uniform neutron matter corresponding to the BCS approximation and to polarisation effects. Under the assumption of a rapid cooling of the core and an initial temperature of 100 keV in the inner crust, the cooling time of the star was estimated at 9 and 34 years, respectively. (author)

New experimental method to study the collective modes in exotic nuclei; influence of the superfluidity on the cooling time of a neutron star

International Nuclear Information System (INIS)

Monrozeau, Ch.

2007-07-01

Giant monopole (GMR) and quadrupole (GQR) resonances have been measured in the 56 Ni using inelastic scattering of 50 A.MeV deuteron at the Grand Accelerateur National d'Ions Lourds facility. This is the first experimental observation of isoscalar collective modes in a short-lived nucleus. The secondary beam was impinged on the active target Maya filled with a pure deuterium gas. Recoiling deuterons were detected in Maya and in a wall of nine silicon detectors. The GMR and GQR are centered at 19.3(0.5) and 16.2(0.5) MeV, respectively. Corresponding angular distributions were extracted from 3 to 7 degrees in the centre of mass frame. DWBA analysis based on RPA transition densities yields the percentage of the energy weighted sum rule exhausted: 136(27) % for the GMR et 76(13) % for the GQR. A finite temperature Hartree-Fock-Bogoliubov model was implemented to describe the 10 Wigner-Seitz cells which compose the inner crust of neutron stars and to microscopically calculate their specific heat. Calculations are performed with two contact pairing forces chosen to simulate the pairing properties of uniform neutron matter corresponding to the BCS approximation and to polarisation effects. Under the assumption of a rapid cooling of the core and an initial temperature of 100 keV in the inner crust, the cooling time of the star was estimated at 9 and 34 years, respectively. (author)

Regularized tripartite continuous variable EPR-type states with Wigner functions and CHSH violations

International Nuclear Information System (INIS)

Jacobsen, Sol H; Jarvis, P D

2008-01-01

We consider tripartite entangled states for continuous variable systems of EPR type, which generalize the famous bipartite CV EPR states (eigenvectors of conjugate choices X 1 - X 2 , P 1 + P 2 , of the systems' relative position and total momentum variables). We give the regularized forms of such tripartite EPR states in second-quantized formulation, and derive their Wigner functions. This is directly compared with the established NOPA-like states from quantum optics. Whereas the multipartite entangled states of NOPA type have singular Wigner functions in the limit of large squeezing, r → ∞, or tanh r → 1 - (approaching the EPR states in the bipartite case), our regularized tripartite EPR states show singular behaviour not only in the approach to the EPR-type region (s → 1 in our notation), but also for an additional, auxiliary regime of the regulator (s→√2). While the s → 1 limit pertains to tripartite CV states with singular eigenstates of the relative coordinates and remaining squeezed in the total momentum, the (s→√2) limit yields singular eigenstates of the total momentum, but squeezed in the relative coordinates. Regarded as expectation values of displaced parity measurements, the tripartite Wigner functions provide the ingredients for generalized CHSH inequalities. Violations of the tripartite CHSH bound (B 3 ≤ 2) are established, with B 3 ≅2.09 in the canonical regime (s → 1 + ), as well as B 3 ≅2.32 in the auxiliary regime (s→√2 + )

Wigner function and tomogram of the excited squeezed vacuum state

International Nuclear Information System (INIS)

Meng Xiangguo; Wang Jisuo; Fan Hongyi

2007-01-01

The excited squeezed light (ESL) can be the outcome of interaction between squeezed light probe and excited atom, which can explore the status and the structure of the atom. We calculate the Wigner function and tomogram of ESL that may be comparable to the experimental measurement of quadrature-amplitude distribution for the light field obtained using balanced homodyne detection. The method of calculation seems new

Wigner function and tomogram of the excited squeezed vacuum state

Energy Technology Data Exchange (ETDEWEB)

Meng Xiangguo [Department of Physics, Liaocheng University, Shandong Province 252059 (China); Wang Jisuo [Department of Physics, Liaocheng University, Shandong Province 252059 (China)]. E-mail: jswang@lcu.edu.cn; Fan Hongyi [Department of Physics, Liaocheng University, Shandong Province 252059 (China); CCAST (World Laboratory), P.O. Box 8730, 100080 Beijing (China)

2007-01-29

The excited squeezed light (ESL) can be the outcome of interaction between squeezed light probe and excited atom, which can explore the status and the structure of the atom. We calculate the Wigner function and tomogram of ESL that may be comparable to the experimental measurement of quadrature-amplitude distribution for the light field obtained using balanced homodyne detection. The method of calculation seems new.

Ring-shaped functions and Wigner 6j-symbols

International Nuclear Information System (INIS)

Mardoyan, L.G.; Erevanskij Gosudarstvennyj Univ., Erevan

2006-01-01

The explicit expression for the ring-shaped matrix connecting the ring-shaped functions relating to different values of the axial parameter is obtained. The connection of this matrix with Wigner 6j-symbols is found out. The motion of quantum particle in the ring-shaped model with the zero priming potential is investigated. The bases of this model, which are factored in spherical cylindrical coordinates, are obtained. The formula generalizing the Rayleigh expansion of a plane wave with respect to spherical waves in the ring-shaped model is deduced [ru

Time Evolution Of The Wigner Function In Discrete Quantum Phase Space For A Soluble Quasi-spin Model

CERN Document Server

Galetti, D

2000-01-01

Summary: The discrete phase space approach to quantum mechanics of degrees of freedom without classical counterparts is applied to the many-fermions/quasi-spin Lipkin model. The Wigner function is written for some chosen states associated to discrete angle and angular momentum variables, and the time evolution is numerically calculated using the discrete von Neumann-Liouville equation. Direct evidences in the time evolution of the Wigner function are extracted that identify a tunnelling effect. A connection with an $SU(2)$-based semiclassical continuous approach to the Lipkin model is also presented.

Out-of-equilibrium nanocrystalline R1-s(Fe,M)5+2s alloys (R=Sm,Pr; M=Co,Si,Ga)

International Nuclear Information System (INIS)

Bessais, L.; Djega-Mariadassou, C.

2005-01-01

The out-of-equilibrium hexagonal P6/mmm R 1-s (Fe,M) 5+2s (R=Sm,Pr and M=Co, Si or Ga) intermetallics are obtained by controlled nanocrystallization. A model is presented to explain the structure of the hexagonal phases, which stoichiometry is consistent with Sm(Fe,M) 9 and R(Fe,Ti,Co) 10 . The Curie temperatures increase versus Ga, Si, Co content. The analysis of the Moessbauer spectra leads to monotonous variation of the hyperfine parameters. The refinement of the Moessbauer spectra was performed on the basis of the correlation between Wigner-Seitz cell volumes obtained from X-ray diffraction results and isomer shifts. The abundance of each magnetic site was calculated by the multinomial distribution law. For a given substituting Co, Si, Ga content, the sequence for the isomer shift in the hexagonal cell is 2e>3g>6l. With increasing M content, the isomer shift of the 3g site remains quasi-constant. Those approaches lead to the location of Si, Ga, Co in 3g site, Ti in 6l site. (copyright 2005 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

The Wigner transition in a magnetic field

International Nuclear Information System (INIS)

Kleppmann, W.G.; Elliott, R.J.

1975-01-01

The criteria for the stabilization of a condensed Wigner phase are re-examined for a low-density free-electron gas (jellium) in a uniform magnetic field. By a new calculation of the Coulomb energy it is shown that below a critical density the lowest energy state has electrons in cigar-shaped charge distributions arranged on an elongated body-centred tetragonal lattice. The critical densities are computed as functions of magnetic-field strength for free electrons in astrophysical situations and for electrons of low effective mass in semiconductors. In the latter case, the results can be used to give a satisfactory interpretation of experimental results in heavily compensated InSb. (author)

Eigenfunctions of quadratic hamiltonians in Wigner representation

International Nuclear Information System (INIS)

Akhundova, Eh.A.; Dodonov, V.V.; Man'ko, V.I.

1984-01-01

Exact solutions of the Schroedinger equation in Wigner representation are obtained for an arbitrary non-stationary N-dimensional quadratic Hamiltonian. It is shown that the complete system of the solutions can always be chosen in the form of the products of Laguerre polynomials, the arguments of which are the quadratic integrals of motion of the corresponding classical problem. The generating function is found for the transition probabilities between Fock states which represent a many-dimensional generatization of a well-known Husimi formula for the oscillator of variable frequency. As an example, the motion of a charged particle in an uniform alternate electromagnetic field is considered in detail

Wigner weight functions and Weyl symbols of non-negative definite linear operators

NARCIS (Netherlands)

Janssen, A.J.E.M.

1989-01-01

In this paper we present several necessary and, for radially symmetric functions, necessary and sufficient conditions for a function of two variables to be a Wigner weight function (Weyl symbol of a non-negative definite linear operator of L2(R)). These necessary conditions are in terms of spread

The 2-D Wigner solid transition in a magnetic field: A perspective

International Nuclear Information System (INIS)

Platzman, P.M.; Song He; Price, R.

1992-01-01

A 2-D electron system in the presence of a perpendicular magnetic field of arbitrary strength is expected to form a Wigner solid in certain regimes of density and filling factor. Some estimates of the phase diagram in these two parameters are presented and a few recent experimental results are reviewed

A test of Wigner's spin-isospin symmetry from double binding energy differences

International Nuclear Information System (INIS)

Van Isacker, P.; Warner, D.D.; Brenner, D.S.

1996-01-01

The spin-isospin or SU(4) symmetry is investigated. It is shown that the N = Z enhancements of |δV np | are an unavoidable consequence of Wigner's SU(4) symmetry and that the degree of the enhancement provides a sensitive test of the quality of the symmetry itself. (K.A.)

Tertiary instability of zonal flows within the Wigner-Moyal formulation of drift turbulence

Science.gov (United States)

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.

Structural and Moessbauer spectral study of the metastable phase Sm(Fe, Co, Ti)10

International Nuclear Information System (INIS)

Bessais, L.; Djega-Mariadassou, C.; Koch, E.

2002-01-01

We have performed a Moessbauer spectral analysis of nanocrystalline metastable P 6/mmm SmTi(Fe 1-x Co x ) 9 , correlated with structural transformation towards its equilibrium derivative I4/mmm SmTi(Fe 1-x Co x ) 11 . The Rietveld analysis shows that the 3g site is fully occupied, while the 6 l occupation is limited to hexagons surrounding the Fe-Fe dumb-bell pairs 2e. A specific programme for the Wigner-Seitz cell (WSC) calculation of the metastable disordered structure was used. The hyperfine parameter assignment based on the isomer shift correlation with the WSC volumes sequence leads to Co 3g preferential occupation, with Ti location in 6 l sites. The mean hyperfine field increases with Co content in connection with the enhancement of the negative core electron polarization term upon additional Co electron filling. The same trend is observed for each individual site leading to the sequence H HF {2e}≥H HF {6 l }≥H HF {3g}. (author)

A SAS2H/KENO-V methodology for 3D fuel burnup analysis

International Nuclear Information System (INIS)

Milosevic, M.; Greenspan, E.; Vujic, J.

2002-01-01

An efficient methodology for 3D fuel burnup analysis of LWR reactors is described in this paper. This methodology is founded on coupling Monte Carlo method for 3D calculation of node power distribution, and transport method for depletion calculation in ID Wigner-Seitz equivalent cell for each node independently. The proposed fuel burnup modeling, based on application of SCALE-4.4a control modules SAS2H and KENO-V.a is verified for the case of 2D x-y model of IRIS 15 x 15 fuel assembly (with reflective boundary condition) by using two well benchmarked code systems. The one is MOCUP, a coupled MCNP-4C and ORIGEN2.1 utility code, and the second is KENO-V.a/ORIGEN2.1 code system recently developed by authors of this paper. The proposed SAS2H/KENO-V.a methodology was applied for 3D burnup analysis of IRIS-1000 benchmark.44 core. Detailed k sub e sub f sub f and power density evolution with burnup are reported. (author)

Computational efficiency improvement with Wigner rotation technique in studying atoms in intense few-cycle circularly polarized pulses

International Nuclear Information System (INIS)

Yuan, Minghu; Feng, Liqiang; Lü, Rui; Chu, Tianshu

2014-01-01

We show that by introducing Wigner rotation technique into the solution of time-dependent Schrödinger equation in length gauge, computational efficiency can be greatly improved in describing atoms in intense few-cycle circularly polarized laser pulses. The methodology with Wigner rotation technique underlying our openMP parallel computational code for circularly polarized laser pulses is described. Results of test calculations to investigate the scaling property of the computational code with the number of the electronic angular basis function l as well as the strong field phenomena are presented and discussed for the hydrogen atom

A note on the time decay of solutions for the linearized Wigner-Poisson system

KAUST Repository

Gamba, Irene; Gualdani, Maria; Sparber, Christof

2009-01-01

We consider the one-dimensional Wigner-Poisson system of plasma physics, linearized around a (spatially homogeneous) Lorentzian distribution and prove that the solution of the corresponding linearized problem decays to zero in time. We also give

Fokker-Planck equation associated with the Wigner function of a quantum system with a finite number of states

International Nuclear Information System (INIS)

Cohendet, O.

1989-01-01

We consider a quantum system with a finite number N of states and we show that a Markov process evolving in an 'extended' discrete phase can be associated with the discrete Wigner function of the system. This Wigner function is built using the Weyl quantization procedure on the group Z N xZ N . Moreover we can use this process to compute the quantum mean values as probabilistic expectations of functions of this process. This probabilistic formulation can be seen as a stochastic mechanics in phase space. (orig.)

Time Evolution of the Wigner Operator as a Quasi-density Operator in Amplitude Dessipative Channel

Science.gov (United States)

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.

On the measurement of Wigner distribution moments in the fractional Fourier transform domain

NARCIS (Netherlands)

Bastiaans, M.J.; Alieva, T.

2002-01-01

It is shown how all global Wigner distribution moments of arbitrary order can be measured as intensity moments in the output plane of an appropriate number of fractional Fourier transform systems (generally anamorphic ones). The minimum number of (anamorphic) fractional power spectra that are needed

Salecker-Wigner-Peres clock and average tunneling times

International Nuclear Information System (INIS)

Lunardi, Jose T.; Manzoni, Luiz A.; Nystrom, Andrew T.

2011-01-01

The quantum clock of Salecker-Wigner-Peres is used, by performing a post-selection of the final state, to obtain average transmission and reflection times associated to the scattering of localized wave packets by static potentials in one dimension. The behavior of these average times is studied for a Gaussian wave packet, centered around a tunneling wave number, incident on a rectangular barrier and, in particular, on a double delta barrier potential. The regime of opaque barriers is investigated and the results show that the average transmission time does not saturate, showing no evidence of the Hartman effect (or its generalized version).

Anomalous current from the covariant Wigner function

Science.gov (United States)

Prokhorov, George; Teryaev, Oleg

2018-04-01

We consider accelerated and rotating media of weakly interacting fermions in local thermodynamic equilibrium on the basis of kinetic approach. Kinetic properties of such media can be described by covariant Wigner function incorporating the relativistic distribution functions of particles with spin. We obtain the formulae for axial current by summation of the terms of all orders of thermal vorticity tensor, chemical potential, both for massive and massless particles. In the massless limit all the terms of fourth and higher orders of vorticity and third order of chemical potential and temperature equal zero. It is shown, that axial current gets a topological component along the 4-acceleration vector. The similarity between different approaches to baryon polarization is established.

Wave equation of a nonlinear triatomic molecule and the adiabatic correction to the Born--Oppenheimer approximation

International Nuclear Information System (INIS)

Bardo, R.D.; Wolfsberg, M.

1977-01-01

The wave equation for a nonlinear polyatomic molecule is formulated in molecule-fixed coordinates by a method originally due to Hirschfelder and Wigner. Application is made to a triatomic molecule, and the wave equation is explicitly presented in a useful molecule-fixed coordinate system. The formula for the adiabatic correction to the Born--Oppenheimer approximation for a triatomic molecule is obtained. The extension of the present formulation to larger polyatomic molecules is pointed out. Some terms in the triatomic molecule wave equation are discussed in detail

Entanglement with negative Wigner function of almost 3,000 atoms heralded by one photon.

Science.gov (United States)

McConnell, Robert; Zhang, Hao; Hu, Jiazhong; Ćuk, Senka; Vuletić, Vladan

2015-03-26

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, but these states display Gaussian spin distribution functions with a non-negative Wigner quasiprobability distribution function. Non-Gaussian entangled states have been produced in small ensembles of ions, and very recently in large atomic ensembles. Here we generate entanglement in a large atomic ensemble via an 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 non-classicality--and verify an entanglement depth (the minimum number of mutually entangled atoms) of 2,910 ± 190 out of 3,100 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. Although 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. More generally, our results demonstrate the power of heralded methods for entanglement generation, and illustrate how the information contained in a single photon can drastically alter the quantum state of a large system.

Effect of cosine current approximation in lattice cell calculations in cylindrical geometry

International Nuclear Information System (INIS)

Mohanakrishnan, P.

1978-01-01

It is found that one-dimensional cylindrical geometry reactor lattice cell calculations using cosine angular current approximation at spatial mesh interfaces give results surprisingly close to the results of accurate neutron transport calculations as well as experimental measurements. This is especially true for tight light water moderated lattices. Reasons for this close agreement are investigated here. By re-examining the effects of reflective and white cell boundary conditions in these calculations it is concluded that one major reason is the use of white boundary condition necessitated by the approximation of the two-dimensional reactor lattice cell by a one-dimensional one. (orig.) [de

Technical assessment of the significance of Wigner energy for disposal of graphite wastes from the Windscale Piles

International Nuclear Information System (INIS)

Guppy, R.M.; Wisbey, S.J.; McCarthy, J.

2001-01-01

Plans to dismantle the core of the Windscale Pile 1 reactor, and to package the waste for interim storage and eventual disposal, are well advanced. UK Nirex Limited, currently responsible for identifying and developing a site primarily for disposal of the wide range of intermediate level wastes, is addressing the suitability of the waste from Windscale Pile 1, for transport to, and disposal at, a deep waste repository. To support the decommissioning of Windscale Pile 1, information on the condition of the graphite has been sought. Despite the fire in 1957, recent sampling of regions of the core has shown that much of the graphite still contains significant residual Wigner energy. Unless it can be shown that Wigner energy will not be released at a significant rate during operations such as waste packaging or handling of the package, or after disposal, future safety cases may be undermined. A model for the release of Wigner energy has been developed, which describes the stored energy as a set of defects with different activation energies. Initial values of stored energy are attributed to each member of the set, and the energy is released using first order decay processes. By appropriate selection of the range of activation energies and stored energies attributable to each population of defects, experimentally determined releases of stored energy as a function of temperature can be reproduced by the model. Within the disposal environment, the packages will be subject to modest heating from external sources, including the host rocks, radioactive decay, corrosion processes and heat from curing of backfill materials in the disposal vaults. The Wigner energy release model has been used in combination with finite element thermal modelling to assess the temperature evolution of stacks of waste packages located within hypothetical disposal vaults. It has also been used to assess the response of individual waste packages exposed to fires. This paper provides a summary of the

A note on the time decay of solutions for the linearized Wigner-Poisson system

KAUST Repository

Gamba, Irene

2009-01-01

We consider the one-dimensional Wigner-Poisson system of plasma physics, linearized around a (spatially homogeneous) Lorentzian distribution and prove that the solution of the corresponding linearized problem decays to zero in time. We also give an explicit algebraic decay rate.

CERN and the Wigner Research Centre for Physics inaugurate CERN data centre’s extension in Budapest, Hungary

CERN Multimedia

Wigner Research Centre for Physics, Hungary

2013-01-01

On 13 June 2013 CERN and the Wigner Research Centre for Physics inaugurated the Hungarian data centre in Budapest, marking the completion of the facility hosting the extension for CERN computing resources. About 500 servers, 20,000 computing cores, and 5.5 Petabytes of storage are already operational at the site. The dedicated and redundant 100 Gbit/s circuits connecting the two sites are functional since February 2013 and are among the first transnational links at this distance. The capacity at Wigner will be remotely managed from CERN, substantially extending the capabilities of the Worldwide LHC Computing Grid (WLCG) Tier-0 activities and bolstering CERN’s infrastructure business continuity.

A test of Wigner's spin-isospin symmetry from double binding energy differences

International Nuclear Information System (INIS)

Van Isacker, P.; Warner, D.D.; Brenner, D.S.

1995-01-01

It is shown that the anomalously large double binding energy differences for even-even N = Z nuclei are a consequence of Wigner's SU(4) symmetry. These, and similar quantities for odd-mass and odd-odd nuclei, provide a simple and distinct signature of this symmetry in N ≅ Z nuclei. (authors). 16 refs., 2 figs., 1 tab

Application of the Wigner-Function Formulation to Mesoscopic Systems in Presence of Electron-Phonon Interaction

National Research Council Canada - National Science Library

Jacoboni, C

1997-01-01

A theoretical and computational analysis of the quantum dynamics of charge carriers in presence of electron-phonon interaction based on the Wigner function is here applied to the study of transport in mesoscopic systems...

Two-Q-boson interferometry and generalization of the Wigner function

Energy Technology Data Exchange (ETDEWEB)

Padula, Sandra S. [Instituto de Fisica Teorica (IFT), Sao Paulo, SP (Brazil)]. E-mail: padula@ift.unesp.br; Zhang, Q.H. [McGill Univ., Montreal (Canada). Physics Dept.

2004-07-01

Bose-Einstein correlations of two identically charged Q-bosons are derived considering those particles to be confined in finite volumes. Boundary effects on single Q-boson spectrum are also studied. We illustrate these effects by two examples: a toy model (one-dimensional box) and a confining sphere. We also confined a generalized expression for the Wigner function depending on the deformation parameter Q, which is reduced to its original functional form in the limit Q {yields} 1. (author)

Two-Q-boson interferometry and generalization of the Wigner function

International Nuclear Information System (INIS)

Padula, Sandra S.; Zhang, Q.H.

2004-01-01

Bose-Einstein correlations of two identically charged Q-bosons are derived considering those particles to be confined in finite volumes. Boundary effects on single Q-boson spectrum are also studied. We illustrate these effects by two examples: a toy model (one-dimensional box) and a confining sphere. We also derive a generalized expression for the Wigner function depending on the deformation parameter Q, which is reduced to its original functional form in the limit Q → 1

Two-Q-boson interferometry and generalization of the Wigner function

International Nuclear Information System (INIS)

Padula, Sandra S.; Zhang, Q.H.

2004-01-01

Bose-Einstein correlations of two identically charged Q-bosons are derived considering those particles to be confined in finite volumes. Boundary effects on single Q-boson spectrum are also studied. We illustrate these effects by two examples: a toy model (one-dimensional box) and a confining sphere. We also confined a generalized expression for the Wigner function depending on the deformation parameter Q, which is reduced to its original functional form in the limit Q → 1. (author)

Qsub(N) approximation for slowing-down in fast reactors

International Nuclear Information System (INIS)

Rocca-Volmerange, Brigitte.

1976-05-01

An accurate and simple determination of the neutron energy spectra in fast reactors poses several problems. The slowing-down models (Fermi, Wigner, Goertzel-Greuling...) which are different forms of the approximation with order N=0 may prove inaccurate, in spite of recent improvements. A new method of approximation is presented which turns out to be a method of higher order: the Qsub(N) method. It is characterized by a rapid convergence with respect to the order N, by the use of some global parameters to represent the slowing-down and by the expression of the Boltzmann integral equation in a differential formalism. Numerous test verify that, for the order N=2 or 3, the method gives precision equivalent to that of the multigroup numerical integration for the spectra with greatly reduced calculational effort. Furthermore, since the Qsub(N) expressions are a kind of synthesis method, they allow calculation of the spatial Green's function, or the use of collision probabilities to find the flux. Both possibilities have been introduced into existing reactor codes: EXCALIBUR, TRALOR, RE MINEUR... Some applications to multi-zone media (core, blanket, reflector of Masurca pile and exponential slabs) are presented in the isotropic collision approximation. The case of linearly anisotropic collisions is theoretically resolved [fr

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

Science.gov (United States)

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.

On Wigner's problem, computability theory, and the definition of life

International Nuclear Information System (INIS)

Swain, J.

1998-01-01

In 1961, Eugene Wigner presented a clever argument that in a world which is adequately described by quantum mechanics, self-reproducing systems in general, and perhaps life in particular, would be incredibly improbable. The problem and some attempts at its solution are examined, and a new solution is presented based on computability theory. In particular, it is shown that computability theory provides limits on what can be known about a system in addition to those which arise from quantum mechanics. (author)

Torus as phase space: Weyl quantization, dequantization, and Wigner formalism

Energy Technology Data Exchange (ETDEWEB)

Ligabò, Marilena, E-mail: marilena.ligabo@uniba.it [Dipartimento di Matematica, Università di Bari, I-70125 Bari (Italy)

2016-08-15

The Weyl quantization of classical observables on the torus (as phase space) without regularity assumptions is explicitly computed. The equivalence class of symbols yielding the same Weyl operator is characterized. The Heisenberg equation for the dynamics of general quantum observables is written through the Moyal brackets on the torus and the support of the Wigner transform is characterized. Finally, a dequantization procedure is introduced that applies, for instance, to the Pauli matrices. As a result we obtain the corresponding classical symbols.

A 2D Wigner Distribution-based multisize windows technique for image fusion

Czech Academy of Sciences Publication Activity Database

Redondo, R.; Fischer, S.; Šroubek, Filip; Cristóbal, G.

2008-01-01

Roč. 19, č. 1 (2008), s. 12-19 ISSN 1047-3203 R&D Projects: GA ČR GA102/04/0155; GA ČR GA202/05/0242 Grant - others:CSIC(CZ) 2004CZ0009 Institutional research plan: CEZ:AV0Z10750506 Keywords : Wigner distribution * image fusion * multifocus Subject RIV: JD - Computer Applications, Robotics Impact factor: 1.342, year: 2008

Stokes vector and its relationship to Discrete Wigner Functions of multiqubit states

Energy Technology Data Exchange (ETDEWEB)

Srinivasan, K., E-mail: sriniphysics@gmail.com; Raghavan, G.

2016-07-29

A Stokes vectors and Discrete Wigner Functions (DWF) provide two alternate ways of representing the state of multiqubit systems. A general relationship between the Stokes vector and the DWF is derived for arbitrary n-qubit states for all possible choices of quantum nets. The Stokes vector and the DWF are shown to be related through a Hadamard Matrix. Using these results, a relationship between the Stokes vector of a spin-flipped state and the DWF is derived. Finally, we also present a method to express the Minkowskian squared norm of the Stokes vector, corresponding to n-concurrence in terms of the DWF. - Highlights: • Relationship between Stokes vector (SV) and discrete Wigner function (DWF) for arbitrary multiqubit states is presented. • It is shown that SV and DWF are related to one another through Hadamard matrices. • We show that the Hadamard matrices depend on the choice of the quantum net. • Relationship between SV of the spin flipped state and the DWF is derived. • Expression to compute n-concurrence of the pure n-qubit systems purely in terms of DWF is given.

Stokes vector and its relationship to Discrete Wigner Functions of multiqubit states

International Nuclear Information System (INIS)

Srinivasan, K.; Raghavan, G.

2016-01-01

A Stokes vectors and Discrete Wigner Functions (DWF) provide two alternate ways of representing the state of multiqubit systems. A general relationship between the Stokes vector and the DWF is derived for arbitrary n-qubit states for all possible choices of quantum nets. The Stokes vector and the DWF are shown to be related through a Hadamard Matrix. Using these results, a relationship between the Stokes vector of a spin-flipped state and the DWF is derived. Finally, we also present a method to express the Minkowskian squared norm of the Stokes vector, corresponding to n-concurrence in terms of the DWF. - Highlights: • Relationship between Stokes vector (SV) and discrete Wigner function (DWF) for arbitrary multiqubit states is presented. • It is shown that SV and DWF are related to one another through Hadamard matrices. • We show that the Hadamard matrices depend on the choice of the quantum net. • Relationship between SV of the spin flipped state and the DWF is derived. • Expression to compute n-concurrence of the pure n-qubit systems purely in terms of DWF is given.

Number-Phase Wigner Representation and Entropic Uncertainty Relations for Binomial and Negative Binomial States

International Nuclear Information System (INIS)

Amitabh, J.; Vaccaro, J.A.; Hill, K.E.

1998-01-01

We study the recently defined number-phase Wigner function S NP (n,θ) for a single-mode field considered to be in binomial and negative binomial states. These states interpolate between Fock and coherent states and coherent and quasi thermal states, respectively, and thus provide a set of states with properties ranging from uncertain phase and sharp photon number to sharp phase and uncertain photon number. The distribution function S NP (n,θ) gives a graphical representation of the complimentary nature of the number and phase properties of these states. We highlight important differences between Wigner's quasi probability function, which is associated with the position and momentum observables, and S NP (n,θ), which is associated directly with the photon number and phase observables. We also discuss the number-phase entropic uncertainty relation for the binomial and negative binomial states and we show that negative binomial states give a lower phase entropy than states which minimize the phase variance

Excitonic Wigner crystal and high T sub c ferromagnetism in RB sub 6

CERN Document Server

Kasuya, T

2000-01-01

The mechanisms for the high T sub c ferromagnetism in La-doped divalent hexaborides DB sub 6 are studied in detail comparing with similar family materials, in particular with YbB sub 6 , EuB sub 6 and Ce monopnictides. It is shown that in DB sub 6 the light-electron-heavy-hole paired excitonic states form the Wigner crystal, or Wigner glass in actual materials, in which the conventional intersite electron exchange interactions similar to that in Ni dominate the pair singlet formation due to the intra pair mixing causing a ferromagnetic spin glass-like ordering of electron spins. In the La-doped system La sub x D sub 1 sub - sub x B sub 6 , the population of molecular La impurity states with giant moments increases as x approaches the optimal value x sub 0 approx 0.005 for high T sub c providing vacant states for the roton-like fluctuations, which cause the high T sub c at the boundary of the delocalization of electron carriers. Therefore, the critical La concentration for delocalization coincides with the opt...

Wigner time-delay distribution in chaotic cavities and freezing transition.

Science.gov (United States)

Texier, Christophe; Majumdar, Satya N

2013-06-21

Using the joint distribution for proper time delays of a chaotic cavity derived by Brouwer, Frahm, and Beenakker [Phys. Rev. Lett. 78, 4737 (1997)], we obtain, in the limit of the large number of channels N, the large deviation function for the distribution of the Wigner time delay (the sum of proper times) by a Coulomb gas method. We show that the existence of a power law tail originates from narrow resonance contributions, related to a (second order) freezing transition in the Coulomb gas.

Atomic probe Wigner tomography of a nanomechanical system

International Nuclear Information System (INIS)

Singh, Swati; Meystre, Pierre

2010-01-01

We propose a scheme to measure the quantum state of a nanomechanical oscillator cooled near its ground state of vibrational motion. This is an extension of the nonlinear atomic homodyning technique scheme first developed to measure the intracavity field in a micromaser. It involves the use of a detector atom that is simultaneously coupled to the resonator via a magnetic interaction and to (classical) optical fields via a Raman transition. We show that the probability for the atom to be found in the ground state is a direct measure of the Wigner characteristic function of the nanomechanical oscillator. We also investigate the back-action effect of this destructive measurement on the state of the resonator.

Inoenue-Wigner contraction and D = 2 + 1 supergravity

Energy Technology Data Exchange (ETDEWEB)

Concha, P.K.; Rodriguez, E.K. [Universidad Adolfo Ibanez, Departamento de Ciencias, Facultad de Artes Liberales, Vina del Mar (Chile); Universidad Austral de Chile, Instituto de Ciencias Fisicas y Matematicas, Valdivia (Chile); Fierro, O. [Universidad Catolica de la Santisima Concepcion, Departamento de Matematica y Fisica Aplicadas, Concepcion (Chile)

2017-01-15

We present a generalization of the standard Inoenue-Wigner contraction by rescaling not only the generators of a Lie superalgebra but also the arbitrary constants appearing in the components of the invariant tensor. The procedure presented here allows one to obtain explicitly the Chern-Simons supergravity action of a contracted superalgebra. In particular we show that the Poincare limit can be performed to a D = 2 + 1 (p,q) AdS Chern-Simons supergravity in presence of the exotic form. We also construct a new three-dimensional (2,0) Maxwell Chern-Simons supergravity theory as a particular limit of (2,0) AdS-Lorentz supergravity theory. The generalization for N = p + q gravitinos is also considered. (orig.)

Rotation-type input-output relationships for Wigner distribution moments in fractional Fourier transform systems

NARCIS (Netherlands)

Bastiaans, M.J.; Alieva, T.

2002-01-01

It is shown how all global Wigner distribution moments of arbitrary order in the output plane of a (generally anamorphic) two-dimensional fractional Fourier transform system can be expressed in terms of the moments in the input plane. This general input-output relationship is then broken down into a

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

DEFF Research Database (Denmark)

Pecker, S.; Kuemmeth, Ferdinand; Secchi, A.

2013-01-01

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...

W∞ and the Racah-Wigner algebra

International Nuclear Information System (INIS)

Pope, C.N.; Shen, X.; Romans, L.J.

1990-01-01

We examine the structure of a recently constructed W ∞ algebra, an extension of the Virasoro algebra that describes an infinite number of fields with all conformal spins 2,3..., with central terms for all spins. By examining its underlying SL(2,R) structure, we are able to exhibit its relation to the algebas of SL(2,R) tensor operators. Based upon this relationship, we generalise W ∞ to a one-parameter family of inequivalent Lie algebras W ∞ (μ), which for general μ requires the introduction of formally negative spins. Furthermore, we display a realisation of the W ∞ (μ) commutation relations in terms of an underlying associative product, which we denote with a lone star. This product structure shares many formal features with the Racah-Wigner algebra in angular-momentum theory. We also discuss the relation between W ∞ and the symplectic algebra on a cone, which can be viewed as a co-adjoint orbit of SL(2,R). (orig.)

Wigner Distribution Functions and the Representation of Canonical Transformations in Time-Dependent Quantum Mechanics

Directory of Open Access Journals (Sweden)

Marcos Moshinsky

2008-07-01

Full Text Available For classical canonical transformations, one can, using the Wigner transformation, pass from their representation in Hilbert space to a kernel in phase space. In this paper it will be discussed how the time-dependence of the uncertainties of the corresponding time-dependent quantum problems can be incorporated into this formalism.

The use of Wigner transformation for the description of the classical aspects of the quantum systems

International Nuclear Information System (INIS)

Baran, V.

1990-01-01

The mutual relation between the classical phase space and the Hilbert space of operators are explicitly written down.In particular, the Wigner transformation maps the Hilbert space onto the classical space of functions defined on two dimensional manifold. (Author)

MD simulation of atomic displacements in metals and metallic bilayers under low energy ion bombardment at 300 K

International Nuclear Information System (INIS)

Kornich, G.V.; Betz, G.; Bazhin, A.I.

1999-01-01

MD simulations of 100 eV Ar ion bombardment of (1 0 0) Ni and Al as well as Al/Ni bilayer crystals at 300 K have been performed and compared to previous calculations at 0 K. The Al/Ni bilayer crystal consisted of one Al layer on a (1 0 0) Ni substrate. Sputtering yields for Ni and Al/Ni show no temperature dependence, while for Al a pronounced increase with temperature was observed. The contributions of different mechanisms to the production of surface and bulk defects are discussed. The mean square displacement (MSD) of atoms is in all cases larger at 300 K as compared to 0 K. The larger MSD at 300 K is mainly due to an increase in lateral (perpendicular to the ion beam) motion of displaced atoms. Similar the number of atomic jumps, in which an atom leaves its original Wigner-Seitz cell, increases in all cases with temperature. For the pure elements the production of bulk vacancies and interstitials decreases with temperature, but the number of surface vacancies and ad-atoms increases with temperature. For the bilayer system practically no temperature dependence for defects was observed

A different approach to obtain Mayer’s extension to stationary single particle Wigner distribution

International Nuclear Information System (INIS)

Bose, Anirban; Janaki, M. S.

2012-01-01

It is shown that the stationary collisionless single-particle Wigner equation in one dimension containing quantum corrections at the lowest order is satisfied by a distribution function that is similar in form to the Maxwellian distribution with an effective mass and a generalized potential. The distribution is used to study quantum corrections to electron hole solutions.

Realistic electrostatic potentials in a neutron star crust

International Nuclear Information System (INIS)

Ebel, Claudio; Mishustin, Igor; Greiner, Walter

2015-01-01

We study the electrostatic properties of inhomogeneous nuclear matter which can be formed in the crusts of neutron stars or in supernova explosions. Such matter is represented by Wigner–Seitz cells of different geometries (spherical, cylindrical, cartesian), which contain nuclei, free neutrons and electrons under the conditions of electrical neutrality. Using the Thomas–Fermi approximation, we have solved the Poisson equation for the electrostatic potential and calculated the corresponding electron density distributions in individual cells. The calculations are done for different shapes and sizes of the cells and different average baryon densities. The electron-to-baryon fraction was fixed at 0.3. Using realistic electron distributions leads to a significant reduction in electrostatic energy and electron chemical potential. (paper)

A WENO-solver combined with adaptive momentum discretization for the Wigner transport equation and its application to resonant tunneling diodes.

Science.gov (United States)

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.

The modified Bargmann-Wigner formalism for bosons of spin 1 and 2

Energy Technology Data Exchange (ETDEWEB)

Dvoeglazov, Valeri V [Universidad de Zacatecas, Apartado Postal 636, Suc. UAZ, Zacatecas 98062, Zac (Mexico)

2007-11-15

On the basis of our recent modifications of the Dirac formalism we generalize the Bargmann-Wigner formalism for higher spins to be compatible with other formalisms for bosons. Relations with dual electrodynamics, with the Ogievetskii-Polubarinov notoph and the Weinberg 2(2J+1) theory are found. Next, we introduce the dual analogues of the Riemann tensor and derive corresponding dynamical equations in the Minkowski space. Relations with the Marques-Spehler chiral gravity theory are discussed.

On the distribution functions in the quantum mechanics and Wigner functions

International Nuclear Information System (INIS)

Kuz'menkov, L.S.; Maksimov, S.G.

2002-01-01

The problem on the distribution functions, leading to the similar local values of the particles number, pulse and energy, as in the quantum mechanics, is formulated and solved. The method is based on the quantum-mechanical determination of the probability density. The derived distribution function coincides with the Wigner function only for the spatial-homogeneous systems. The Bogolyubov equations chain, the Liouville equation for the distribution quantum functions by any number of particles in the system, the general expression for the tensor of the dielectric permittivity of the plasma electron component are obtained [ru

A generalized Wigner function for quantum systems with the SU(2) dynamical symmetry group

International Nuclear Information System (INIS)

Klimov, A B; Romero, J L

2008-01-01

We introduce a Wigner-like quasidistribution function to describe quantum systems with the SU(2) dynamic symmetry group. This function is defined in a three-dimensional group manifold and can be used to represent the states defined in several SU(2) invariant subspaces. The explicit differential Moyal-like form of the star product is found and analyzed in the semiclassical limit

Neutron bombardment of single wall carbon nanohorn (SWCNH). DSC determination of the stored Wigner-Szilard energy

International Nuclear Information System (INIS)

Franco Cataldo; Susana Iglesias-Groth; Yaser Hafez; Giancarlo Angelini

2014-01-01

Single wall carbon nanohorn (SWCNH) were neutron-bombarded to a dose of 3.28 × 10 16 n/cm 2 . The Wigner or stored energy was determined by a differential scanning calorimeter and was found 5.49 J/g, 50 times higher than the Wigner energy measured on graphite flakes treated at the same neutron dose. The activation energy for the thermal annealing of the accumulated radiation damage in SWCNH was determined in the range 6.3-6.6 eV against a typical activation energy for the annealing of the radiation-damaged graphite which is in the range of 1.4-1.5 eV. Furthermore the stored energy in neutron-damaged SWCNH is released at 400-430 deg C while the main peak in the neutron-damaged graphite occurs at 200-220 deg C. The radiation damaged SWCNH were examined with FT-IR spectroscopy showing the formation of acetylenic and aliphatic moieties suggesting the aromatic C=C breakdown caused by the neutron bombardment. (author)

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

Energy Technology Data Exchange (ETDEWEB)

Gadella, M. [Departamento de Física Teórica, Atómica y Óptica and IMUVA, Universidad de Valladolid, E-47011 Valladolid (Spain); Kuru, Ş. [Department of Physics, Faculty of Science, Ankara University, 06100 Ankara (Turkey); Negro, J., E-mail: jnegro@fta.uva.es [Departamento de Física Teórica, Atómica y Óptica and IMUVA, Universidad de Valladolid, E-47011 Valladolid (Spain)

2017-04-15

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 for 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.

Optical sectioning for optical scanning holography using phase-space filtering with Wigner distribution functions.

Science.gov (United States)

Kim, Hwi; Min, Sung-Wook; Lee, Byoungho; Poon, Ting-Chung

2008-07-01

We propose a novel optical sectioning method for optical scanning holography, which is performed in phase space by using Wigner distribution functions together with the fractional Fourier transform. The principle of phase-space optical sectioning for one-dimensional signals, such as slit objects, and two-dimensional signals, such as rectangular objects, is first discussed. Computer simulation results are then presented to substantiate the proposed idea.

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

International Nuclear Information System (INIS)

Miller, William H.; Cotton, Stephen J.

2016-01-01

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.

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.

Science.gov (United States)

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.

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

Energy Technology Data Exchange (ETDEWEB)

Miller, William H., E-mail: millerwh@berkeley.edu; Cotton, Stephen J., E-mail: StephenJCotton47@gmail.com [Department of Chemistry and Kenneth S. Pitzer Center for Theoretical Chemistry, University of California, and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States)

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.

Effective medium super-cell approximation for interacting disordered systems: an alternative real-space derivation of generalized dynamical cluster approximation

International Nuclear Information System (INIS)

Moradian, Rostam

2006-01-01

We develop a generalized real-space effective medium super-cell approximation (EMSCA) method to treat the electronic states of interacting disordered systems. This method is general and allows randomness both in the on-site energies and in the hopping integrals. For a non-interacting disordered system, in the special case of randomness in the on-site energies, this method is equivalent to the non-local coherent potential approximation (NLCPA) derived previously. Also, for an interacting system the EMSCA method leads to the real-space derivation of the generalized dynamical cluster approximation (DCA) for a general lattice structure. We found that the original DCA and the NLCPA are two simple cases of this technique, so the EMSCA is equivalent to the generalized DCA where there is included interaction and randomness in the on-site energies and in the hopping integrals. All of the equations of this formalism are derived by using the effective medium theory in real space

Near-threshold infrared photodetachment of Al-: A determination of the electron affinity of aluminum and the range of validity of the Wigner law

International Nuclear Information System (INIS)

Calabrese, D.; Covington, A.M.; Thompson, J.S.; Marawar, R.W.; Farley, J.W.

1996-01-01

The relative photodetachment cross section of Al - has been measured in the wavelength range 2420 endash 2820 nm (0.440 endash 0.512 eV), using a coaxial ion-laser beams apparatus, in which a 2.98-keV Al - beam is merged with a beam from an F-center laser. The cross-section data near the 3 P 0,1,2 → 2 P 1/2,3/2 photodetachment threshold have been fitted to the Wigner threshold law and to the zero-core-contribution theory of photodetachment. The electron affinity of aluminum was determined to be 0.44094(+0.00066/-0.00048) eV, after correcting the experimental threshold for unresolved fine structure in the ground states of Al - and Al. The new measurement is in agreement with the best previous measurement (0.441±0.010 eV) and is 20 times more precise. The Wigner law agrees with experiment within a few percent for photon energies within 3% of threshold. A proposed leading correction to the Wigner law is discussed. copyright 1996 The American Physical Society

Characterization of tomographically faithful states in terms of their Wigner function

International Nuclear Information System (INIS)

D'Ariano, G M; Sacchi, M F

2005-01-01

A bipartite quantum state is tomographically faithful when it can be used as an input of a quantum operation acting on one of the two quantum systems, such that the joint output state carries complete information about the operation itself. Tomographically faithful states are a necessary ingredient for the tomography of quantum operations and for complete quantum calibration of measuring apparatuses. In this paper we provide a complete classification of such states for continuous variables in terms of the Wigner function of the state. For two-mode Gaussian states faithfulness simply resorts to correlation between the modes

Generalized synthetic kernel approximation for elastic moderation of fast neutrons

International Nuclear Information System (INIS)

Yamamoto, Koji; Sekiya, Tamotsu; Yamamura, Yasunori.

1975-01-01

A method of synthetic kernel approximation is examined in some detail with a view to simplifying the treatment of the elastic moderation of fast neutrons. A sequence of unified kernel (fsub(N)) is introduced, which is then divided into two subsequences (Wsub(n)) and (Gsub(n)) according to whether N is odd (Wsub(n)=fsub(2n-1), n=1,2, ...) or even (Gsub(n)=fsub(2n), n=0,1, ...). The W 1 and G 1 kernels correspond to the usual Wigner and GG kernels, respectively, and the Wsub(n) and Gsub(n) kernels for n>=2 represent generalizations thereof. It is shown that the Wsub(n) kernel solution with a relatively small n (>=2) is superior on the whole to the Gsub(n) kernel solution for the same index n, while both converge to the exact values with increasing n. To evaluate the collision density numerically and rapidly, a simple recurrence formula is derived. In the asymptotic region (except near resonances), this recurrence formula allows calculation with a relatively coarse mesh width whenever hsub(a)<=0.05 at least. For calculations in the transient lethargy region, a mesh width of order epsilon/10 is small enough to evaluate the approximate collision density psisub(N) with an accuracy comparable to that obtained analytically. It is shown that, with the present method, an order of approximation of about n=7 should yield a practically correct solution diviating not more than 1% in collision density. (auth.)

The Nuclear Scissors Mode by Two Approaches (Wigner Function Moments Versus RPA)

CERN Document Server

Balbutsev, E B

2004-01-01

Two complementary methods to describe the collective motion, RPA and Wigner Function Moments (WFM) method, are compared on an example of a simple model - harmonic oscillator with quadrupole-quadrupole residual interaction. It is shown that they give identical formulae for eigenfrequencies and transition probabilities of all collective excitations of the model including the scissors mode, which is a subject of our especial attention. The normalization factor of the "synthetic" scissors state and its overlap with physical states are calculated analytically. The orthogonality of the spurious state to all physical states is proved rigorously.

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

Science.gov (United States)

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.

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

KAUST Repository

Chen, Jyun-Hong

2018-03-12

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 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 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 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.

About SIC POVMs and discrete Wigner distributions

International Nuclear Information System (INIS)

Colin, Samuel; Corbett, John; Durt, Thomas; Gross, David

2005-01-01

A set of d 2 vectors in a Hilbert space of dimension d is called equiangular if each pair of vectors encloses the same angle. The projection operators onto these vectors define a POVM which is distinguished by its high degree of symmetry. Measures of this kind are called symmetric informationally complete, or SIC POVMs for short, and could be applied for quantum state tomography. Despite its simple geometrical description, the problem of constructing SIC POVMs or even proving their existence seems to be very hard. It is our purpose to introduce two applications of discrete Wigner functions to the analysis of the problem at hand. First, we will present a method for identifying symmetries of SIC POVMs under Clifford operations. This constitutes an alternative approach to a structure described before by Zauner and Appleby. Further, a simple and geometrically motivated construction for an SIC POVM in dimensions two and three is given (which, unfortunately, allows no generalization). Even though no new structures are found, we hope that the re-formulation of the problem may prove useful for future inquiries

The role of scalar product and Wigner distribution in optical and quantum mechanical measurements

International Nuclear Information System (INIS)

Wodkiewicz, K.

1984-01-01

In this paper we present a unified approach to the phase-space description of optical and quantum measurements. We find that from the operational point of view the notion of a time dependent spectrum of light and a joint measurement of position and momentum in quantum mechanics can be formulated in one common approach in which the scalar product, the Wigner function and the phase-space proximity are closely related to a realistic measuring process

Wigner-Kirkwood expansion of the quasi-elastic nuclear responses and application to spin-isospin responses

International Nuclear Information System (INIS)

Chanfray, G.

1988-01-01

We derive a semi-classical Wigner-Kirkwood expansion (Planck constant expansion) of the linear response functions. We find that the semi-classical results compare very well to the quantum mechanical calculations. We apply our formalism to the spin-isospin responses and show that surface-peaked Planck constant 2 corrections considerably decrease the ratio longitudinal/transverse as obtained through the Los Alamos (longitudinal momentum) experiment

The Collected Works of Eugene Paul Wigner Historical, Philosophical, and Socio-Political Papers

CERN Document Server

Wigner, Eugene Paul

2001-01-01

Not only was EP Wigner one of the most active creators of 20th century physics, he was also always interested in expressing his opinion in philosophical, political or sociological matters This volume of his collected works covers a wide selection of his essays about science and society, about himself and his colleagues Annotated by J Mehra, this volume will become an important source of reference for historians of science, and it will be pleasant reading for every physicist interested in forming ideas in modern physics

Quasi-static electron density fluctuations of atoms in hot compressed matter

International Nuclear Information System (INIS)

Grimaldi, F.; Grimaldi-Lecourt, A.

1982-01-01

The standard theoretical methods for the calculation of properties of hot compressed matter lead to a description based on the Average Atom model. In this model the degenerate orbitals are populated with the Fermi-Dirac (FD) density, partitioned according to the binomial distribution. Since the one particle picture is inadequate to evaluate reliable optical properties, a method involving correlated population fluctuations, but limited to unrelaxed orbitals and lacking time dependence, has been examined. The probability distribution of fluctuations in a particular level is evaluated through a decoupling procedure. The method is carried out self consistently. For each level this leads to the definition of an effective 1st order ionization energy as a statistical sum of all possible transition energies. As a result the effective number of electrons exchanged with the outside weights the chemical potential. This defines an effective chemical potential μsup(k) for each level. In many cases of interest the statistics leads to FD type average occupation numbers. This allows a treatment of the continuum in a Thomas-Fermi like model using the effective ionization energy and μsup(k). We obtain a simultaneous description of charge rearrangements and net fluctuations in the Wigner-Seitz cell. The discussion is supported by numerical results for iron. (author)

Approximate method for solving the velocity dependent transport equation in a slab lattice

International Nuclear Information System (INIS)

Ferrari, A.

1966-01-01

A method is described that is intended to provide an approximate solution of the transport equation in a medium simulating a water-moderated plate filled reactor core. This medium is constituted by a periodic array of water channels and absorbing plates. The velocity dependent transport equation in slab geometry is included. The computation is performed in a water channel: the absorbing plates are accounted for by the boundary conditions. The scattering of neutrons in water is assumed isotropic, which allows the use of a double Pn approximation to deal with the angular dependence. This method is able to represent the discontinuity of the angular distribution at the channel boundary. The set of equations thus obtained is dependent only on x and v and the coefficients are independent on x. This solution suggests to try solutions involving Legendre polynomials. This scheme leads to a set of equations v dependent only. To obtain an explicit solution, a thermalization model must now be chosen. Using the secondary model of Cadilhac a solution of this set is easy to get. The numerical computations were performed with a particular secondary model, the well-known model of Wigner and Wilkins. (author) [fr

Interference effects of neutral MSSM Higgs bosons with a generalised narrow-width approximation

International Nuclear Information System (INIS)

Fuchs, Elina

2014-11-01

Mixing effects in the MSSM Higgs sector can give rise to a sizeable interference between the neutral Higgs bosons. On the other hand, factorising a more complicated process into production and decay parts by means of the narrow-width approximation (NWA) simplifies the calculation. The standard NWA, however, does not account for interference terms. Therefore, we introduce a generalisation of the NWA (gNWA) which allows for a consistent treatment of interference effects between nearly mass-degenerate particles. Furthermore, we apply the gNWA at the tree and 1-loop level to an example process where the neutral Higgs bosons h and H are produced in the decay of a heavy neutralino and subsequently decay into a fermion pair. The h-H propagator mixing is found to agree well with the approximation of Breit-Wigner propagators times finite wave-function normalisation factors, both leading to a significant interference contribution. The factorisation of the interference term based on on-shell matrix elements reproduces the full interference result within a precision of better than 1% for the considered process. The gNWA also enables the inclusion of contributions beyond the 1-loop order into the most precise prediction.

Wigner Transport Simulation of Resonant Tunneling Diodes with Auxiliary Quantum Wells

Science.gov (United States)

Lee, Joon-Ho; Shin, Mincheol; Byun, Seok-Joo; Kim, Wangki

2018-03-01

Resonant-tunneling diodes (RTDs) with auxiliary quantum wells ( e.g., emitter prewell, subwell, and collector postwell) are studied using a Wigner transport equation (WTE) discretized by a thirdorder upwind differential scheme. A flat-band potential profile is used for the WTE simulation. Our calculations revealed functions of the auxiliary wells as follows: The prewell increases the current density ( J) and the peak voltage ( V p ) while decreasing the peak-to-valley current ratio (PVCR), and the postwell decreases J while increasing the PVCR. The subwell affects J and PVCR, but its main effect is to decrease V p . When multiple auxiliary wells are used, each auxiliary well contributes independently to the transport without producing side effects.

The Wigner distribution function in modal characterisation

CSIR Research Space (South Africa)

Mredlana, Prince

2016-07-01

Full Text Available function in modal characterisation P. MREDLANA1, D. NAIDOO1, C MAFUSIRE2, T. KRUGER2, A. DUDLEY1,3, A. FORBES1,3 1CSIR National Laser Centre, PO BOX 395, Pretoria 0001, South Africa. 2Department of Physics, Faculty of Natural and Agricultural..., the Wigner distribution of 𝑓 𝑥 is an integral of the correlation function 𝑓 𝑥 + 1 2 𝑥′ 𝑓 ∗ 𝑥 + 1 2 𝑥′ represented as: 𝑊𝑓 𝑥, 𝑒 = 𝑓 𝑥 + 1 2 𝑥′ 𝑓 ∗ 𝑥 + 1 2 𝑥′ 𝑒−𝑖𝑒𝑥′𝑑ð...

Formulation of state projected centroid molecular dynamics: Microcanonical ensemble and connection to the Wigner distribution.

Science.gov (United States)

Orr, Lindsay; Hernández de la Peña, Lisandro; Roy, Pierre-Nicholas

2017-06-07

A derivation of quantum statistical mechanics based on the concept of a Feynman path centroid is presented for the case of generalized density operators using the projected density operator formalism of Blinov and Roy [J. Chem. Phys. 115, 7822-7831 (2001)]. The resulting centroid densities, centroid symbols, and centroid correlation functions are formulated and analyzed in the context of the canonical equilibrium picture of Jang and Voth [J. Chem. Phys. 111, 2357-2370 (1999)]. The case where the density operator projects onto a particular energy eigenstate of the system is discussed, and it is shown that one can extract microcanonical dynamical information from double Kubo transformed correlation functions. It is also shown that the proposed projection operator approach can be used to formally connect the centroid and Wigner phase-space distributions in the zero reciprocal temperature β limit. A Centroid Molecular Dynamics (CMD) approximation to the state-projected exact quantum dynamics is proposed and proven to be exact in the harmonic limit. The state projected CMD method is also tested numerically for a quartic oscillator and a double-well potential and found to be more accurate than canonical CMD. In the case of a ground state projection, this method can resolve tunnelling splittings of the double well problem in the higher barrier regime where canonical CMD fails. Finally, the state-projected CMD framework is cast in a path integral form.

Formulation of state projected centroid molecular dynamics: Microcanonical ensemble and connection to the Wigner distribution

Science.gov (United States)

Orr, Lindsay; Hernández de la Peña, Lisandro; Roy, Pierre-Nicholas

2017-06-01

A derivation of quantum statistical mechanics based on the concept of a Feynman path centroid is presented for the case of generalized density operators using the projected density operator formalism of Blinov and Roy [J. Chem. Phys. 115, 7822-7831 (2001)]. The resulting centroid densities, centroid symbols, and centroid correlation functions are formulated and analyzed in the context of the canonical equilibrium picture of Jang and Voth [J. Chem. Phys. 111, 2357-2370 (1999)]. The case where the density operator projects onto a particular energy eigenstate of the system is discussed, and it is shown that one can extract microcanonical dynamical information from double Kubo transformed correlation functions. It is also shown that the proposed projection operator approach can be used to formally connect the centroid and Wigner phase-space distributions in the zero reciprocal temperature β limit. A Centroid Molecular Dynamics (CMD) approximation to the state-projected exact quantum dynamics is proposed and proven to be exact in the harmonic limit. The state projected CMD method is also tested numerically for a quartic oscillator and a double-well potential and found to be more accurate than canonical CMD. In the case of a ground state projection, this method can resolve tunnelling splittings of the double well problem in the higher barrier regime where canonical CMD fails. Finally, the state-projected CMD framework is cast in a path integral form.

Aharonov-Bohm oscillations with fractional period in a multichannel Wigner crystal ring

International Nuclear Information System (INIS)

Krive, I.V.; Krokhin, A.A.

1997-01-01

We study the persistent current in a quasi 1D ring with strongly correlated electrons forming a multichannel Wigner crystal (WC). The influence of the Coulomb interaction manifests itself only in the presence of external scatterers that pin the WC. Two regimes of weak and strong pinning are considered. For strong pinning we predict the Aharonov-Bohm oscillations with fractional period. Fractionalization is due to the interchannel coupling in the process of quantum tunneling of the WC. The fractional period depends on the filling of the channels and may serve as an indicator of non-Fermi-liquid behaviour of interacting electrons in quasi 1D rings. (author). 20 refs

Wigner-Smith delay times and the non-Hermitian Hamiltonian for the HOCl molecule

International Nuclear Information System (INIS)

Barr, A.M.; Reichl, L.E.

2013-01-01

We construct the scattering matrix for a two-dimensional model of a Cl atom scattering from an OH dimer. We show that the scattering matrix can be written in terms of a non-Hermitian Hamiltonian whose complex energy eigenvalues can be used to compute Wigner-Smith delay times for the Cl-OH scattering process. We compute the delay times for a range of energies, and show that the scattering states with the longest delay times are strongly influenced by unstable periodic orbits in the classical dynamics. (Copyright copyright 2013 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

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

Science.gov (United States)

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).

Towards an unified microscopic approach of the description of the nuclear structure and reaction

International Nuclear Information System (INIS)

Hoang, Sy-Than

2009-01-01

This thesis contains 3 main parts: 1. Nuclear matter: The properties of nuclear matter are examined using finite range effective interactions, either derived from the Brueckner theory (M3Y-type interactions) or determined in a purely phenomenological way (Gogny-type interactions). Skyrme-type interactions are also used for comparison. The motivation of the study is to establish a link between the bare NN interaction and nuclear matter properties via the effective Brueckner G-matrix parameterized in the M3Y form. We have concentrated our discussion on several main aspects: the pressure in symmetric nuclear matter and in neutron matter, the density dependence of the symmetry energy S, the neutron star cooling, and the nuclear matter incompressibility for the symmetric and asymmetric nuclear matter. 2. Structure of finite nuclei and of the inner crust of neutron stars: We present the non-relativistic HF and HF-BCS approaches in coordinate representation using finite-range density-dependent interactions in both the mean field and pairing channels. The method for solving the HF equations in coordinate space is presented. We limit the study to the spherical symmetry case. An iterative scheme is used for solving the integro-differential HF equations. We adopt the method of Brueckner-Gammel-Weizner which is free of poles in the local equivalent potentials, in contrast to the usually used Vautherin-Veneroni method. Alternatively, we have developed a method using a basis of spherical Bessel functions. The latter method is useful for treating systems containing many nucleons in large boxes like the Wigner-Seitz (WS) cells of the neutron star inner crust. We have thus studied, using the effective interactions mentioned above, the doubly magic nuclei, the Sn isotopes, and the possible occurrence of bubble structures in the nuclei 22 O, 34 Si, 46 Ar and 68 Ar. We also present for the first time a study of Wigner-Seitz cells in the inner crust of neutron stars using finite range

Rotating Wigner molecules and spin-related behaviors in quantum rings

International Nuclear Information System (INIS)

Yang Ning; Zhu Jialin; Dai Zhensheng

2008-01-01

The trial wavefunctions for few-electron quantum rings are presented to describe the spin-dependent rotating Wigner molecule states. The wavefunctions are constructed from the single-particle orbits which contain two variational parameters to describe the shape and size dependence of electron localization in the ring-like confinement. They can explicitly show the size dependence of single-particle orbital occupation to give an understanding of the spin rules of ground states without magnetic fields. They can also correctly describe the spin and angular momentum transitions in magnetic fields. By examining the von Neumann entropy, it is demonstrated that the wavefunctions can illustrate the entanglement between electrons in quantum rings, including the AB oscillations as well as the spin and size dependence of the entropy. Such trial wavefunctions will be useful in investigating spin-related quantum behaviors of a few electrons in quantum rings

Directional Wigner-Ville distribution and its application for rotating-machinery condition monitoring

International Nuclear Information System (INIS)

Kim, Dong Wan; Ha, Jae HOng; Shin, Hae Gon; Lee, Yoon Hee; Kim, Young Baik

1996-01-01

Vibration analysis is one of the most powerful tools available for the detection and isolation of incipient faults in mechanical systems. The methods of vibration analysis in use today and under continuous study are broad band vibration monitoring, time domain analysis, and frequency domain analysis. In recent years, great interest has been generated concerning the use of time-frequency representation and its application for a machinery diagnostics and condition monitoring system. The objective of the research described in this paper was to develop a new diagnostic tool for the rotating machinery. This paper introduces a new time-frequency representation, Directional Wigner-Ville Distribution, which analyses the time-frequency structure of the rotating machinery vibration

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

Science.gov (United States)

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.

Quality parameters analysis of optical imaging systems with enhanced focal depth using the Wigner distribution function

Science.gov (United States)

Zalvidea; Colautti; Sicre

2000-05-01

An analysis of the Strehl ratio and the optical transfer function as imaging quality parameters of optical elements with enhanced focal length is carried out by employing the Wigner distribution function. To this end, we use four different pupil functions: a full circular aperture, a hyper-Gaussian aperture, a quartic phase plate, and a logarithmic phase mask. A comparison is performed between the quality parameters and test images formed by these pupil functions at different defocus distances.

One-electron densities of freely rotating Wigner molecules

Science.gov (United States)

Cioslowski, Jerzy

2017-12-01

A formalism enabling computation of the one-particle density of a freely rotating assembly of identical particles that vibrate about their equilibrium positions with amplitudes much smaller than their average distances is presented. It produces densities as finite sums of products of angular and radial functions, the length of the expansion being determined by the interplay between the point-group and permutational symmetries of the system in question. Obtaining from a convolution of the rotational and bosonic components of the parent wavefunction, the angular functions are state-dependent. On the other hand, the radial functions are Gaussians with maxima located at the equilibrium lengths of the position vectors of individual particles and exponents depending on the scalar products of these vectors and the eigenvectors of the corresponding Hessian as well as the respective eigenvalues. Although the new formalism is particularly useful for studies of the Wigner molecules formed by electrons subject to weak confining potentials, it is readily adaptable to species (such as ´balliums’ and Coulomb crystals) composed of identical particles with arbitrary spin statistics and permutational symmetry. Several examples of applications of the present approach to the harmonium atoms within the strong-correlation regime are given.

Prometeo I. A program for averaging thermal constants over a Wigner-Wilkins flux spectrum on the Univac UCT of J.E.N.; Prometo I. Progrma para promediar las constantes termicas con el espectro Wigner-Wikins en la Univac UCT de la J.E.N.

Energy Technology Data Exchange (ETDEWEB)

Corella, M R; Iglesias, T

1964-07-01

The Prometeo I program for the Univac UCT of J.E.N., determines the spectrum of thermal neutrons in equilibrium with a hydrogen-moderated homogeneous mixture from the Wigner-Wilkins differential equation, and averages various, cross sections over the spectrum. The present cross section libraries, available for the Prometeo I , are tabulated. (Author) 4 refs.

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

Science.gov (United States)

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.

A benchmark study of the Signed-particle Monte Carlo algorithm for the Wigner equation

Directory of Open Access Journals (Sweden)

Muscato Orazio

2017-12-01

Full Text Available The Wigner equation represents a promising model for the simulation of electronic nanodevices, which allows the comprehension and prediction of quantum mechanical phenomena in terms of quasi-distribution functions. During these years, a Monte Carlo technique for the solution of this kinetic equation has been developed, based on the generation and annihilation of signed particles. This technique can be deeply understood in terms of the theory of pure jump processes with a general state space, producing a class of stochastic algorithms. One of these algorithms has been validated successfully by numerical experiments on a benchmark test case.

Relationship between the Wigner function and the probability density function in quantum phase space representation

International Nuclear Information System (INIS)

Li Qianshu; Lue Liqiang; Wei Gongmin

2004-01-01

This paper discusses the relationship between the Wigner function, along with other related quasiprobability distribution functions, and the probability density distribution function constructed from the wave function of the Schroedinger equation in quantum phase space, as formulated by Torres-Vega and Frederick (TF). At the same time, a general approach in solving the wave function of the Schroedinger equation of TF quantum phase space theory is proposed. The relationship of the wave functions between the TF quantum phase space representation and the coordinate or momentum representation is thus revealed

Progress in Application of Generalized Wigner Distribution to Growth and Other Problems

Science.gov (United States)

Einstein, T. L.; Morales-Cifuentes, Josue; Pimpinelli, Alberto; Gonzalez, Diego Luis

We recap the use of the (single-parameter) Generalized Wigner Distribution (GWD) to analyze capture-zone distributions associated with submonolayer epitaxial growth. We discuss recent applications to physical systems, as well as key simulations. We pay particular attention to how this method compares with other methods to assess the critical nucleus size characterizing growth. The following talk discusses a particular case when special insight is needed to reconcile the various methods. We discuss improvements that can be achieved by going to a 2-parameter fragmentation approach. At a much larger scale we have applied this approach to various distributions in socio-political phenomena (areas of secondary administrative units [e.g., counties] and distributions of subway stations). Work at UMD supported by NSF CHE 13-05892.

Numerical approximation for HIV infection of CD4+ T cells mathematical model

Directory of Open Access Journals (Sweden)

Vineet K. Srivastava

2014-06-01

Full Text Available A dynamical model of HIV infection of CD4+ T cells is solved numerically using an approximate analytical method so-called the differential transform method (DTM. The solution obtained by the method is an infinite power series for appropriate initial condition, without any discretization, transformation, perturbation, or restrictive conditions. A comparative study between the present method, the classical Euler’s and Runge–Kutta fourth order (RK4 methods is also carried out.

Rovibrational states of Wigner molecules in spherically symmetric confining potentials

Energy Technology Data Exchange (ETDEWEB)

Cioslowski, Jerzy [Institute of Physics, University of Szczecin, Wielkopolska 15, 70-451 Szczecin, Poland and Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, D-01187 Dresden (Germany)

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. 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.

Time evolution of the coarse-graining-smoothed Wigner operator in an amplitude dissipative channel: from a pure state to a mixed state

International Nuclear Information System (INIS)

He, Rui; Fan, Hong-yi

2014-01-01

Based on the solution to the master equation of the density operator describing the amplitude dissipative channel, we derive the time evolution law of the coarse-graining-smoothed Wigner operator in this channel, which demonstrates how an initial pure state evolves into a mixed state, exhibiting decoherence

Ionic and Wigner Glasses, Superionic Conductors, and Spinodal Electrostatic Gels: Dynamically Arrested Phases of the Primitive Model

International Nuclear Information System (INIS)

Sanchez-Diaz, L. E.; Juarez-Maldonado, R.; Vizcarra-Rendon, A.

2009-01-01

Based on the recently proposed self-consistent generalized Langevin equation theory of dynamic arrest, in this letter we show that the ergodic-nonergodic phase diagram of a classical mixture of charged hard spheres (the so-called 'primitive model' of ionic solutions and molten salts) includes arrested phases corresponding to nonconducting ionic glasses, partially arrested states that represent solid electrolytes (or 'superionic' conductors), low-density colloidal Wigner glasses, and low-density electrostatic gels associated with arrested spinodal decomposition.

Experimental evidence for a Mott-Wigner glass phase of magnetite above the Verwey temperature

International Nuclear Information System (INIS)

Boekema, C.; Lichti, R.L.; Chan, K.C.B.; Brabers, V.A.M.; Denison, A.B.; Cooke, D.W.; Heffner, R.H.; Hutson, R.L.; Schillaci, M.E.

1986-01-01

New muon-spin-relaxation (μSR) results on magnetite are reported and discussed in light of earlier Moessbauer, neutron, and μSR results. Modification of the μSR anomaly (observed at 247 K in zero field), when an external magnetic field is applied, provides evidence that the anomaly results from cross relaxation between the muon Larmor precession and the electron-correlation process in the B sublattice. The combined results strongly indicate that phonon-assisted electron hopping is the principal conduction mechanism above the Verwey transition temperature (T/sub V/). Together with theoretical evidence, these data support Mott's suggestion that above T/sub V/ magnetite is in the Wigner-glass state

Creation, Storage, and On-Demand Release of Optical Quantum States with a Negative Wigner Function

Directory of Open Access Journals (Sweden)

Jun-ichi Yoshikawa

2013-12-01

Full Text Available Highly nonclassical quantum states of light, characterized by Wigner functions with negative values, have been all-optically created so far only in a heralded fashion. In this case, the desired output emerges rarely and randomly from a quantum-state generator. An important example is the heralded production of high-purity single-photon states, typically based on some nonlinear optical interaction. In contrast, on-demand single-photon sources are also reported, exploiting the quantized level structure of matter systems. These sources, however, lead to highly impure output states, composed mostly of vacuum. While such impure states may still exhibit certain single-photon-like features such as antibunching, they are not nonclassical enough for advanced quantum-information processing. On the other hand, the intrinsic randomness of pure, heralded states can be circumvented by first storing and then releasing them on demand. Here, we propose such a controlled release, and we experimentally demonstrate it for heralded single photons. We employ two optical cavities, where the photons are both created and stored inside one cavity and finally released through a dynamical tuning of the other cavity. We demonstrate storage times of up to 300 ns while keeping the single-photon purity around 50% after storage. Our experiment is the first demonstration of a negative Wigner function at the output of an on-demand photon source or a quantum memory. In principle, our storage system is compatible with all kinds of nonclassical states, including those known to be essential for many advanced quantum-information protocols.

Wigner's little group as a gauge generator in linearized gravity theories

International Nuclear Information System (INIS)

Scaria, Tomy; Chakraborty, Biswajit

2002-01-01

We show that the translational subgroup of Wigner's little group for massless particles in 3 + 1 dimensions generates gauge transformation in linearized Einstein gravity. Similarly, a suitable representation of the one-dimensional translational group T(1) is shown to generate gauge transformation in the linearized Einstein-Chern-Simons theory in 2 + 1 dimensions. These representations are derived systematically from appropriate representations of translational groups which generate gauge transformations in gauge theories living in spacetime of one higher dimension by the technique of dimensional descent. The unified picture thus obtained is compared with a similar picture available for vector gauge theories in 3 + 1 and 2 + 1 dimensions. Finally, the polarization tensor of the Einstein-Pauli-Fierz theory in 2 + 1 dimensions is shown to split into the polarization tensors of a pair of Einstein-Chern-Simons theories with opposite helicities suggesting a doublet structure for the Einstein-Pauli-Fierz theory

Scale magnetic effect in quantum electrodynamics and the Wigner-Weyl formalism

Science.gov (United States)

Chernodub, M. N.; Zubkov, M. A.

2017-09-01

The scale magnetic effect (SME) is the generation of electric current due to a conformal anomaly in an external magnetic field in curved spacetime. The effect appears in a vacuum with electrically charged massless particles. Similarly to the Hall effect, the direction of the induced anomalous current is perpendicular to the direction of the external magnetic field B and to the gradient of the conformal factor τ , while the strength of the current is proportional to the beta function of the theory. In massive electrodynamics the SME remains valid, but the value of the induced current differs from the current generated in the system of massless fermions. In the present paper we use the Wigner-Weyl formalism to demonstrate that in accordance with the decoupling property of heavy fermions the corresponding anomalous conductivity vanishes in the large-mass limit with m2≫|e B | and m ≫|∇τ | .

Prometeo I. A program for averaging thermal constants over a Wigner-Wilkins flux spectrum on the Univac UCT of J.E.N

International Nuclear Information System (INIS)

Corella, M. R.; Iglesias, T.

1964-01-01

The Prometeo I program for the Univac UCT of J.E.N., determines the spectrum of thermal neutrons in equilibrium with a hydrogen-moderated homogeneous mixture from the Wigner-Wilkins differential equation, and averages various, cross sections over the spectrum. The present cross section libraries, available for the Prometeo I , are tabulated. (Author) 4 refs

Experimental validation of the Wigner distributions theory of phase-contrast imaging

International Nuclear Information System (INIS)

Donnelly, Edwin F.; Price, Ronald R.; Pickens, David R.

2005-01-01

Recently, a new theory of phase-contrast imaging has been proposed by Wu and Liu [Med. Phys. 31, 2378-2384 (2004)]. This theory, based upon Wigner distributions, provides a much stronger foundation for the evaluation of phase-contrast imaging systems than did the prior theories based upon Fresnel-Kirchhoff diffraction theory. In this paper, we compare results of measurements made in our laboratory of phase contrast for different geometries and tube voltages to the predictions of the Wu and Liu model. In our previous publications, we have used an empirical measurement (the edge enhancement index) to parametrize the degree of phase-contrast effects in an image. While the Wu and Liu model itself does not predict image contrast, it does measure the degree of phase contrast that the system can image for a given spatial frequency. We have found that our previously published experimental results relating phase-contrast effects to geometry and x-ray tube voltage are consistent with the predictions of the Wu and Liu model

Study of the dynamics of the lower hybrid wave during current drive in tokamaks and of the Weyl-Wigner in quantum mechanics

International Nuclear Information System (INIS)

Bizarro, J.P.

1993-10-01

A comprehensive and detailed investigation is presented on the dynamics of the lower hybrid wave during current drive in tokamaks in situations where toroidally induced ray stochasticity is important and on the Weyl-Wigner formalism for rotation angle and angular momentum variables in quantum mechanics. It is shown that ray-tracing and Fokker-Planck codes are reliable tools for modelling the physics of lower-hybrid current drive provided a large number of rays is used when stochastic effects are important, and, in particular, that such codes are capable of reproducing the experimentally observed features of the hard X-ray emission. The balance between the wave damping and the stochastic divergence of nearby ray trajectories appears to be of great importance in governing the dynamics of the launched power spectrum and in establishing the characteristics of the deposition patterns. The implications of rotational periodicity and of angular momentum quantization for the Weyl-Wigner formalism are analyzed. Particular attention is paid to discreteness and its consequences: importance of evenness and oddness, use of two difference operators instead of one differential operator. 24 refs

Wigner transformation in curved space-time and the curvature correction of the Vlasov equation for semiclassical gravitating systems

International Nuclear Information System (INIS)

Winter, J.

1985-01-01

A covariant generalization of the Wigner transformation of quantum equations is proposed for gravitating many-particle systems, which modifies the Einstein-Liouville equations for the coupled gravity-matter problem by inclusion of quantum effects of the matter moving in its self-consistent classical gravitational field, in order to extend their realm of validity to higher particle densities. The corrections of the Vlasov equation (Liouville equation in one-particle phase space) are exhibited as combined effects of quantum mechanics and the curvature of space-time arranged in a semiclassical expansion in powers of h 2 , the first-order term of which is explicitly calculated. It is linear in the Riemann tensor and in its gradient; the Riemann tensor occurs in a similar position as the tensor of the Yang-Mills field strength in a corresponding Vlasov equation for systems with local gauge invariance in the purely classical limit. The performance of the Wigner transformation is based on expressing the equation of motion for the two-point function of the Klein-Gordon field, in particular the Beltrami operator, in terms of a midpoint and a distance vector covariantly defined for the two points. This implies the calculation of deviations of the geodesic between these points, the standard concept of which has to be refined to include infinitesimal variations of the second order. A differential equation for the second-order deviation is established

A random matrix approach to the crossover of energy-level statistics from Wigner to Poisson

International Nuclear Information System (INIS)

Datta, Nilanjana; Kunz, Herve

2004-01-01

We analyze a class of parametrized random matrix models, introduced by Rosenzweig and Porter, which is expected to describe the energy level statistics of quantum systems whose classical dynamics varies from regular to chaotic as a function of a parameter. We compute the generating function for the correlations of energy levels, in the limit of infinite matrix size. The crossover between Poisson and Wigner statistics is measured by a renormalized coupling constant. The model is exactly solved in the sense that, in the limit of infinite matrix size, the energy-level correlation functions and their generating function are given in terms of a finite set of integrals

Semiclassical Wigner distribution for a two-mode entangled state generated by an optical parametric oscillator

International Nuclear Information System (INIS)

Dechoum, K.; Hahn, M. D.; Khoury, A. Z.; Vallejos, R. O.

2010-01-01

We derive the steady-state solution of the Fokker-Planck equation that describes the dynamics of the nondegenerate optical parametric oscillator in the truncated Wigner representation of the density operator. We assume that the pump mode is strongly damped, which permits its adiabatic elimination. When the elimination is correctly executed, the resulting stochastic equations contain multiplicative noise terms and do not admit a potential solution. However, we develop a heuristic scheme leading to a satisfactory steady-state solution. This provides a clear view of the intracavity two-mode entangled state valid in all operating regimes of the optical parametric oscillator. A non-Gaussian distribution is obtained for the above threshold solution.

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

Science.gov (United States)

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.

Continuous Transition between Brillouin-Wigner and Rayleigh-Schrödinger Perturbation Theory, Generalized Bloch Equation, and Hilbert Space Multireference Coupled Cluster

Czech Academy of Sciences Publication Activity Database

Pittner, Jiří

2003-01-01

Roč. 118, č. 24 (2003), s. 10876-10889 ISSN 0021-9606 R&D Projects: GA MŠk OC D23.001; GA ČR GA203/99/D009; GA AV ČR IAA4040108 Institutional research plan: CEZ:AV0Z4040901 Keywords : continuous transition * Brillouin-Wigner * Rayleigh-Schrödinger Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 2.950, year: 2003

Exact Wigner surmise type evaluation of the spacing distribution in the bulk of the scaled random matrix ensembles

International Nuclear Information System (INIS)

Forrester, P.J.; Witte, N.S.

2000-01-01

Random matrix ensembles with orthogonal and unitary symmetry correspond to the cases of real symmetric and Hermitian random matrices respectively. We show that the probability density function for the corresponding spacings between consecutive eigenvalues can be written exactly in the Wigner surmise type form a(s) e-b(s) for a simply related to a Painleve transcendent and b its anti-derivative. A formula consisting of the sum of two such terms is given for the symplectic case (Hermitian matrices with real quaternion elements)

Some connections between relativistic classical mechanics, statistical mechanics, and quantum field theory

International Nuclear Information System (INIS)

Remler, E.A.

1977-01-01

A gauge-invariant version of the Wigner representation is used to relate relativistic mechanics, statistical mechanics, and quantum field theory in the context of the electrodynamics of scalar particles. A unified formulation of quantum field theory and statistical mechanics is developed which clarifies the physics interpretation of the single-particle Wigner function. A covariant form of Ehrenfest's theorem is derived. Classical electrodynamics is derived from quantum field theory after making a random-phase approximation. The validity of this approximation is discussed

FRAUD/SABOTAGE Killing Nuclear-Reactors!!! ``Super"alloys GENERIC ENDEMIC Wigner's-Disease IN-stability!!!

Science.gov (United States)

Asphahani, Aziz; Siegel, Sidney; Siegel, Edward

2010-03-01

Siegel [[J.Mag.Mag.Mtls.7,312(78); PSS(a)11,45(72); Semis.& Insuls.5(79)] (at: ORNL, ANS, Westin``KL"ouse, PSEG, IAEA, ABB) warning of old/new nuclear-reactors/spent-fuel-casks/refineries/ jet/missile/rocket-engines austenitic/FCC Ni/Fe-based (so MIS- called)``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(46)]; Ostwald-ripening; spinodal- decomposition; overageing-embrittlement; thermomechanical- INstability: Mayo[Google: ``If Leaks Could Kill"; at flickr.com search on ``Giant-Magnotoresistance"; find: [SiegelPolitics(79)]; Hoffman[animatedsoftware.com],...what DOE/NRC MISlabels as ``butt-welds" ``stress-corrosion cracking" endpoint's ROOT-CAUSE ULTIMATE-ORIGIN is WD overageing-embrit- tlement caused brittle-fracture cracking from early/ongoing AEC/DOE-n``u''tional-la``v''atories sabotage!!!

Metal chemistry of the transactinides

International Nuclear Information System (INIS)

Eichler, B.

2000-12-01

The elements with atomic numbers between 104 and 116 are expected to behave as metals. Their interaction with metal surfaces is of uppermost importance both to design experimental separation procedures as well as for their chemical characterization. This interaction is quantified by the net adsorption enthalpy. The determination of the net adsorption enthalpy requires the calculation of the solution enthalpy of transactinides in the bulk-phases of the solid adsorbent metals. These solution enthalpies have been calculated with the Miedema-model. For that purpose the necessary parameters of the transactinides: the metal radius, the molar volume, the electronic density at the Wigner-Seitz-Cell boundary and the electronegativity (Miedema Scale) have been obtained on the basis of empirical correlations starting from the entropies of solid transactinides. These entropies were estimated by extrapolations as a function of atomic masses along the groups of the periodic table. The results of the calculations show a strong dependence on the cohesion energy of the solid adsorbent metals as well as on the solution enthalpies of transactinides in the bulk-phase of these metals. The enthalpies of segregation of transactinides from the metallic bulk-phases as the 'driving forces' of the surface enrichment process were calculated. The calculated data allow the selection of the best suitable materials for the gas phase transport as well as of the adsorbent metal for chromatographic separations, for sampling and for electrochemical deposition in experiments with the transactinides. (author)

Metal chemistry of the transactinides; Metallchemie der Transaktinoide

Energy Technology Data Exchange (ETDEWEB)

Eichler, B

2000-12-01

The elements with atomic numbers between 104 and 116 are expected to behave as metals. Their interaction with metal surfaces is of uppermost importance both to design experimental separation procedures as well as for their chemical characterization. This interaction is quantified by the net adsorption enthalpy. The determination of the net adsorption enthalpy requires the calculation of the solution enthalpy of transactinides in the bulk-phases of the solid adsorbent metals. These solution enthalpies have been calculated with the Miedema-model. For that purpose the necessary parameters of the transactinides: the metal radius, the molar volume, the electronic density at the Wigner-Seitz-Cell boundary and the electronegativity (Miedema Scale) have been obtained on the basis of empirical correlations starting from the entropies of solid transactinides. These entropies were estimated by extrapolations as a function of atomic masses along the groups of the periodic table. The results of the calculations show a strong dependence on the cohesion energy of the solid adsorbent metals as well as on the solution enthalpies of transactinides in the bulk-phase of these metals. The enthalpies of segregation of transactinides from the metallic bulk-phases as the 'driving forces' of the surface enrichment process were calculated. The calculated data allow the selection of the best suitable materials for the gas phase transport as well as of the adsorbent metal for chromatographic separations, for sampling and for electrochemical deposition in experiments with the transactinides. (author)

Breit-Wigner resonances and the quasinormal modes of anti-de Sitter black holes

International Nuclear Information System (INIS)

Berti, Emanuele; Cardoso, Vitor; Pani, Paolo

2009-01-01

We show that the theory of Breit-Wigner resonances can be used as an efficient numerical tool to compute black hole quasinormal modes. For illustration, we focus on the Schwarzschild anti-de Sitter (SAdS) spacetime. The resonance method is better suited to small SAdS black holes than the traditional series expansion method, allowing us to confirm that the damping time scale of small SAdS black holes for scalar and gravitational fields is proportional to r + -2l-2 , where r + is the horizon radius. The proportionality coefficients are in good agreement with analytic calculations. We also examine the eikonal limit of SAdS quasinormal modes, confirming quantitatively Festuccia and Liu's [arXiv:0811.1033] prediction of the existence of very long-lived modes. Our results are particularly relevant for the AdS/CFT correspondence, since long-lived modes presumably dominate the decay time scale of the perturbations.

Rotational damping motion in nuclei

International Nuclear Information System (INIS)

Egido, J.L.; Faessler, A.

1991-01-01

The recently proposed model to explain the mechanism of the rotational motion damping in nuclei is exactly solved. When compared with the earlier approximative solution, we find significative differences in the low excitation energy limit (i.e. Γ μ 0 ). For the strength functions we find distributions going from the Wigner semicircle through gaussians to Breit-Wigner shapes. (orig.)

Methods for the neutronic design of a Supersara experimental loop

International Nuclear Information System (INIS)

Casali, F.; Cepraga, D.

1982-01-01

This paper describes a method for the neutronic design of experimental loops irradiated in D 2 O experimental reactors, like Essor. The calculation approach concerns the definition of a Weigner-Seitz cell where the loop under examination be subjected to the same neutronic conditions as in the actual reactor

Wigner’s phase-space function and atomic structure: II. Ground states for closed-shell atoms

DEFF Research Database (Denmark)

Springborg, Michael; Dahl, Jens Peder

1987-01-01

We present formulas for reduced Wigner phase-space functions for atoms, with an emphasis on the first-order spinless Wigner function. This function can be written as the sum of separate contributions from single orbitals (the natural orbitals). This allows a detailed study of the function. Here we...... display and analyze the function for the closed-shell atoms helium, beryllium, neon, argon, and zinc in the Hartree-Fock approximation. The quantum-mechanical exact results are compared with those obtained with the approximate Thomas-Fermi description of electron densities in phase space....

Classical and Quantum Models in Non-Equilibrium Statistical Mechanics: Moment Methods and Long-Time Approximations

Directory of Open Access Journals (Sweden)

Ramon F. Alvarez-Estrada

2012-02-01

Full Text Available We consider non-equilibrium open statistical systems, subject to potentials and to external “heat baths” (hb at thermal equilibrium at temperature T (either with ab initio dissipation or without it. Boltzmann’s classical equilibrium distributions generate, as Gaussian weight functions in momenta, orthogonal polynomials in momenta (the position-independent Hermite polynomialsHn’s. The moments of non-equilibrium classical distributions, implied by the Hn’s, fulfill a hierarchy: for long times, the lowest moment dominates the evolution towards thermal equilibrium, either with dissipation or without it (but under certain approximation. We revisit that hierarchy, whose solution depends on operator continued fractions. We review our generalization of that moment method to classical closed many-particle interacting systems with neither a hb nor ab initio dissipation: with initial states describing thermal equilibrium at T at large distances but non-equilibrium at finite distances, the moment method yields, approximately, irreversible thermalization of the whole system at T, for long times. Generalizations to non-equilibrium quantum interacting systems meet additional difficulties. Three of them are: (i equilibrium distributions (represented through Wigner functions are neither Gaussian in momenta nor known in closed form; (ii they may depend on dissipation; and (iii the orthogonal polynomials in momenta generated by them depend also on positions. We generalize the moment method, dealing with (i, (ii and (iii, to some non-equilibrium one-particle quantum interacting systems. Open problems are discussed briefly.

Vesicle computers: Approximating a Voronoi diagram using Voronoi automata

International Nuclear Information System (INIS)

Adamatzky, Andrew; De Lacy Costello, Ben; Holley, Julian; Gorecki, Jerzy; Bull, Larry

2011-01-01

Highlights: → We model irregular arrangements of vesicles filled with chemical systems. → We examine influence of precipitation threshold on the system's computational potential. → We demonstrate computation of Voronoi diagram and skeleton. - Abstract: Irregular arrangements of vesicles filled with excitable and precipitating chemical systems are imitated by Voronoi automata - finite-state machines defined on a planar Voronoi diagram. Every Voronoi cell takes four states: resting, excited, refractory and precipitate. A resting cell excites if it has at least one neighbour in an excited state. The cell precipitates if the ratio of excited cells in its neighbourhood versus the number of neighbours exceeds a certain threshold. To approximate a Voronoi diagram on Voronoi automata we project a planar set onto the automaton lattice, thus cells corresponding to data-points are excited. Excitation waves propagate across the Voronoi automaton, interact with each other and form precipitate at the points of interaction. The configuration of the precipitate represents the edges of an approximated Voronoi diagram. We discover the relationship between the quality of the Voronoi diagram approximation and the precipitation threshold, and demonstrate the feasibility of our model in approximating Voronoi diagrams of arbitrary-shaped objects and in constructing a skeleton of a planar shape.

Wigner formula of rotation matrices and quantum walks

International Nuclear Information System (INIS)

Miyazaki, Takahiro; Katori, Makoto; Konno, Norio

2007-01-01

Quantization of a random-walk model is performed by giving a qudit (a multicomponent wave function) to a walker at site and by introducing a quantum coin, which is a matrix representation of a unitary transformation. In quantum walks, the qudit of the walker is mixed according to the quantum coin at each time step, when the walker hops to other sites. As special cases of the quantum walks driven by high-dimensional quantum coins generally studied by Brun, Carteret, and Ambainis, we study the models obtained by choosing rotation as the unitary transformation, whose matrix representations determine quantum coins. We show that Wigner's (2j+1)-dimensional unitary representations of rotations with half-integers j's are useful to analyze the probability laws of quantum walks. For any value of half-integer j, convergence of all moments of walker's pseudovelocity in the long-time limit is proved. It is generally shown for the present models that, if (2j+1) is even, the probability measure of limit distribution is given by a superposition of (2j+1)/2 terms of scaled Konno's density functions, and if (2j+1) is odd, it is a superposition of j terms of scaled Konno's density functions and a Dirac's delta function at the origin. For the two-, three-, and four-component models, the probability densities of limit distributions are explicitly calculated and their dependence on the parameters of quantum coins and on the initial qudit of walker is completely determined. Comparison with computer simulation results is also shown

Thermoelectric properties of periodic quantum structures in the Wigner-Rode formalism

Science.gov (United States)

Kommini, Adithya; Aksamija, Zlatan

2018-01-01

Improving the thermoelectric Seebeck coefficient, while simultaneously reducing thermal conductivity, is required in order to boost thermoelectric (TE) figure of merit (ZT). A common approach to improve the Seebeck coefficient is electron filtering where ‘cold’ (low energy) electrons are restricted from participating in transport by an energy barrier (Kim and Lundstrom 2011 J. Appl. Phys. 110 034511, Zide et al 2010 J. Appl. Phys. 108 123702). However, the impact of electron tunneling through thin barriers and resonant states on TE properties has been given less attention, despite the widespread use of quantum wells and superlattices (SLs) in TE applications. In our work, we develop a comprehensive transport model using the Wigner-Rode formalism. We include the full electronic bandstructure and all the relevant scattering mechanisms, allowing us to simulate both energy relaxation and quantum effects from periodic potential barriers. We study the impact of barrier shape on TE performance and find that tall, sharp barriers with small period lengths lead to the largest increase in both Seebeck coefficient and conductivity, thus boosting power factor and TE efficiency. Our findings are robust against additional elastic scattering such as atomic-scale roughness at side-walls of SL nanowires.

Incorporation of Duffing Oscillator and Wigner-Ville Distribution in Traffic Flow Prediction

Directory of Open Access Journals (Sweden)

Anamarija L. Mrgole

2017-02-01

Full Text Available The main purpose of this study was to investigate the use of various chaotic pattern recognition methods for traffic flow prediction. Traffic flow is a variable, dynamic and complex system, which is non-linear and unpredictable. The emergence of traffic flow congestion in road traffic is estimated when the traffic load on a specific section of the road in a specific time period is close to exceeding the capacity of the road infrastructure. Under certain conditions, it can be seen in concentrating chaotic traffic flow patterns. The literature review of traffic flow theory and its connection with chaotic features implies that this kind of method has great theoretical and practical value. Researched methods of identifying chaos in traffic flow have shown certain restrictions in their techniques but have suggested guidelines for improving the identification of chaotic parameters in traffic flow. The proposed new method of forecasting congestion in traffic flow uses Wigner-Ville frequency distribution. This method enables the display of a chaotic attractor without the use of reconstruction phase space.

Wigner's dynamical transition state theory in phase space: classical and quantum

International Nuclear Information System (INIS)

Waalkens, Holger; Schubert, Roman; Wiggins, Stephen

2008-01-01

We develop Wigner's approach to a dynamical transition state theory in phase space in both the classical and quantum mechanical settings. The key to our development is the construction of a normal form for describing the dynamics in the neighbourhood of a specific type of saddle point that governs the evolution from reactants to products in high dimensional systems. In the classical case this is the standard Poincaré–Birkhoff normal form. In the quantum case we develop a normal form based on the Weyl calculus and an explicit algorithm for computing this quantum normal form. The classical normal form allows us to discover and compute the phase space structures that govern classical reaction dynamics. From this knowledge we are able to provide a direct construction of an energy dependent dividing surface in phase space having the properties that trajectories do not locally 're-cross' the surface and the directional flux across the surface is minimal. Using this, we are able to give a formula for the directional flux through the dividing surface that goes beyond the harmonic approximation. We relate this construction to the flux–flux autocorrelation function which is a standard ingredient in the expression for the reaction rate in the chemistry community. We also give a classical mechanical interpretation of the activated complex as a normally hyperbolic invariant manifold (NHIM), and further describe the structure of the NHIM. The quantum normal form provides us with an efficient algorithm to compute quantum reaction rates and we relate this algorithm to the quantum version of the flux–flux autocorrelation function formalism. The significance of the classical phase space structures for the quantum mechanics of reactions is elucidated by studying the phase space distribution of scattering states. The quantum normal form also provides an efficient way of computing Gamov–Siegert resonances. We relate these resonances to the lifetimes of the quantum activated

Diophantine approximation and badly approximable sets

DEFF Research Database (Denmark)

Kristensen, S.; Thorn, R.; Velani, S.

2006-01-01

. The classical set Bad of `badly approximable' numbers in the theory of Diophantine approximation falls within our framework as do the sets Bad(i,j) of simultaneously badly approximable numbers. Under various natural conditions we prove that the badly approximable subsets of Omega have full Hausdorff dimension...

Liouville equation of relativistic charged fermion

International Nuclear Information System (INIS)

Wang Renchuan; Zhu Dongpei; Huang Zhuoran; Ko Che-ming

1991-01-01

As a form of density martrix, the Wigner function is the distribution in quantum phase space. It is a 2 X 2 matrix function when one uses it to describe the non-relativistic fermion. While describing the relativistic fermion, it is usually represented by 4 x 4 matrix function. In this paper authors obtain a Wigner function for the relativistic fermion in the form of 2 x 2 matrix, and the Liouville equation satisfied by the Wigner function. this equivalent to the Dirac equation of changed fermion in QED. The equation is also equivalent to the Dirac equation in the Walecka model applied to the intermediate energy nuclear collision while the nucleon is coupled to the vector meson only (or taking mean field approximation for the scalar meson). Authors prove that the 2 x 2 Wigner function completely describes the quantum system just the same as the relativistic fermion wave function. All the information about the observables can be obtained with above Wigner function

Validity of the cumulant method for a pulse nonlinear Kerr oscillator

International Nuclear Information System (INIS)

Grygiel, K.; Leonski, W.; Szlachetka, P.

1998-01-01

We study the dynamics of an anharmonic oscillator driven by a train of pulses. The cumulant expansion and quantum evolution operator approaches are presented and compared. The modifications introduced by quantum mechanics into the dynamics of classical systems which manifest chaos are a problem of great importance. It is known that quantization modifies the dynamics of classical system is usually studied by means of the equation for the Wigner function derived from the quantum Liouville equation. In Wigner's formulation of quantum mechanics we treat a quantum system in a 'classical way' including all their quantum features. And what is more, we can contrast the quantum and classical dynamics within the framework of one formalism. The problem is, that the equations for the Wigner functions are mathematically cumbersome and their analytic solutions for most nonlinear systems are unknown. However, instead of the equation for the Wigner function we can use the set of equations for statistical moments generated by our equation for the Wigner function. It is obvious that in this approach a quantum system is governed by an infinite set of equations. Therefore, for numerical reasons the set of equations for statistical moments has to be truncated at a finite number, which means approximating it. It is known that first cumulant approximation represents the classical dynamics. The second cumulant approximation adds the first quantum corrections to the classical dynamics. In this paper we compare some aspects of the cumulant method and the method used by Leonski and Tanas to study an anharmonic oscillator driven by a train of pulses. The Kerr oscillator model is the same ad that is discussed in an earlier paper albeit without the damping mechanism

A Signal Decomposition Method for Ultrasonic Guided Wave Generated from Debonding Combining Smoothed Pseudo Wigner-Ville Distribution and Vold–Kalman Filter Order Tracking

Directory of Open Access Journals (Sweden)

Junhua Wu

2017-01-01

Full Text Available Carbon fibre composites have a promising application future of the vehicle, due to its excellent physical properties. Debonding is a major defect of the material. Analyses of wave packets are critical for identification of the defect on ultrasonic nondestructive evaluation and testing. In order to isolate different components of ultrasonic guided waves (GWs, a signal decomposition algorithm combining Smoothed Pseudo Wigner-Ville distribution and Vold–Kalman filter order tracking is presented. In the algorithm, the time-frequency distribution of GW is first obtained by using Smoothed Pseudo Wigner-Ville distribution. The frequencies of different modes are computed based on summation of the time-frequency coefficients in the frequency direction. On the basis of these frequencies, isolation of different modes is done by Vold–Kalman filter order tracking. The results of the simulation signal and the experimental signal reveal that the presented algorithm succeeds in decomposing the multicomponent signal into monocomponents. Even though components overlap in corresponding Fourier spectrum, they can be isolated by using the presented algorithm. So the frequency resolution of the presented method is promising. Based on this, we can do research about defect identification, calculation of the defect size, and locating the position of the defect.

Brillouin-Wigner theory of mixed-valence impurities in BCS superconductor: Tc/TcO and ΔC/ΔCO

International Nuclear Information System (INIS)

Li Jun; Gong Changde.

1986-08-01

The (lowest order) Brillouin-Wigner perturbational expansion theory is adopted to describe the mixed-valence impurities in the BCS superconductor. Two substantial quantities characterizing the superconducting state, i.e. the reduced transition temperature T c /T cO and the reduced specific heat jump ΔC/ΔC O are calculated numerically as a function of the impurity concentration x and the energy level difference E f between two 4f configurations. A comparison with the experimental data of the Th 1-x Ce x and Th 1-x U x alloy is also included with a more reasonable fitting than Kaiser's theory. (author)

Estimates of point defect production in α-quartz using molecular dynamics simulations

Science.gov (United States)

Cowen, Benjamin J.; El-Genk, Mohamed S.

2017-07-01

Molecular dynamics (MD) simulations are performed to investigate the production of point defects in α-quartz by oxygen and silicon primary knock-on atoms (PKAs) of 0.25-2 keV. The Wigner-Seitz (WS) defect analysis is used to identify the produced vacancies, interstitials, and antisites, and the coordination defect analysis is used to identify the under and over-coordinated oxygen and silicon atoms. The defects at the end of the ballistic phase and the residual defects, after annealing, increase with increased PKA energy, and are statistically the same for the oxygen and silicon PKAs. The WS defect analysis results show that the numbers of the oxygen vacancies and interstitials (VO, Oi) at the end of the ballistic phase is the highest, followed closely by those of the silicon vacancies and interstitials (VSi, Sii). The number of the residual oxygen and silicon vacancies and interstitials are statistically the same. In addition, the under-coordinated OI and SiIII, which are the primary defects during the ballistic phase, have high annealing efficiencies (>89%). The over-coordinated defects of OIII and SiV, which are not nearly as abundant in the ballistic phase, have much lower annealing efficiencies (PKA energy.

Strongly coupled semiclassical plasma: interaction model and some properties

International Nuclear Information System (INIS)

Baimbetov, N.F.; Bekenov, N.A.

1999-01-01

In the report a fully ionized strongly coupled hydrogen plasma is considered. The density number is considered within range n=n e =n i ≅(10 21 -2·10 25 )sm -3 , and the temperature domian is T≅(5·10 4 -10 6 ) K. The coupling parameter Γ is defined by Γ=e 2 /αk B T, where k B is the Boltzmann constant and e is electrical charge, α=(3/4πn) 1/3 is the average distance between the particles (Wigner-Seitz radius). The dimensionless density parameter r s =α/α B is given in terms of the Bohr radius α B =ℎ 2 /me 2 ∼0.529·10 - 8 sm. The degeneracy parameter for the electron was defined by the ratio between the thermal energy k B T and the Fermi energy E F :Θ=k B T/E F ∼0.54·r s /Γ. The intermediate temperature-density region, where Γ≥1; Θ≅1; T>13.6 eV is examined. A semiclassical effective potential which account for the short-range, quantum diffraction and symmetry effects of charge carriers screening

Unified equation of state for neutron stars on a microscopic basis

Science.gov (United States)

Sharma, B. K.; Centelles, M.; Viñas, X.; Baldo, M.; Burgio, G. F.

2015-12-01

We derive a new equation of state (EoS) for neutron stars (NS) from the outer crust to the core based on modern microscopic calculations using the Argonne v18 potential plus three-body forces computed with the Urbana model. To deal with the inhomogeneous structures of matter in the NS crust, we use a recent nuclear energy density functional that is directly based on the same microscopic calculations, and which is able to reproduce the ground-state properties of nuclei along the periodic table. The EoS of the outer crust requires the masses of neutron-rich nuclei, which are obtained through Hartree-Fock-Bogoliubov calculations with the new functional when they are unknown experimentally. To compute the inner crust, Thomas-Fermi calculations in Wigner-Seitz cells are performed with the same functional. Existence of nuclear pasta is predicted in a range of average baryon densities between ≃0.067 fm-3 and ≃0.0825 fm-3, where the transition to the core takes place. The NS core is computed from the new nuclear EoS assuming non-exotic constituents (core of npeμ matter). In each region of the star, we discuss the comparison of the new EoS with previous EoSs for the complete NS structure, widely used in astrophysical calculations. The new microscopically derived EoS fulfills at the same time a NS maximum mass of 2 M⊙ with a radius of 10 km, and a 1.5 M⊙ NS with a radius of 11.6 km.

Polyelectrolyte-mediated bridging interactions: columnar macromolecular phases

International Nuclear Information System (INIS)

Licer, Matjaz; Podgornik, Rudolf

2010-01-01

We present a mean-field theory for charged polymer chains in an external electrostatic field in the weak and strong coupling limits. We apply the theory to describe the statistical mechanics of flexible polyelectrolyte chains in a hexagonal columnar lattice of stiff cylindrical macroions, such as DNA, in a bathing solution of a uni-univalent salt (e.g. NaCl). The salt effects are first described in the Debye-Hueckel framework. This yields the macroion electrostatic field in the screened Coulomb form, which we take to represent the mean field into which the chains are immersed. We introduce the Green's function for the polyelectrolyte chains and derive the corresponding Edwards equation which we solve numerically in the Wigner-Seitz cylindrical cell using the ground state dominance ansatz. The solutions indicate the presence of polyelectrolyte bridging, which results in a like-charge attraction between stiff macroions. Then we reformulate the Edwards theory for the strong coupling case and use the standard Poisson-Boltzmann picture to describe the salt solution. We begin with the free energy which we minimize to obtain the Euler-Lagrange equations. The solutions yield self-consistently determined monomer density and electrostatic fields. We furthermore calculate the free energy density as well as the total osmotic pressure in the system. We again show that bridging implicates like-charge attractions of entropic origin between stiff cylindrical macroions. By analyzing the osmotic pressure we demonstrate that, in certain parts of the parameter space, a phase transition occurs between two phases of the same hexagonal symmetry.

Pulse processing in optical fibers using the temporal Radon-Wigner transform

Energy Technology Data Exchange (ETDEWEB)

Bulus-Rossini, L A; Costanzo-Caso, P A; Duchowicz, R [Centro de Investigaciones Opticas, CONICET La Plata - CIC, Camino Parque Centenario y 506, C.C. 3 (1897) La Plata (Argentina); Sicre, E E, E-mail: lbulus@ing.unlp.edu.ar [Instituto de Tecnologia, Facultad de Ingenieria y Ciencias Exactas, Universidad Argentina de la Empresa, Lima 717, C1073AAO Buenos Aires (Argentina)

2011-01-01

It is presented the use of the temporal Radon-Wigner transform (RWT), which is the squared modulus of the fractional Fourier transform (FRT) for a varying fractional order p, as a processing tool for pulses with FWHM of ps-tens of ps. For analysis purposes, the complete numerical generation of the RWT with 0 < p < 1 is proposed to select a particular pulse shape related to a determined value of p. To this end, the amplitude and phase of the signal to be processed are obtained using a pulse characterization technique. To synthesize the processed pulse, the selected FRT irradiance is optically produced employing a photonic device that combines phase modulation and dispersive transmission. The practical implementation of this device involves a scaling factor that depends on the modulation and dispersive parameters. It is explored the variation of this factor in order to obtain an enhancement of the particular characteristic sought in the pulse to be synthesized. To illustrate the implementation of the proposed method, numerical simulations of its application to compress signals commonly found in fiber optic transmission systems, are performed. The examples presented consider chirped Gaussian pulses and pulses distorted by group velocity dispersion and self-phase modulation.

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

Science.gov (United States)

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)]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!!!

Dentate Gyrus circuitry features improve performance of sparse approximation algorithms.

Directory of Open Access Journals (Sweden)

Panagiotis C Petrantonakis

Full Text Available Memory-related activity in the Dentate Gyrus (DG is characterized by sparsity. Memory representations are seen as activated neuronal populations of granule cells, the main encoding cells in DG, which are estimated to engage 2-4% of the total population. This sparsity is assumed to enhance the ability of DG to perform pattern separation, one of the most valuable contributions of DG during memory formation. In this work, we investigate how features of the DG such as its excitatory and inhibitory connectivity diagram can be used to develop theoretical algorithms performing Sparse Approximation, a widely used strategy in the Signal Processing field. Sparse approximation stands for the algorithmic identification of few components from a dictionary that approximate a certain signal. The ability of DG to achieve pattern separation by sparsifing its representations is exploited here to improve the performance of the state of the art sparse approximation algorithm "Iterative Soft Thresholding" (IST by adding new algorithmic features inspired by the DG circuitry. Lateral inhibition of granule cells, either direct or indirect, via mossy cells, is shown to enhance the performance of the IST. Apart from revealing the potential of DG-inspired theoretical algorithms, this work presents new insights regarding the function of particular cell types in the pattern separation task of the DG.

Spectral properties of embedded Gaussian unitary ensemble of random matrices with Wigner's SU(4) symmetry

International Nuclear Information System (INIS)

Vyas, Manan; Kota, V.K.B.

2010-01-01

For m fermions in Ω number of single particle orbitals, each fourfold degenerate, we introduce and analyze in detail embedded Gaussian unitary ensemble of random matrices generated by random two-body interactions that are SU(4) scalar [EGUE(2)-SU(4)]. Here the SU(4) algebra corresponds to the Wigner's supermultiplet SU(4) symmetry in nuclei. Embedding algebra for the EGUE(2)-SU(4) ensemble is U(4Ω) contains U(Ω) x SU(4). Exploiting the Wigner-Racah algebra of the embedding algebra, analytical expression for the ensemble average of the product of any two m particle Hamiltonian matrix elements is derived. Using this, formulas for a special class of U(Ω) irreducible representations (irreps) {4 r , p}, p = 0, 1, 2, 3 are derived for the ensemble averaged spectral variances and also for the covariances in energy centroids and spectral variances. On the other hand, simplifying the tabulations of Hecht for SU(Ω) Racah coefficients, numerical calculations are carried out for general U(Ω) irreps. Spectral variances clearly show, by applying Jacquod and Stone prescription, that the EGUE(2)-SU(4) ensemble generates ground state structure just as the quadratic Casimir invariant (C 2 ) of SU(4). This is further corroborated by the calculation of the expectation values of C 2 [SU(4)] and the four periodicity in the ground state energies. Secondly, it is found that the covariances in energy centroids and spectral variances increase in magnitude considerably as we go from EGUE(2) for spinless fermions to EGUE(2) for fermions with spin to EGUE(2)-SU(4) implying that the differences in ensemble and spectral averages grow with increasing symmetry. Also for EGUE(2)-SU(4) there are, unlike for GUE, non-zero cross-correlations in energy centroids and spectral variances defined over spaces with different particle numbers and/or U(Ω) [equivalently SU(4)] irreps. In the dilute limit defined by Ω → ∞, r >> 1 and r/Ω → 0, for the {4 r , p} irreps, we have derived analytical

On the dilute gas two particle density matrices of p--H2 and He4

International Nuclear Information System (INIS)

Weres, O.

1976-01-01

In the preceding paper we demonstrated that the reduced two- particle density matrix of simple quantum liquids could profitably be re-expressed in terms of a Taylor expansion of its logarithm about the diagonal. In the present publication we examine the Taylor coefficients which arise when the dilute gas two particle density matrix is expanded in this way. In particular, we evaluate the leading coefficients of p-H 2 and He 4 exactly and extend the Wigner--Kirkwood approximation to provided approximate expressions for them. We demonstrate how these approximate expressions may be applied to yield results superior to those yielded by the ordinary Wigner--Kirkwood approximation. In an appendix we demonstrate how the Block equation for the dilute gas two particle density matrix may be reduced to an equivalent closed set of equations for the leading Taylor coefficients

Error Estimates for the Approximation of the Effective Hamiltonian

International Nuclear Information System (INIS)

Camilli, Fabio; Capuzzo Dolcetta, Italo; Gomes, Diogo A.

2008-01-01

We study approximation schemes for the cell problem arising in homogenization of Hamilton-Jacobi equations. We prove several error estimates concerning the rate of convergence of the approximation scheme to the effective Hamiltonian, both in the optimal control setting and as well as in the calculus of variations setting

Dynamics and quantum Zeno effect for a qubit in either a low- or high-frequency bath beyond the rotating-wave approximation

International Nuclear Information System (INIS)

Cao Xiufeng; You, J. Q.; Zheng, H.; Kofman, A. G.; Nori, Franco

2010-01-01

We use a non-Markovian approach to study the decoherence dynamics of a qubit in either a low- or high-frequency bath modeling the qubit environment. This is done for two separate cases: either with measurements or without them. This approach is based on a unitary transformation and does not require the rotating-wave approximation. In the case without measurement, we show that, for low-frequency noise, the bath shifts the qubit energy toward higher energies (blue shift), while the ordinary high-frequency cutoff Ohmic bath shifts the qubit energy toward lower energies (red shift). In order to preserve the coherence of the qubit, we also investigate the dynamics of the qubit subject to measurements (quantum Zeno regime) in two cases: low- and high-frequency baths. For very frequent projective measurements, the low-frequency bath gives rise to the quantum anti-Zeno effect on the qubit. The quantum Zeno effect only occurs in the high-frequency-cutoff Ohmic bath, after counterrotating terms are considered. In the condition that the decay rate due to the two kinds of baths are equal under the Wigner-Weisskopf approximation, we find that without the approximation, for a high-frequency environment, the decay rate should be faster (without measurements) or slower (with frequent measurements, in the Zeno regime), compared to the low-frequency bath case. The experimental implementation of our results here could distinguish the type of bath (either a low- or high-frequency one) and protect the coherence of the qubit by modulating the dominant frequency of its environment.

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

Science.gov (United States)

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.

Hierarchical low-rank approximation for high dimensional approximation

KAUST Repository

Nouy, Anthony

2016-01-07

Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. Such high-dimensional approximation problems naturally arise in stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high-dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we present algorithms for the approximation in hierarchical tensor format using statistical methods. Sparse representations in a given tensor format are obtained with adaptive or convex relaxation methods, with a selection of parameters using crossvalidation methods.

Hierarchical low-rank approximation for high dimensional approximation

KAUST Repository

Nouy, Anthony

2016-01-01

Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. Such high-dimensional approximation problems naturally arise in stochastic analysis and uncertainty quantification. In many practical situations, the approximation of high-dimensional functions is made computationally tractable by using rank-structured approximations. In this talk, we present algorithms for the approximation in hierarchical tensor format using statistical methods. Sparse representations in a given tensor format are obtained with adaptive or convex relaxation methods, with a selection of parameters using crossvalidation methods.

U.S. Department Of Energy's nuclear engineering education research: highlights of recent and current research-II. 1. Comparison of Angular Approximations for PWR Cell Calculations

International Nuclear Information System (INIS)

Smith, M.A.; Tsoulfanidis, N.; Lewis, E.E.; Palmiotti, G.

2001-01-01

Increasing computer power is allowing higher-order angular approximations to replace diffusion theory methods in whole core reactor physics computations. Spherical harmonic (P n ), simplified spherical harmonic (SP n ), and discrete ordinates (S n ) methods are capable of performing such calculations in three dimensions. Most advantages of such transport methods are gained by eliminating fuel assembly homogenization, thus allowing pin powers to be calculated directly. A further step, currently under investigation, is the elimination of spatial homogenization at the pin cell level as well. The fuel-moderator interfaces may be treated explicitly in P n , S n , or SP n calculations by applying triangular finite elements (FEM) to the spatial variables. Early results using a modified form of the VARIANT code, however, indicate that without pin cell homogenization, high-order angular approximations may be required to represent the lattice effects accurately within the whole-core calculations. To examine these lattice effects further, a modified form of VARIANT was created to use the spatial triangular finite element scheme. The program was set up to treat a single heterogeneous pin cell coupled with P n , SP n , or S n angular approximations. Additional modifications replaced the nodal interface approximations with exact reflected boundary conditions to increase the accuracy of the results. Several pressurized water reactor pin cells, taken from a previous benchmark specification, were examined. However, the results shown here focus only on the most severe case, i.e., a pin cell containing 8.7% mixed-oxide enriched fuel. The DRAGON collision probability code was used to collapse a 69-group cross-section library to a more manageable 7-group library that contained cross sections for the fuel-cladding mixture and for the water. Eigenvalue results are shown in Figs. 1 and 2 using the modified VARIANT code with P n , SP n , and S n angular approximations. A 7-group MCNP Monte

January: IBM 7094 programme for the resolution of cell problems in planar, spherical and cylindrical geometry using the double Pn approximation

International Nuclear Information System (INIS)

Amouyal, A.; Tariel, H.

1966-01-01

Code name: January 1 st SCEA 011S. 2) Computer: IBM 7094; Programme system: Fortran II, 2 nd version. 3) Nature of the problem: resolution of cell problems with one space variable (planar, spherical and cylindrical geometries) and with one energy group, with isotropic sources in the double P n approximation (DP 1 and DP 3 approximation in planar and spherical geometries, DP 1 and DP 2 in cylindrical geometry). 4) Method used: the differential equations with limiting conditions are transformed into differential system with initial conditions which are integrated by a separate-step method. 5) Restrictions: number of physical media [fr

A New Approximate Chimera Donor Cell Search Algorithm

Science.gov (United States)

Holst, Terry L.; Nixon, David (Technical Monitor)

1998-01-01

The objectives of this study were to develop chimera-based full potential methodology which is compatible with overflow (Euler/Navier-Stokes) chimera flow solver and to develop a fast donor cell search algorithm that is compatible with the chimera full potential approach. Results of this work included presenting a new donor cell search algorithm suitable for use with a chimera-based full potential solver. This algorithm was found to be extremely fast and simple producing donor cells as fast as 60,000 per second.

Space-angle approximations in the variational nodal method

International Nuclear Information System (INIS)

Lewis, E. E.; Palmiotti, G.; Taiwo, T.

1999-01-01

The variational nodal method is formulated such that the angular and spatial approximations maybe examined separately. Spherical harmonic, simplified spherical harmonic, and discrete ordinate approximations are coupled to the primal hybrid finite element treatment of the spatial variables. Within this framework, two classes of spatial trial functions are presented: (1) orthogonal polynomials for the treatment of homogeneous nodes and (2) bilinear finite subelement trial functions for the treatment of fuel assembly sized nodes in which fuel-pin cell cross sections are represented explicitly. Polynomial and subelement trial functions are applied to benchmark water-reactor problems containing MOX fuel using spherical harmonic and simplified spherical harmonic approximations. The resulting accuracy and computing costs are compared

Evolution of Wigner function in laser process under the action of linear resonance force and its application

Science.gov (United States)

Dao-ming, Lu

2018-05-01

The negativity of Wigner function (WF) is one of the important symbols of non-classical properties of light field. Therefore, it is of great significance to study the evolution of WF in dissipative process. The evolution formula of WF in laser process under the action of linear resonance force is given by virtue of thermo entangled state representation and the technique of integration within an ordered product of operator. As its application, the evolution of WF of thermal field and that of single-photon-added coherent state are discussed. The results show that the WF of thermal field maintains its original character. On the other hand, the negative region size and the depth of negativity of WF of single- photon-added coherent state decrease until it vanishes with dissipation. This shows that the non-classical property of single-photon-added coherent state is weakened, until it disappears with dissipation time increasing.

Relativistic quantum kinetic analysis of a pion--nucleon system

International Nuclear Information System (INIS)

Alonso, J.D.

1985-01-01

A relativistic plasma of nucleons interacting through pions via the usual isospin-invariant Yukawa coupling is analyzed in the framework of the covariant Wigner function technique. The method is manifestly covariant and the temperature effects are considered. The relativistic quantum BBGKY hierarchy for the pion--nucleon system is derived. By generalizing the Bogolioubov analysis of the classical BBGKY hierarchy a non-perturbative renormalizable method is elaborated which allows the solution of the kinetic problem in form of power series of two cluster parameters which measure the importance of correlations. In the lowest order of the cluster expansion (Hartree approximation of zero-order approximation) the quasi-nucleon Fock space is introduced, the fermion Wigner function in the thermodynamic equilibrium is obtained and the vacuum effects are renormalized. In this approximation the plasma behaves as a perfect Fermi gas of nucleons and antinucleons, but there exists an abnormal configuration with a uniform pion condensate which is unstable. In the next approximation (quadratic in the small parameters) the quasi-pion dispersion relation is obtained and the vacuum polarization tensor is renormalized. The quasi-pion rest-mass spectra (''plasma frequency'') and the effective-coupling behaviour as functions of the thermodynamic state are given. By estimating the size of the cluster parameters the self-consistency of the approximation scheme is proved. The quasi-pion Fock space is introduced and the quasi-pion equilibrium Wigner function is obtained. From these results the problem of the higher-order corrections to the Hartree thermodynamics is outlined

Calculation of spherical harmonics and Wigner d functions by FFT. Applications to fast rotational matching in molecular replacement and implementation into AMoRe.

Science.gov (United States)

Trapani, Stefano; Navaza, Jorge

2006-07-01

The FFT calculation of spherical harmonics, Wigner D matrices and rotation function has been extended to all angular variables in the AMoRe molecular replacement software. The resulting code avoids singularity issues arising from recursive formulas, performs faster and produces results with at least the same accuracy as the original code. The new code aims at permitting accurate and more rapid computations at high angular resolution of the rotation function of large particles. Test calculations on the icosahedral IBDV VP2 subviral particle showed that the new code performs on the average 1.5 times faster than the original code.

Symmetry and history quantum theory: An analog of Wigner close-quote s theorem

International Nuclear Information System (INIS)

Schreckenberg, S.

1996-01-01

The basic ingredients of the open-quote open-quote consistent histories close-quote close-quote approach to quantum theory are a space UP of open-quote open-quote history propositions close-quote close-quote and a space D of open-quote open-quote decoherence functionals.close-quote close-quote In this article we consider such history quantum theories in the case where UP is given by the set of projectors P(V) on some Hilbert space V. We define the notion of a open-quote open-quote physical symmetry of a history quantum theory close-quote close-quote (PSHQT) and specify such objects exhaustively with the aid of an analog of Wigner close-quote s theorem. In order to prove this theorem we investigate the structure of D, define the notion of an open-quote open-quote elementary decoherence functional,close-quote close-quote and show that each decoherence functional can be expanded as a certain combination of these functionals. We call two history quantum theories that are related by a PSHQT open-quote open-quote physically equivalent close-quote close-quote and show explicitly, in the case of history quantum mechanics, how this notion is compatible with one that has appeared previously. copyright 1996 American Institute of Physics

Eugene Paul Wigner – A Tribute*

Indian Academy of Sciences (India)

, w hen a tall, slender young m an entered the dining room , looked at ..... an approxim ate,not an exact,consequence ofquantum m echanics;so departures .... w ith the SU (4) superm ultiplet theory to system atize the low -lying energy levels.

Implementation of Eugene Wigner Training Course at University of 'Politehnica' of Bucharest, Power Engineering Faculty, Nuclear Power Plant Department

International Nuclear Information System (INIS)

Ghizdeanu, E.N.

2004-01-01

The 'Eugene Wigner' training Course for Reactor Physics Experiments has been supported by the 5th Framework Programme of the European Commission, and it has been integrated in the ENEN (European Nuclear Engineering Network) program. This project has been prepared for the future European Nuclear Education schemes and degrees. Starting from a general presentation of the course this paper presents my opinion as a former student about the course impact. In this paper is written my opinion about the following: The content of theoretical courses; The usefulness of the textbook; The content of the practical experiments; The usefulness of the textbook for the practical experiments, and evaluations. Moreover, parts of this course were implemented to my seminars. Results, expectations and conclusions about the usefulness of the course are presented. (author)

Statistical properties of spectra in harmonically trapped spin-orbit coupled systems

DEFF Research Database (Denmark)

V. Marchukov, O.; G. Volosniev, A.; V. Fedorov, D.

2014-01-01

We compute single-particle energy spectra for a one-body Hamiltonian consisting of a two-dimensional deformed harmonic oscillator potential, the Rashba spin-orbit coupling and the Zeeman term. To investigate the statistical properties of the obtained spectra as functions of deformation, spin......-orbit and Zeeman strengths we examine the distributions of the nearest neighbor spacings. We find that the shapes of these distributions depend strongly on the three potential parameters. We show that the obtained shapes in some cases can be well approximated with the standard Poisson, Brody and Wigner...... distributions. The Brody and Wigner distributions characterize irregular motion and help identify quantum chaotic systems. We present a special choices of deformation and spin-orbit strengths without the Zeeman term which provide a fair reproduction of the fourth-power repelling Wigner distribution. By adding...

Semiclassical evolution of dissipative Markovian systems

International Nuclear Information System (INIS)

Ozorio de Almeida, A M; Rios, P de M; Brodier, O

2009-01-01

A semiclassical approximation for an evolving density operator, driven by a 'closed' Hamiltonian operator and 'open' Markovian Lindblad operators, is obtained. The theory is based on the chord function, i.e. the Fourier transform of the Wigner function. It reduces to an exact solution of the Lindblad master equation if the Hamiltonian operator is a quadratic function and the Lindblad operators are linear functions of positions and momenta. Initially, the semiclassical formulae for the case of Hermitian Lindblad operators are reinterpreted in terms of a (real) double phase space, generated by an appropriate classical double Hamiltonian. An extra 'open' term is added to the double Hamiltonian by the non-Hermitian part of the Lindblad operators in the general case of dissipative Markovian evolution. The particular case of generic Hamiltonian operators, but linear dissipative Lindblad operators, is studied in more detail. A Liouville-type equivariance still holds for the corresponding classical evolution in double phase space, but the centre subspace, which supports the Wigner function, is compressed, along with expansion of its conjugate subspace, which supports the chord function. Decoherence narrows the relevant region of double phase space to the neighbourhood of a caustic for both the Wigner function and the chord function. This difficulty is avoided by a propagator in a mixed representation, so that a further 'small-chord' approximation leads to a simple generalization of the quadratic theory for evolving Wigner functions

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

Science.gov (United States)

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 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.

Semiclassical expansions of the nuclear relativistic Hartree-Fock theory

International Nuclear Information System (INIS)

Weigel, M.K.; Haddad, S.

1991-01-01

Semiclassical expansions for Green functions, self-energy, phase-space density and density are given and discussed. The many-body problem was treated in the relativistic Hartree-Fock approximation with a Lagrangian with a standard OBE potential structure including the possibility of space-dependent couplings. The expansions are obtained by formulating the many-body problem in the mixed position-momentum (Wigner) representation and application of the (h/2π)-Wigner-Kirkwood expansion scheme. The resulting self-consistency problems for the zeroth and second order are formulated in three versions. (author)

Reduction of motion artifact in pulse oximetry by smoothed pseudo Wigner-Ville distribution

Directory of Open Access Journals (Sweden)

Zhang Yuan-ting

2005-03-01

Full Text Available Abstract Background The pulse oximeter, a medical device capable of measuring blood oxygen saturation (SpO2, has been shown to be a valuable device for monitoring patients in critical conditions. In order to incorporate the technique into a wearable device which can be used in ambulatory settings, the influence of motion artifacts on the estimated SpO2 must be reduced. This study investigates the use of the smoothed psuedo Wigner-Ville distribution (SPWVD for the reduction of motion artifacts affecting pulse oximetry. Methods The SPWVD approach is compared with two techniques currently used in this field, i.e. the weighted moving average (WMA and the fast Fourier transform (FFT approaches. SpO2 and pulse rate were estimated from a photoplethysmographic (PPG signal recorded when subject is in a resting position as well as in the act of performing four types of motions: horizontal and vertical movements of the hand, and bending and pressing motions of the finger. For each condition, 24 sets of PPG signals collected from 6 subjects, each of 30 seconds, were studied with reference to the PPG signal recorded simultaneously from the subject's other hand, which was stationary at all times. Results and Discussion The SPWVD approach shows significant improvement (p Conclusion The results suggested that the SPWVD approach could potentially be used to reduce motion artifact on wearable pulse oximeters.

Quantum maximum-entropy principle for closed quantum hydrodynamic transport within a Wigner function formalism

International Nuclear Information System (INIS)

Trovato, M.; Reggiani, L.

2011-01-01

By introducing a quantum entropy functional of the reduced density matrix, the principle of quantum maximum entropy is asserted as fundamental principle of quantum statistical mechanics. Accordingly, we develop a comprehensive theoretical formalism to construct rigorously a closed quantum hydrodynamic transport within a Wigner function approach. The theoretical formalism is formulated in both thermodynamic equilibrium and nonequilibrium conditions, and the quantum contributions are obtained by only assuming that the Lagrange multipliers can be expanded in powers of (ℎ/2π) 2 . In particular, by using an arbitrary number of moments, we prove that (1) on a macroscopic scale all nonlocal effects, compatible with the uncertainty principle, are imputable to high-order spatial derivatives, both of the numerical density n and of the effective temperature T; (2) the results available from the literature in the framework of both a quantum Boltzmann gas and a degenerate quantum Fermi gas are recovered as a particular case; (3) the statistics for the quantum Fermi and Bose gases at different levels of degeneracy are explicitly incorporated; (4) a set of relevant applications admitting exact analytical equations are explicitly given and discussed; (5) the quantum maximum entropy principle keeps full validity in the classical limit, when (ℎ/2π)→0.

The Wigner-Ville Transform, An Approach to Interpret GPR Data: Outlining a Rik Zone

Science.gov (United States)

Chavez, R. E.; Samano, M. A.; Camara, M. E.; Tejero, A.; Flores-Marquez, L. E.; Arango, C.; Velazco, V.

2006-12-01

In this investigation, a time-frequency analysis is performed, based in the decomposition of the GPR signal in high- and low-frequencies. This process is combined with a statistical approach to detect signal changes in time and position simultaneously. The spectral analysis is carried out through the Wigner-Ville distribution (WVD). A cross-correlation can be computed between the original signal and the time-frequency components to obtain structural anomalies in the GPR observations, and to perform a correlation with the available geology. An example of this methodology is presented, where a series of traces where analyzed from a GPR profile surveyed in an eastern area of Mexico City. This is a heavily urbanized region built on the bottom of an ancient lake. The sediments are poorly consolidated and the extraction water rate has increased the areas of subsidence. Nowadays, most of family homes and public buildings, mainly schools have started to suffer heavy damages. The geophysical study carried out in the area permitted to detect areas of high risk. The data analysis combined with previous geological studies, which included stratigraphic columns allowed to identify the geophysical characteristics of the area, which will allow to the authorities to plan the future development of the area.

Multi-compartment linear noise approximation

International Nuclear Information System (INIS)

Challenger, Joseph D; McKane, Alan J; Pahle, Jürgen

2012-01-01

The ability to quantify the stochastic fluctuations present in biochemical and other systems is becoming increasing important. Analytical descriptions of these fluctuations are attractive, as stochastic simulations are computationally expensive. Building on previous work, a linear noise approximation is developed for biochemical models with many compartments, for example cells. The procedure is then implemented in the software package COPASI. This technique is illustrated with two simple examples and is then applied to a more realistic biochemical model. Expressions for the noise, given in the form of covariance matrices, are presented. (paper)

A phase space approach to wave propagation with dispersion.

Science.gov (United States)

Ben-Benjamin, Jonathan S; Cohen, Leon; Loughlin, Patrick J

2015-08-01

A phase space approximation method for linear dispersive wave propagation with arbitrary initial conditions is developed. The results expand on a previous approximation in terms of the Wigner distribution of a single mode. In contrast to this previously considered single-mode case, the approximation presented here is for the full wave and is obtained by a different approach. This solution requires one to obtain (i) the initial modal functions from the given initial wave, and (ii) the initial cross-Wigner distribution between different modal functions. The full wave is the sum of modal functions. The approximation is obtained for general linear wave equations by transforming the equations to phase space, and then solving in the new domain. It is shown that each modal function of the wave satisfies a Schrödinger-type equation where the equivalent "Hamiltonian" operator is the dispersion relation corresponding to the mode and where the wavenumber is replaced by the wavenumber operator. Application to the beam equation is considered to illustrate the approach.

Self-similar factor approximants

International Nuclear Information System (INIS)

Gluzman, S.; Yukalov, V.I.; Sornette, D.

2003-01-01

The problem of reconstructing functions from their asymptotic expansions in powers of a small variable is addressed by deriving an improved type of approximants. The derivation is based on the self-similar approximation theory, which presents the passage from one approximant to another as the motion realized by a dynamical system with the property of group self-similarity. The derived approximants, because of their form, are called self-similar factor approximants. These complement the obtained earlier self-similar exponential approximants and self-similar root approximants. The specific feature of self-similar factor approximants is that their control functions, providing convergence of the computational algorithm, are completely defined from the accuracy-through-order conditions. These approximants contain the Pade approximants as a particular case, and in some limit they can be reduced to the self-similar exponential approximants previously introduced by two of us. It is proved that the self-similar factor approximants are able to reproduce exactly a wide class of functions, which include a variety of nonalgebraic functions. For other functions, not pertaining to this exactly reproducible class, the factor approximants provide very accurate approximations, whose accuracy surpasses significantly that of the most accurate Pade approximants. This is illustrated by a number of examples showing the generality and accuracy of the factor approximants even when conventional techniques meet serious difficulties

Implementation of the multireference Brillouin-Wigner and Mukherjee’s coupled cluster methods with non-iterative triple excitations utilizing reference-level parallelism

Energy Technology Data Exchange (ETDEWEB)

Bhaskaran-Nair, Kiran; Brabec, Jiri; Apra, Edoardo; van Dam, Hubertus JJ; Pittner, Jiri; Kowalski, Karol

2012-09-07

In this paper we discuss the performance of the non-iterative State-Specific Mul- tireference Coupled Cluster (SS-MRCC) methods accounting for the effect of triply excited cluster amplitudes. The corrections to the Brillouin-Wigner and Mukherjee MRCC models based on the manifold of singly and doubly excited cluster amplitudes (BW-MRCCSD and Mk-MRCCSD, respectively) are tested and compared with the exact full configuration interaction results (FCI) for small systems (H2O, N2, and Be3). For larger systems (naphthyne isomers and -carotene), the non-iterative BW-MRCCSD(T) and Mk-MRCCSD(T) methods are compared against the results obtained with the single reference coupled cluster methods. We also report on the parallel performance of the non-iterative implementations based on the use of pro- cessor groups.

Volatilization behavior of transactinides from metal surfaces and melts (thermochemical calculation); Verfluechtigungsverhalten der Transaktinoide von Metalloberflaechen und aus Schmelzen (Thermochemische Kalkulation)

Energy Technology Data Exchange (ETDEWEB)

Eichler, B

2003-01-01

Volatilization properties of elements with the atomic numbers Z=104 to 116 are determined on the basis of empirical relations. These empirical correlations are deduced from the analysis of thermochemical data of metallic elements in the periodic table and their relations to the material constant: Structure specific connections are shown to exist between the electron densities at the 'Wigner-Seitz' cell borders of metals and the specific surface energies of solid metals with hexagonal, cubic face-centred, cubic body-centred and rhombohedral lattices. Analogously, structure specific relations can be found between the standard enthalpies of the gaseous monoatomic metals and their surface energies. Linear correlations with exceptionally high correlation coefficients are observed between the standard sublimation enthalpies of isotypic metals in the dimeric state and the surface energies. Volatilization properties are deduced for the transactinides on the basis of these established relations, applying a predicted structure and further empirical correlations. These volatilization properties are in detail: the standard enthalpies of the gaseous monomers; the standard sublimation enthalpies of the dimers; the standard dissociation enthalpies of the dimers; the standard enthalpies of adsorption on metal surfaces; the volatilization enthalpies from molten metals, and the standard formation enthalpies of hetero binuclear intermetallic molecules. Thermochemical constants required for the calculation of the intermetallic interactions are determined using the Miedema model. The closed systematic approach facilitate: the assessment of the calculated data considering the agreement with known rules of metal chemistry, trends in the 7{sup t}h row and along the groups of the periodic table, the coherence of the data, and the action of closed shell effects in the electron configurations. From the obtained data conclusions are possible regarding the design of volatilization

Critic: a new program for the topological analysis of solid-state electron densities

Science.gov (United States)

Otero-de-la-Roza, A.; Blanco, M. A.; Pendás, A. Martín; Luaña, Víctor

2009-01-01

In this paper we introduce CRITIC, a new program for the topological analysis of the electron densities of crystalline solids. Two different versions of the code are provided, one adapted to the LAPW (Linear Augmented Plane Wave) density calculated by the WIEN2K package and the other to the ab initio Perturbed Ion ( aiPI) density calculated with the PI7 code. Using the converged ground state densities, CRITIC can locate their critical points, determine atomic basins and integrate properties within them, and generate several graphical representations which include topological atomic basins and primary bundles, contour maps of ρ and ∇ρ, vector maps of ∇ρ, chemical graphs, etc. Program summaryProgram title: CRITIC Catalogue identifier: AECB_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECB_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GPL, version 3 No. of lines in distributed program, including test data, etc.: 1 206 843 No. of bytes in distributed program, including test data, etc.: 12 648 065 Distribution format: tar.gz Programming language: FORTRAN 77 and 90 Computer: Any computer capable of compiling Fortran Operating system: Unix, GNU/Linux Classification: 7.3 Nature of problem: Topological analysis of the electron density in periodic solids. Solution method: The automatic localization of the electron density critical points is based on a recursive partitioning of the Wigner-Seitz cell into tetrahedra followed by a Newton search from significant points on each tetrahedra. Plotting of and integration on the atomic basins is currently based on a new implementation of Keith's promega algorithm. Running time: Variable, depending on the task. From seconds to a few minutes for the localization of critical points. Hours to days for the determination of the atomic basins shape and properties. Times correspond to a typical 2007 PC.

Modulated Pade approximant

International Nuclear Information System (INIS)

Ginsburg, C.A.

1980-01-01

In many problems, a desired property A of a function f(x) is determined by the behaviour of f(x) approximately equal to g(x,A) as x→xsup(*). In this letter, a method for resuming the power series in x of f(x) and approximating A (modulated Pade approximant) is presented. This new approximant is an extension of a resumation method for f(x) in terms of rational functions. (author)

Approximate Dynamic Programming: Combining Regional and Local State Following Approximations.

Science.gov (United States)

Deptula, Patryk; Rosenfeld, Joel A; Kamalapurkar, Rushikesh; Dixon, Warren E

2018-06-01

An infinite-horizon optimal regulation problem for a control-affine deterministic system is solved online using a local state following (StaF) kernel and a regional model-based reinforcement learning (R-MBRL) method to approximate the value function. Unlike traditional methods such as R-MBRL that aim to approximate the value function over a large compact set, the StaF kernel approach aims to approximate the value function in a local neighborhood of the state that travels within a compact set. In this paper, the value function is approximated using a state-dependent convex combination of the StaF-based and the R-MBRL-based approximations. As the state enters a neighborhood containing the origin, the value function transitions from being approximated by the StaF approach to the R-MBRL approach. Semiglobal uniformly ultimately bounded (SGUUB) convergence of the system states to the origin is established using a Lyapunov-based analysis. Simulation results are provided for two, three, six, and ten-state dynamical systems to demonstrate the scalability and performance of the developed method.

Effects of Al substitution in Nd2Fe17 studied by first-principles calculations

International Nuclear Information System (INIS)

Huang, M.; Ching, W.Y.

1994-01-01

We have studied the effect of Al substitution in Nd 2 Fe 17 compound by means of first-principles calculations. We first obtain the site-decomposed potentials for Fe from self-consistent calculation on Y 2 Fe 17 and the atomiclike potentials in the crystalline environment for Al and Nd. Calculations are carried out for a single Al substituting one Fe at four different Fe sites (6c), (9d), (18f ), and (18h), two Al substituting two Fe (18h), and four Al substituting three Fe (18h) and one Fe (18f ). Our results show that the Al moment is oppositely polarized to Fe. The average moment per Fe atom actually increases for Al substituting Fe (18h) and Fe (18f ) is about the same for Al substituting Fe (6c), and is drastically reduced when replacing Fe (9d). Experimentally, Al is shown to be excluded from the (9d) sites because of the small Wigner--Seitz volume. When two Fe atoms are replaced by two Al atoms, the total moment is only slightly less than when only one Fe atom is replaced, and the M s per Fe site actually increases, in agreement with the Moessbauer data. These results are analyzed in terms of the local atomic geometry and the charge transfer effect from the neighboring Fe to Al

Geometrical approach to the distribution of the zeros for the Husimi function

International Nuclear Information System (INIS)

Toscano, Fabricio; Almeida, M. Ozorio de

1999-03-01

We construct a semiclassical expression for the Husimi function of autonomous systems in one degree of freedom, by smoothing with a Gaussian function an expression that captures the essential features of the Wigner function in the semiclassical limit. Our approximation reveals the center and chord structure that the Husimi function inherits from the Wigner function, down to very shallow valleys, where lie the Husimi zeros. This explanation for the distribution of zeros along curves relies on the geometry of the classical torus, rather the complex analytic properties of the WKB method in the Bargmann representation. We evaluate the zeros for several examples. (author)

The fiftieth anniversary of the first public announcement of the successful test of fission: Proceedings

International Nuclear Information System (INIS)

1989-01-01

This report contains comments and discussions on the history of fission. The following people comments and lectures are discussed in this report: Remarks and introduction of Maxine F. Singer; president's message, Maxine F. Singer; introduction of Stephen Joel Trachtenberg; President's message, Stephen Joel Trachtenberg; introduction of Frederick Seitz; lecture: ''Nuclear Science: Promises and Perceptions, '' Frederick Seitz; introduction of K. Alex Mueller; lecture: ''High Temperature Ferroelectricity and Superconductivity,'' introduction of Edward Teller; and lecture: ''Toward a More Secure World,'' Edward Teller

The fiftieth anniversary of the first public announcement of the successful test of fission: Proceedings

Energy Technology Data Exchange (ETDEWEB)

1989-12-31

This report contains comments and discussions on the history of fission. The following people comments and lectures are discussed in this report: Remarks and introduction of Maxine F. Singer; president`s message, Maxine F. Singer; introduction of Stephen Joel Trachtenberg; President`s message, Stephen Joel Trachtenberg; introduction of Frederick Seitz; lecture: ``Nuclear Science: Promises and Perceptions, `` Frederick Seitz; introduction of K. Alex Mueller; lecture: ``High Temperature Ferroelectricity and Superconductivity,`` introduction of Edward Teller; and lecture: ``Toward a More Secure World,`` Edward Teller.

Finite element approximation to the even-parity transport equation

International Nuclear Information System (INIS)

Lewis, E.E.

1981-01-01

This paper studies the finite element method, a procedure for reducing partial differential equations to sets of algebraic equations suitable for solution on a digital computer. The differential equation is cast into the form of a variational principle, the resulting domain then subdivided into finite elements. The dependent variable is then approximated by a simple polynomial, and these are linked across inter-element boundaries by continuity conditions. The finite element method is tailored to a variety of transport problems. Angular approximations are formulated, and the extent of ray effect mitigation is examined. Complex trial functions are introduced to enable the inclusion of buckling approximations. The ubiquitous curved interfaces of cell calculations, and coarse mesh methods are also treated. A concluding section discusses limitations of the work to date and suggests possible future directions

Approximate solutions of the two-dimensional integral transport equation by collision probability methods

International Nuclear Information System (INIS)

Sanchez, Richard

1977-01-01

A set of approximate solutions for the isotropic two-dimensional neutron transport problem has been developed using the Interface Current formalism. The method has been applied to regular lattices of rectangular cells containing a fuel pin, cladding and water, or homogenized structural material. The cells are divided into zones which are homogeneous. A zone-wise flux expansion is used to formulate a direct collision probability problem within a cell. The coupling of the cells is made by making extra assumptions on the currents entering and leaving the interfaces. Two codes have been written: the first uses a cylindrical cell model and one or three terms for the flux expansion; the second uses a two-dimensional flux representation and does a truly two-dimensional calculation inside each cell. In both codes one or three terms can be used to make a space-independent expansion of the angular fluxes entering and leaving each side of the cell. The accuracies and computing times achieved with the different approximations are illustrated by numerical studies on two benchmark pr

A novel joint timing/frequency synchronization scheme based on Radon-Wigner transform of LFM signals in CO-OFDM systems

Science.gov (United States)

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.

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

Science.gov (United States)

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.

An exact formalism for Doppler-broadened neutron cross-sections

International Nuclear Information System (INIS)

Catsaros, Nicolas.

1985-07-01

An exact formalism (Ψ, Φ) is proposed for the calculation of Breit-Wigner or Adler-Adler Doppler-broadened neutron cross-sections. The well-known (Ψ, Φ) formalism is shown to be a zero-order approximation of the generalized (Ψ, Φ) formalism. (author)

Approximate symmetries of Hamiltonians

Science.gov (United States)

Chubb, Christopher T.; Flammia, Steven T.

2017-08-01

We explore the relationship between approximate symmetries of a gapped Hamiltonian and the structure of its ground space. We start by considering approximate symmetry operators, defined as unitary operators whose commutators with the Hamiltonian have norms that are sufficiently small. We show that when approximate symmetry operators can be restricted to the ground space while approximately preserving certain mutual commutation relations. We generalize the Stone-von Neumann theorem to matrices that approximately satisfy the canonical (Heisenberg-Weyl-type) commutation relations and use this to show that approximate symmetry operators can certify the degeneracy of the ground space even though they only approximately form a group. Importantly, the notions of "approximate" and "small" are all independent of the dimension of the ambient Hilbert space and depend only on the degeneracy in the ground space. Our analysis additionally holds for any gapped band of sufficiently small width in the excited spectrum of the Hamiltonian, and we discuss applications of these ideas to topological quantum phases of matter and topological quantum error correcting codes. Finally, in our analysis, we also provide an exponential improvement upon bounds concerning the existence of shared approximate eigenvectors of approximately commuting operators under an added normality constraint, which may be of independent interest.

The fiftieth anniversary of the first public announcement of the successful test of fission: Proceedings

Energy Technology Data Exchange (ETDEWEB)

1989-01-01

This report contains comments and discussions on the history of fission. The following people comments and lectures are discussed in this report: Remarks and introduction of Maxine F. Singer; president's message, Maxine F. Singer; introduction of Stephen Joel Trachtenberg; President's message, Stephen Joel Trachtenberg; introduction of Frederick Seitz; lecture: Nuclear Science: Promises and Perceptions, '' Frederick Seitz; introduction of K. Alex Mueller; lecture: High Temperature Ferroelectricity and Superconductivity,'' introduction of Edward Teller; and lecture: Toward a More Secure World,'' Edward Teller.

Geometric approximation algorithms

CERN Document Server

Har-Peled, Sariel

2011-01-01

Exact algorithms for dealing with geometric objects are complicated, hard to implement in practice, and slow. Over the last 20 years a theory of geometric approximation algorithms has emerged. These algorithms tend to be simple, fast, and more robust than their exact counterparts. This book is the first to cover geometric approximation algorithms in detail. In addition, more traditional computational geometry techniques that are widely used in developing such algorithms, like sampling, linear programming, etc., are also surveyed. Other topics covered include approximate nearest-neighbor search, shape approximation, coresets, dimension reduction, and embeddings. The topics covered are relatively independent and are supplemented by exercises. Close to 200 color figures are included in the text to illustrate proofs and ideas.

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

Science.gov (United States)

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!!!

Sparse approximation with bases

CERN Document Server

2015-01-01

This book systematically presents recent fundamental results on greedy approximation with respect to bases. Motivated by numerous applications, the last decade has seen great successes in studying nonlinear sparse approximation. Recent findings have established that greedy-type algorithms are suitable methods of nonlinear approximation in both sparse approximation with respect to bases and sparse approximation with respect to redundant systems. These insights, combined with some previous fundamental results, form the basis for constructing the theory of greedy approximation. Taking into account the theoretical and practical demand for this kind of theory, the book systematically elaborates a theoretical framework for greedy approximation and its applications.  The book addresses the needs of researchers working in numerical mathematics, harmonic analysis, and functional analysis. It quickly takes the reader from classical results to the latest frontier, but is written at the level of a graduate course and do...

Distribution of Steps with Finite-Range Interactions: Analytic Approximations and Numerical Results

Science.gov (United States)

GonzáLez, Diego Luis; Jaramillo, Diego Felipe; TéLlez, Gabriel; Einstein, T. L.

2013-03-01

While most Monte Carlo simulations assume only nearest-neighbor steps interact elastically, most analytic frameworks (especially the generalized Wigner distribution) posit that each step elastically repels all others. In addition to the elastic repulsions, we allow for possible surface-state-mediated interactions. We investigate analytically and numerically how next-nearest neighbor (NNN) interactions and, more generally, interactions out to q'th nearest neighbor alter the form of the terrace-width distribution and of pair correlation functions (i.e. the sum over n'th neighbor distribution functions, which we investigated recently.[2] For physically plausible interactions, we find modest changes when NNN interactions are included and generally negligible changes when more distant interactions are allowed. We discuss methods for extracting from simulated experimental data the characteristic scale-setting terms in assumed potential forms.

Approximating distributions from moments

Science.gov (United States)

Pawula, R. F.

1987-11-01

A method based upon Pearson-type approximations from statistics is developed for approximating a symmetric probability density function from its moments. The extended Fokker-Planck equation for non-Markov processes is shown to be the underlying foundation for the approximations. The approximation is shown to be exact for the beta probability density function. The applicability of the general method is illustrated by numerous pithy examples from linear and nonlinear filtering of both Markov and non-Markov dichotomous noise. New approximations are given for the probability density function in two cases in which exact solutions are unavailable, those of (i) the filter-limiter-filter problem and (ii) second-order Butterworth filtering of the random telegraph signal. The approximate results are compared with previously published Monte Carlo simulations in these two cases.

General Rytov approximation.

Science.gov (United States)

Potvin, Guy

2015-10-01

We examine how the Rytov approximation describing log-amplitude and phase fluctuations of a wave propagating through weak uniform turbulence can be generalized to the case of turbulence with a large-scale nonuniform component. We show how the large-scale refractive index field creates Fermat rays using the path integral formulation for paraxial propagation. We then show how the second-order derivatives of the Fermat ray action affect the Rytov approximation, and we discuss how a numerical algorithm would model the general Rytov approximation.

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

Science.gov (United States)

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

Discrete space structure of the sl(1 vertical bar 3) Wigner quantum oscillator

International Nuclear Information System (INIS)

King, R.C.; Palev, T.D.; Stoilova, N.I.; Jeugt, J. van der

2002-09-01

The properties of a noncanonical 3D Wigner quantum oscillator, whose position and momentum operators generate the Lie superalgebra sl(1 vertical bar 3), are further investigated. Within each state space W(p), p=1,2,..., the energy E q , q=0,1,2,3, takes no more than 4 different values. If the oscillator is in a stationary state ψ q is an element of W(p) then measurements of the non-commuting Cartesian coordinates of the particle are such that their allowed values are consistent with it being found at a finite number of sites, called 'nests'. These lie on a sphere centered on the origin of fixed, finite radius p q . The nests themselves are at the vertices of a rectangular parallelepiped. In the typical cases (p>2) the number of nests is 8 for q=0 and 3, and varies from 8 to 24, depending on the state, for q=1 and 2. The number of nests is less in the atypical cases (p=1,2), but it is never less than two. In certain states in W(2) (resp. in W(1)) the oscillator is 'polarized' so that all the nests lie on a plane (resp. on a line). The particle cannot be localized in any one of the available nests alone since the coordinates do not commute. The probabilities of measuring particular values of the coordinates are discussed. The mean trajectories and the standard deviations of the coordinates and momenta are computed, and conclusions are drawn about uncertainty relations. The rotational invariance of the system is also discussed. (author)

ππ P-wave resonant scattering from lattice QCD

Directory of Open Access Journals (Sweden)

Paul Srijit

2018-01-01

Full Text Available 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(16stat(14sys and gρππ = 5:69(13stat(16sys. In our comparison with other lattice QCD results, we consider the dimensionless ratios amρ/amN and amπ/amN to avoid scale setting ambiguities.

ππ P-wave resonant scattering from lattice QCD

Science.gov (United States)

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.

Peculiarities of the momentum distribution functions of strongly correlated charged fermions

Science.gov (United States)

Larkin, A. S.; Filinov, V. S.; Fortov, V. E.

2018-01-01

New numerical version of the Wigner approach to quantum thermodynamics of strongly coupled systems of particles has been developed for extreme conditions, when analytical approximations based on different kinds of perturbation theories cannot be applied. An explicit analytical expression of the Wigner function has been obtained in linear and harmonic approximations. Fermi statistical effects are accounted for by effective pair pseudopotential depending on coordinates, momenta and degeneracy parameter of particles and taking into account Pauli blocking of fermions. A new quantum Monte-Carlo method for calculations of average values of arbitrary quantum operators has been developed. Calculations of the momentum distribution functions and the pair correlation functions of degenerate ideal Fermi gas have been carried out for testing the developed approach. Comparison of the obtained momentum distribution functions of strongly correlated Coulomb systems with the Maxwell-Boltzmann and the Fermi distributions shows the significant influence of interparticle interaction both at small momenta and in high energy quantum ‘tails’.

Lorentz transformations, sideways shift and massless spinning particles

Science.gov (United States)

Bolonek-Lasoń, K.; Kosiński, P.; Maślanka, P.

2017-06-01

Recently (Stone et al. (2015) [16]) the influence of the so called ;Wigner translations; (more generally-Lorentz transformations) on circularly polarized Gaussian packets (providing the solution to Maxwell equations in paraxial approximation) has been studied. It appears that, within this approximation, the Wigner translations have an effect of shifting the wave packet trajectory parallel to itself by an amount proportional to the photon helicity. It has been suggested that this shift may result from specific properties of the algebra of Poincare generators for massless particles. In the present letter we describe the general relation between transformation properties of electromagnetic field on quantum and classical levels. It allows for a straightforward derivation of the helicity-dependent transformation rules. We present also an elementary derivation of the formula for sideways shift based on classical Maxwell theory. Some comments are made concerning the generalization to higher helicities and the relation to the coordinate operator defined long time ago by Pryce.

Lorentz transformations, sideways shift and massless spinning particles

Directory of Open Access Journals (Sweden)

K. Bolonek-Lasoń

2017-06-01

Full Text Available Recently (Stone et al. (2015 [16] the influence of the so called “Wigner translations” (more generally-Lorentz transformations on circularly polarized Gaussian packets (providing the solution to Maxwell equations in paraxial approximation has been studied. It appears that, within this approximation, the Wigner translations have an effect of shifting the wave packet trajectory parallel to itself by an amount proportional to the photon helicity. It has been suggested that this shift may result from specific properties of the algebra of Poincare generators for massless particles. In the present letter we describe the general relation between transformation properties of electromagnetic field on quantum and classical levels. It allows for a straightforward derivation of the helicity-dependent transformation rules. We present also an elementary derivation of the formula for sideways shift based on classical Maxwell theory. Some comments are made concerning the generalization to higher helicities and the relation to the coordinate operator defined long time ago by Pryce.

Lorentz transformations, sideways shift and massless spinning particles

Energy Technology Data Exchange (ETDEWEB)

Bolonek-Lasoń, K. [Department of Statistical Methods, Faculty of Economics and Sociology (Poland); Kosiński, P. [Department of Computer Science, Faculty of Physics and Applied Informatics, University of Łódź, Pomorska 149/153, 90-236 Łódź (Poland); Maślanka, P., E-mail: pmaslan@uni.lodz.pl [Department of Computer Science, Faculty of Physics and Applied Informatics, University of Łódź, Pomorska 149/153, 90-236 Łódź (Poland)

2017-06-10

Recently (Stone et al. (2015) ) the influence of the so called “Wigner translations” (more generally-Lorentz transformations) on circularly polarized Gaussian packets (providing the solution to Maxwell equations in paraxial approximation) has been studied. It appears that, within this approximation, the Wigner translations have an effect of shifting the wave packet trajectory parallel to itself by an amount proportional to the photon helicity. It has been suggested that this shift may result from specific properties of the algebra of Poincare generators for massless particles. In the present letter we describe the general relation between transformation properties of electromagnetic field on quantum and classical levels. It allows for a straightforward derivation of the helicity-dependent transformation rules. We present also an elementary derivation of the formula for sideways shift based on classical Maxwell theory. Some comments are made concerning the generalization to higher helicities and the relation to the coordinate operator defined long time ago by Pryce.

The Wigner-Ville Distribution Based on the Linear Canonical Transform and Its Applications for QFM Signal Parameters Estimation

Directory of Open Access Journals (Sweden)

Yu-E Song

2014-01-01

Full Text Available The Wigner-Ville distribution (WVD based on the linear canonical transform (LCT (WDL not only has the advantages of the LCT but also has the good properties of WVD. In this paper, some new and important properties of the WDL are derived, and the relationships between WDL and some other time-frequency distributions are discussed, such as the ambiguity function based on LCT (LCTAF, the short-time Fourier transform (STFT, and the wavelet transform (WT. The WDLs of some signals are also deduced. A novel definition of the WVD based on the LCT and generalized instantaneous autocorrelation function (GWDL is proposed and its applications in the estimation of parameters for QFM signals are also discussed. The GWDL of the QFM signal generates an impulse and the third-order phase coefficient of QFM signal can be estimated in accordance with the position information of such impulse. The proposed algorithm is fast because it only requires 1-dimensional maximization. Also the new algorithm only has fourth-order nonlinearity thus it has accurate estimation and low signal-to-noise ratio (SNR threshold. The simulation results are provided to support the theoretical results.

Approximation techniques for engineers

CERN Document Server

Komzsik, Louis

2006-01-01

Presenting numerous examples, algorithms, and industrial applications, Approximation Techniques for Engineers is your complete guide to the major techniques used in modern engineering practice. Whether you need approximations for discrete data of continuous functions, or you''re looking for approximate solutions to engineering problems, everything you need is nestled between the covers of this book. Now you can benefit from Louis Komzsik''s years of industrial experience to gain a working knowledge of a vast array of approximation techniques through this complete and self-contained resource.

International Conference Approximation Theory XV

CERN Document Server

Schumaker, Larry

2017-01-01

These proceedings are based on papers presented at the international conference Approximation Theory XV, which was held May 22–25, 2016 in San Antonio, Texas. The conference was the fifteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 146 participants. The book contains longer survey papers by some of the invited speakers covering topics such as compressive sensing, isogeometric analysis, and scaling limits of polynomials and entire functions of exponential type. The book also includes papers on a variety of current topics in Approximation Theory drawn from areas such as advances in kernel approximation with applications, approximation theory and algebraic geometry, multivariate splines for applications, practical function approximation, approximation of PDEs, wavelets and framelets with applications, approximation theory in signal processing, compressive sensing, rational interpolation, spline approximation in isogeometric analysis, a...

The non-commutative and discrete spatial structure of a 3D Wigner quantum oscillator

International Nuclear Information System (INIS)

King, R C; Palev, T D; Stoilova, N I; Jeugt, J Van der

2003-01-01

The properties of a non-canonical 3D Wigner quantum oscillator, whose position and momentum operators generate the Lie superalgebra sl(1|3), are further investigated. Within each state space W(p), p = 1, 2, ..., the energy E q , q = 0, 1, 2, 3, takes no more than four different values. If the oscillator is in a stationary state ψ q element of W(p) then measurements of the non-commuting Cartesian coordinates of the particle are such that their allowed values are consistent with it being found at a finite number of sites, called 'nests'. These lie on a sphere centred on the origin of fixed, finite radius ρ q . The nests themselves are at the vertices of a rectangular parallelepiped. In the typical cases (p > 2) the number of nests is 8 for q = 0 and 3, and varies from 8 to 24, depending on the state, for q = 1 and 2. The number of nests is less in the atypical cases (p = 1, 2), but it is never less than 2. In certain states in W(2) (respectively in W(1)) the oscillator is 'polarized' so that all the nests lie on a plane (respectively on a line). The particle cannot be localized in any one of the available nests alone since the coordinates do not commute. The probabilities of measuring particular values of the coordinates are discussed. The mean trajectories and the standard deviations of the coordinates and momenta are computed, and conclusions are drawn about uncertainty relations

Semiclassical scar functions in phase space

International Nuclear Information System (INIS)

Rivas, Alejandro M F

2007-01-01

We develop a semiclassical approximation for the scar function in the Weyl-Wigner representation in the neighborhood of a classically unstable periodic orbit of chaotic two-dimensional systems. The prediction of hyperbolic fringes, asymptotic to the stable and unstable manifolds, is verified computationally for a (linear) cat map, after the theory is adapted to a discrete phase space appropriate to a quantized torus. Characteristic fringe patterns can be distinguished even for quasi-energies where the fixed point is not Bohr-quantized. Also the patterns are highly localized in the neighborhood of the periodic orbit and along its stable and unstable manifolds without any long distance patterns that appear for the case of the spectral Wigner function

On unitarity relations and their application to meson–antimeson mixing

Indian Academy of Sciences (India)

Abstract. In view of the recent observation of nonexponential decay features for a certain quantum- mechanical system, we revisit our earlier study of the small-time behaviour of the meson–antimeson complex wherein the commonly employed Weisskopf–Wigner approximation could be tested, in principle. We find that the ...

Abnormal Gait Behavior Detection for Elderly Based on Enhanced Wigner-Ville Analysis and Cloud Incremental SVM Learning

Directory of Open Access Journals (Sweden)

Jian Luo

2016-01-01

Full Text Available A cloud based health care system is proposed in this paper for the elderly by providing abnormal gait behavior detection, classification, online diagnosis, and remote aid service. Intelligent mobile terminals with triaxial acceleration sensor embedded are used to capture the movement and ambulation information of elderly. The collected signals are first enhanced by a Kalman filter. And the magnitude of signal vector features is then extracted and decomposed into a linear combination of enhanced Gabor atoms. The Wigner-Ville analysis method is introduced and the problem is studied by joint time-frequency analysis. In order to solve the large-scale abnormal behavior data lacking problem in training process, a cloud based incremental SVM (CI-SVM learning method is proposed. The original abnormal behavior data are first used to get the initial SVM classifier. And the larger abnormal behavior data of elderly collected by mobile devices are then gathered in cloud platform to conduct incremental training and get the new SVM classifier. By the CI-SVM learning method, the knowledge of SVM classifier could be accumulated due to the dynamic incremental learning. Experimental results demonstrate that the proposed method is feasible and can be applied to aged care, emergency aid, and related fields.

Ordered cones and approximation

CERN Document Server

Keimel, Klaus

1992-01-01

This book presents a unified approach to Korovkin-type approximation theorems. It includes classical material on the approximation of real-valuedfunctions as well as recent and new results on set-valued functions and stochastic processes, and on weighted approximation. The results are notonly of qualitative nature, but include quantitative bounds on the order of approximation. The book is addressed to researchers in functional analysis and approximation theory as well as to those that want to applythese methods in other fields. It is largely self- contained, but the readershould have a solid background in abstract functional analysis. The unified approach is based on a new notion of locally convex ordered cones that are not embeddable in vector spaces but allow Hahn-Banach type separation and extension theorems. This concept seems to be of independent interest.

TEMPEST-2, Thermalization Program for Neutron Spectra and Multigroup Cross-Sections

International Nuclear Information System (INIS)

Gowins, G.

1984-01-01

Description of problem or function: TEMPEST2 is a neutron thermalization program based upon the Wigner-Wilkins approximation for light moderators and the Wilkins approximation for heavy moderators. A Maxwellian distribution may also be used. The model used may be selected as a function of energy. The second-order differential equations are integrated directly rather than transformed to the Riccati equation. The program provides microscopic and macroscopic cross-section averages over the thermal neutron spectrum