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 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

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.)

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....

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.

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

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.

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

Science.gov (United States)

Sels, Dries; Brosens, Fons

2013-10-01

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

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

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.

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.

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)

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.)

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.

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.

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.)

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.

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 >

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.)

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.

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

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.

Semiclassical propagation of Wigner functions.

Science.gov (United States)

Dittrich, T; Gómez, E A; Pachón, L A

2010-06-07

We present a comprehensive study of semiclassical phase-space propagation in the Wigner representation, emphasizing numerical applications, in particular as an initial-value representation. Two semiclassical approximation schemes are discussed. The propagator of the Wigner function based on van Vleck's approximation replaces the Liouville propagator by a quantum spot with an oscillatory pattern reflecting the interference between pairs of classical trajectories. Employing phase-space path integration instead, caustics in the quantum spot are resolved in terms of Airy functions. We apply both to two benchmark models of nonlinear molecular potentials, the Morse oscillator and the quartic double well, to test them in standard tasks such as computing autocorrelation functions and propagating coherent states. The performance of semiclassical Wigner propagation is very good even in the presence of marked quantum effects, e.g., in coherent tunneling and in propagating Schrodinger cat states, and of classical chaos in four-dimensional phase space. We suggest options for an effective numerical implementation of our method and for integrating it in Monte-Carlo-Metropolis algorithms suitable for high-dimensional systems.

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.

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

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

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)

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.

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

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)

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

Discrete linear canonical transforms based on dilated Hermite functions.

Science.gov (United States)

Pei, Soo-Chang; Lai, Yun-Chiu

2011-08-01

Linear canonical transform (LCT) is very useful and powerful in signal processing and optics. In this paper, discrete LCT (DLCT) is proposed to approximate LCT by utilizing the discrete dilated Hermite functions. The Wigner distribution function is also used to investigate DLCT performances in the time-frequency domain. Compared with the existing digital computation of LCT, our proposed DLCT possess additivity and reversibility properties with no oversampling involved. In addition, the length of input/output signals will not be changed before and after the DLCT transformations, which is consistent with the time-frequency area-preserving nature of LCT; meanwhile, the proposed DLCT has very good approximation of continuous LCT.

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...

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.

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.

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

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

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

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

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.

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

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

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

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.

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

Discrete phase space based on finite fields

International Nuclear Information System (INIS)

Gibbons, Kathleen S.; Hoffman, Matthew J.; Wootters, William K.

2004-01-01

The original Wigner function provides a way of representing in phase space the quantum states of systems with continuous degrees of freedom. Wigner functions have also been developed for discrete quantum systems, one popular version being defined on a 2Nx2N discrete phase space for a system with N orthogonal states. Here we investigate an alternative class of discrete Wigner functions, in which the field of real numbers that labels the axes of continuous phase space is replaced by a finite field having N elements. There exists such a field if and only if N is a power of a prime; so our formulation can be applied directly only to systems for which the state-space dimension takes such a value. Though this condition may seem limiting, we note that any quantum computer based on qubits meets the condition and can thus be accommodated within our scheme. The geometry of our NxN phase space also leads naturally to a method of constructing a complete set of N+1 mutually unbiased bases for the state space

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

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.

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

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

Strong semiclassical approximation of Wigner functions for the Hartree dynamics

KAUST Repository

Athanassoulis, Agissilaos; Paul, Thierry; Pezzotti, Federica; Pulvirenti, Mario

2011-01-01

We consider the Wigner equation corresponding to a nonlinear Schrödinger evolution of the Hartree type in the semiclassical limit h → 0. Under appropriate assumptions on the initial data and the interaction potential, we show that the Wigner function is close in L 2 to its weak limit, the solution of the corresponding Vlasov equation. The strong approximation allows the construction of semiclassical operator-valued observables, approximating their quantum counterparts in Hilbert-Schmidt topology. The proof makes use of a pointwise-positivity manipulation, which seems necessary in working with the L 2 norm and the precise form of the nonlinearity. We employ the Husimi function as a pivot between the classical probability density and the Wigner function, which - as it is well known - is not pointwise positive in general.

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.

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)

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...

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 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

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.

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.

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.

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)

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.

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 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.

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.

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...

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.

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

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

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 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

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.

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.

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

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.

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

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)

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

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.

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.

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

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

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.

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.

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 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

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.

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....

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.

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 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 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

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.

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.

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

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.)

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 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

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...

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.)

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.

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....

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

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.)

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.

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)

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.

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.

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

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.

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.

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

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.

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.

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.

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)

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....

The Wigner transform and the semi-classical approximations

International Nuclear Information System (INIS)

Shlomo, S.

1985-01-01

The Wigner transform provides a reformulation of quantum mechanics in terms of classical concepts. Some properties of the Wigner transform of the density matrix which justify its interpretation as the quantum-mechanical analog of the classical phase-space distribution function are presented. Considering some applications, it is demonstrated that the Wigner distribution function serves as a good starting point for semi-classical approximations to properties of the (nuclear) many-body system

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.

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.

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

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

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)

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 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.

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

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.

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 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.

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

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.

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 + )

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.

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.

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.

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.

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.

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.

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...

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.

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...

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.

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

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 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...

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

Analysis of Discrete Mittag - Leffler Functions

Directory of Open Access Journals (Sweden)

N. Shobanadevi

2015-03-01

Full Text Available Discrete Mittag - Leffler functions play a major role in the development of the theory of discrete fractional calculus. In the present article, we analyze qualitative properties of discrete Mittag - Leffler functions and establish sufficient conditions for convergence, oscillation and summability of the infinite series associated with discrete Mittag - Leffler functions.

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

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

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

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.

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.

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

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....

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

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.

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.

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.

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

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.

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.

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.

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 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

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.

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

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.

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.)

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...

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.

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.

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 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.

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.

Mittag-Leffler function for discrete fractional modelling

Directory of Open Access Journals (Sweden)

Guo-Cheng Wu

2016-01-01

Full Text Available From the difference equations on discrete time scales, this paper numerically investigates one discrete fractional difference equation in the Caputo delta’s sense which has an explicit solution in form of the discrete Mittag-Leffler function. The exact numerical values of the solutions are given in comparison with the truncated Mittag-Leffler function.

Notes on qubit phase space and discrete symplectic structures

International Nuclear Information System (INIS)

Livine, Etera R

2010-01-01

We start from Wootter's construction of discrete phase spaces and Wigner functions for qubits and more generally for finite-dimensional Hilbert spaces. We look at this framework from a non-commutative space perspective and we focus on the Moyal product and the differential calculus on these discrete phase spaces. In particular, the qubit phase space provides the simplest example of a four-point non-commutative phase space. We give an explicit expression of the Moyal bracket as a differential operator. We then compare the quantum dynamics encoded by the Moyal bracket to the classical dynamics: we show that the classical Poisson bracket does not satisfy the Jacobi identity thus leaving the Moyal bracket as the only consistent symplectic structure. We finally generalize our analysis to Hilbert spaces of prime dimensions d and their associated d x d phase spaces.

Discretization of four types of Weyl group orbit functions

International Nuclear Information System (INIS)

Hrivnák, Jiří

2013-01-01

The discrete Fourier calculus of the four families of special functions, called C–, S–, S s – and S l -functions, is summarized. Functions from each of the four families of special functions are discretely orthogonal over a certain finite set of points. The generalizations of discrete cosine and sine transforms of one variable — the discrete S s – and S l -transforms of the group F 4 — are considered in detail required for their exploitation in discrete Fourier spectral methods. The continuous interpolations, induced by the discrete expansions, are presented

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.

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.

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).

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

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.

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

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.

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

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

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

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.

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

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)

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.

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 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)

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

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.

Discrete Morse functions for graph configuration spaces

International Nuclear Information System (INIS)

Sawicki, A

2012-01-01

We present an alternative application of discrete Morse theory for two-particle graph configuration spaces. In contrast to previous constructions, which are based on discrete Morse vector fields, our approach is through Morse functions, which have a nice physical interpretation as two-body potentials constructed from one-body potentials. We also give a brief introduction to discrete Morse theory. Our motivation comes from the problem of quantum statistics for particles on networks, for which generalized versions of anyon statistics can appear. (paper)

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)

Uniform analytic approximation of Wigner rotation matrices

Science.gov (United States)

Hoffmann, Scott E.

2018-02-01

We derive the leading asymptotic approximation, for low angle θ, of the Wigner rotation matrix elements, dm1m2 j(θ ) , uniform in j, m1, and m2. The result is in terms of a Bessel function of integer order. We numerically investigate the error for a variety of cases and find that the approximation can be useful over a significant range of angles. This approximation has application in the partial wave analysis of wavepacket scattering.

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....

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 ...

The boundary value problem for discrete analytic functions

KAUST Repository

Skopenkov, Mikhail

2013-01-01

This paper is on further development of discrete complex analysis introduced by R.Isaacs, J.Ferrand, R.Duffin, and C.Mercat. We consider a graph lying in the complex plane and having quadrilateral faces. A function on the vertices is called discrete

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.

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

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.

A discrete stress-strength interference model based on universal generating function

International Nuclear Information System (INIS)

An Zongwen; Huang Hongzhong; Liu Yu

2008-01-01

Continuous stress-strength interference (SSI) model regards stress and strength as continuous random variables with known probability density function. This, to some extent, results in a limitation of its application. In this paper, stress and strength are treated as discrete random variables, and a discrete SSI model is presented by using the universal generating function (UGF) method. Finally, case studies demonstrate the validity of the discrete model in a variety of circumstances, in which stress and strength can be represented by continuous random variables, discrete random variables, or two groups of experimental data

Truncated Wigner dynamics and conservation laws

Science.gov (United States)

Drummond, Peter D.; Opanchuk, Bogdan

2017-10-01

Ultracold Bose gases can be used to experimentally test many-body theory predictions. Here we point out that both exact conservation laws and dynamical invariants exist in the topical case of the one-dimensional Bose gas, and these provide an important validation of methods. We show that the first four quantum conservation laws are exactly conserved in the approximate truncated Wigner approach to many-body quantum dynamics. Center-of-mass position variance is also exactly calculable. This is nearly exact in the truncated Wigner approximation, apart from small terms that vanish as N-3 /2 as N →∞ with fixed momentum cutoff. Examples of this are calculated in experimentally relevant, mesoscopic cases.

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

Adaptive Control and Function Projective Synchronization in 2D Discrete-Time Chaotic Systems

International Nuclear Information System (INIS)

Li Yin; Chen Yong; Li Biao

2009-01-01

This study addresses the adaptive control and function projective synchronization problems between 2D Rulkov discrete-time system and Network discrete-time system. Based on backstepping design with three controllers, a systematic, concrete and automatic scheme is developed to investigate the function projective synchronization of discrete-time chaotic systems. In addition, the adaptive control function is applied to achieve the state synchronization of two discrete-time systems. Numerical results demonstrate the effectiveness of the proposed control scheme.

Discrete expansions of continuum wave functions

International Nuclear Information System (INIS)

Bang, J.; Ershov, S.N.; Gareev, F.A.; Kazacha, G.S.

1980-01-01

Different methods of expanding continuum wave functions in terms of discrete basis sets are discussed. The convergence properties of these expansions are investigated, both from a mathematical and a numerical point of view, for the case of potentials of Woods-Saxon and square well type. (orig.)

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.

Discrete-Trial Functional Analysis and Functional Communication Training with Three Adults with Intellectual Disabilities and Problem Behavior

Science.gov (United States)

Chezan, Laura C.; Drasgow, Erik; Martin, Christian A.

2014-01-01

We conducted a sequence of two studies on the use of discrete-trial functional analysis and functional communication training. First, we used discrete-trial functional analysis (DTFA) to identify the function of problem behavior in three adults with intellectual disabilities and problem behavior. Results indicated clear patterns of problem…

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

The boundary value problem for discrete analytic functions

KAUST Repository

Skopenkov, Mikhail

2013-06-01

This paper is on further development of discrete complex analysis introduced by R.Isaacs, J.Ferrand, R.Duffin, and C.Mercat. We consider a graph lying in the complex plane and having quadrilateral faces. A function on the vertices is called discrete analytic, if for each face the difference quotients along the two diagonals are equal.We prove that the Dirichlet boundary value problem for the real part of a discrete analytic function has a unique solution. In the case when each face has orthogonal diagonals we prove that this solution uniformly converges to a harmonic function in the scaling limit. This solves a problem of S.Smirnov from 2010. This was proved earlier by R.Courant-K.Friedrichs-H.Lewy and L.Lusternik for square lattices, by D.Chelkak-S.Smirnov and implicitly by P.G.Ciarlet-P.-A.Raviart for rhombic lattices.In particular, our result implies uniform convergence of the finite element method on Delaunay triangulations. This solves a problem of A.Bobenko from 2011. The methodology is based on energy estimates inspired by alternating-current network theory. © 2013 Elsevier Ltd.

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

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.

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.

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

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)

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...

Discrete expansions of continuum functions. General concepts

International Nuclear Information System (INIS)

Bang, J.; Ershov, S.N.; Gareev, F.A.; Kazacha, G.S.

1979-01-01

Different discrete expansions of the continuum wave functions are considered: pole expansion (according to the Mittag-Lefler theorem), Weinberg states. The general property of these groups of states is their completeness in the finite region of space. They satisfy the Schroedinger type equations and are matched with free solutions of the Schroedinger equation at the boundary. Convergence of expansions for the S matrix, the Green functions and the continuous-spectrum wave functions is studied. A new group of states possessing the best convergence is introduced

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

Evaluation of the Utility of a Discrete-Trial Functional Analysis in Early Intervention Classrooms

Science.gov (United States)

Kodak, Tiffany; Fisher, Wayne W.; Paden, Amber; Dickes, Nitasha

2013-01-01

We evaluated a discrete-trial functional analysis implemented by regular classroom staff in a classroom setting. The results suggest that the discrete-trial functional analysis identified a social function for each participant and may require fewer staff than standard functional analysis procedures.

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.

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.

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

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.

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.

Relating zeta functions of discrete and quantum graphs

Science.gov (United States)

Harrison, Jonathan; Weyand, Tracy

2018-02-01

We write the spectral zeta function of the Laplace operator on an equilateral metric graph in terms of the spectral zeta function of the normalized Laplace operator on the corresponding discrete graph. To do this, we apply a relation between the spectrum of the Laplacian on a discrete graph and that of the Laplacian on an equilateral metric graph. As a by-product, we determine how the multiplicity of eigenvalues of the quantum graph, that are also in the spectrum of the graph with Dirichlet conditions at the vertices, depends on the graph geometry. Finally we apply the result to calculate the vacuum energy and spectral determinant of a complete bipartite graph and compare our results with those for a star graph, a graph in which all vertices are connected to a central vertex by a single edge.

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

Function Projective Synchronization in Discrete-Time Chaotic System with Uncertain Parameters

International Nuclear Information System (INIS)

Chen Yong; Li Xin

2009-01-01

The function projective synchronization of discrete-time chaotic systems is presented. Based on backstepping design with three controllers, a systematic, concrete and automatic scheme is developed to investigate function projective synchronization (FPS) of discrete-time chaotic systems with uncertain parameters. With the aid of symbolic-numeric computation, we use the proposed scheme to illustrate FPS between two identical 3D Henon-like maps with uncertain parameters. Numeric simulations are used to verify the effectiveness of our scheme. (general)

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.

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.

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.

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

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.

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)

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.

The Information Content of Discrete Functions and Their Application in Genetic Data Analysis.

Science.gov (United States)

Sakhanenko, Nikita A; Kunert-Graf, James; Galas, David J

2017-12-01

The complex of central problems in data analysis consists of three components: (1) detecting the dependence of variables using quantitative measures, (2) defining the significance of these dependence measures, and (3) inferring the functional relationships among dependent variables. We have argued previously that an information theory approach allows separation of the detection problem from the inference of functional form problem. We approach here the third component of inferring functional forms based on information encoded in the functions. We present here a direct method for classifying the functional forms of discrete functions of three variables represented in data sets. Discrete variables are frequently encountered in data analysis, both as the result of inherently categorical variables and from the binning of continuous numerical variables into discrete alphabets of values. The fundamental question of how much information is contained in a given function is answered for these discrete functions, and their surprisingly complex relationships are illustrated. The all-important effect of noise on the inference of function classes is found to be highly heterogeneous and reveals some unexpected patterns. We apply this classification approach to an important area of biological data analysis-that of inference of genetic interactions. Genetic analysis provides a rich source of real and complex biological data analysis problems, and our general methods provide an analytical basis and tools for characterizing genetic problems and for analyzing genetic data. We illustrate the functional description and the classes of a number of common genetic interaction modes and also show how different modes vary widely in their sensitivity to noise.

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)

Bifurcations in a discrete time model composed of Beverton-Holt function and Ricker function.

Science.gov (United States)

Shang, Jin; Li, Bingtuan; Barnard, Michael R

2015-05-01

We provide rigorous analysis for a discrete-time model composed of the Ricker function and Beverton-Holt function. This model was proposed by Lewis and Li [Bull. Math. Biol. 74 (2012) 2383-2402] in the study of a population in which reproduction occurs at a discrete instant of time whereas death and competition take place continuously during the season. We show analytically that there exists a period-doubling bifurcation curve in the model. The bifurcation curve divides the parameter space into the region of stability and the region of instability. We demonstrate through numerical bifurcation diagrams that the regions of periodic cycles are intermixed with the regions of chaos. We also study the global stability of the model. Copyright © 2015 Elsevier Inc. All rights reserved.

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)

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

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)

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

Baecklund transformations for discrete Painleve equations: Discrete PII-PV

International Nuclear Information System (INIS)

Sakka, A.; Mugan, U.

2006-01-01

Transformation properties of discrete Painleve equations are investigated by using an algorithmic method. This method yields explicit transformations which relates the solutions of discrete Painleve equations, discrete P II -P V , with different values of parameters. The particular solutions which are expressible in terms of the discrete analogue of the classical special functions of discrete Painleve equations can also be obtained from these transformations

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

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

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).

Sliding mode control-based linear functional observers for discrete-time stochastic systems

Science.gov (United States)

Singh, Satnesh; Janardhanan, Sivaramakrishnan

2017-11-01

Sliding mode control (SMC) is one of the most popular techniques to stabilise linear discrete-time stochastic systems. However, application of SMC becomes difficult when the system states are not available for feedback. This paper presents a new approach to design a SMC-based functional observer for discrete-time stochastic systems. The functional observer is based on the Kronecker product approach. Existence conditions and stability analysis of the proposed observer are given. The control input is estimated by a novel linear functional observer. This approach leads to a non-switching type of control, thereby eliminating the fundamental cause of chatter. Furthermore, the functional observer is designed in such a way that the effect of process and measurement noise is minimised. Simulation example is given to illustrate and validate the proposed design method.

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

Discrete Mathematics

DEFF Research Database (Denmark)

Sørensen, John Aasted

2011-01-01

; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics...... to new problems. Relations and functions: Define a product set; define and apply equivalence relations; construct and apply functions. Apply these concepts to new problems. Natural numbers and induction: Define the natural numbers; apply the principle of induction to verify a selection of properties...

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...

Discrete-Trial Functional Analysis and Functional Communication Training with Three Individuals with Autism and Severe Problem Behavior

Science.gov (United States)

Schmidt, Jonathan D.; Drasgow, Erik; Halle, James W.; Martin, Christian A.; Bliss, Sacha A.

2014-01-01

Discrete-trial functional analysis (DTFA) is an experimental method for determining the variables maintaining problem behavior in the context of natural routines. Functional communication training (FCT) is an effective method for replacing problem behavior, once identified, with a functionally equivalent response. We implemented these procedures…

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.

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

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.

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...

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

Quantum computers in phase space

International Nuclear Information System (INIS)

Miquel, Cesar; Paz, Juan Pablo; Saraceno, Marcos

2002-01-01

We represent both the states and the evolution of a quantum computer in phase space using the discrete Wigner function. We study properties of the phase space representation of quantum algorithms: apart from analyzing important examples, such as the Fourier transform and Grover's search, we examine the conditions for the existence of a direct correspondence between quantum and classical evolutions in phase space. Finally, we describe how to measure directly the Wigner function in a given phase-space point by means of a tomographic method that, itself, can be interpreted as a simple quantum algorithm

Orthogonal functions, discrete variable representation, and generalized gauss quadratures

DEFF Research Database (Denmark)

Schneider, B. I.; Nygaard, Nicolai

2002-01-01

in the original representation. This has been exploited in bound-state, scattering, and time-dependent problems using the so-called, discrete variable representation (DVR). At the core of this approach is the mathematical three-term recursion relationship satisfied by the classical orthogonal functions...... functions, this is not the case. However, they may be computed in a stable numerical fashion, via the recursion. In essence, this is an application of the well-known Lanczos recursion approach. Once the recursion coefficients are known, it is possible to compute the points and weights of quadratures on...

Discrete Green's Theorem, Green's Functions and Stable Radiative FDTD Boundary Conditions

NARCIS (Netherlands)

Arnold, J.M.; Hon, de B.P.

2007-01-01

We propose a radiative boundary condition for the discrete-grid formulation of Helmholtz’ equation, based on rational approximation in the frequency domain of a Green’s function for the discretised system. This boundary condition is free from instabilities.

On quantum mechanical phase-space wave functions

DEFF Research Database (Denmark)

Wlodarz, Joachim J.

1994-01-01

An approach to quantum mechanics based on the notion of a phase-space wave function is proposed within the Weyl-Wigner-Moyal representation. It is shown that the Schrodinger equation for the phase-space wave function is equivalent to the quantum Liouville equation for the Wigner distribution...... function. The relationship to the recent results by Torres-Vega and Frederick [J. Chem. Phys. 98, 3103 (1993)] is also discussed....

Quantum distribution function of nonequilibrium system

International Nuclear Information System (INIS)

Sogo, Kiyoshi; Fujimoto, Yasushi.

1990-03-01

A path integral representation is derived for the Wigner distribution function of a nonequilibrium system coupled with heat bath. Under appropriate conditions, the Wigner distribution function approaches an equilibrium distribution, which manifests shifting and broadening of spectral lines due to the interaction with heat bath. It is shown that the equilibrium distribution becomes the quantum canonical distribution in the vanishing coupling constant limit. (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.

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.

VMF3/GPT3: refined discrete and empirical troposphere mapping functions

Science.gov (United States)

Landskron, Daniel; Böhm, Johannes

2018-04-01

Incorrect modeling of troposphere delays is one of the major error sources for space geodetic techniques such as Global Navigation Satellite Systems (GNSS) or Very Long Baseline Interferometry (VLBI). Over the years, many approaches have been devised which aim at mapping the delay of radio waves from zenith direction down to the observed elevation angle, so-called mapping functions. This paper contains a new approach intended to refine the currently most important discrete mapping function, the Vienna Mapping Functions 1 (VMF1), which is successively referred to as Vienna Mapping Functions 3 (VMF3). It is designed in such a way as to eliminate shortcomings in the empirical coefficients b and c and in the tuning for the specific elevation angle of 3°. Ray-traced delays of the ray-tracer RADIATE serve as the basis for the calculation of new mapping function coefficients. Comparisons of modeled slant delays demonstrate the ability of VMF3 to approximate the underlying ray-traced delays more accurately than VMF1 does, in particular at low elevation angles. In other words, when requiring highest precision, VMF3 is to be preferable to VMF1. Aside from revising the discrete form of mapping functions, we also present a new empirical model named Global Pressure and Temperature 3 (GPT3) on a 5°× 5° as well as a 1°× 1° global grid, which is generally based on the same data. Its main components are hydrostatic and wet empirical mapping function coefficients derived from special averaging techniques of the respective (discrete) VMF3 data. In addition, GPT3 also contains a set of meteorological quantities which are adopted as they stand from their predecessor, Global Pressure and Temperature 2 wet. Thus, GPT3 represents a very comprehensive troposphere model which can be used for a series of geodetic as well as meteorological and climatological purposes and is fully consistent with VMF3.

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)

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.

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

Functional envelope of a non-autonomous discrete system

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Barzanouni Ali

2017-11-01

Full Text Available Let (X, F = {fn}n =0∞ be a non-autonomous discrete system by a compact metric space X and continuous maps fn : X → X, n = 0, 1, ....We introduce functional envelope (S(X, G = {Gn}n =0∞, of (X, F = {fn}n =0∞, where S(X is the space of all continuous self maps of X and the map Gn : S(X → S(X is defined by Gn(ϕ = Fn ∘ ϕ, Fn = fn ∘ fn-1 ∘ . . . ∘ f1 ∘ f0. The paper mainly deals with the connection between the properties of a system and the properties of its functional envelope.

Discrete imaging models for three-dimensional optoacoustic tomography using radially symmetric expansion functions.

Science.gov (United States)

Wang, Kun; Schoonover, Robert W; Su, Richard; Oraevsky, Alexander; Anastasio, Mark A

2014-05-01

Optoacoustic tomography (OAT), also known as photoacoustic tomography, is an emerging computed biomedical imaging modality that exploits optical contrast and ultrasonic detection principles. Iterative image reconstruction algorithms that are based on discrete imaging models are actively being developed for OAT due to their ability to improve image quality by incorporating accurate models of the imaging physics, instrument response, and measurement noise. In this work, we investigate the use of discrete imaging models based on Kaiser-Bessel window functions for iterative image reconstruction in OAT. A closed-form expression for the pressure produced by a Kaiser-Bessel function is calculated, which facilitates accurate computation of the system matrix. Computer-simulation and experimental studies are employed to demonstrate the potential advantages of Kaiser-Bessel function-based iterative image reconstruction in OAT.

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)

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.

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.

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.

Permanence of a predator-prey discrete system with Holling-IV functional response and distributed delays.

Science.gov (United States)

Zhang, X; Wu, Z; Zhou, T

2016-01-01

A predator-prey discrete-time model with Holling-IV functional response and distributed delays is investigated in this paper. By using the comparison theorem of the difference equation and some analysis technique, some sufficient conditions are obtained for the permanence of the discrete predator-prey system. Two examples are given to illustrate the feasibility of the obtained result.

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

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.

Preserved re-experience of discrete emotions: Amnesia and executive function.

Science.gov (United States)

Stanciu, Marian Andrei; Rafal, Robert D; Turnbull, Oliver H

2018-02-07

Amnesic patients can re-experience emotions elicited by forgotten events, suggesting that brain systems for episodic and emotional memory are independent. However, the range of such emotional memories remains under-investigated (most studies employing just positive-negative emotion dyads), and executive function may also play a role in the re-experience of emotions. This is the first investigation of the intensity of the emotional re-experience of a range of discrete emotions (anger, fear, sadness, and happiness) for a group of amnesic patients. Twenty Korsakoff syndrome (KS) patients and 20 neurologically normal controls listened to four novel emotional vignettes selectively eliciting the four basic emotions. Emotional experience was measured using pen-and-paper Visual Analogue Mood Scales and episodic memory using verbal recollections. After 30 min, the recollection of stories was severely impaired for the patient group, but the emotional re-experience was no different from that of controls. Notably, there was no relationship between episodic recall and the intensity of the four emotions, such that even profoundly amnesic patients reported moderate levels of the target emotion. Exploratory analyses revealed negative correlations between the intensity of basic emotions and executive functions (e.g., cognitive flexibility and response inhibition) for controls but not patients. The results suggest that discrete emotions can be re-experienced independently of episodic memory, and that the re-experience of certain discrete emotions appears to be dampened by executive control. KS patients with absent or mild cognitive symptoms should benefit from emotion-regulation interventions aimed at reducing the recognized affective burden associated with their episodic memory deficit. © 2018 The British Psychological Society.

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

Ion association at discretely-charged dielectric interfaces: Giant charge inversion

Science.gov (United States)

Wang, Zhi-Yong; Wu, Jianzhong

2017-07-01

Giant charge reversal has been identified for the first time by Monte Carlo simulation for a discretely charged surface in contact with a trivalent electrolyte solution. It takes place regardless of the surface charge density under study and the monovalent salt. In stark contrast to earlier predictions based on the 2-dimensional Wigner crystal model to describe strong correlation of counterions at the macroion surface, we find that giant charge reversal reflects an intricate interplay of ionic volume effects, electrostatic correlations, surface charge heterogeneity, and the dielectric response of the confined fluids. While the novel phenomenon is yet to be confirmed with experiment, the simulation results appear in excellent agreement with a wide range of existing observations in the subregime of charge inversion. Our findings may have far-reaching implications to understanding complex electrochemical phenomena entailing ionic fluids under dielectric confinements.

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

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.

A more accurate half-discrete Hardy-Hilbert-type inequality with the logarithmic function.

Science.gov (United States)

Wang, Aizhen; Yang, Bicheng

2017-01-01

By means of the weight functions, the technique of real analysis and Hermite-Hadamard's inequality, a more accurate half-discrete Hardy-Hilbert-type inequality related to the kernel of logarithmic function and a best possible constant factor is given. Moreover, the equivalent forms, the operator expressions, the reverses and some particular cases are also considered.

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.

Nonclassicality indicator for the real phase-space distribution functions

International Nuclear Information System (INIS)

Sadeghi, Parvin; Khademi, Siamak; Nasiri, Sadollah

2010-01-01

Benedict et al. and Kenfack et al. advocated nonclassicality indicators based on the measurement of negativity of the Wigner distribution functions. These indicators have some applications in quantum mechanics and quantum optics. In this paper we define a nonclassicality indicator in terms of the interference in phase space, which is applicable to some real distribution functions including those of Wigner. As a special case one may reproduce the previous results using our indicator for the Wigner distribution functions. This indicator is examined for cases of the Schroedinger cat state and the thermal states and the results are compared with those obtained by previous methods. It seems that the physical behavior of nonclassicality indicators originates in the uncertainty principle. This is shown by an onto correspondence between these indicators and the uncertainty principle.

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

Zero of the discrete beta function in SU(3) lattice gauge theory with color sextet fermions

International Nuclear Information System (INIS)

Shamir, Yigal; Svetitsky, Benjamin; DeGrand, Thomas

2008-01-01

We have carried out a Schrodinger functional calculation for the SU(3) lattice gauge theory with two flavors of Wilson fermions in the sextet representation of the gauge group. We find that the discrete beta function, which governs the change in the running coupling under a discrete change of spatial scale, changes sign when the Schrodinger functional renormalized coupling is in the neighborhood of g 2 =2.0. The simplest explanation is that the theory has an infrared-attractive fixed point, but more complicated possibilities are allowed by the data. While we compare rescalings by factors of 2 and 4/3, we work at a single lattice spacing.

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.

Application of discrete function and software control flow to dependability assessment of embedded digital system

International Nuclear Information System (INIS)

Choi, Jong Gyun; Seong, Poong Hyun

2001-01-01

This article describes a combinatorial model for estimating the reliability of the embedded digital system by means of discrete function theory and software control flow. This model includes a coverage model for fault processing mechanisms implemented in digital system. Furthermore, the model considers the interaction between hardware and software. The fault processing mechanisms make it difficult for many types of components in digital system to be treated as binary state, good or bad. The discrete function theory provides a complete analysis of multi-state system as which the digital system can be regarded Through adaptation software control flow to discrete function theory, the HW/SW interaction is considered for estimation of the reliability of digital system. Using this model, we predict the reliability of one board controller in a digital system, Interposing Logic System(ILS), which is installed in YGN nuclear power units 3 and 4. Since the proposed model is general combinatinal model, the simplification of this model becomes a conservative model that treats the system as binary state. Moreover, if information for coverage factor of fault tolerance mechanisms implemented in system through fault injection experiment is obtained, this model can consider detailed interaction of system components

Exact Travelling Solutions of Discrete sine-Gordon Equation via Extended Tanh-Function Approach

International Nuclear Information System (INIS)

Dai Chaoqing; Zhang Jiefang

2006-01-01

In this paper, we generalize the extended tanh-function approach, which was used to find new exact travelling wave solutions of nonlinear partial differential equations or coupled nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, two series of exact travelling wave solutions of the discrete sine-Gordon equation are obtained by means of the extended tanh-function approach.

A more accurate half-discrete Hardy-Hilbert-type inequality with the logarithmic function

Directory of Open Access Journals (Sweden)

Aizhen Wang

2017-06-01

Full Text Available Abstract By means of the weight functions, the technique of real analysis and Hermite-Hadamard’s inequality, a more accurate half-discrete Hardy-Hilbert-type inequality related to the kernel of logarithmic function and a best possible constant factor is given. Moreover, the equivalent forms, the operator expressions, the reverses and some particular cases are also considered.

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.

Explicit solutions to the semi-discrete modified KdV equation and motion of discrete plane curves

International Nuclear Information System (INIS)

Inoguchi, Jun-ichi; Kajiwara, Kenji; Matsuura, Nozomu; Ohta, Yasuhiro

2012-01-01

We construct explicit solutions to continuous motion of discrete plane curves described by a semi-discrete potential modified KdV equation. Explicit formulas in terms of the τ function are presented. Bäcklund transformations of the discrete curves are also discussed. We finally consider the continuous limit of discrete motion of discrete plane curves described by the discrete potential modified KdV equation to motion of smooth plane curves characterized by the potential modified KdV equation. (paper)

Factorizations of rational matrix functions with application to discrete isomonodromic transformations and difference Painleve equations

International Nuclear Information System (INIS)

Dzhamay, Anton

2009-01-01

We study factorizations of rational matrix functions with simple poles on the Riemann sphere. For the quadratic case (two poles) we show, using multiplicative representations of such matrix functions, that a good coordinate system on this space is given by a mix of residue eigenvectors of the matrix and its inverse. Our approach is motivated by the theory of discrete isomonodromic transformations and their relationship with difference Painleve equations. In particular, in these coordinates, basic isomonodromic transformations take the form of the discrete Euler-Lagrange equations. Secondly we show that dPV equations, previously obtained in this context by D Arinkin and A Borodin, can be understood as simple relationships between the residues of such matrices and their inverses.

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)

Decomposing a Utility Function Based on Discrete Distribution Independence

DEFF Research Database (Denmark)

He, Ying; Dyer, James; Butler, John

2014-01-01

For two-attribute decision-making problems, the multilinear utility model cannot be applied when the risk aversion on one attribute depends on the level of the other attribute. We propose a family of general preference conditions called nth-degree discrete distribution independence that can...... accommodate a variety of dependence relationships between two attributes. The special case of second-degree discrete distribution independence is equivalent to the utility independence condition. We focus on third-degree discrete distribution independence that leads to a decomposition formula that contains...

Orthogonal functions, discrete variable representation, and generalized gauss quadratures

DEFF Research Database (Denmark)

Schneider, B. I.; Nygaard, Nicolai

2002-01-01

in the original representation. This has been exploited in bound-state, scattering, and time-dependent problems using the so-called, discrete variable representation (DVR). At the core of this approach is the mathematical three-term recursion relationship satisfied by the classical orthogonal functions......, the distinction between spectral and grid approaches becomes blurred. In fact, the two approaches can be related by a similarity transformation. By the exploitation of this idea, calculations can be considerably simplified by removing the need to compute difficult matrix elements of the Hamiltonian...... functions, this is not the case. However, they may be computed in a stable numerical fashion, via the recursion. In essence, this is an application of the well-known Lanczos recursion approach. Once the recursion coefficients are known, it is possible to compute the points and weights of quadratures on...

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 | .

Discrete Green’s function diakoptics for stable FDTD interaction between multiply-connected domains

NARCIS (Netherlands)

Hon, de B.P.; Arnold, J.M.; Graglia, R.D.

2007-01-01

We have developed FDTD boundary conditions based on discrete Green's function diakoptics for arbitrary multiply-connected 2D domains. The associated Z-domain boundary operator is symmetric, with an imaginary part that can be proved to be positive semi-definite on the upper half of the unit circle in

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.

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

A particular inverse problem for Schroedinger discrete equation in two and higher dimensions under apriori information of wave functions

International Nuclear Information System (INIS)

Pavlus, M.

1997-01-01

The entire potential and the rest of wave functions are determined in parallelepiped domain if the entire discrete spectrum and the apriori information about the wave functions on one side of parallelepiped are given. Formulation for solving the Schroedinger discrete equation in two and higher dimensions is proposed and new formulas are derived for their solution. Two examples for a 2D case and one example for a 3D case are demonstrated

Discrete repulsive oscillator wavefunctions

International Nuclear Information System (INIS)

Munoz, Carlos A; Rueda-Paz, Juvenal; Wolf, Kurt Bernardo

2009-01-01

For the study of infinite discrete systems on phase space, the three-dimensional Lorentz algebra and group, so(2,1) and SO(2,1), provide a discrete model of the repulsive oscillator. Its eigenfunctions are found in the principal irreducible representation series, where the compact generator-that we identify with the position operator-has the infinite discrete spectrum of the integers Z, while the spectrum of energies is a double continuum. The right- and left-moving wavefunctions are given by hypergeometric functions that form a Dirac basis for l 2 (Z). Under contraction, the discrete system limits to the well-known quantum repulsive oscillator. Numerical computations of finite approximations raise further questions on the use of Dirac bases for infinite discrete systems.

On the Importance of Both Dimensional and Discrete Models of Emotion.

Science.gov (United States)

Harmon-Jones, Eddie; Harmon-Jones, Cindy; Summerell, Elizabeth

2017-09-29

We review research on the structure and functions of emotions that has benefitted from a serious consideration of both discrete and dimensional perspectives on emotion. To illustrate this point, we review research that demonstrates: (1) how affective valence within discrete emotions differs as a function of individuals and situations, and how these differences relate to various functions; (2) that anger (and other emotional states) should be considered as a discrete emotion but there are dimensions around and within anger; (3) that similarities exist between approach-related positive and negative discrete emotions and they have unique motivational functions; (4) that discrete emotions and broad dimensions of emotions both have unique functions; and (5) evidence that a "new" discrete emotion with discrete functions exists within a broader emotion family. We hope that this consideration of both discrete and dimensional perspectives on emotion will assist in understanding the functions of emotions.

On the Importance of Both Dimensional and Discrete Models of Emotion

Science.gov (United States)

Harmon-Jones, Eddie

2017-01-01

We review research on the structure and functions of emotions that has benefitted from a serious consideration of both discrete and dimensional perspectives on emotion. To illustrate this point, we review research that demonstrates: (1) how affective valence within discrete emotions differs as a function of individuals and situations, and how these differences relate to various functions; (2) that anger (and other emotional states) should be considered as a discrete emotion but there are dimensions around and within anger; (3) that similarities exist between approach-related positive and negative discrete emotions and they have unique motivational functions; (4) that discrete emotions and broad dimensions of emotions both have unique functions; and (5) evidence that a “new” discrete emotion with discrete functions exists within a broader emotion family. We hope that this consideration of both discrete and dimensional perspectives on emotion will assist in understanding the functions of emotions. PMID:28961185

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).

On the Importance of Both Dimensional and Discrete Models of Emotion

Directory of Open Access Journals (Sweden)

Eddie Harmon-Jones

2017-09-01

Full Text Available We review research on the structure and functions of emotions that has benefitted from a serious consideration of both discrete and dimensional perspectives on emotion. To illustrate this point, we review research that demonstrates: (1 how affective valence within discrete emotions differs as a function of individuals and situations, and how these differences relate to various functions; (2 that anger (and other emotional states should be considered as a discrete emotion but there are dimensions around and within anger; (3 that similarities exist between approach-related positive and negative discrete emotions and they have unique motivational functions; (4 that discrete emotions and broad dimensions of emotions both have unique functions; and (5 evidence that a “new” discrete emotion with discrete functions exists within a broader emotion family. We hope that this consideration of both discrete and dimensional perspectives on emotion will assist in understanding the functions of emotions.

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)

Interpolation of the discrete logarithm in a finite field of characteristic two by Boolean functions

DEFF Research Database (Denmark)

Brandstaetter, Nina; Lange, Tanja; Winterhof, Arne

2005-01-01

We obtain bounds on degree, weight, and the maximal Fourier coefficient of Boolean functions interpolating the discrete logarithm in finite fields of characteristic two. These bounds complement earlier results for finite fields of odd characteristic....

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)

Semigroup evolution in the Wigner-Weisskopf pole approximation with Markovian spectral coupling

International Nuclear Information System (INIS)

Shikerman, F.; Peer, A.; Horwitz, L. P.

2011-01-01

We establish the relation between the Wigner-Weisskopf theory for the description of an unstable system and the theory of coupling to an environment. According to the Wigner-Weisskopf general approach, even within the pole approximation, the evolution of a total system subspace is not an exact semigroup for multichannel decay unless the projectors into eigenstates of the reduced evolution generator W(z) are orthogonal. With multichannel decay, the projectors must be evaluated at different pole locations z α ≠z β , and since the orthogonality relation does not generally hold at different values of z, the semigroup evolution is a poor approximation for the multichannel decay, even for very weak coupling. Nevertheless, if the theory is generalized to take into account interactions with an environment, one can ensure orthogonality of the W(z) projectors regardless of the number of poles. Such a possibility occurs when W(z), and hence its eigenvectors, is independent of z, which corresponds to the Markovian limit of the coupling to the continuum spectrum.

Semigroup evolution in the Wigner-Weisskopf pole approximation with Markovian spectral coupling

Energy Technology Data Exchange (ETDEWEB)

Shikerman, F.; Peer, A. [Physics department and BINA center for nano-technology, Bar Ilan University, Ramat Gan 52900 (Israel); Horwitz, L. P. [Physics department and BINA center for nano-technology, Bar Ilan University, Ramat Gan 52900 (Israel); School of Physics, Tel-Aviv University, Ramat-Aviv 69978 (Israel); Department of Physics, Ariel University Center of Samaria, Ariel 40700 (Israel)

2011-07-15

We establish the relation between the Wigner-Weisskopf theory for the description of an unstable system and the theory of coupling to an environment. According to the Wigner-Weisskopf general approach, even within the pole approximation, the evolution of a total system subspace is not an exact semigroup for multichannel decay unless the projectors into eigenstates of the reduced evolution generator W(z) are orthogonal. With multichannel decay, the projectors must be evaluated at different pole locations z{sub {alpha}}{ne}z{sub {beta}}, and since the orthogonality relation does not generally hold at different values of z, the semigroup evolution is a poor approximation for the multichannel decay, even for very weak coupling. Nevertheless, if the theory is generalized to take into account interactions with an environment, one can ensure orthogonality of the W(z) projectors regardless of the number of poles. Such a possibility occurs when W(z), and hence its eigenvectors, is independent of z, which corresponds to the Markovian limit of the coupling to the continuum spectrum.

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.

A study of discrete nonlinear systems

International Nuclear Information System (INIS)

Dhillon, H.S.

2001-04-01

An investigation of various spatially discrete time-independent nonlinear models was undertaken. These models are generically applicable to many different physical systems including electron-phonon interactions in solids, magnetic multilayers, layered superconductors and classical lattice systems. To characterise the possible magnetic structures created on magnetic multilayers a model has been formulated and studied. The Euler-Lagrange equation for this model is a discrete version of the Sine-Gordon equation. Solutions of this equation are generated by applying the methods of Chaotic Dynamics - treating the space variable associated with the layer number as a discrete time variable. The states found indicate periodic, quasiperiodic and chaotic structures. Analytic solutions to the discrete nonlinear Schroedinger Equation (DNSE) with cubic nonlinearity are presented in the strong coupling limit. Using these as a starting point, a procedure is developed to determine the wave function and the energy eigenvalue for moderate coupling. The energy eigenvalues of the different structures of the wave function are found to be in excellent agreement with the exact strong coupling result. The solutions to the DNSE indicate commensurate and incommensurate spatial structures associated with different localisation patterns of the wave function. The states which arise may be fractal, periodic, quasiperiodic or chaotic. This work is then extended to solve a first order discrete nonlinear equation. The exact solutions for both the first and second order discrete nonlinear equations with cubic nonlinearity suggests that this method of studying discrete nonlinear equations may be applied to solve discrete equations with any order difference and cubic nonlinearity. (author)

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

Recent Advances in the Korringa-Kohn-Rostoker Green Function Method

Directory of Open Access Journals (Sweden)

Zeller Rudolf

2014-01-01

Full Text Available The Korringa-Kohn-Rostoker (KKR Green function (GF method is a technique for all-electron full-potential density-functional calculations. Similar to the historical Wigner-Seitz cellular method, the KKR-GF method uses a partitioning of space into atomic Wigner-Seitz cells. However, the numerically demanding wave-function matching at the cell boundaries is avoided by use of an integral equation formalism based on the concept of reference Green functions. The advantage of this formalism will be illustrated by the recent progress made for very large systems with thousands of inequivalent atoms and for very accurate calculations of atomic forces and total energies.

Breit-Wigner approximation for propagators of mixed unstable states

International Nuclear Information System (INIS)

Fuchs, Elina

2016-10-01

For systems of unstable particles that mix with each other, an approximation of the fully momentum- dependent propagator matrix is presented in terms of a sum of simple Breit-Wigner propagators that are multiplied with finite on-shell wave function normalisation factors. The latter are evaluated at the complex poles of the propagators. The pole structure of general propagator matrices is carefully analysed, and it is demonstrated that in the proposed approximation imaginary parts arising from absorptive parts of loop integrals are properly taken into account. Applying the formalism to the neutral MSSM Higgs sector with complex parameters, very good numerical agreement is found between cross sections based on the full propagators and the corresponding cross sections based on the described approximation. The proposed approach does not only technically simplify the treatment of propagators with non-vanishing off-diagonal contributions, it is shown that it can also facilitate an improved theoretical prediction of the considered observables via a more precise implementation of the total widths of the involved particles. It is also well-suited for the incorporation of interference effects arising from overlapping resonances.

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

Discrete computational structures

CERN Document Server

Korfhage, Robert R

1974-01-01

Discrete Computational Structures describes discrete mathematical concepts that are important to computing, covering necessary mathematical fundamentals, computer representation of sets, graph theory, storage minimization, and bandwidth. The book also explains conceptual framework (Gorn trees, searching, subroutines) and directed graphs (flowcharts, critical paths, information network). The text discusses algebra particularly as it applies to concentrates on semigroups, groups, lattices, propositional calculus, including a new tabular method of Boolean function minimization. The text emphasize

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....

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

The magic of universal quantum computing with permutations

OpenAIRE

Planat, Michel; Rukhsan-Ul-Haq

2017-01-01

The role of permutation gates for universal quantum computing is investigated. The \\lq magic' of computation is clarified in the permutation gates, their eigenstates, the Wootters discrete Wigner function and state-dependent contextuality (following many contributions on this subject). A first classification of main types of resulting magic states in low dimensions $d \\le 9$ is performed.

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

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

Discrete density of states

International Nuclear Information System (INIS)

Aydin, Alhun; Sisman, Altug

2016-01-01

By considering the quantum-mechanically minimum allowable energy interval, we exactly count number of states (NOS) and introduce discrete density of states (DOS) concept for a particle in a box for various dimensions. Expressions for bounded and unbounded continua are analytically recovered from discrete ones. Even though substantial fluctuations prevail in discrete DOS, they're almost completely flattened out after summation or integration operation. It's seen that relative errors of analytical expressions of bounded/unbounded continua rapidly decrease for high NOS values (weak confinement or high energy conditions), while the proposed analytical expressions based on Weyl's conjecture always preserve their lower error characteristic. - Highlights: • Discrete density of states considering minimum energy difference is proposed. • Analytical DOS and NOS formulas based on Weyl conjecture are given. • Discrete DOS and NOS functions are examined for various dimensions. • Relative errors of analytical formulas are much better than the conventional ones.

Time evolution of a Gaussian class of quasi-distribution functions under quadratic Hamiltonian.

Science.gov (United States)

Ginzburg, D; Mann, A

2014-03-10

A Lie algebraic method for propagation of the Wigner quasi-distribution function (QDF) under quadratic Hamiltonian was presented by Zoubi and Ben-Aryeh. We show that the same method can be used in order to propagate a rather general class of QDFs, which we call the "Gaussian class." This class contains as special cases the well-known Wigner, Husimi, Glauber, and Kirkwood-Rihaczek QDFs. We present some examples of the calculation of the time evolution of those functions.

Graph-cut based discrete-valued image reconstruction.

Science.gov (United States)

Tuysuzoglu, Ahmet; Karl, W Clem; Stojanovic, Ivana; Castañòn, David; Ünlü, M Selim

2015-05-01

Efficient graph-cut methods have been used with great success for labeling and denoising problems occurring in computer vision. Unfortunately, the presence of linear image mappings has prevented the use of these techniques in most discrete-amplitude image reconstruction problems. In this paper, we develop a graph-cut based framework for the direct solution of discrete amplitude linear image reconstruction problems cast as regularized energy function minimizations. We first analyze the structure of discrete linear inverse problem cost functions to show that the obstacle to the application of graph-cut methods to their solution is the variable mixing caused by the presence of the linear sensing operator. We then propose to use a surrogate energy functional that overcomes the challenges imposed by the sensing operator yet can be utilized efficiently in existing graph-cut frameworks. We use this surrogate energy functional to devise a monotonic iterative algorithm for the solution of discrete valued inverse problems. We first provide experiments using local convolutional operators and show the robustness of the proposed technique to noise and stability to changes in regularization parameter. Then we focus on nonlocal, tomographic examples where we consider limited-angle data problems. We compare our technique with state-of-the-art discrete and continuous image reconstruction techniques. Experiments show that the proposed method outperforms state-of-the-art techniques in challenging scenarios involving discrete valued unknowns.

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 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

Discrete density of states

Energy Technology Data Exchange (ETDEWEB)

Aydin, Alhun; Sisman, Altug, E-mail: sismanal@itu.edu.tr

2016-03-22

By considering the quantum-mechanically minimum allowable energy interval, we exactly count number of states (NOS) and introduce discrete density of states (DOS) concept for a particle in a box for various dimensions. Expressions for bounded and unbounded continua are analytically recovered from discrete ones. Even though substantial fluctuations prevail in discrete DOS, they're almost completely flattened out after summation or integration operation. It's seen that relative errors of analytical expressions of bounded/unbounded continua rapidly decrease for high NOS values (weak confinement or high energy conditions), while the proposed analytical expressions based on Weyl's conjecture always preserve their lower error characteristic. - Highlights: • Discrete density of states considering minimum energy difference is proposed. • Analytical DOS and NOS formulas based on Weyl conjecture are given. • Discrete DOS and NOS functions are examined for various dimensions. • Relative errors of analytical formulas are much better than the conventional ones.

Homogenization of discrete media

International Nuclear Information System (INIS)

Pradel, F.; Sab, K.

1998-01-01

Material such as granular media, beam assembly are easily seen as discrete media. They look like geometrical points linked together thanks to energetic expressions. Our purpose is to extend discrete kinematics to the one of an equivalent continuous material. First we explain how we build the localisation tool for periodic materials according to estimated continuum medium type (classical Cauchy, and Cosserat media). Once the bridge built between discrete and continuum media, we exhibit its application over two bidimensional beam assembly structures : the honey comb and a structural reinforced variation. The new behavior is then applied for the simple plan shear problem in a Cosserat continuum and compared with the real discrete solution. By the mean of this example, we establish the agreement of our new model with real structures. The exposed method has a longer range than mechanics and can be applied to every discrete problems like electromagnetism in which relationship between geometrical points can be summed up by an energetic function. (orig.)

Homogenization of discrete media

Energy Technology Data Exchange (ETDEWEB)

Pradel, F.; Sab, K. [CERAM-ENPC, Marne-la-Vallee (France)

1998-11-01

Material such as granular media, beam assembly are easily seen as discrete media. They look like geometrical points linked together thanks to energetic expressions. Our purpose is to extend discrete kinematics to the one of an equivalent continuous material. First we explain how we build the localisation tool for periodic materials according to estimated continuum medium type (classical Cauchy, and Cosserat media). Once the bridge built between discrete and continuum media, we exhibit its application over two bidimensional beam assembly structures : the honey comb and a structural reinforced variation. The new behavior is then applied for the simple plan shear problem in a Cosserat continuum and compared with the real discrete solution. By the mean of this example, we establish the agreement of our new model with real structures. The exposed method has a longer range than mechanics and can be applied to every discrete problems like electromagnetism in which relationship between geometrical points can be summed up by an energetic function. (orig.) 7 refs.

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.)

Quantum mechanics with non-negative quantum distribution function

International Nuclear Information System (INIS)

Zorin, A.V.; Sevastianov, L.A.

2010-01-01

Full text: (author)Among numerous approaches to probabilistic interpretation of the conventional quantum mechanics the most close to the N. Bohr idea of the correspondence principle is the D.I. Blokhintzev - Ya.P. Terletsky approach using the quantum distribution function on the coordinate- momentum space. The detailed investigation of this approach has lead to the correspondence rule of V.V. Kuryshkin. Quantum mechanics of Kuryshkin (QMK) embody the program proposed by Yu.M. Shirokov for unifying classical and quantum mechanics in similar mathematical models. QMK develops and enhances Wigner's proposal concerning the calculation of quantum corrections to classical thermodynamic parameters using a phase distribution function. The main result of QMK is the possibility of description by mean of a positively-valued distribution function. This represents an important step towards a completely statistical model of quantum phenomena, compared with the quasi-probabilistic nature of Wigner distribution. Wigner's model does not permit to perform correctly the classical limit in quantum mechanics as well. On the other hand, QMK has a much more complex structure of operators of observables. One of the unsolved problems of QMK is the absence of a priori rules for establishing of auxiliary functions. Nevertheless, while it is impossible to overcome the complex form of operators, we find it quite possible to derive some methods of filing sets of auxiliary functions

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)

The Magic of Universal Quantum Computing with Permutations

Directory of Open Access Journals (Sweden)

Michel Planat

2017-01-01

Full Text Available The role of permutation gates for universal quantum computing is investigated. The “magic” of computation is clarified in the permutation gates, their eigenstates, the Wootters discrete Wigner function, and state-dependent contextuality (following many contributions on this subject. A first classification of a few types of resulting magic states in low dimensions d≤9 is performed.

Finite Discrete Gabor Analysis

DEFF Research Database (Denmark)

Søndergaard, Peter Lempel

2007-01-01

frequency bands at certain times. Gabor theory can be formulated for both functions on the real line and for discrete signals of finite length. The two theories are largely the same because many aspects come from the same underlying theory of locally compact Abelian groups. The two types of Gabor systems...... can also be related by sampling and periodization. This thesis extends on this theory by showing new results for window construction. It also provides a discussion of the problems associated to discrete Gabor bases. The sampling and periodization connection is handy because it allows Gabor systems...... on the real line to be well approximated by finite and discrete Gabor frames. This method of approximation is especially attractive because efficient numerical methods exists for doing computations with finite, discrete Gabor systems. This thesis presents new algorithms for the efficient computation of finite...

Discrete non-parametric kernel estimation for global sensitivity analysis

International Nuclear Information System (INIS)

Senga Kiessé, Tristan; Ventura, Anne

2016-01-01

This work investigates the discrete kernel approach for evaluating the contribution of the variance of discrete input variables to the variance of model output, via analysis of variance (ANOVA) decomposition. Until recently only the continuous kernel approach has been applied as a metamodeling approach within sensitivity analysis framework, for both discrete and continuous input variables. Now the discrete kernel estimation is known to be suitable for smoothing discrete functions. We present a discrete non-parametric kernel estimator of ANOVA decomposition of a given model. An estimator of sensitivity indices is also presented with its asymtotic convergence rate. Some simulations on a test function analysis and a real case study from agricultural have shown that the discrete kernel approach outperforms the continuous kernel one for evaluating the contribution of moderate or most influential discrete parameters to the model output. - Highlights: • We study a discrete kernel estimation for sensitivity analysis of a model. • A discrete kernel estimator of ANOVA decomposition of the model is presented. • Sensitivity indices are calculated for discrete input parameters. • An estimator of sensitivity indices is also presented with its convergence rate. • An application is realized for improving the reliability of environmental models.

Discrete gradients in discrete classical mechanics

International Nuclear Information System (INIS)

Renna, L.

1987-01-01

A simple model of discrete classical mechanics is given where, starting from the continuous Hamilton equations, discrete equations of motion are established together with a proper discrete gradient definition. The conservation laws of the total discrete momentum, angular momentum, and energy are demonstrated

Non-classicality criteria: Glauber-Sudarshan P function and Mandel ? parameter

Science.gov (United States)

Alexanian, Moorad

2018-01-01

We calculate exactly the quantum mechanical, temporal Wigner quasiprobability density for a single-mode, degenerate parametric amplifier for a system in the Gaussian state, viz., a displaced-squeezed thermal state. The Wigner function allows us to calculate the fluctuations in photon number and the quadrature variance. We contrast the difference between the non-classicality criteria, which is independent of the displacement parameter ?, based on the Glauber-Sudarshan quasiprobability distribution ? and the classical/non-classical behaviour of the Mandel ? parameter, which depends strongly on ?. We find a phase transition as a function of ? such that at the critical point ?, ?, as a function of ?, goes from strictly classical, for ?, to a mixed classical/non-classical behaviour, for ?.

On the mixed discretization of the time domain magnetic field integral equation

KAUST Repository

Ulku, Huseyin Arda

2012-09-01

Time domain magnetic field integral equation (MFIE) is discretized using divergence-conforming Rao-Wilton-Glisson (RWG) and curl-conforming Buffa-Christiansen (BC) functions as spatial basis and testing functions, respectively. The resulting mixed discretization scheme, unlike the classical scheme which uses RWG functions as both basis and testing functions, is proper: Testing functions belong to dual space of the basis functions. Numerical results demonstrate that the marching on-in-time (MOT) solution of the mixed discretized MFIE yields more accurate results than that of classically discretized MFIE. © 2012 IEEE.

Discrete dispersion models and their Tweedie asymptotics

DEFF Research Database (Denmark)

Jørgensen, Bent; Kokonendji, Célestin C.

2016-01-01

The paper introduce a class of two-parameter discrete dispersion models, obtained by combining convolution with a factorial tilting operation, similar to exponential dispersion models which combine convolution and exponential tilting. The equidispersed Poisson model has a special place in this ap......The paper introduce a class of two-parameter discrete dispersion models, obtained by combining convolution with a factorial tilting operation, similar to exponential dispersion models which combine convolution and exponential tilting. The equidispersed Poisson model has a special place...... in this approach, whereas several overdispersed discrete distributions, such as the Neyman Type A, Pólya-Aeppli, negative binomial and Poisson-inverse Gaussian, turn out to be Poisson-Tweedie factorial dispersion models with power dispersion functions, analogous to ordinary Tweedie exponential dispersion models...... with power variance functions. Using the factorial cumulant generating function as tool, we introduce a dilation operation as a discrete analogue of scaling, generalizing binomial thinning. The Poisson-Tweedie factorial dispersion models are closed under dilation, which in turn leads to a Poisson...

Novel stability criteria for uncertain delayed Cohen-Grossberg neural networks using discretized Lyapunov functional

International Nuclear Information System (INIS)

Souza, Fernando O.; Palhares, Reinaldo M.; Ekel, Petr Ya.

2009-01-01

This paper deals with the stability analysis of delayed uncertain Cohen-Grossberg neural networks (CGNN). The proposed methodology consists in obtaining new robust stability criteria formulated as linear matrix inequalities (LMIs) via the Lyapunov-Krasovskii theory. Particularly one stability criterion is derived from the selection of a parameter-dependent Lyapunov-Krasovskii functional, which allied with the Gu's discretization technique and a simple strategy that decouples the system matrices from the functional matrices, assures a less conservative stability condition. Two computer simulations are presented to support the improved theoretical results.

Design of the Coordinate Transformation Function for Cylindrical Acoustic Cloaks with a Quantity of Discrete Layers

International Nuclear Information System (INIS)

Cai Li; Wen Ji-Hong; Yu Dian-Long; Lu Zhi-Miao; Wen Xi-Sen

2014-01-01

Acoustic cloak based on coordinate transformation is of great topical interest and has promise in potential applications such as sound transparency and insulation. The frequency response of acoustic cloaks with a quantity of discrete homogeneous layers is analyzed by the acoustic scattering theory. The effect of coordinate transformation function on the acoustic total scattering cross section is discussed to achieve low scattering with only a few layers of anisotropic metamaterials. Also, the physics of acoustic wave interaction with the interfaces between the discrete layers inside the cloak shell is discussed. These results provide a better way of designing a multilayered acoustic cloak with fewer layers. (fundamental areas of phenomenology(including applications))

Design of the Coordinate Transformation Function for Cylindrical Acoustic Cloaks with a Quantity of Discrete Layers

Science.gov (United States)

Cai, Li; Wen, Ji-Hong; Yu, Dian-Long; Lu, Zhi-Miao; Wen, Xi-Sen

2014-09-01

Acoustic cloak based on coordinate transformation is of great topical interest and has promise in potential applications such as sound transparency and insulation. The frequency response of acoustic cloaks with a quantity of discrete homogeneous layers is analyzed by the acoustic scattering theory. The effect of coordinate transformation function on the acoustic total scattering cross section is discussed to achieve low scattering with only a few layers of anisotropic metamaterials. Also, the physics of acoustic wave interaction with the interfaces between the discrete layers inside the cloak shell is discussed. These results provide a better way of designing a multilayered acoustic cloak with fewer layers.

Discrete mKdV and discrete sine-Gordon flows on discrete space curves

International Nuclear Information System (INIS)

Inoguchi, Jun-ichi; Kajiwara, Kenji; Matsuura, Nozomu; Ohta, Yasuhiro

2014-01-01

In this paper, we consider the discrete deformation of the discrete space curves with constant torsion described by the discrete mKdV or the discrete sine-Gordon equations, and show that it is formulated as the torsion-preserving equidistant deformation on the osculating plane which satisfies the isoperimetric condition. The curve is reconstructed from the deformation data by using the Sym–Tafel formula. The isoperimetric equidistant deformation of the space curves does not preserve the torsion in general. However, it is possible to construct the torsion-preserving deformation by tuning the deformation parameters. Further, it is also possible to make an arbitrary choice of the deformation described by the discrete mKdV equation or by the discrete sine-Gordon equation at each step. We finally show that the discrete deformation of discrete space curves yields the discrete K-surfaces. (paper)

Discrete Curvatures and Discrete Minimal Surfaces

KAUST Repository

Sun, Xiang

2012-06-01

This thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads to great interest in studying discrete surfaces. With the rich smooth surface theory in hand, one would hope that this elegant theory can still be applied to the discrete counter part. Such a generalization, however, is not always successful. While discrete surfaces have the advantage of being finite dimensional, thus easier to treat, their geometric properties such as curvatures are not well defined in the classical sense. Furthermore, the powerful calculus tool can hardly be applied. The methods in this thesis, including angular defect formula, cotangent formula, parallel meshes, relative geometry etc. are approaches based on offset meshes or generalized offset meshes. As an important application, we discuss discrete minimal surfaces and discrete Koenigs meshes.

Discrete-time inverse optimal control for nonlinear systems

CERN Document Server

Sanchez, Edgar N

2013-01-01

Discrete-Time Inverse Optimal Control for Nonlinear Systems proposes a novel inverse optimal control scheme for stabilization and trajectory tracking of discrete-time nonlinear systems. This avoids the need to solve the associated Hamilton-Jacobi-Bellman equation and minimizes a cost functional, resulting in a more efficient controller. Design More Efficient Controllers for Stabilization and Trajectory Tracking of Discrete-Time Nonlinear Systems The book presents two approaches for controller synthesis: the first based on passivity theory and the second on a control Lyapunov function (CLF). Th

Image Encryption Technology Based on Fractional Two-Dimensional Triangle Function Combination Discrete Chaotic Map Coupled with Menezes-Vanstone Elliptic Curve Cryptosystem

Directory of Open Access Journals (Sweden)

Zeyu Liu

2018-01-01

Full Text Available A new fractional two-dimensional triangle function combination discrete chaotic map (2D-TFCDM with the discrete fractional difference is proposed. We observe the bifurcation behaviors and draw the bifurcation diagrams, the largest Lyapunov exponent plot, and the phase portraits of the proposed map, respectively. On the application side, we apply the proposed discrete fractional map into image encryption with the secret keys ciphered by Menezes-Vanstone Elliptic Curve Cryptosystem (MVECC. Finally, the image encryption algorithm is analysed in four main aspects that indicate the proposed algorithm is better than others.

Infant differential behavioral responding to discrete emotions.

Science.gov (United States)

Walle, Eric A; Reschke, Peter J; Camras, Linda A; Campos, Joseph J

2017-10-01

Emotional communication regulates the behaviors of social partners. Research on individuals' responding to others' emotions typically compares responses to a single negative emotion compared with responses to a neutral or positive emotion. Furthermore, coding of such responses routinely measure surface level features of the behavior (e.g., approach vs. avoidance) rather than its underlying function (e.g., the goal of the approach or avoidant behavior). This investigation examined infants' responding to others' emotional displays across 5 discrete emotions: joy, sadness, fear, anger, and disgust. Specifically, 16-, 19-, and 24-month-old infants observed an adult communicate a discrete emotion toward a stimulus during a naturalistic interaction. Infants' responses were coded to capture the function of their behaviors (e.g., exploration, prosocial behavior, and security seeking). The results revealed a number of instances indicating that infants use different functional behaviors in response to discrete emotions. Differences in behaviors across emotions were clearest in the 24-month-old infants, though younger infants also demonstrated some differential use of behaviors in response to discrete emotions. This is the first comprehensive study to identify differences in how infants respond with goal-directed behaviors to discrete emotions. Additionally, the inclusion of a function-based coding scheme and interpersonal paradigms may be informative for future emotion research with children and adults. Possible developmental accounts for the observed behaviors and the benefits of coding techniques emphasizing the function of social behavior over their form are discussed. (PsycINFO Database Record (c) 2017 APA, all rights reserved).

Closed-form expressions for time-frequency operations involving Hermite functions

NARCIS (Netherlands)

Korevaar, C.W.; Oude Alink, M.S.; de Boer, Pieter-Tjerk; Kokkeler, Andre B.J.; Smit, Gerardus Johannes Maria

2016-01-01

The product, convolution, correlation, Wigner distribution function (WDF) and ambiguity function (AF) of two Hermite functions of arbitrary order n and m are derived and expressed as a bounded, weighted sum of n+m Hermite functions. It was already known that these mathematical operations performed

Geometric description of a discrete power function associated with the sixth Painlevé equation.

Science.gov (United States)

Joshi, Nalini; Kajiwara, Kenji; Masuda, Tetsu; Nakazono, Nobutaka; Shi, Yang

2017-11-01

In this paper, we consider the discrete power function associated with the sixth Painlevé equation. This function is a special solution of the so-called cross-ratio equation with a similarity constraint. We show in this paper that this system is embedded in a cubic lattice with [Formula: see text] symmetry. By constructing the action of [Formula: see text] as a subgroup of [Formula: see text], i.e. the symmetry group of P VI , we show how to relate [Formula: see text] to the symmetry group of the lattice. Moreover, by using translations in [Formula: see text], we explain the odd-even structure appearing in previously known explicit formulae in terms of the τ function.

Bilinear phase-plane distribution functions and positivity

NARCIS (Netherlands)

Janssen, A.J.E.M.

1985-01-01

There is a theorem of Wigner that states that phase-plane distribution functions involving the state bilinearly and having correct marginals must take negative values for certain states. The purpose of this paper is to support the statement that these phase-plane distribution functions are for

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.

Integrable lattices and their sublattices: From the discrete Moutard (discrete Cauchy-Riemann) 4-point equation to the self-adjoint 5-point scheme

International Nuclear Information System (INIS)

Doliwa, A.; Grinevich, P.; Nieszporski, M.; Santini, P. M.

2007-01-01

We present the sublattice approach, a procedure to generate, from a given integrable lattice, a sublattice which inherits its integrability features. We consider, as illustrative example of this approach, the discrete Moutard 4-point equation and its sublattice, the self-adjoint 5-point scheme on the star of the square lattice, which are relevant in the theory of the integrable discrete geometries and in the theory of discrete holomorphic and harmonic functions (in this last context, the discrete Moutard equation is called discrete Cauchy-Riemann equation). Therefore an integrable, at one energy, discretization of elliptic two-dimensional operators is considered. We use the sublattice point of view to derive, from the Darboux transformations and superposition formulas of the discrete Moutard equation, the Darboux transformations and superposition formulas of the self-adjoint 5-point scheme. We also construct, from algebro-geometric solutions of the discrete Moutard equation, algebro-geometric solutions of the self-adjoint 5-point scheme. In particular, we show that the corresponding restrictions on the finite-gap data are of the same type as those for the fixed energy problem for the two-dimensional Schroedinger operator. We finally use these solutions to construct explicit examples of discrete holomorphic and harmonic functions, as well as examples of quadrilateral surfaces in R 3

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)

Symmetries in discrete-time mechanics

International Nuclear Information System (INIS)

Khorrami, M.

1996-01-01

Based on a general formulation for discrete-time quantum mechanics, introduced by M. Khorrami (Annals Phys. 224 (1995), 101), symmetries in discrete-time quantum mechanics are investigated. It is shown that any classical continuous symmetry leads to a conserved quantity in classical mechanics, as well as quantum mechanics. The transformed wave function, however, has the correct evolution if and only if the symmetry is nonanomalous. Copyright copyright 1996 Academic Press, Inc

On E-discretization of tori of compact simple Lie groups. II

Science.gov (United States)

Hrivnák, Jiří; Juránek, Michal

2017-10-01

Ten types of discrete Fourier transforms of Weyl orbit functions are developed. Generalizing one-dimensional cosine, sine, and exponential, each type of the Weyl orbit function represents an exponential symmetrized with respect to a subgroup of the Weyl group. Fundamental domains of even affine and dual even affine Weyl groups, governing the argument and label symmetries of the even orbit functions, are determined. The discrete orthogonality relations are formulated on finite sets of points from the refinements of the dual weight lattices. Explicit counting formulas for the number of points of the discrete transforms are deduced. Real-valued Hartley orbit functions are introduced, and all ten types of the corresponding discrete Hartley transforms are detailed.

Many-Body Quantum Spin Dynamics with Monte Carlo Trajectories on a Discrete Phase Space

Directory of Open Access Journals (Sweden)

J. Schachenmayer

2015-02-01

Full Text Available Interacting spin systems are of fundamental relevance in different areas of physics, as well as in quantum information science and biology. These spin models represent the simplest, yet not fully understood, manifestation of quantum many-body systems. An important outstanding problem is the efficient numerical computation of dynamics in large spin systems. Here, we propose a new semiclassical method to study many-body spin dynamics in generic spin lattice models. The method is based on a discrete Monte Carlo sampling in phase space in the framework of the so-called truncated Wigner approximation. Comparisons with analytical and numerically exact calculations demonstrate the power of the technique. They show that it correctly reproduces the dynamics of one- and two-point correlations and spin squeezing at short times, thus capturing entanglement. Our results open the possibility to study the quantum dynamics accessible to recent experiments in regimes where other numerical methods are inapplicable.

Exact discretization of Schrödinger equation

Energy Technology Data Exchange (ETDEWEB)

Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru

2016-01-08

There are different approaches to discretization of the Schrödinger equation with some approximations. In this paper we derive a discrete equation that can be considered as exact discretization of the continuous Schrödinger equation. The proposed discrete equation is an equation with difference of integer order that is represented by infinite series. We suggest differences, which are characterized by power-law Fourier transforms. These differences can be considered as exact discrete analogs of derivatives of integer orders. Physically the suggested discrete equation describes a chain (or lattice) model with long-range interaction of power-law form. Mathematically it is a uniquely highlighted difference equation that exactly corresponds to the continuous Schrödinger equation. Using the Young's inequality for convolution, we prove that suggested differences are operators on the Hilbert space of square-summable sequences. We prove that the wave functions, which are exact discrete analogs of the free particle and harmonic oscillator solutions of the continuous Schrödinger equations, are solutions of the suggested discrete Schrödinger equations. - Highlights: • Exact discretization of the continuous Schrödinger equation is suggested. • New long-range interactions of power-law form are suggested. • Solutions of discrete Schrödinger equation are exact discrete analogs of continuous solutions.

Exact discretization of Schrödinger equation

International Nuclear Information System (INIS)

Tarasov, Vasily E.

2016-01-01

There are different approaches to discretization of the Schrödinger equation with some approximations. In this paper we derive a discrete equation that can be considered as exact discretization of the continuous Schrödinger equation. The proposed discrete equation is an equation with difference of integer order that is represented by infinite series. We suggest differences, which are characterized by power-law Fourier transforms. These differences can be considered as exact discrete analogs of derivatives of integer orders. Physically the suggested discrete equation describes a chain (or lattice) model with long-range interaction of power-law form. Mathematically it is a uniquely highlighted difference equation that exactly corresponds to the continuous Schrödinger equation. Using the Young's inequality for convolution, we prove that suggested differences are operators on the Hilbert space of square-summable sequences. We prove that the wave functions, which are exact discrete analogs of the free particle and harmonic oscillator solutions of the continuous Schrödinger equations, are solutions of the suggested discrete Schrödinger equations. - Highlights: • Exact discretization of the continuous Schrödinger equation is suggested. • New long-range interactions of power-law form are suggested. • Solutions of discrete Schrödinger equation are exact discrete analogs of continuous solutions.

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.

Discrete Green’s functions for propagators between complex objects in discrete space-time nonlinear electromagnetics

NARCIS (Netherlands)

Arnold, J.M.; Hon, de B.P.; Graglia, R.D.

2007-01-01

We propose a potential-based form of the FDTD scheme, with potentials driven by sources that are themselves simple dynamical systems. This formulation admits a radiative boundary condition for the discrete-mesh Maxwell's equations in a multiply connected exterior domain, which facilitates

Quantum Numbers and the Eigenfunction Approach to Obtain Symmetry Adapted Functions for Discrete Symmetries

Directory of Open Access Journals (Sweden)

Renato Lemus

2012-11-01

Full Text Available The eigenfunction approach used for discrete symmetries is deduced from the concept of quantum numbers. We show that the irreducible representations (irreps associated with the eigenfunctions are indeed a shorthand notation for the set of eigenvalues of the class operators (character table. The need of a canonical chain of groups to establish a complete set of commuting operators is emphasized. This analysis allows us to establish in natural form the connection between the quantum numbers and the eigenfunction method proposed by J.Q. Chen to obtain symmetry adapted functions. We then proceed to present a friendly version of the eigenfunction method to project functions.

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)

Discrete ellipsoidal statistical BGK model and Burnett equations

Science.gov (United States)

Zhang, Yu-Dong; Xu, Ai-Guo; Zhang, Guang-Cai; Chen, Zhi-Hua; Wang, Pei

2018-06-01

A new discrete Boltzmann model, the discrete ellipsoidal statistical Bhatnagar-Gross-Krook (ESBGK) model, is proposed to simulate nonequilibrium compressible flows. Compared with the original discrete BGK model, the discrete ES-BGK has a flexible Prandtl number. For the discrete ES-BGK model in the Burnett level, two kinds of discrete velocity model are introduced and the relations between nonequilibrium quantities and the viscous stress and heat flux in the Burnett level are established. The model is verified via four benchmark tests. In addition, a new idea is introduced to recover the actual distribution function through the macroscopic quantities and their space derivatives. The recovery scheme works not only for discrete Boltzmann simulation but also for hydrodynamic ones, for example, those based on the Navier-Stokes or the Burnett equations.

Current Density and Continuity in Discretized Models

Science.gov (United States)

Boykin, Timothy B.; Luisier, Mathieu; Klimeck, Gerhard

2010-01-01

Discrete approaches have long been used in numerical modelling of physical systems in both research and teaching. Discrete versions of the Schrodinger equation employing either one or several basis functions per mesh point are often used by senior undergraduates and beginning graduate students in computational physics projects. In studying…

q-Gamow states as continuous linear functionals on analytical test functions

Energy Technology Data Exchange (ETDEWEB)

Plastino, A.; Rocca, M.C., E-mail: mariocarlosrocca@gmail.com

2016-04-15

We define here q-Gamow states corresponding to Tsallis' q-statistics. We compute for them their norm, mean energy value and the q-analogue of the Breit–Wigner distribution (a q-Breit–Wigner).

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

Comparison of the auxiliary function method and the discrete-ordinate method for solving the radiative transfer equation for light scattering.

Science.gov (United States)

da Silva, Anabela; Elias, Mady; Andraud, Christine; Lafait, Jacques

2003-12-01

Two methods for solving the radiative transfer equation are compared with the aim of computing the angular distribution of the light scattered by a heterogeneous scattering medium composed of a single flat layer or a multilayer. The first method [auxiliary function method (AFM)], recently developed, uses an auxiliary function and leads to an exact solution; the second [discrete-ordinate method (DOM)] is based on the channel concept and needs an angular discretization. The comparison is applied to two different media presenting two typical and extreme scattering behaviors: Rayleigh and Mie scattering with smooth or very anisotropic phase functions, respectively. A very good agreement between the predictions of the two methods is observed in both cases. The larger the number of channels used in the DOM, the better the agreement. The principal advantages and limitations of each method are also listed.

Discrete Sparse Coding.

Science.gov (United States)

Exarchakis, Georgios; Lücke, Jörg

2017-11-01

Sparse coding algorithms with continuous latent variables have been the subject of a large number of studies. However, discrete latent spaces for sparse coding have been largely ignored. In this work, we study sparse coding with latents described by discrete instead of continuous prior distributions. We consider the general case in which the latents (while being sparse) can take on any value of a finite set of possible values and in which we learn the prior probability of any value from data. This approach can be applied to any data generated by discrete causes, and it can be applied as an approximation of continuous causes. As the prior probabilities are learned, the approach then allows for estimating the prior shape without assuming specific functional forms. To efficiently train the parameters of our probabilistic generative model, we apply a truncated expectation-maximization approach (expectation truncation) that we modify to work with a general discrete prior. We evaluate the performance of the algorithm by applying it to a variety of tasks: (1) we use artificial data to verify that the algorithm can recover the generating parameters from a random initialization, (2) use image patches of natural images and discuss the role of the prior for the extraction of image components, (3) use extracellular recordings of neurons to present a novel method of analysis for spiking neurons that includes an intuitive discretization strategy, and (4) apply the algorithm on the task of encoding audio waveforms of human speech. The diverse set of numerical experiments presented in this letter suggests that discrete sparse coding algorithms can scale efficiently to work with realistic data sets and provide novel statistical quantities to describe the structure of the data.

On a correspondence between regular and non-regular operator monotone functions

DEFF Research Database (Denmark)

Gibilisco, P.; Hansen, Frank; Isola, T.

2009-01-01

We prove the existence of a bijection between the regular and the non-regular operator monotone functions satisfying a certain functional equation. As an application we give a new proof of the operator monotonicity of certain functions related to the Wigner-Yanase-Dyson skew information....

Homogenisation of a Wigner-Seitz cell in two group diffusion theory

International Nuclear Information System (INIS)

Allen, F.R.

1968-02-01

Two group diffusion theory is used to develop a theory for the homogenisation of a Wigner-Seitz cell, neglecting azimuthal flux components of higher order than dipoles. An iterative method of solution is suggested for linkage with reactor calculations. The limiting theory for no cell leakage leads to cell edge flux normalisation of cell parameters, the current design method for SGHW reactor design calculations. Numerical solutions are presented for a cell-plus-environment model with monopoles only. The results demonstrate the exact theory in comparison with the approximate recipes of normalisation to cell edge, moderator average, or cell average flux levels. (author)

Discrete systems and integrability

CERN Document Server

Hietarinta, J; Nijhoff, F W

2016-01-01

This first introductory text to discrete integrable systems introduces key notions of integrability from the vantage point of discrete systems, also making connections with the continuous theory where relevant. While treating the material at an elementary level, the book also highlights many recent developments. Topics include: Darboux and Bäcklund transformations; difference equations and special functions; multidimensional consistency of integrable lattice equations; associated linear problems (Lax pairs); connections with Padé approximants and convergence algorithms; singularities and geometry; Hirota's bilinear formalism for lattices; intriguing properties of discrete Painlevé equations; and the novel theory of Lagrangian multiforms. The book builds the material in an organic way, emphasizing interconnections between the various approaches, while the exposition is mostly done through explicit computations on key examples. Written by respected experts in the field, the numerous exercises and the thoroug...

One-way functions based on the discrete logarithm problem in the groups meeting conditions C(3-T (6

Directory of Open Access Journals (Sweden)

N. V. Bezverkhniy

2014-01-01

Full Text Available In this work we are consider a possibility to create schemes of open key distribution in the groups meeting conditions C(3-T(6. Our constructions use the following algorithms.1. The algorithm that solves the membership problem for cyclic subgroups, also known as the discrete logarithm problem.2. The algorithm that solves the word problem in this class of groups.Our approach is based on the geometric methods of combinatorial group theory (the method of diagrams in groups.In a cryptographic scheme based on the open key distribution one-way functions are used, i.e. functions direct calculation of which must be much easier than that of the inverse one. Our task was to construct a one-way function using groups with small cancelation conditions C(3-T(6 and to compare the calculation complexity of this function with the calculation complexity of its inverse.P.W. Shor has shown in the paper that there exists a polynomial algorithm that can be implemented in a quantum computer to solve the discrete logarithm problem in the groups of units of finite fields and the rings of congruences mod n. This stimulated a series of investigations trying to find alternative complicated mathematical problems that can be used for construction of new asymmetric cryptosystems. For example, open key distribution systems based on the conjugacy problem in matrix groups and the braid groups were proposed.In the other papers the constructions used the discrete logarithm problem in the groups of inner automorphisms of semi-direct products of SL(2,Z and Zp and GL(2,Zp and Zp. groups. The paper of E. Sakalauskas, P. Tvarijonas, A. Raulinaitis proposed a scheme that uses a composition of two problems of group theory, namely the conjugacy problem and the discrete logarithm problem.Our results show that the scheme that we propose is of polynomial complexity. Therefore its security is not sufficient for further applications in communications. However the security can be improved

Functional forms and price elasticities in a discrete continuous choice model of the residential water demand

Science.gov (United States)

Vásquez Lavín, F. A.; Hernandez, J. I.; Ponce, R. D.; Orrego, S. A.

2017-07-01

During recent decades, water demand estimation has gained considerable attention from scholars. From an econometric perspective, the most used functional forms include log-log and linear specifications. Despite the advances in this field and the relevance for policymaking, little attention has been paid to the functional forms used in these estimations, and most authors have not provided justifications for their selection of functional forms. A discrete continuous choice model of the residential water demand is estimated using six functional forms (log-log, full-log, log-quadratic, semilog, linear, and Stone-Geary), and the expected consumption and price elasticity are evaluated. From a policy perspective, our results highlight the relevance of functional form selection for both the expected consumption and price elasticity.

Quantum cosmology based on discrete Feynman paths

International Nuclear Information System (INIS)

Chew, Geoffrey F.

2002-01-01

Although the rules for interpreting local quantum theory imply discretization of process, Lorentz covariance is usually regarded as precluding time quantization. Nevertheless a time-discretized quantum representation of redshifting spatially-homogeneous universe may be based on discrete-step Feynman paths carrying causal Lorentz-invariant action--paths that not only propagate the wave function but provide a phenomenologically-promising elementary-particle Hilbert-space basis. In a model under development, local path steps are at Planck scale while, at a much larger ''wave-function scale'', global steps separate successive wave-functions. Wave-function spacetime is but a tiny fraction of path spacetime. Electromagnetic and gravitational actions are ''at a distance'' in Wheeler-Feynman sense while strong (color) and weak (isospin) actions, as well as action of particle motion, are ''local'' in a sense paralleling the action of local field theory. ''Nonmaterial'' path segments and ''trivial events'' collaborate to define energy and gravity. Photons coupled to conserved electric charge enjoy privileged model status among elementary fermions and vector bosons. Although real path parameters provide no immediate meaning for ''measurement'', the phase of the complex wave function allows significance for ''information'' accumulated through ''gentle'' electromagnetic events involving charged matter and ''soft'' photons. Through its soft-photon content the wave function is an ''information reservoir''

Similarities of discrete and continuous Sturm-Liouville problems

Directory of Open Access Journals (Sweden)

Kazem Ghanbari

2007-12-01

Full Text Available In this paper we present a study on the analogous properties of discrete and continuous Sturm-Liouville problems arising in matrix analysis and differential equations, respectively. Green's functions in both cases have analogous expressions in terms of the spectral data. Most of the results associated to inverse problems in both cases are identical. In particular, in both cases Weyl's m-function determines the Sturm-Liouville operators uniquely. Moreover, the well known Rayleigh-Ritz Theorem in linear algebra can be proved by using the concept of Green's function in discrete case.

Rational solutions of the discrete time Toda lattice and the alternate discrete Painleve II equation

International Nuclear Information System (INIS)

Common, Alan K; Hone, Andrew N W

2008-01-01

The Yablonskii-Vorob'ev polynomials y n (t), which are defined by a second-order bilinear differential-difference equation, provide rational solutions of the Toda lattice. They are also polynomial tau-functions for the rational solutions of the second Painleve equation (P II ). Here we define two-variable polynomials Y n (t, h) on a lattice with spacing h, by considering rational solutions of the discrete time Toda lattice as introduced by Suris. These polynomials are shown to have many properties that are analogous to those of the Yablonskii-Vorob'ev polynomials, to which they reduce when h = 0. They also provide rational solutions for a particular discretization of P II , namely the so-called alternate discrete P II , and this connection leads to an expression in terms of the Umemura polynomials for the third Painleve equation (P III ). It is shown that the Baecklund transformation for the alternate discrete Painleve equation is a symplectic map, and the shift in time is also symplectic. Finally we present a Lax pair for the alternate discrete P II , which recovers Jimbo and Miwa's Lax pair for P II in the continuum limit h → 0

Discrete Mathematics

DEFF Research Database (Denmark)

Sørensen, John Aasted

2011-01-01

The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics......; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...

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.

One-Way Functions and Composition of Conjugacy and Discrete Logarithm Problems in the Small Cancellation Groups

Directory of Open Access Journals (Sweden)

N. V. Bezverkhniy

2015-01-01

Full Text Available The paper considers the possibility for building a one-way function in the small cancellation group. Thus, it uses the algorithm to solve the problem for a cyclic subgroup, also known as a discrete logarithm problem, and the algorithm to solve the word problem in this class of groups.Research is conducted using geometric methods of combinatorial group theory (the method of diagrams in groups.In public channel exchange of information are used one-way functions, direct calculation of which should be much less complicated than the calculation of the inverse function. The paper considers the combination of two problems: discrete logarithms and conjugacy. This leads to the problem of conjugate membership for a cyclic subgroup. The work proposes an algorithm based on this problem, which can be used as a basis in investigation of the appropriate one-way function for its fitness to build a public key distribution scheme.The study used doughnut charts of word conjugacy, and for one special class of such charts has been proven a property of the layer-based periodicity. The presence of such properties is obviously leads to a solution of the power conjugacy of words in the considered class of groups. Unfortunately, this study failed to show any periodicity of a doughnut chart, but for one of two possible classes this periodicity has been proven.The building process of one-way function considered in the paper was studied in terms of possibility to calculate both direct and inverse mappings. The computational complexity was not considered. Thus, the following two tasks were yet unresolved: determining the quality of one-way function in the above protocol of the public key distribution and completing the study of the periodicity of doughnut charts of word conjugacy, leading to a positive solution of the power conjugacy of words in the class groups under consideration.

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

Current density and continuity in discretized models

International Nuclear Information System (INIS)

Boykin, Timothy B; Luisier, Mathieu; Klimeck, Gerhard

2010-01-01

Discrete approaches have long been used in numerical modelling of physical systems in both research and teaching. Discrete versions of the Schroedinger equation employing either one or several basis functions per mesh point are often used by senior undergraduates and beginning graduate students in computational physics projects. In studying discrete models, students can encounter conceptual difficulties with the representation of the current and its divergence because different finite-difference expressions, all of which reduce to the current density in the continuous limit, measure different physical quantities. Understanding these different discrete currents is essential and requires a careful analysis of the current operator, the divergence of the current and the continuity equation. Here we develop point forms of the current and its divergence valid for an arbitrary mesh and basis. We show that in discrete models currents exist only along lines joining atomic sites (or mesh points). Using these results, we derive a discrete analogue of the divergence theorem and demonstrate probability conservation in a purely localized-basis approach.

Discrete Calculus as a Bridge between Scales

Science.gov (United States)

Degiuli, Eric; McElwaine, Jim

2012-02-01

Understanding how continuum descriptions of disordered media emerge from the microscopic scale is a fundamental challenge in condensed matter physics. In many systems, it is necessary to coarse-grain balance equations at the microscopic scale to obtain macroscopic equations. We report development of an exact, discrete calculus, which allows identification of discrete microscopic equations with their continuum equivalent [1]. This allows the application of powerful techniques of calculus, such as the Helmholtz decomposition, the Divergence Theorem, and Stokes' Theorem. We illustrate our results with granular materials. In particular, we show how Newton's laws for a single grain reproduce their continuum equivalent in the calculus. This allows introduction of a discrete Airy stress function, exactly as in the continuum. As an application of the formalism, we show how these results give the natural mean-field variation of discrete quantities, in agreement with numerical simulations. The discrete calculus thus acts as a bridge between discrete microscale quantities and continuous macroscale quantities. [4pt] [1] E. DeGiuli & J. McElwaine, PRE 2011. doi: 10.1103/PhysRevE.84.041310

Quantum chaos on discrete graphs

International Nuclear Information System (INIS)

Smilansky, Uzy

2007-01-01

Adapting a method developed for the study of quantum chaos on quantum (metric) graphs (Kottos and Smilansky 1997 Phys. Rev. Lett. 79 4794, Kottos and Smilansky 1999 Ann. Phys., NY 274 76), spectral ζ functions and trace formulae for discrete Laplacians on graphs are derived. This is achieved by expressing the spectral secular equation in terms of the periodic orbits of the graph and obtaining functions which belong to the class of ζ functions proposed originally by Ihara (1966 J. Mat. Soc. Japan 18 219) and expanded by subsequent authors (Stark and Terras 1996 Adv. Math. 121 124, Kotani and Sunada 2000 J. Math. Sci. Univ. Tokyo 7 7). Finally, a model of 'classical dynamics' on the discrete graph is proposed. It is analogous to the corresponding classical dynamics derived for quantum graphs (Kottos and Smilansky 1997 Phys. Rev. Lett. 79 4794, Kottos and Smilansky 1999 Ann. Phys., NY 274 76). (fast track communication)

Discrete Curvatures and Discrete Minimal Surfaces

KAUST Repository

Sun, Xiang

2012-01-01

This thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads

Ion association at discretely-charged dielectric interfaces: Giant charge inversion [Dielectric response controlled ion association at physically heterogeneous surfaces: Giant charge reversal

Energy Technology Data Exchange (ETDEWEB)

Wang, Zhi -Yong [Chongqing Univ. of Technology, Chongqing (China); Univ. of California, Riverside, CA (United States); Wu, Jianzhong [Univ. of California, Riverside, CA (United States)

2017-07-11

Giant charge reversal has been identified for the first time by Monte Carlo simulation for a discretely charged surface in contact with a trivalent electrolyte solution. It takes place regardless of the surface charge density under study and the monovalent salt. In stark contrast to earlier predictions based on the 2-dimensional Wigner crystal model to describe strong correlation of counterions at the macroion surface, we find that giant charge reversal reflects an intricate interplay of ionic volume effects, electrostatic correlations, surface charge heterogeneity, and the dielectric response of the confined fluids. While the novel phenomenon is yet to be confirmed with experiment, the simulation results appear in excellent agreement with a wide range of existing observations in the subregime of charge inversion. Lastly, our findings may have far-reaching implications to understanding complex electrochemical phenomena entailing ionic fluids under dielectric confinements.

Reconfiguration of face expressions based on the discrete capture data of radial basis function interpolation

Institute of Scientific and Technical Information of China (English)

ZHENG Guangguo; ZHOU Dongsheng; WEI Xiaopeng; ZHANG Qiang

2012-01-01

Compactly supported radial basis function can enable the coefficient matrix of solving weigh linear system to have a sparse banded structure, thereby reducing the complexity of the algorithm. Firstly, based on the compactly supported radial basis function, the paper makes the complex quadratic function （Multiquadric, MQ for short） to be transformed and proposes a class of compactly supported MQ function. Secondly, the paper describes a method that interpolates discrete motion capture data to solve the motion vectors of the interpolation points and they are used in facial expression reconstruction. Finally, according to this characteris- tic of the uneven distribution of the face markers, the markers are numbered and grouped in accordance with the density level, and then be interpolated in line with each group. The approach not only ensures the accuracy of the deformation of face local area and smoothness, but also reduces the time complexity of computing.

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’.

Implementation of quantum and classical discrete fractional Fourier transforms

Science.gov (United States)

Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N.; Szameit, Alexander

2016-01-01

Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools. PMID:27006089

Implementation of quantum and classical discrete fractional Fourier transforms.

Science.gov (United States)

Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N; Szameit, Alexander

2016-03-23

Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools.

The discrete Painleve II equations: Miura and auto-Baecklund transformations

International Nuclear Information System (INIS)

Carstea, A S; Ramani, A; Willox, R; Grammaticos, B

2003-01-01

We present Miura transformations for all discrete Painleve II equations known to date. We then use these Miuras to derive special solutions in terms of discrete Airy functions and to construct auto-Baecklund transformations for the discrete Painleve equations. These transformations are then used to generate rational solutions. Some new forms of d-P II and d-P 34 are obtained as well

Progress in optics

CERN Document Server

Wolf, Emil

2008-01-01

In the fourty-six years that have gone by since the first volume of Progress in Optics was published, optics has become one of the most dynamic fields of science. The volumes in this series which have appeared up to now contain more than 300 review articles by distinguished research workers, which have become permanent records for many important developments.- Metamaterials- Polarization Techniques- Linear Baisotropic Mediums- Ultrafast Optical Pulses- Quantum Imaging- Point-Spread Funcions- Discrete Wigner Functions

Foundations of a discrete physics

International Nuclear Information System (INIS)

McGoveran, D.; Noyes, P.

1988-01-01

Starting from the principles of finiteness, discreteness, finite computability and absolute nonuniqueness, we develop the ordering operator calculus, a strictly constructive mathematical system having the empirical properties required by quantum mechanical and special relativistic phenomena. We show how to construct discrete distance functions, and both rectangular and spherical coordinate systems(with a discrete version of ''π''). The richest discrete space constructible without a preferred axis and preserving translational and rotational invariance is shown to be a discrete 3-space with the usual symmetries. We introduce a local ordering parameter with local (proper) time-like properties and universal ordering parameters with global (cosmological) time-like properties. Constructed ''attribute velocities'' connect ensembles with attributes that are invariant as the appropriate time-like parameter increases. For each such attribute, we show how to construct attribute velocities which must satisfy the '' relativistic Doppler shift'' and the ''relativistic velocity composition law,'' as well as the Lorentz transformations. By construction, these velocities have finite maximum and minimum values. In the space of all attributes, the minimum of these maximum velocities will predominate in all multiple attribute computations, and hence can be identified as a fundamental limiting velocity, General commutation relations are constructed which under the physical interpretation are shown to reduce to the usual quantum mechanical commutation relations. 50 refs., 18 figs

Minimization of Linear Functionals Defined on| Solutions of Large-Scale Discrete Ill-Posed Problems

DEFF Research Database (Denmark)

Elden, Lars; Hansen, Per Christian; Rojas, Marielba

2003-01-01

The minimization of linear functionals de ned on the solutions of discrete ill-posed problems arises, e.g., in the computation of con dence intervals for these solutions. In 1990, Elden proposed an algorithm for this minimization problem based on a parametric-programming reformulation involving...... the solution of a sequence of trust-region problems, and using matrix factorizations. In this paper, we describe MLFIP, a large-scale version of this algorithm where a limited-memory trust-region solver is used on the subproblems. We illustrate the use of our algorithm in connection with an inverse heat...

Theoretical Basics of Teaching Discrete Mathematics

Directory of Open Access Journals (Sweden)

Y. A. Perminov

2012-01-01

Full Text Available  The paper deals with the research findings concerning the process of mastering the theoretical basics of discrete mathematics by the students of vocational pedagogic profile. The methodological analysis is based on the subject and functions of the modern discrete mathematics and its role in mathematical modeling and computing. The modern discrete mathematics (i.e. mathematics of the finite type structures plays the important role in modernization of vocational training. It is especially rele- vant to training students for vocational pedagogic qualifications, as in the future they will be responsible for training the middle and the senior level specialists in engineer- ing and technical spheres. Nowadays in different industries, there arise the problems which require for their solving both continual – based on the classical mathematical methods – and discrete modeling. The teaching course of discrete mathematics for the future vocational teachers should be relevant to the target qualification and aimed at mastering the mathematical modeling, systems of computer mathematics and computer technologies. The author emphasizes the fundamental role of mastering the language of algebraic and serial structures, as well as the logical, algorithmic, combinatory schemes dominating in dis- crete mathematics. The guidelines for selecting the content of the course in discrete mathematics are specified. The theoretical findings of the research can be put into practice whilst developing curricula and working programs for bachelors and masters’ training. 

Foundations of the probabilistic mechanics of discrete media

CERN Document Server

Axelrad, D R

1984-01-01

This latest volume in the Foundations & Philosophy of Science & Technology series provides an account of probabilistic functional analysis and shows its applicability in the formulation of the behaviour of discrete media with the inclusion of microstructural effects. Although quantum mechanics have long been recognized as a stochastic theory, the introduction of probabilistic concepts and principles to classical mechanics has in general not been attempted. In this study the author takes the view that the significant field quantities of a discrete medium are random variables or functions of s

Mimetic discretization methods

CERN Document Server

Castillo, Jose E

2013-01-01

To help solve physical and engineering problems, mimetic or compatible algebraic discretization methods employ discrete constructs to mimic the continuous identities and theorems found in vector calculus. Mimetic Discretization Methods focuses on the recent mimetic discretization method co-developed by the first author. Based on the Castillo-Grone operators, this simple mimetic discretization method is invariably valid for spatial dimensions no greater than three. The book also presents a numerical method for obtaining corresponding discrete operators that mimic the continuum differential and

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

Symmetric discrete coherent states for n-qubits

International Nuclear Information System (INIS)

Muñoz, C; Klimov, A B; Sánchez-Soto, L L

2012-01-01

We put forward a method of constructing discrete coherent states for n qubits. After establishing appropriate displacement operators, the coherent states appear as displaced versions of a fiducial vector that is fixed by imposing a number of natural symmetry requirements on its Q-function. Using these coherent states, we establish a partial order in the discrete phase space, which allows us to picture some n-qubit states as apparent distributions. We also analyze correlations in terms of sums of squared Q-functions. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’. (paper)

Application of multivariate splines to discrete mathematics

OpenAIRE

Xu, Zhiqiang

2005-01-01

Using methods developed in multivariate splines, we present an explicit formula for discrete truncated powers, which are defined as the number of non-negative integer solutions of linear Diophantine equations. We further use the formula to study some classical problems in discrete mathematics as follows. First, we extend the partition function of integers in number theory. Second, we exploit the relation between the relative volume of convex polytopes and multivariate truncated powers and giv...

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)

Continuous versus discrete structures II -- Discrete Hamiltonian systems and Helmholtz conditions

OpenAIRE

Cresson, Jacky; Pierret, Frédéric

2015-01-01

We define discrete Hamiltonian systems in the framework of discrete embeddings. An explicit comparison with previous attempts is given. We then solve the discrete Helmholtz's inverse problem for the discrete calculus of variation in the Hamiltonian setting. Several applications are discussed.

Hopf Bifurcation Analysis for a Stochastic Discrete-Time Hyperchaotic System

Directory of Open Access Journals (Sweden)

Jie Ran

2015-01-01

Full Text Available The dynamics of a discrete-time hyperchaotic system and the amplitude control of Hopf bifurcation for a stochastic discrete-time hyperchaotic system are investigated in this paper. Numerical simulations are presented to exhibit the complex dynamical behaviors in the discrete-time hyperchaotic system. Furthermore, the stochastic discrete-time hyperchaotic system with random parameters is transformed into its equivalent deterministic system with the orthogonal polynomial theory of discrete random function. In addition, the dynamical features of the discrete-time hyperchaotic system with random disturbances are obtained through its equivalent deterministic system. By using the Hopf bifurcation conditions of the deterministic discrete-time system, the specific conditions for the existence of Hopf bifurcation in the equivalent deterministic system are derived. And the amplitude control with random intensity is discussed in detail. Finally, the feasibility of the control method is demonstrated by numerical simulations.

Digital Discretion

DEFF Research Database (Denmark)

Busch, Peter Andre; Zinner Henriksen, Helle

2018-01-01

discretion is suggested to reduce this footprint by influencing or replacing their discretionary practices using ICT. What is less researched is whether digital discretion can cause changes in public policy outcomes, and under what conditions such changes can occur. Using the concept of public service values......This study reviews 44 peer-reviewed articles on digital discretion published in the period from 1998 to January 2017. Street-level bureaucrats have traditionally had a wide ability to exercise discretion stirring debate since they can add their personal footprint on public policies. Digital......, we suggest that digital discretion can strengthen ethical and democratic values but weaken professional and relational values. Furthermore, we conclude that contextual factors such as considerations made by policy makers on the macro-level and the degree of professionalization of street...

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

Orbital angular momentum in phase space

International Nuclear Information System (INIS)

Rigas, I.; Sanchez-Soto, L.L.; Klimov, A.B.; Rehacek, J.; Hradil, Z.

2011-01-01

Research highlights: → We propose a comprehensive Weyl-Wigner formalism for the canonical pair angle-angular momentum. → We present a simple and useful toolkit for the practitioner. → We derive simple evolution equations in terms of a star product in the semiclassical limit. - Abstract: A comprehensive theory of the Weyl-Wigner formalism for the canonical pair angle-angular momentum is presented. Special attention is paid to the problems linked to rotational periodicity and angular-momentum discreteness.

Discrete variable theory of triatomic photodissociation

International Nuclear Information System (INIS)

Heather, R.W.; Light, J.C.

1983-01-01

The coupled equations describing the photodissociation process are expressed in the discrete variable representation (DVR) in which the coupled equations are labeled by quadrature points rather than by internal basis functions. A large reduction in the dimensionality of the coupled equations can be realized since the spatially localized bound state nuclear wave function vanishes at most of the quadrature points, making only certain orientations of the fragments important in the region of strong interaction (small separation). The discrete variable theory of photodissociation is applied to the model dissociation of bent HCN in which the CN fragment is treated as a rigid rotor. The truncated DVR rotational distributions are compared with the exact close coupled rotational distributions, and excellent agreement with greatly reduced dimensionality of the equations is found

The discrete additive Weibull distribution: A bathtub-shaped hazard for discontinuous failure data

International Nuclear Information System (INIS)

Bebbington, Mark; Lai, Chin-Diew; Wellington, Morgan; Zitikis, Ričardas

2012-01-01

Although failure data are usually treated as being continuous, they may have been collected in a discrete manner, or in fact be discrete in nature. Reliability models with bathtub-shaped hazard rate are fundamental to the concepts of burn-in and maintenance, but how well do they incorporate discrete data? We explore discrete versions of the additive Weibull distribution, which has the twin virtues of mathematical tractability and the ability to produce bathtub-shaped hazard rate functions. We derive conditions on the parameters for the hazard rate function to be increasing, decreasing, or bathtub shaped. While discrete versions may have the same shaped hazard rate for the same parameter values, we find that when fitted to data the fitted hazard rate shapes can vary between versions. Our results are illustrated using several real-life data sets, and the implications of using continuous models for discrete data discussed.