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

Science.gov (United States)

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

2000-12-01

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

Wigner 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

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

CERN Document Server

Galetti, D

2000-01-01

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

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.

Hydrogen atom in phase space: the Wigner representation

International Nuclear Information System (INIS)

Praxmeyer, Ludmila; Mostowski, Jan; Wodkiewicz, Krzysztof

2006-01-01

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

Wigner 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 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

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.

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.

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

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

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...

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

Quantum mechanics in phase space

DEFF Research Database (Denmark)

Hansen, Frank

1984-01-01

A reformulation of quantum mechanics for a finite system is given using twisted multiplication of functions on phase space and Tomita's theory of generalized Hilbert algebras. Quantization of a classical observable h is achieved when the twisted exponential Exp0(-h) is defined as a tempered....... Generalized Weyl-Wigner maps related to the notion of Hamiltonian weight are studied and used in the formulation of a twisted spectral theory for functions on phase space. Some inequalities for Wigner functions on phase space are proven. A brief discussion of the classical limit obtained through dilations...

Phase-space quantization of field theory

International Nuclear Information System (INIS)

Curtright, T.; Zachos, C.

1999-01-01

In this lecture, a limited introduction of gauge invariance in phase-space is provided, predicated on canonical transformations in quantum phase-space. Exact characteristic trajectories are also specified for the time-propagating Wigner phase-space distribution function: they are especially simple--indeed, classical--for the quantized simple harmonic oscillator. This serves as the underpinning of the field theoretic Wigner functional formulation introduced. Scalar field theory is thus reformulated in terms of distributions in field phase-space. This is a pedagogical selection from work published and reported at the Yukawa Institute Workshop ''Gauge Theory and Integrable Models'', 26-29 January, 1999

Wigner functions from the two-dimensional wavelet group.

Science.gov (United States)

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

2000-12-01

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

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

International Nuclear Information System (INIS)

Waalkens, Holger; Schubert, Roman; Wiggins, Stephen

2008-01-01

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

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

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....

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.

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 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.

Quantum mechanics in coherent algebras on phase space

International Nuclear Information System (INIS)

Lesche, B.; Seligman, T.H.

1986-01-01

Quantum mechanics is formulated on a quantum mechanical phase space. The algebra of observables and states is represented by an algebra of functions on phase space that fulfills a certain coherence condition, expressing the quantum mechanical superposition principle. The trace operation is an integration over phase space. In the case where the canonical variables independently run from -infinity to +infinity the formalism reduces to the representation of quantum mechanics by Wigner distributions. However, the notion of coherent algebras allows to apply the formalism to spaces for which the Wigner mapping is not known. Quantum mechanics of a particle in a plane in polar coordinates is discussed as an example. (author)

Quark imaging in the proton via quantum phase-space distributions

International Nuclear Information System (INIS)

Belitsky, A.V.; Ji Xiangdong; Yuan Feng

2004-01-01

We develop the concept of quantum phase-space (Wigner) distributions for quarks and gluons in the proton. To appreciate their physical content, we analyze the contraints from special relativity on the interpretation of elastic form factors, and examine the physics of the Feynman parton distributions in the proton's rest frame. We relate the quark Wigner functions to the transverse-momentum dependent parton distributions and generalized parton distributions, emphasizing the physical role of the skewness parameter. We show that the Wigner functions allow us to visualize quantum quarks and gluons using the language of classical phase space. We present two examples of the quark Wigner distributions and point out some model-independent features

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

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

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

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

Quantum dynamical time evolutions as stochastic flows on phase space

International Nuclear Information System (INIS)

Combe, P.; Rodriguez, R.; Guerra, F.; Sirigue, M.; Sirigue-Collin, M.

1984-01-01

We are mainly interested in describing the time development of the Wigner functions by means of stochastic processes. In the second section we recall the main properties of the Wigner functions as well as those of their Fourier transform. In the next one we derive the evolution equation of these functions for a class of Hamiltonians and we give a probabilistic expression for the solution of these equations by means of a stochastic flow in phase space which reminds of the classical flows. In the last section we remark that the previously defined flow can be extended to the bounded continuous functions on phase space and that this flow conserves the cone generated by the Wigner functions. (orig./HSI)

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.

On phase-space representations of quantum mechanics using

Indian Academy of Sciences (India)

space representations of quantum mechanics using Glauber coherent states. DIÓGENES CAMPOS. Research Article Volume 87 Issue 2 August ... Keywords. Phase-space quantum mechanics, coherent states, Husimi function, Wigner function ...

The Bohr-Heisenberg correspondence principle viewed from phase space

DEFF Research Database (Denmark)

Dahl, Jens Peder

2002-01-01

Phase-space representations play an increasingly important role in several branches of physics. Here, we review the author's studies of the Bohr-Heisenberg correspondence principle within the Weyl-Wigner phase-space representation. The analysis leads to refined correspondence rules that can...

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 >

Revealing virtual processes of a quantum Brownian particle in phase space

International Nuclear Information System (INIS)

Maniscalco, S

2005-01-01

The short-time dynamics of a quantum Brownian particle in a harmonic potential is studied in phase space. An exact non-Markovian analytic approach to calculate the time evolution of the Wigner function is presented. The dynamics of the Wigner function of an initially squeezed state is analysed. It is shown that virtual exchanges of energy between the particle and the reservoir, characterizing the non-Lindblad short-time dynamics where system-reservoir correlations are not negligible, show up in phase space

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.)

The eigenvalue problem in phase space.

Science.gov (United States)

Cohen, Leon

2018-06-30

We formulate the standard quantum mechanical eigenvalue problem in quantum phase space. The equation obtained involves the c-function that corresponds to the quantum operator. We use the Wigner distribution for the phase space function. We argue that the phase space eigenvalue equation obtained has, in addition to the proper solutions, improper solutions. That is, solutions for which no wave function exists which could generate the distribution. We discuss the conditions for ascertaining whether a position momentum function is a proper phase space distribution. We call these conditions psi-representability conditions, and show that if these conditions are imposed, one extracts the correct phase space eigenfunctions. We also derive the phase space eigenvalue equation for arbitrary phase space distributions functions. © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

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

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.

Quantum Shuttle in Phase Space

DEFF Research Database (Denmark)

Novotny, Tomas; Donarini, Andrea; Jauho, Antti-Pekka

2003-01-01

Abstract: We present a quantum theory of the shuttle instability in electronic transport through a nanostructure with a mechanical degree of freedom. A phase space formulation in terms of the Wigner function allows us to identify a crossover from the tunneling to the shuttling regime, thus...

The Morse oscillator in position space, momentum space, and phase space

DEFF Research Database (Denmark)

Dahl, Jens Peder; Springborg, Michael

1988-01-01

We present a unified description of the position-space wave functions, the momentum-space wave functions, and the phase-space Wigner functions for the bound states of a Morse oscillator. By comparing with the functions for the harmonic oscillator the effects of anharmonicity are visualized....... Analytical expressions for the wave functions and the phase space functions are given, and it is demonstrated how a numerical problem arising from the summation of an alternating series in evaluating Laguerre functions can be circumvented. The method is applicable also for other problems where Laguerre...... functions are to be calculated. The wave and phase space functions are displayed in a series of curves and contour diagrams. An Appendix discusses the calculation of the modified Bessel functions of real, positive argument and complex order, which is required for calculating the phase space functions...

Phase-space distributions and orbital angular momentum

Directory of Open Access Journals (Sweden)

Pasquini B.

2014-06-01

Full Text Available We review the concept of Wigner distributions to describe the phase-space distributions of quarks in the nucleon, emphasizing the information encoded in these functions about the quark orbital angular momentum.

The quantum state vector in phase space and Gabor's windowed Fourier transform

International Nuclear Information System (INIS)

Bracken, A J; Watson, P

2010-01-01

Representations of quantum state vectors by complex phase space amplitudes, complementing the description of the density operator by the Wigner function, have been defined by applying the Weyl-Wigner transform to dyadic operators, linear in the state vector and anti-linear in a fixed 'window state vector'. Here aspects of this construction are explored, and a connection is established with Gabor's 'windowed Fourier transform'. The amplitudes that arise for simple quantum states from various choices of windows are presented as illustrations. Generalized Bargmann representations of the state vector appear as special cases, associated with Gaussian windows. For every choice of window, amplitudes lie in a corresponding linear subspace of square-integrable functions on phase space. A generalized Born interpretation of amplitudes is described, with both the Wigner function and a generalized Husimi function appearing as quantities linear in an amplitude and anti-linear in its complex conjugate. Schroedinger's time-dependent and time-independent equations are represented on phase space amplitudes, and their solutions described in simple cases.

Relativistic algebraic spinors and quantum motions in phase space

International Nuclear Information System (INIS)

Holland, P.R.

1986-01-01

Following suggestions of Schonberg and Bohm, we study the tensorial phase space representation of the Dirac and Feynman-Gell-Mann equations in terms of the complex Dirac algebra C 4 , a Jordan-Wigner algebra G 4 , and Wigner transformations. To do this we solve the problem of the conditions under which elements in C 4 generate minimal ideals, and extend this to G 4 . This yields the linear theory of Dirac spin spaces and tensor representations of Dirac spinors, and the spin-1/2 wave equations are represented through fermionic state vectors in a higher space as a set of interconnected tensor relations

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.

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

Phase-space spinor amplitudes for spin-1/2 systems

International Nuclear Information System (INIS)

Watson, P.; Bracken, A. J.

2011-01-01

The concept of phase-space amplitudes for systems with continuous degrees of freedom is generalized to finite-dimensional spin systems. Complex amplitudes are obtained on both a sphere and a finite lattice, in each case enabling a more fundamental description of pure spin states than that previously given by Wigner functions. In each case the Wigner function can be expressed as the star product of the amplitude and its conjugate, so providing a generalized Born interpretation of amplitudes that emphasizes their more fundamental status. The ordinary product of the amplitude and its conjugate produces a (generalized) spin Husimi function. The case of spin-(1/2) is treated in detail, and it is shown that phase-space amplitudes on the sphere transform correctly as spinors under rotations, despite their expression in terms of spherical harmonics. Spin amplitudes on a lattice are also found to transform as spinors. Applications are given to the phase space description of state superposition, and to the evolution in phase space of the state of a spin-(1/2) magnetic dipole in a time-dependent magnetic field.

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

Coherent and squeezed states in phase space

International Nuclear Information System (INIS)

Jannussis, A.; Bartzis, V.; Vlahos, E.

1990-01-01

In the present paper, the coherent and the squeezed states in phase space have been studied. From the wave functions of the coherent and the squeezed state, their corresponding Wigner distribution functions are calculated. Especially the calculation of the corresponding Wigner functions for the above states permits the determination of the mean values of position and momentum and thus the Heisenberg uncertainty relation. In fact, from the related results, it is concluded that the uncertainty relation of the coherent and associated squeezed states is the same

A new type of phase-space path integral

International Nuclear Information System (INIS)

Marinov, M.S.

1991-01-01

Evolution of Wigner's quasi-distribution of a quantum system is represented by means of a path integral in phase space. Instead of the Hamiltonian action, a new functional is present in the integral, and its extrema in the functional space are also given by the classical trajectories. The phase-space paths appear in the integral with real weights, so complex integrals are not necessary. The semiclassical approximation and some applications are discussed briefly. (orig.)

On the phase space representations. 1

International Nuclear Information System (INIS)

Polubarinov, I.V.

1978-01-01

The Dirac representation theory deals usually with the amplitude formalism of the quantum theory. An introduction is given into a theory of some other representations, which are applicable in the density matrix formalism and can naturally be called phase space representations (PSR). They use terms of phase space variables (x and p simultaneously) and give a description, close to the classical phase space description. Definitions and algebraic properties are given in quantum mechanics for such PSRs as the Wigner representation, coherent state representation and others. Completeness relations of a matrix type are used as a starting point. The case of quantum field theory is also outlined

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.)

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.

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.

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

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.

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.

Phase-space evolution of x-ray coherence in phase-sensitive imaging.

Science.gov (United States)

Wu, Xizeng; Liu, Hong

2008-08-01

X-ray coherence evolution in the imaging process plays a key role for x-ray phase-sensitive imaging. In this work we present a phase-space formulation for the phase-sensitive imaging. The theory is reformulated in terms of the cross-spectral density and associated Wigner distribution. The phase-space formulation enables an explicit and quantitative account of partial coherence effects on phase-sensitive imaging. The presented formulas for x-ray spectral density at the detector can be used for performing accurate phase retrieval and optimizing the phase-contrast visibility. The concept of phase-space shearing length derived from this phase-space formulation clarifies the spatial coherence requirement for phase-sensitive imaging with incoherent sources. The theory has been applied to x-ray Talbot interferometric imaging as well. The peak coherence condition derived reveals new insights into three-grating-based Talbot-interferometric imaging and gratings-based x-ray dark-field imaging.

Discrete Wigner Function Derivation of the Aaronson–Gottesman Tableau Algorithm

Directory of Open Access Journals (Sweden)

Lucas Kocia

2017-07-01

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

Generalized Reduction Formula for Discrete Wigner Functions of Multiqubit Systems

Science.gov (United States)

Srinivasan, K.; Raghavan, G.

2018-03-01

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

On a phase space quantum description of the spherical 2-brane

International Nuclear Information System (INIS)

Cordero, R; Turrubiates, F J; Vera, J C

2014-01-01

The quantum properties of the two-dimensional relativistic spherical membrane in phase space are analyzed using the Wigner function. Specifically, the true vacuum and rigid bubble nucleation cases are treated. Inspired by quantum cosmology, the Hartle–Hawking, Linde and Vilenkin boundary conditions are employed to calculate the bubble wave functions and their corresponding Wigner functions. Furthermore, the asymptotic behavior of the wave function using three different methods is explored and the Wigner functions are calculated numerically. Some aspects of the semiclassical properties for each boundary condition and their possible implications for quantum cosmology are discussed. (papers)

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

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

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....

Lattice Wigner equation

Science.gov (United States)

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

2018-01-01

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

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.

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...

Linear entropy in quantum phase space

International Nuclear Information System (INIS)

Rosales-Zarate, Laura E. C.; Drummond, P. D.

2011-01-01

We calculate the quantum Renyi entropy in a phase-space representation for either fermions or bosons. This can also be used to calculate purity and fidelity, or the entanglement between two systems. We show that it is possible to calculate the entropy from sampled phase-space distributions in normally ordered representations, although this is not possible for all quantum states. We give an example of the use of this method in an exactly soluble thermal case. The quantum entropy cannot be calculated at all using sampling methods in classical symmetric (Wigner) or antinormally ordered (Husimi) phase spaces, due to inner-product divergences. The preferred method is to use generalized Gaussian phase-space methods, which utilize a distribution over stochastic Green's functions. We illustrate this approach by calculating the reduced entropy and entanglement of bosonic or fermionic modes coupled to a time-evolving, non-Markovian reservoir.

Linear entropy in quantum phase space

Energy Technology Data Exchange (ETDEWEB)

Rosales-Zarate, Laura E. C.; Drummond, P. D. [Centre for Atom Optics and Ultrafast Spectroscopy, Swinburne University of Technology, Melbourne 3122 (Australia)

2011-10-15

We calculate the quantum Renyi entropy in a phase-space representation for either fermions or bosons. This can also be used to calculate purity and fidelity, or the entanglement between two systems. We show that it is possible to calculate the entropy from sampled phase-space distributions in normally ordered representations, although this is not possible for all quantum states. We give an example of the use of this method in an exactly soluble thermal case. The quantum entropy cannot be calculated at all using sampling methods in classical symmetric (Wigner) or antinormally ordered (Husimi) phase spaces, due to inner-product divergences. The preferred method is to use generalized Gaussian phase-space methods, which utilize a distribution over stochastic Green's functions. We illustrate this approach by calculating the reduced entropy and entanglement of bosonic or fermionic modes coupled to a time-evolving, non-Markovian reservoir.

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.

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.

Comparison of phase space dynamics of Kopenhagen and causal interpretations of quantum mechanics

Energy Technology Data Exchange (ETDEWEB)

Tempel, Christoph; Schleich, Wolfgang P. [Institut fuer Quantenphysik, Universitaet Ulm, D-89069 Ulm (Germany)

2013-07-01

Recent publications pursue the attempt to reconstruct Bohm trajectories experimentally utilizing the technique of weak measurements. We study the phase space dynamics of a specific double slit setup in terms of the Bohm de-Broglie formulation of quantum mechanics. We want to compare the results of those Bohmian phase space dynamics to the usual quantum mechanical phase space formulation with the Wigner function as a quasi probability density.

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

Science.gov (United States)

Luzanov, A V

2008-09-07

The Wigner function for the pure quantum states is used as an integral kernel of the non-Hermitian operator K, to which the standard singular value decomposition (SVD) is applied. It provides a set of the squared singular values treated as probabilities of the individual phase-space processes, the latter being described by eigenfunctions of KK(+) (for coordinate variables) and K(+)K (for momentum variables). Such a SVD representation is employed to obviate the well-known difficulties in the definition of the phase-space entropy measures in terms of the Wigner function that usually allows negative values. In particular, the new measures of nonclassicality are constructed in the form that automatically satisfies additivity for systems composed of noninteracting parts. Furthermore, the emphasis is given on the geometrical interpretation of the full entropy measure as the effective phase-space volume in the Wigner picture of quantum mechanics. The approach is exemplified by considering some generic vibrational systems. Specifically, for eigenstates of the harmonic oscillator and a superposition of coherent states, the singular value spectrum is evaluated analytically. Numerical computations are given for the nonlinear problems (the Morse and double well oscillators, and the Henon-Heiles system). We also discuss the difficulties in implementation of a similar technique for electronic problems.

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

Science.gov (United States)

Banach, Zbigniew; Piekarski, Sławomir

1993-01-01

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

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

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

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.

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

Simple procedure for phase-space measurement and entanglement validation

Science.gov (United States)

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

2017-08-01

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

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.

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.

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

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.

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.

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

International Nuclear Information System (INIS)

Oste, Roy; Jeugt, Joris Van der

2014-01-01

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

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)

Incomplete Detection of Nonclassical Phase-Space Distributions

Science.gov (United States)

Bohmann, M.; Tiedau, J.; Bartley, T.; Sperling, J.; Silberhorn, C.; Vogel, W.

2018-02-01

We implement the direct sampling of negative phase-space functions via unbalanced homodyne measurement using click-counting detectors. The negativities significantly certify nonclassical light in the high-loss regime using a small number of detectors which cannot resolve individual photons. We apply our method to heralded single-photon states and experimentally demonstrate the most significant certification of nonclassicality for only two detection bins. By contrast, the frequently applied Wigner function fails to directly indicate such quantum characteristics for the quantum efficiencies present in our setup without applying additional reconstruction algorithms. Therefore, we realize a robust and reliable approach to characterize nonclassical light in phase space under realistic conditions.

Quantum algorithms for phase-space tomography

International Nuclear Information System (INIS)

Paz, Juan Pablo; Roncaglia, Augusto Jose; Saraceno, Marcos

2004-01-01

We present efficient circuits that can be used for the phase-space tomography of quantum states. The circuits evaluate individual values or selected averages of the Wigner, Kirkwood, and Husimi distributions. These quantum gate arrays can be programmed by initializing appropriate computational states. The Husimi circuit relies on a subroutine that is also interesting in its own right: the efficient preparation of a coherent state, which is the ground state of the Harper Hamiltonian

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.

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.)

Phase-space quantum control

International Nuclear Information System (INIS)

Fechner, Susanne

2008-01-01

The von Neumann-representation introduced in this thesis describes each laser pulse in a one-to-one manner as a sum of bandwidth-limited, Gaussian laser pulses centered around different points in phase space. These pulses can be regarded as elementary building blocks from which every single laser pulse can be constructed. The von Neumann-representation combines different useful properties for applications in quantum control. First, it is a one-to-one map between the degrees of freedom of the pulse shaper and the phase-space representation of the corresponding shaped laser pulse. In other words: Every possible choice of pulse shaper parameters corresponds to exactly one von Neumann-representation and vice versa. Moreover, since temporal and spectral structures become immediately sizable, the von Neumann-representation, as well as the Husimi- or the Wigner-representations, allows for an intuitive interpretation of the represented laser pulse. (orig.)

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)

A phase space approach to wave propagation with dispersion.

Science.gov (United States)

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

2015-08-01

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

Slowing Quantum Decoherence by Squeezing in Phase Space

Science.gov (United States)

Le Jeannic, H.; Cavaillès, A.; Huang, K.; Filip, R.; Laurat, J.

2018-02-01

Non-Gaussian states, and specifically the paradigmatic cat state, are well known to be very sensitive to losses. When propagating through damping channels, these states quickly lose their nonclassical features and the associated negative oscillations of their Wigner function. However, by squeezing the superposition states, the decoherence process can be qualitatively changed and substantially slowed down. Here, as a first example, we experimentally observe the reduced decoherence of squeezed optical coherent-state superpositions through a lossy channel. To quantify the robustness of states, we introduce a combination of a decaying value and a rate of decay of the Wigner function negativity. This work, which uses squeezing as an ancillary Gaussian resource, opens new possibilities to protect and manipulate quantum superpositions in phase space.

Quantum phase space with a basis of Wannier functions

Science.gov (United States)

Fang, Yuan; Wu, Fan; Wu, Biao

2018-02-01

A quantum phase space with Wannier basis is constructed: (i) classical phase space is divided into Planck cells; (ii) a complete set of Wannier functions are constructed with the combination of Kohn’s method and Löwdin method such that each Wannier function is localized at a Planck cell. With these Wannier functions one can map a wave function unitarily onto phase space. Various examples are used to illustrate our method and compare it to Wigner function. The advantage of our method is that it can smooth out the oscillations in wave functions without losing any information and is potentially a better tool in studying quantum-classical correspondence. In addition, we point out that our method can be used for time-frequency analysis of signals.

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

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

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)

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.

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.

Non-commutative geometry on quantum phase-space

International Nuclear Information System (INIS)

Reuter, M.

1995-06-01

A non-commutative analogue of the classical differential forms is constructed on the phase-space of an arbitrary quantum system. The non-commutative forms are universal and are related to the quantum mechanical dynamics in the same way as the classical forms are related to classical dynamics. They are constructed by applying the Weyl-Wigner symbol map to the differential envelope of the linear operators on the quantum mechanical Hilbert space. This leads to a representation of the non-commutative forms considered by A. Connes in terms of multiscalar functions on the classical phase-space. In an appropriate coincidence limit they define a quantum deformation of the classical tensor fields and both commutative and non-commutative forms can be studied in a unified framework. We interprete the quantum differential forms in physical terms and comment on possible applications. (orig.)

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

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.

Quantum Optics in Phase Space

Science.gov (United States)

Schleich, Wolfgang P.

2001-04-01

Quantum Optics in Phase Space provides a concise introduction to the rapidly moving field of quantum optics from the point of view of phase space. Modern in style and didactically skillful, Quantum Optics in Phase Space prepares students for their own research by presenting detailed derivations, many illustrations and a large set of workable problems at the end of each chapter. Often, the theoretical treatments are accompanied by the corresponding experiments. An exhaustive list of references provides a guide to the literature. Quantum Optics in Phase Space also serves advanced researchers as a comprehensive reference book. Starting with an extensive review of the experiments that define quantum optics and a brief summary of the foundations of quantum mechanics the author Wolfgang P. Schleich illustrates the properties of quantum states with the help of the Wigner phase space distribution function. His description of waves ala WKB connects semi-classical phase space with the Berry phase. These semi-classical techniques provide deeper insight into the timely topics of wave packet dynamics, fractional revivals and the Talbot effect. Whereas the first half of the book deals with mechanical oscillators such as ions in a trap or atoms in a standing wave the second half addresses problems where the quantization of the radiation field is of importance. Such topics extensively discussed include optical interferometry, the atom-field interaction, quantum state preparation and measurement, entanglement, decoherence, the one-atom maser and atom optics in quantized light fields. Quantum Optics in Phase Space presents the subject of quantum optics as transparently as possible. Giving wide-ranging references, it enables students to study and solve problems with modern scientific literature. The result is a remarkably concise yet comprehensive and accessible text- and reference book - an inspiring source of information and insight for students, teachers and researchers alike.

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.

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.

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

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

International Nuclear Information System (INIS)

Wodkiewicz, K.

1984-01-01

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

Wigner 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.

Multiplexed phase-space imaging for 3D fluorescence microscopy.

Science.gov (United States)

Liu, Hsiou-Yuan; Zhong, Jingshan; Waller, Laura

2017-06-26

Optical phase-space functions describe spatial and angular information simultaneously; examples of optical phase-space functions include light fields in ray optics and Wigner functions in wave optics. Measurement of phase-space enables digital refocusing, aberration removal and 3D reconstruction. High-resolution capture of 4D phase-space datasets is, however, challenging. Previous scanning approaches are slow, light inefficient and do not achieve diffraction-limited resolution. Here, we propose a multiplexed method that solves these problems. We use a spatial light modulator (SLM) in the pupil plane of a microscope in order to sequentially pattern multiplexed coded apertures while capturing images in real space. Then, we reconstruct the 3D fluorescence distribution of our sample by solving an inverse problem via regularized least squares with a proximal accelerated gradient descent solver. We experimentally reconstruct a 101 Megavoxel 3D volume (1010×510×500µm with NA 0.4), demonstrating improved acquisition time, light throughput and resolution compared to scanning aperture methods. Our flexible patterning scheme further allows sparsity in the sample to be exploited for reduced data capture.

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 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

Quantum Potential and Symmetries in Extended Phase Space

Directory of Open Access Journals (Sweden)

Sadollah Nasiri

2006-06-01

Full Text Available The behavior of the quantum potential is studied for a particle in a linear and a harmonic potential by means of an extended phase space technique. This is done by obtaining an expression for the quantum potential in momentum space representation followed by the generalization of this concept to extended phase space. It is shown that there exists an extended canonical transformation that removes the expression for the quantum potential in the dynamical equation. The situation, mathematically, is similar to disappearance of the centrifugal potential in going from the spherical to the Cartesian coordinates that changes the physical potential to an effective one. The representation where the quantum potential disappears and the modified Hamilton-Jacobi equation reduces to the familiar classical form, is one in which the dynamical equation turns out to be the Wigner equation.

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.

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.

Quantum dynamics via a time propagator in Wigner's phase space

DEFF Research Database (Denmark)

Grønager, Michael; Henriksen, Niels Engholm

1995-01-01

We derive an expression for a short-time phase space propagator. We use it in a new propagation scheme and demonstrate that it works for a Morse potential. The propagation scheme is used to propagate classical distributions which do not obey the Heisenberg uncertainty principle. It is shown that ...... as a part of the sampling function. ©1995 American Institute of Physics....

Augmenting Phase Space Quantization to Introduce Additional Physical Effects

Science.gov (United States)

Robbins, Matthew P. G.

Quantum mechanics can be done using classical phase space functions and a star product. The state of the system is described by a quasi-probability distribution. A classical system can be quantized in phase space in different ways with different quasi-probability distributions and star products. A transition differential operator relates different phase space quantizations. The objective of this thesis is to introduce additional physical effects into the process of quantization by using the transition operator. As prototypical examples, we first look at the coarse-graining of the Wigner function and the damped simple harmonic oscillator. By generalizing the transition operator and star product to also be functions of the position and momentum, we show that additional physical features beyond damping and coarse-graining can be introduced into a quantum system, including the generalized uncertainty principle of quantum gravity phenomenology, driving forces, and decoherence.

Visualizing the quantum interaction picture in phase space

International Nuclear Information System (INIS)

Mehmani, Bahar; Aiello, Andrea

2012-01-01

We present a graphical example of the interaction picture-time evolution. Our aim is to help students understand in a didactic manner the simplicity that this picture provides. Visualizing the interaction picture unveils its advantages, which are hidden behind the involved mathematics. Specifically, we show that the time evolution of a driven harmonic oscillator in the interaction picture corresponds to a local transformation of a phase space-reference frame into the one that is co-rotating with the Wigner function. (paper)

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

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

International Nuclear Information System (INIS)

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

2005-01-01

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

Moshinsky atom and density functional theory - A phase space view(1)

DEFF Research Database (Denmark)

Dahl, Jens Peder

2009-01-01

Le probleme de deux particules dans un potentiel d'oscillateur harmonique commun interagissant par le biais de forces d'oscillateur harmonique est discute dans la representation phase-espace de Weyl-Wigner. La fonction de Wigner du systeme est une fonction ordinaire des constantes phase-espace du...

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.

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.

States in the Hilbert space formulation and in the phase space formulation of quantum mechanics

International Nuclear Information System (INIS)

Tosiek, J.; Brzykcy, P.

2013-01-01

We consider the problem of testing whether a given matrix in the Hilbert space formulation of quantum mechanics or a function considered in the phase space formulation of quantum theory represents a quantum state. We propose several practical criteria for recognising states in these two versions of quantum physics. After minor modifications, they can be applied to check positivity of any operators acting in a Hilbert space or positivity of any functions from an algebra with a ∗-product of Weyl type. -- Highlights: ► Methods of testing whether a given matrix represents a quantum state. ► The Stratonovich–Weyl correspondence on an arbitrary symplectic manifold. ► Criteria for checking whether a function on a symplectic space is a Wigner function

Phase-space representation of non-classical behaviour of scalar wave-fields

International Nuclear Information System (INIS)

Canas-Cardona, Gustavo; Castaneda, Roman; Vinck-Posada, Herbert

2011-01-01

The modelling of optical fields by using radiant and virtual point sources for the spatial coherence wavelets in the phase-space representation evidences some effects, conventionally attributed to non-classical correlations of light, although such type of correlations are not explicitly included in the model. Specifically, a light state is produced that has similar morphology to the Wigner Distribution Function of the well-known quantum Schroedinger cat and squeezed states.

Frame transforms, star products and quantum mechanics on phase space

International Nuclear Information System (INIS)

Aniello, P; Marmo, G; Man'ko, V I

2008-01-01

Using the notions of frame transform and of square integrable projective representation of a locally compact group G, we introduce a class of isometries (tight frame transforms) from the space of Hilbert-Schmidt operators in the carrier Hilbert space of the representation into the space of square integrable functions on the direct product group G x G. These transforms have remarkable properties. In particular, their ranges are reproducing kernel Hilbert spaces endowed with a suitable 'star product' which mimics, at the level of functions, the original product of operators. A 'phase space formulation' of quantum mechanics relying on the frame transforms introduced in the present paper, and the link of these maps with both the Wigner transform and the wavelet transform are discussed

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.

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.

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

Nuclear dynamics in phase space

International Nuclear Information System (INIS)

Di Toro, M.

1984-07-01

We present a unified semiclassical picture of nuclear dynamics, from collective states to heavy ion physics, based on a study of the time evolution of the Wigner distribution function. We discuss in particular the mean field dynamics, in this ''quantal'' phase space, which is ruled by the nuclear Vlasov equation. Simple approximate solutions are worked out for rotational and vibrational collective motions. Giant resonances are shown to be quite well described as scaling modes, which are equivalent to a lowest multipole (up to 1sub(max)=2) distortions of the momentum distribution. Applications are shown to heavy ion physics to study giant resonances on high spin states and dynamical collective effects in subthreshold π-production. Several possible extensions and in particular the inclusion of two-body collision terms are finally discussed

Qubits in phase space: Wigner-function approach to quantum-error correction and the mean-king problem

International Nuclear Information System (INIS)

Paz, Juan Pablo; Roncaglia, Augusto Jose; Saraceno, Marcos

2005-01-01

We analyze and further develop a method to represent the quantum state of a system of n qubits in a phase-space grid of NxN points (where N=2 n ). The method, which was recently proposed by Wootters and co-workers (Gibbons et al., Phys. Rev. A 70, 062101 (2004).), is based on the use of the elements of the finite field GF(2 n ) to label the phase-space axes. We present a self-contained overview of the method, we give insights into some of its features, and we apply it to investigate problems which are of interest for quantum-information theory: We analyze the phase-space representation of stabilizer states and quantum error-correction codes and present a phase-space solution to the so-called mean king problem

Phase-space quantum control; Quantenkontrolle im Zeit-Frequenz-Phasenraum

Energy Technology Data Exchange (ETDEWEB)

Fechner, Susanne

2008-08-06

The von Neumann-representation introduced in this thesis describes each laser pulse in a one-to-one manner as a sum of bandwidth-limited, Gaussian laser pulses centered around different points in phase space. These pulses can be regarded as elementary building blocks from which every single laser pulse can be constructed. The von Neumann-representation combines different useful properties for applications in quantum control. First, it is a one-to-one map between the degrees of freedom of the pulse shaper and the phase-space representation of the corresponding shaped laser pulse. In other words: Every possible choice of pulse shaper parameters corresponds to exactly one von Neumann-representation and vice versa. Moreover, since temporal and spectral structures become immediately sizable, the von Neumann-representation, as well as the Husimi- or the Wigner-representations, allows for an intuitive interpretation of the represented laser pulse. (orig.)

Entropy and wigner functions

Science.gov (United States)

Manfredi; Feix

2000-10-01

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

Entropy and Wigner Functions

OpenAIRE

Manfredi, G.; Feix, M. R.

2002-01-01

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

Phase-space description of wave packet approach to electronic transport in nanoscale systems

International Nuclear Information System (INIS)

Szydłowski, D; Wołoszyn, M; Spisak, B J

2013-01-01

The dynamics of conduction electrons in resonant tunnelling nanosystems is studied within the phase-space approach based on the Wigner distribution function. The time evolution of the distribution function is calculated from the time-dependent quantum kinetic equation for which an effective numerical method is presented. Calculations of the transport properties of a double-barrier resonant tunnelling diode are performed to illustrate the proposed techniques. Additionally, analysis of the transient effects in the nanosystem is carried out and it is shown that for some range of the bias voltage the temporal variations of electronic current can take negative values. The explanation of this effect is based on the analysis of the time changes of the Wigner distribution function. The decay time of the temporal current oscillations in the nanosystem as a function of the bias voltage is determined. (paper)

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

International Nuclear Information System (INIS)

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

2009-01-01

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

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.

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.

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 Functions on a Lattice

OpenAIRE

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

2000-01-01

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

Wigner 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.

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

Science.gov (United States)

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

2018-05-01

We study the phase diagram of a symmetric electron–hole bilayer system at absolute zero temperature and in zero magnetic field within the quantum Monte Carlo approach. In particular, we conduct variational Monte Carlo simulations for various phases, i.e. the paramagnetic fluid phase, the ferromagnetic fluid phase, the anti-ferromagnetic Wigner crystal phase, the ferromagnetic Wigner crystal phase and the excitonic phase, to estimate the ground-state energy at different values of in-layer density and inter-layer spacing. Slater–Jastrow style trial wave functions, with single-particle orbitals appropriate for different phases, are used to construct the phase diagram in the (r s , d) plane by finding the relative stability of trial wave functions. At very small layer separations, we find that the fluid phases are stable, with the paramagnetic fluid phase being particularly stable at and the ferromagnetic fluid phase being particularly stable at . As the layer spacing increases, we first find that there is a phase transition from the ferromagnetic fluid phase to the ferromagnetic Wigner crystal phase when d reaches 0.4 a.u. at r s   =  20, and before there is a return to the ferromagnetic fluid phase when d approaches 1 a.u. However, for r s   Wigner crystal is stable over the considered range of r s and d. We also find that as r s increases, the critical layer separations for Wigner crystallization increase.

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

Science.gov (United States)

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

2018-05-10

We study the phase diagram of a symmetric electron-hole bilayer system at absolute zero temperature and in zero magnetic field within the quantum Monte Carlo approach. In particular, we conduct variational Monte Carlo simulations for various phases, i.e. the paramagnetic fluid phase, the ferromagnetic fluid phase, the anti-ferromagnetic Wigner crystal phase, the ferromagnetic Wigner crystal phase and the excitonic phase, to estimate the ground-state energy at different values of in-layer density and inter-layer spacing. Slater-Jastrow style trial wave functions, with single-particle orbitals appropriate for different phases, are used to construct the phase diagram in the (r s , d) plane by finding the relative stability of trial wave functions. At very small layer separations, we find that the fluid phases are stable, with the paramagnetic fluid phase being particularly stable at [Formula: see text] and the ferromagnetic fluid phase being particularly stable at [Formula: see text]. As the layer spacing increases, we first find that there is a phase transition from the ferromagnetic fluid phase to the ferromagnetic Wigner crystal phase when d reaches 0.4 a.u. at r s   =  20, and before there is a return to the ferromagnetic fluid phase when d approaches 1 a.u. However, for r s   Wigner crystal is stable over the considered range of r s and d. We also find that as r s increases, the critical layer separations for Wigner crystallization increase.

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.

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

Nondeterministic noiseless amplification via non-symplectic phase space transformations

International Nuclear Information System (INIS)

Walk, Nathan; Lund, Austin P; Ralph, Timothy C

2013-01-01

We analyse the action of an ideal noiseless linear amplifier operator, g a-hat † a-hat, using the Wigner function phase space representation. In this setting we are able to clarify the gain g for which a physical output is produced when this operator is acted upon inputs other than coherent states. We derive compact closed form expressions for the action of N local amplifiers, with potentially different gains, on arbitrary N-mode Gaussian states and provide several examples of the utility of this formalism for determining important quantities including amplification and the strength and purity of the distilled entanglement, and for optimizing the use of the amplification in quantum information protocols. (paper)

Zonal-flow dynamics from a phase-space perspective

Science.gov (United States)

Ruiz, D. E.; Parker, J. B.; Shi, E. L.; Dodin, I. Y.

2017-10-01

The wave kinetic equation (WKE) describing drift-wave (DW) turbulence is widely used in the studies of zonal flows (ZFs) emerging from DW turbulence. However, this formulation neglects the exchange of enstrophy between DWs and ZFs and also ignores effects beyond the geometrical-optics (GO) limit. Here we present a new theory that captures both of these effects, while still treating DW quanta (``driftons'') as particles in phase space. In this theory, the drifton dynamics is described by an equation of the Wigner-Moyal type, which is analogous to the phase-space formulation of quantum mechanics. The ``Hamiltonian'' and the ``dissipative'' parts of the DW-ZF interactions are clearly identified. Moreover, this theory can be interpreted as a phase-space representation of the second-order cumulant expansion (CE2). In the GO limit, this formulation features additional terms missing in the traditional WKE that ensure conservation of the total enstrophy of the system, in addition to the total energy, which is the only conserved invariant in previous theories based on the traditional WKE. Numerical simulations are presented to illustrate the importance of these additional terms. Supported by the U.S. DOE through Contract Nos. DE-AC02-09CH11466 and DE-AC52-07NA27344, by the NNSA SSAA Program through DOE Research Grant No. DE-NA0002948, and by the U.S. DOD NDSEG Fellowship through Contract No. 32-CFR-168a.

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.

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.

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 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

A concise treatise on quantum mechanics in phase space

CERN Document Server

Curtright, Thomas L; Zachos, Cosmas K

2014-01-01

This is a text on quantum mechanics formulated simultaneously in terms of position and momentum, i.e. in phase space. It is written at an introductory level, drawing on the remarkable history of the subject for inspiration and motivation. Wigner functions density -- matrices in a special Weyl representation -- and star products are the cornerstones of the formalism. The resulting framework is a rich source of physical intuition. It has been used to describe transport in quantum optics, structure and dynamics in nuclear physics, chaos, and decoherence in quantum computing. It is also of importance in signal processing and the mathematics of algebraic deformation. A remarkable aspect of its internal logic, pioneered by Groenewold and Moyal, has only emerged in the last quarter-century: it furnishes a third, alternative way to formulate and understand quantum mechanics, independent of the conventional Hilbert space or path integral approaches to the subject. In this logically complete and self-standing formula...

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

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

Discrete Wigner functions and quantum computation

International Nuclear Information System (INIS)

Galvao, E.

2005-01-01

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

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.

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)

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 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....

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).

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

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)

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....

Nonclassicality of Photon-Added Displaced Thermal State via Quantum Phase-Space Distributions

Science.gov (United States)

Zhang, Ran; Meng, Xiang-Guo; Du, Chuan-Xun; Wang, Ji-Suo

2018-02-01

We introduce a new kind of nonclassical mixed state generated by adding arbitrary photons to a displaced thermal state, i.e., the photon-added displaced thermal state (PADTS), and obtain the normalization factor, which is simply related to two-variable Hermite polynomials. We also discuss the nonclassicality of the PADTS by considering quantum phase-space distributions. The results indicate that the value of the photon count statistics is maximum when the number of detected photons is equal to the number of added photons, and that the photon-added operation has a similar modulation effect with increasing displacement. Moreover, the negative volume of the Wigner function for the PADTS takes a maximal value for a specific photon-added number.

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)

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)

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)

Linear and nonlinear optical signals in probability and phase-space representations

International Nuclear Information System (INIS)

Man'ko, Margarita A

2006-01-01

Review of different representations of signals including the phase-space representations and tomographic representations is presented. The signals under consideration are either linear or nonlinear ones. The linear signals satisfy linear quantumlike Schroedinger and von Neumann equations. Nonlinear signals satisfy nonlinear Schroedinger equations as well as Gross-Pitaevskii equation describing solitons in Bose-Einstein condensate. The Ville-Wigner distributions for solitons are considered in comparison with tomographic-probability densities describing solitons completely. different kinds of tomographies - symplectic tomography, optical tomography and Fresnel tomography are reviewed. New kind of map of the signals onto probability distributions of discrete photon number-like variable is discussed. Mutual relations between different transformations of signal functions are established in explicit form. Such characteristics of the signal-probability distribution as entropy is discussed

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.

Nonequilibrium dynamics of spin-boson models from phase-space methods

Science.gov (United States)

Piñeiro Orioli, Asier; Safavi-Naini, Arghavan; Wall, Michael L.; Rey, Ana Maria

2017-09-01

An accurate description of the nonequilibrium dynamics of systems with coupled spin and bosonic degrees of freedom remains theoretically challenging, especially for large system sizes and in higher than one dimension. Phase-space methods such as the truncated Wigner approximation (TWA) have the advantage of being easily scalable and applicable to arbitrary dimensions. In this work we adapt the TWA to generic spin-boson models by making use of recently developed algorithms for discrete phase spaces [J. Schachenmayer, A. Pikovski, and A. M. Rey, Phys. Rev. X 5, 011022 (2015), 10.1103/PhysRevX.5.011022]. Furthermore we go beyond the standard TWA approximation by applying a scheme based on the Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of equations to our coupled spin-boson model. This allows us, in principle, to study how systematically adding higher-order corrections improves the convergence of the method. To test various levels of approximation we study an exactly solvable spin-boson model, which is particularly relevant for trapped-ion arrays. Using TWA and its BBGKY extension we accurately reproduce the time evolution of a number of one- and two-point correlation functions in several dimensions and for an arbitrary number of bosonic modes.

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.

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

Phase space representation of quantum mechanics

DEFF Research Database (Denmark)

Henriksen, Niels Engholm; Billing, G. D.; Hansen, Flemming Yssing

1988-01-01

The accuracy of the Wigner propagation method is studied for stationary as well as non-stationary states of Morse oscillators. We investigate the possibility of improving the approach by introducing an effective potential. We find that the Wigner propagation method is accurate only for the ground...

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

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.

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.

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...

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.

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

Discrete Wigner Function Reconstruction and Compressed Sensing

OpenAIRE

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

2011-01-01

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

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.

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.

Wigner distribution function for an oscillator

International Nuclear Information System (INIS)

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

1975-01-01

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

Radon-Wigner transform for optical field analysis

NARCIS (Netherlands)

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

1998-01-01

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

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

An approach for generating trajectory-based dynamics which conserves the canonical distribution in the phase space formulation of quantum mechanics. II. Thermal correlation functions.

Science.gov (United States)

Liu, Jian; Miller, William H

2011-03-14

We show the exact expression of the quantum mechanical time correlation function in the phase space formulation of quantum mechanics. The trajectory-based dynamics that conserves the quantum canonical distribution-equilibrium Liouville dynamics (ELD) proposed in Paper I is then used to approximately evaluate the exact expression. It gives exact thermal correlation functions (of even nonlinear operators, i.e., nonlinear functions of position or momentum operators) in the classical, high temperature, and harmonic limits. Various methods have been presented for the implementation of ELD. Numerical tests of the ELD approach in the Wigner or Husimi phase space have been made for a harmonic oscillator and two strongly anharmonic model problems, for each potential autocorrelation functions of both linear and nonlinear operators have been calculated. It suggests ELD can be a potentially useful approach for describing quantum effects for complex systems in condense phase.

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

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.

Wigner particle theory and local quantum physics

International Nuclear Information System (INIS)

Fassarella, Lucio; Schroer, Bert

2002-01-01

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

Time-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.

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

International Nuclear Information System (INIS)

Fan Hongyi

2002-01-01

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

Thermal Wigner Operator in Coherent Thermal State Representation and Its Application

Institute of Scientific and Technical Information of China (English)

FAN HongYi

2002-01-01

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

Scars of the Wigner Function.

Science.gov (United States)

Toscano; de Aguiar MA; Ozorio De Almeida AM

2001-01-01

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

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 Function of Thermo-Invariant Coherent State

International Nuclear Information System (INIS)

Xue-Fen, Xu; Shi-Qun, Zhu

2008-01-01

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

Relativistic Wigner functions

Directory of Open Access Journals (Sweden)

Bialynicki-Birula Iwo

2014-01-01

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

Probing the liquid and solid phases in closely spaced two-dimensional systems

Energy Technology Data Exchange (ETDEWEB)

Zhang, Ding

2014-03-06

Gas, liquid and solid phases are the most common states of matter in our daily encountered 3-dimensional space. The school example is the H{sub 2}O molecule with its phases vapor, water and ice. Interestingly, electrons - with their point-like nature and negative charges - can also organize themselves under certain conditions to bear properties of these three common phases. At relatively high temperature, where Boltzmann statistics prevails, the ensemble of electrons without interactions can be treated as a gas of free particles. Cooling down the system, this electron gas condenses into a Fermi liquid. Finally, as a result of the repulsive Coulomb forces, electrons try to avoid each other by maximizing their distances. When the Coulomb interaction becomes sufficiently strong, a regular lattice emerges - an electron solid. The story however does not end here. Nature has much more in store for us. Electronic systems in fact exhibit a large variety of phases induced by spatial confinement, an external magnetic field, Coulomb interactions, or interactions involving degrees of freedom other than charge such as spin and valley. Here in this thesis, we restrict ourselves to the study of electrons in a 2-dimenisonal (2D) plane. Already in such a 2D electron system (2DES), several distinct states of matter appear: integer and fractional quantum Hall liquids, the 2D Wigner solid, stripe and bubble phases etc. In 2DES it is sufficient to sweep the perpendicular magnetic field to pass from one of these phases into another. Experimentally, many of these phases can be revealed by simply measuring the resistance. For a quantum Hall state, the longitudinal resistance vanishes, while the Hall resistance exhibits a plateau. The quantum Hall plateau is a manifestation of localization induced by the inevitable sample disorder. Coulomb interaction can also play an important role to localize charges. Even in the disorder-free case, electrons - more precisely quasi-particles in the

Probing the liquid and solid phases in closely spaced two-dimensional systems

International Nuclear Information System (INIS)

Zhang, Ding

2014-01-01

Gas, liquid and solid phases are the most common states of matter in our daily encountered 3-dimensional space. The school example is the H 2 O molecule with its phases vapor, water and ice. Interestingly, electrons - with their point-like nature and negative charges - can also organize themselves under certain conditions to bear properties of these three common phases. At relatively high temperature, where Boltzmann statistics prevails, the ensemble of electrons without interactions can be treated as a gas of free particles. Cooling down the system, this electron gas condenses into a Fermi liquid. Finally, as a result of the repulsive Coulomb forces, electrons try to avoid each other by maximizing their distances. When the Coulomb interaction becomes sufficiently strong, a regular lattice emerges - an electron solid. The story however does not end here. Nature has much more in store for us. Electronic systems in fact exhibit a large variety of phases induced by spatial confinement, an external magnetic field, Coulomb interactions, or interactions involving degrees of freedom other than charge such as spin and valley. Here in this thesis, we restrict ourselves to the study of electrons in a 2-dimenisonal (2D) plane. Already in such a 2D electron system (2DES), several distinct states of matter appear: integer and fractional quantum Hall liquids, the 2D Wigner solid, stripe and bubble phases etc. In 2DES it is sufficient to sweep the perpendicular magnetic field to pass from one of these phases into another. Experimentally, many of these phases can be revealed by simply measuring the resistance. For a quantum Hall state, the longitudinal resistance vanishes, while the Hall resistance exhibits a plateau. The quantum Hall plateau is a manifestation of localization induced by the inevitable sample disorder. Coulomb interaction can also play an important role to localize charges. Even in the disorder-free case, electrons - more precisely quasi-particles in the partially

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)

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

Wigner's Symmetry Representation Theorem

Indian Academy of Sciences (India)

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

Fractional Wigner Crystal in the Helical Luttinger Liquid.

Science.gov (United States)

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

2015-11-13

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

Specification of optical components using Wigner distribution function

International Nuclear Information System (INIS)

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

2010-01-01

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

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)

Phase space information in a non-linear quantum system containing a Kerr-like medium through Su(1, 1)-algebraic treatment

Science.gov (United States)

Mohamed, Abdel-Baset A.

2018-05-01

Analytical description for a Su(2)-quantum system interacting with a damped Su(1, 1)-cavity, which is filled with a non-linear Kerr medium, is presented. The dynamics of non-classicality of Su(1, 1)-state is investigated via the negative part of the Wigner function. We show that the negative part depends on the unitary interaction and the Kerr-like medium and it can be disappeared by increasing the dissipation rate and the detuning parameter. The phase space information of the Husimi function and its Wehrl density is very sensitive not only to the coupling to the environment and the unitary interaction but also to the detuning as well as to the Kerr-like medium. The phase space information may be completely erased by increasing the coupling to the environment. The coherence loss of the Su(2)-state is investigated via the Husimi Wehrl entropy. If the effects of the detuning parameter or/and of the Kerr-like medium are combined with the damping effect, the damping effect of the coupling to the environment may be weaken, and the Wehrl entropy is delayed to reach its steady-state value. At the steady-state value, the phase space information and the coherence are quickly lost.

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

Science.gov (United States)

Mohamed, Abdel-Baset A.

2017-10-01

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

Phase locking and quantum statistics in a parametrically driven nonlinear resonator

OpenAIRE

Hovsepyan, G. H.; Shahinyan, A. R.; Chew, Lock Yue; Kryuchkyan, G. Yu.

2016-01-01

We discuss phase-locking phenomena at low-level of quanta for parametrically driven nonlinear Kerr resonator (PDNR) in strong quantum regime. Oscillatory mode of PDNR is created in the process of a degenerate down-conversion of photons under interaction with a train of external Gaussian pulses. We calculate the Wigner functions of cavity mode showing two-fold symmetry in phase space and analyse formation of phase-locked states in the regular as well as the quantum chaotic regime.

Geometrical approach to the discrete Wigner function in prime power dimensions

International Nuclear Information System (INIS)

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

2006-01-01

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

Gymnastics in Phase Space

Energy Technology Data Exchange (ETDEWEB)

Chao, Alexander Wu; /SLAC

2012-03-01

As accelerator technology advances, the requirements on accelerator beam quality become increasingly demanding. Facing these new demands, the topic of phase space gymnastics is becoming a new focus of accelerator physics R&D. In a phase space gymnastics, the beam's phase space distribution is manipulated and precision tailored to meet the required beam qualities. On the other hand, all realization of such gymnastics will have to obey accelerator physics principles as well as technological limitations. Recent examples of phase space gymnastics include Emittance exchanges, Phase space exchanges, Emittance partitioning, Seeded FELs and Microbunched beams. The emittance related topics of this list are reviewed in this report. The accelerator physics basis, the optics design principles that provide these phase space manipulations, and the possible applications of these gymnastics, are discussed. This fascinating new field promises to be a powerful tool of the future.

Quantum phase fluctuations in the Jaynes-cummings model: effects of cavity damping

International Nuclear Information System (INIS)

Ho Trung Dung; Shumovskij, A.S.

1992-01-01

Phase properties of a coherent field interacting with a two-level atom in a cavity with very high but finite Q are studied. It is shown that due to the cavity damping the field phase is randomized more quickly than in the ideal-losslesscavity case. The Hermitian phase distribution and the phase distributions associated with the Q function and the Wigner function are compared. The similarities between them have clear interpretation in terms of the area-of-overlap in phase space. 29 refs.; 3 figs

Quantum Hamiltonian differential geometry: how does quantization affect space?

International Nuclear Information System (INIS)

Aldrovandi, R.

1993-01-01

Quantum phase space is given a description which entirely parallels the usual presentation of Classical Phase Space. A particular Schwinger unitary operator basis, in which the expansion of each operator is its own Weyl expression, is specially convenient for the purpose. The quantum Hamiltonian structure obtains from the classical structure by the conversion of the classical pointwise product of dynamical quantities into the noncommutative star product of Wigner functions. The main qualitative difference in the general structure is that, in the quantum case, the inverse symplectic matrix is not simply antisymmetric. This difference leads to the presence of braiding in the backstage of Quantum Mechanics. (author)

Non-commutative phase space and its space-time symmetry

International Nuclear Information System (INIS)

Li Kang; Dulat Sayipjamal

2010-01-01

First a description of 2+1 dimensional non-commutative (NC) phase space is presented, and then we find that in this formulation the generalized Bopp's shift has a symmetric representation and one can easily and straightforwardly define the star product on NC phase space. Then we define non-commutative Lorentz transformations both on NC space and NC phase space. We also discuss the Poincare symmetry. Finally we point out that our NC phase space formulation and the NC Lorentz transformations are applicable to any even dimensional NC space and NC phase space. (authors)

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

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

Decoherence of odd compass states in the phase-sensitive amplifying/dissipating environment

Energy Technology Data Exchange (ETDEWEB)

Dodonov, V.V., E-mail: vdodonov@fis.unb.br [Instituto de Física, Universidade de Brasília, Caixa Postal 04455, 70919-970 Brasília, DF (Brazil); Valverde, C. [Unidade de Ciências Exatas e Tecnológicas, Universidade Estadual de Goiás, BR 153, km 98, 75001-970 Anápolis, GO (Brazil); Universidade Paulista, BR 153, km 7, 74845-090 Goiânia, GO (Brazil); Souza, L.S. [Unidade de Ciências Exatas e Tecnológicas, Universidade Estadual de Goiás, BR 153, km 98, 75001-970 Anápolis, GO (Brazil); Baseia, B. [Instituto de Física, Universidade Federal de Goiás, 74.690-900 Goiânia, GO (Brazil); Departamento de Física, Universidade Federal da Paraíba, 58.051-970 João Pessoa, PB (Brazil)

2016-08-15

We study the evolution of odd compass states (specific superpositions of four coherent states), governed by the standard master equation with phase-sensitive amplifying/attenuating terms, in the presence of a Hamiltonian describing a parametric degenerate linear amplifier. Explicit expressions for the time-dependent Wigner function are obtained. The time of disappearance of the so called “sub-Planck structures” is calculated using the negative value of the Wigner function at the origin of phase space. It is shown that this value rapidly decreases during a short “conventional interference degradation time” (CIDT), which is inversely proportional to the size of quantum superposition, provided the anti-Hermitian terms in the master equation are of the same order (or stronger) as the Hermitian ones (governing the parametric amplification). The CIDT is compared with the final positivization time (FPT), when the Wigner function becomes positive. It appears that the FPT does not depend on the size of superpositions, moreover, it can be much bigger in the amplifying media than in the attenuating ones. Paradoxically, strengthening the Hamiltonian part results in decreasing the CIDT, so that the CIDT almost does not depend on the size of superpositions in the asymptotical case of very weak reservoir coupling. We also analyze the evolution of the Mandel factor, showing that for some sets of parameters this factor remains significantly negative, even when the Wigner function becomes positive.

Wigner Ville Distribution in Signal Processing, using Scilab Environment

Directory of Open Access Journals (Sweden)

Petru Chioncel

2011-01-01

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

Adaption of optical Fresnel transform to optical Wigner transform

International Nuclear Information System (INIS)

Lv Cuihong; Fan Hongyi

2010-01-01

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

Rigorous solution to Bargmann-Wigner equation for integer spin

CERN Document Server

Huang Shi Zhong; Wu Ning; Zheng Zhi Peng

2002-01-01

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

Nodal Structure of the Electronic Wigner Function

DEFF Research Database (Denmark)

Schmider, Hartmut; Dahl, Jens Peder

1996-01-01

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

The Wigner distribution function applied to optical signals and systems

NARCIS (Netherlands)

Bastiaans, M.J.

1978-01-01

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

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

International Nuclear Information System (INIS)

Wang Jisuo; Meng Xiangguo

2008-01-01

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

Quantum harmonic Brownian motion in a general environment: A modified phase-space approach

International Nuclear Information System (INIS)

Yeh, L.

1993-01-01

After extensive investigations over three decades, the linear-coupling model and its equivalents have become the standard microscopic models for quantum harmonic Brownian motion, in which a harmonically bound Brownian particle is coupled to a quantum dissipative heat bath of general type modeled by infinitely many harmonic oscillators. The dynamics of these models have been studied by many authors using the quantum Langevin equation, the path-integral approach, quasi-probability distribution functions (e.g., the Wigner function), etc. However, the quantum Langevin equation is only applicable to some special problems, while other approaches all involve complicated calculations due to the inevitable reduction (i.e., contraction) operation for ignoring/eliminating the degrees of freedom of the heat bath. In this dissertation, the author proposes an improved methodology via a modified phase-space approach which employs the characteristic function (the symplectic Fourier transform of the Wigner function) as the representative of the density operator. This representative is claimed to be the most natural one for performing the reduction, not only because of its simplicity but also because of its manifestation of geometric meaning. Accordingly, it is particularly convenient for studying the time evolution of the Brownian particle with an arbitrary initial state. The power of this characteristic function is illuminated through a detailed study of several physically interesting problems, including the environment-induced damping of quantum interference, the exact quantum Fokker-Planck equations, and the relaxation of non-factorizable initial states. All derivations and calculations axe shown to be much simplified in comparison with other approaches. In addition to dynamical problems, a novel derivation of the fluctuation-dissipation theorem which is valid for all quantum linear systems is presented

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.

Measurement of complete and continuous Wigner functions for discrete atomic systems

Science.gov (United States)

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

2018-01-01

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

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.

Positive Wigner functions render classical simulation of quantum computation efficient.

Science.gov (United States)

Mari, A; Eisert, J

2012-12-07

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

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.

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

Directory of Open Access Journals (Sweden)

Anamarija L. Mrgole

2017-02-01

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

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

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.

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.

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.

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 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

Synthesizing lattice structures in phase space

International Nuclear Information System (INIS)

Guo, Lingzhen; Marthaler, Michael

2016-01-01

In one dimensional systems, it is possible to create periodic structures in phase space through driving, which is called phase space crystals (Guo et al 2013 Phys. Rev. Lett. 111 205303). This is possible even if for particles trapped in a potential without periodicity. In this paper we discuss ultracold atoms in a driven optical lattice, which is a realization of such a phase space crystals. The corresponding lattice structure in phase space is complex and contains rich physics. A phase space lattice differs fundamentally from a lattice in real space, because its coordinate system, i.e., phase space, has a noncommutative geometry, which naturally provides an artificial gauge (magnetic) field. We study the behavior of the quasienergy band structure and investigate the dissipative dynamics. Synthesizing lattice structures in phase space provides a new platform to simulate the condensed matter phenomena and study the intriguing phenomena of driven systems far away from equilibrium. (paper)

Wigner function and the probability representation of quantum states

Directory of Open Access Journals (Sweden)

Man’ko Margarita A.

2014-01-01

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

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

International Nuclear Information System (INIS)

Levanda, M.; Fleurov, V.

2001-01-01

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

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.

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

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.

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.

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

NARCIS (Netherlands)

Bastiaans, M.J.

1979-01-01

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

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

Science.gov (United States)

Siyouri, Fatima-Zahra

2017-12-01

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

Interpretation of the Wigner transform

International Nuclear Information System (INIS)

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

1990-01-01

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

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).

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

International Nuclear Information System (INIS)

Jiang, Haiyan; Lu, Tiao; Cai, Wei

2014-01-01

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

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

CERN Document Server

Slutskin, A A; Pepper, M

2002-01-01

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

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

International Nuclear Information System (INIS)

Bizarro, João P S

2013-01-01

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

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.

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

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

The Wigner semi-circle law in quantum electro dynamics

International Nuclear Information System (INIS)

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

1996-01-01

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

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

International Nuclear Information System (INIS)

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

1986-01-01

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

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.)

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

Stochastic Nuclear Reaction Theory: Breit-Wigner nuclear noise

International Nuclear Information System (INIS)

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

1988-01-01

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

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

Science.gov (United States)

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

2017-11-01

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

Diagrammatic methods in phase-space regularization

International Nuclear Information System (INIS)

Bern, Z.; Halpern, M.B.; California Univ., Berkeley

1987-11-01

Using the scalar prototype and gauge theory as the simplest possible examples, diagrammatic methods are developed for the recently proposed phase-space form of continuum regularization. A number of one-loop and all-order applications are given, including general diagrammatic discussions of the nogrowth theorem and the uniqueness of the phase-space stochastic calculus. The approach also generates an alternate derivation of the equivalence of the large-β phase-space regularization to the more conventional coordinate-space regularization. (orig.)

Nearest neighbor spacing distributions of low-lying levels of vibrational nuclei

International Nuclear Information System (INIS)

Abul-Magd, A.Y.; Simbel, M.H.

1996-01-01

Energy-level statistics are considered for nuclei whose Hamiltonian is divided into intrinsic and collective-vibrational terms. The levels are described as a random superposition of independent sequences, each corresponding to a given number of phonons. The intrinsic motion is assumed chaotic. The level spacing distribution is found to be intermediate between the Wigner and Poisson distributions and similar in form to the spacing distribution of a system with classical phase space divided into separate regular and chaotic domains. We have obtained approximate expressions for the nearest neighbor spacing and cumulative spacing distribution valid when the level density is described by a constant-temperature formula and not involving additional free parameters. These expressions have been able to achieve good agreement with the experimental spacing distributions. copyright 1996 The American Physical Society

Schrödinger like equation for wavelets

Directory of Open Access Journals (Sweden)

A. Zúñiga-Segundo

2016-01-01

Full Text Available An explicit phase space representation of the wave function is build based on a wavelet transformation. The wavelet transformation allows us to understand the relationship between s − ordered Wigner function, (or Wigner function when s = 0, and the Torres-Vega-Frederick’s wave functions. This relationship is necessary to find a general solution of the Schrödinger equation in phase-space.

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.

Phase-space networks of geometrically frustrated systems.

Science.gov (United States)

Han, Yilong

2009-11-01

We illustrate a network approach to the phase-space study by using two geometrical frustration models: antiferromagnet on triangular lattice and square ice. Their highly degenerated ground states are mapped as discrete networks such that the quantitative network analysis can be applied to phase-space studies. The resulting phase spaces share some comon features and establish a class of complex networks with unique Gaussian spectral densities. Although phase-space networks are heterogeneously connected, the systems are still ergodic due to the random Poisson processes. This network approach can be generalized to phase spaces of some other complex systems.

Scattering of wave packets with phases

Energy Technology Data Exchange (ETDEWEB)

Karlovets, Dmitry V. [Department of Physics, Tomsk State University, Lenina Ave. 36, 634050 Tomsk (Russian Federation)

2017-03-09

A general problem of 2→N{sub f} scattering is addressed with all the states being wave packets with arbitrary phases. Depending on these phases, one deals with coherent states in (3+1) D, vortex particles with orbital angular momentum, the Airy beams, and their generalizations. A method is developed in which a number of events represents a functional of the Wigner functions of such states. Using width of a packet σ{sub p}/〈p〉 as a small parameter, the Wigner functions, the number of events, and a cross section are represented as power series in this parameter, the first non-vanishing corrections to their plane-wave expressions are derived, and generalizations for beams are made. Although in this regime the Wigner functions turn out to be everywhere positive, the cross section develops new specifically quantum features, inaccessible in the plane-wave approximation. Among them is dependence on an impact parameter between the beams, on phases of the incoming states, and on a phase of the scattering amplitude. A model-independent analysis of these effects is made. Two ways of measuring how a Coulomb phase and a hadronic one change with a transferred momentum t are discussed.

Klein-Gordon oscillators in noncommutative phase space

International Nuclear Information System (INIS)

Wang Jianhua

2008-01-01

We study the Klein-Gordon oscillators in non-commutative (NC) phase space. We find that the Klein-Gordon oscillators in NC space and NC phase-space have a similar behaviour to the dynamics of a particle in commutative space moving in a uniform magnetic field. By solving the Klein-Gordon equation in NC phase space, we obtain the energy levels of the Klein-Gordon oscillators, where the additional terms related to the space-space and momentum-momentum non-commutativity are given explicitly. (authors)

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

International Nuclear Information System (INIS)

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

2002-01-01

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

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

Science.gov (United States)

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

2013-01-01

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

Phase Space Exchange in Thick Wedge Absorbers

Energy Technology Data Exchange (ETDEWEB)

Neuffer, David [Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)

2017-01-01

The problem of phase space exchange in wedge absorbers with ionization cooling is discussed. The wedge absorber exchanges transverse and longitudinal phase space by introducing a position-dependent energy loss. In this paper we note that the wedges used with ionization cooling are relatively thick, so that single wedges cause relatively large changes in beam phase space. Calculation methods adapted to such “thick wedge” cases are presented, and beam phase-space transformations through such wedges are discussed.

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

Science.gov (United States)

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

1993-01-01

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

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

Science.gov (United States)

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

2014-10-01

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

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

International Nuclear Information System (INIS)

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

2013-10-01

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

Classicalization times of parametrically amplified 'Schroedinger cat' states coupled to phase-sensitive reservoirs

International Nuclear Information System (INIS)

Dodonov, V.V.; Valverde, C.; Souza, L.S.; Baseia, B.

2011-01-01

The exact Wigner function of a parametrically excited quantum oscillator in a phase-sensitive amplifying/attenuating reservoir is found for initial even/odd coherent states. Studying the evolution of negativity of the Wigner function we show the difference between the 'initial positivization time' (IPT), which is inversely proportional to the square of the initial size of the superposition, and the 'final positivization time' (FPT), which does not depend on this size. Both these times can be made arbitrarily long in maximally squeezed high-temperature reservoirs. Besides, we find the conditions when some (small) squeezing can exist even after the Wigner function becomes totally positive. -- Highlights: → We study parametric excitation of a quantum oscillator in phase-sensitive baths. → Exact time-dependent Wigner function for initial even/odd coherent states is found. → The evolution of negativity of Wigner function is compared with the squeezing dynamics. → The difference between initial and final 'classicalization times' is emphasized. → Both these times can be arbitrarily long for rigged reservoirs at infinite temperature.

Impenetrable Barriers in Phase-Space

International Nuclear Information System (INIS)

Wiggins, S.; Wiesenfeld, L.; Jaffe, C.; Uzer, T.

2001-01-01

Dynamical systems theory is used to construct a general phase-space version of transition state theory. Special multidimensional separatrices are found which act as impenetrable barriers in phase-space between reacting and nonreacting trajectories. The elusive momentum-dependent transition state between reactants and products is thereby characterized. A practical algorithm is presented and applied to a strongly coupled Hamiltonian

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.

Equivalence between contextuality and negativity of the Wigner function for qudits

Science.gov (United States)

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

2017-12-01

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

Entanglement versus negative domains of Wigner functions

DEFF Research Database (Denmark)

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

2006-01-01

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

Phase space diffusion in turbulent plasmas

International Nuclear Information System (INIS)

Pecseli, H.L.

1990-01-01

Turbulent diffusion of charged test particles in electrostatic plasma turbulence is reviewed. Two different types of test particles can be distinguished. First passice particles which are subject to the fluctuating electric fields without themselves contributing to the local space charge. The second type are particles introduced at a prescribed phase space position at a certain time and which then self-consistently participate in the phase space dynamics of the turbulent. The latter ''active'' type of particles can be subjected to an effective frictional force due to radiation of plasma waves. In terms of these test particle types, two basically different problems can be formulated. One deals with the diffusion of a particle with respect to its point of release in phase space. Alternatively the relative diffusion between many, or just two, particles can be analyzed. Analytical expressions for the mean square particle displacements in phase space are discussed. More generally equations for the full probability densities are derived and these are solved analytically in special limits. (orig.)

Noncommutative phase spaces on Aristotle group

Directory of Open Access Journals (Sweden)

Ancille Ngendakumana

2012-03-01

Full Text Available We realize noncommutative phase spaces as coadjoint orbits of extensions of the Aristotle group in a two dimensional space. Through these constructions the momenta of the phase spaces do not commute due to the presence of a naturally introduced magnetic eld. These cases correspond to the minimal coupling of the momentum with a magnetic potential.

Quantum to classical transition in the Hořava-Lifshitz quantum cosmology

Science.gov (United States)

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

2018-02-01

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

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)

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

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.

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.

Phase-space topography characterization of nonlinear ultrasound waveforms.

Science.gov (United States)

Dehghan-Niri, Ehsan; Al-Beer, Helem

2018-03-01

Fundamental understanding of ultrasound interaction with material discontinuities having closed interfaces has many engineering applications such as nondestructive evaluation of defects like kissing bonds and cracks in critical structural and mechanical components. In this paper, to analyze the acoustic field nonlinearities due to defects with closed interfaces, the use of a common technique in nonlinear physics, based on a phase-space topography construction of ultrasound waveform, is proposed. The central idea is to complement the "time" and "frequency" domain analyses with the "phase-space" domain analysis of nonlinear ultrasound waveforms. A nonlinear time series method known as pseudo phase-space topography construction is used to construct equivalent phase-space portrait of measured ultrasound waveforms. Several nonlinear models are considered to numerically simulate nonlinear ultrasound waveforms. The phase-space response of the simulated waveforms is shown to provide different topographic information, while the frequency domain shows similar spectral behavior. Thus, model classification can be substantially enhanced in the phase-space domain. Experimental results on high strength aluminum samples show that the phase-space transformation provides a unique detection and classification capabilities. The Poincaré map of the phase-space domain is also used to better understand the nonlinear behavior of ultrasound waveforms. It is shown that the analysis of ultrasound nonlinearities is more convenient and informative in the phase-space domain than in the frequency domain. Copyright © 2017 Elsevier B.V. All rights reserved.

Phase space diffusion in turbulent plasmas

DEFF Research Database (Denmark)

Pécseli, Hans

1990-01-01

. The second type are particles introduced at a prescribed phase space position at a certain time and which then self-consistently participate in the phase space dynamics of the turbulence. The latter "active" type of particles can be subject to an effective frictional force due to radiation of plasma waves....... In terms of these test particle types, two basically different problems can be formulated. One deals with the diffusion of a particle with respect to its point of release in phase space. Alternatively the relative diffusion between many, or just two, particles can be analyzed. Analytical expressions...

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

Science.gov (United States)

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

2014-02-28

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

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

Energy Technology Data Exchange (ETDEWEB)

Ryabinkin, Ilya G.; Izmaylov, Artur F. [Department of Physical and Environmental Sciences, University of Toronto Scarborough, Toronto, Ontario M1C 1A4 (Canada); Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6 (Canada); Hsieh, Chang-Yu; Kapral, Raymond [Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6 (Canada)

2014-02-28

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

Phase space structure of generalized Gaussian cat states

International Nuclear Information System (INIS)

Nicacio, Fernando; Maia, Raphael N.P.; Toscano, Fabricio; Vallejos, Raul O.

2010-01-01

We analyze generalized Gaussian cat states obtained by superposing arbitrary Gaussian states. The structure of the interference term of the Wigner function is always hyperbolic, surviving the action of a thermal reservoir. We also consider certain superpositions of mixed Gaussian states. An application to semiclassical dynamics is discussed.

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

Science.gov (United States)

de Gosson, Maurice A; de Gosson, Serge M

2012-01-09

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

Wigner 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

Longitudinal Phase Space Tomography with Space Charge

CERN Document Server

Hancock, S; Lindroos, M

2000-01-01

Tomography is now a very broad topic with a wealth of algorithms for the reconstruction of both qualitative and quantitative images. In an extension in the domain of particle accelerators, one of the simplest algorithms has been modified to take into account the non-linearity of large-amplitude synchrotron motion. This permits the accurate reconstruction of longitudinal phase space density from one-dimensional bunch profile data. The method is a hybrid one which incorporates particle tracking. Hitherto, a very simple tracking algorithm has been employed because only a brief span of measured profile data is required to build a snapshot of phase space. This is one of the strengths of the method, as tracking for relatively few turns relaxes the precision to which input machine parameters need to be known. The recent addition of longitudinal space charge considerations as an optional refinement of the code is described. Simplicity suggested an approach based on the derivative of bunch shape with the properties of...

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

Modeling beams with elements in phase space

International Nuclear Information System (INIS)

Nelson, E.M.

1998-01-01

Conventional particle codes represent beams as a collection of macroparticles. An alternative is to represent the beam as a collection of current carrying elements in phase space. While such a representation has limitations, it may be less noisy than a macroparticle model, and it may provide insights about the transport of space charge dominated beams which would otherwise be difficult to gain from macroparticle simulations. The phase space element model of a beam is described, and progress toward an implementation and difficulties with this implementation are discussed. A simulation of an axisymmetric beam using 1d elements in phase space is demonstrated

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

Science.gov (United States)

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

2009-07-14

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

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

Science.gov (United States)

Carré, Frank

2014-09-01

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

The Phase-Space Transformer Instrument (PASTIS) and the Phase-Space Transformation on Ultra-Cold Neutrons

International Nuclear Information System (INIS)

Henggeler, W.; Boehm, M.

2003-11-01

Both reports - part I by Wolfgang Henggeler and part II by Martin Boehm - serve as a comprehensive basis for the realisation of a PST (phase-space transformation) instrument coupled either to cold or ultra-cold neutrons, respectively. This publication accidentally coincides with the 200 th birthday of the Austrian physicist C.A. Doppler who discovered the principle (i.e., the effect denoted later by his name) giving rise to the phase-space transformation described in the present work. (author)

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...

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)

Phase space approach to quantum dynamics

International Nuclear Information System (INIS)

Leboeuf, P.

1991-03-01

The Schroedinger equation for the time propagation of states of a quantised two-dimensional spherical phase space is replaced by the dynamics of a system of N particles lying in phase space. This is done through factorization formulae of analytic function theory arising in coherent-state representation, the 'particles' being the zeros of the quantum state. For linear Hamiltonians, like a spin in a uniform magnetic field, the motion of the particles is classical. However, non-linear terms induce interactions between the particles. Their time propagation is studied and it is shown that, contrary to integrable systems, for chaotic maps they tend to fill, as their classical counterpart, the whole phase space. (author) 13 refs., 3 figs

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.

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

Science.gov (United States)

Tanaka, Takashi

2017-04-15

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

Entanglement and Wigner Function Negativity of Multimode Non-Gaussian States

Science.gov (United States)

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

2017-11-01

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

Experimental Observations of Ion Phase-Space Vortices

DEFF Research Database (Denmark)

Pécseli, Hans; Armstrong, R. J.; Trulsen, J.

1981-01-01

Experimental observations of ion phase-space vortices are reported. The ion phase-space vortices form in the region of heated ions behind electrostatic ion acoustic shocks. The results are in qualitative agreement with numerical and analytic studies....

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...

Incomplete information and fractal phase space

International Nuclear Information System (INIS)

Wang, Qiuping A.

2004-01-01

The incomplete statistics for complex systems is characterized by a so called incompleteness parameter ω which equals unity when information is completely accessible to our treatment. This paper is devoted to the discussion of the incompleteness of accessible information and of the physical signification of ω on the basis of fractal phase space. ω is shown to be proportional to the fractal dimension of the phase space and can be linked to the phase volume expansion and information growth during the scale refining process

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

Czech Academy of Sciences Publication Activity Database

Pittner, Jiří

2003-01-01

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

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.

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

RADON reconstruction in longitudinal phase space

International Nuclear Information System (INIS)

Mane, V.; Peggs, S.; Wei, J.

1997-01-01

Longitudinal particle motion in circular accelerators is typically monitoring by one dimensional (1-D) profiles. Adiabatic particle motion in two dimensional (2-D) phase space can be reconstructed with tomographic techniques, using 1-D profiles. A computer program RADON has been developed in C++ to process digitized mountain range data and perform the phase space reconstruction for the AGS, and later for Relativistic Heavy Ion Collider (RHIC)

Noncommutative Phase Spaces by Coadjoint Orbits Method

Directory of Open Access Journals (Sweden)

Ancille Ngendakumana

2011-12-01

Full Text Available We introduce noncommutative phase spaces by minimal couplings (usual one, dual one and their mixing. We then realize some of them as coadjoint orbits of the anisotropic Newton-Hooke groups in two- and three-dimensional spaces. Through these constructions the positions and the momenta of the phase spaces do not commute due to the presence of a magnetic field and a dual magnetic field.

Quantum magnification of classical sub-Planck phase space features

International Nuclear Information System (INIS)

Hensinger, W.K.; Heckenberg, N.; Rubinsztein-Dunlop, H.; Delande, D.

2002-01-01

Full text: To understand the relationship between quantum mechanics and classical physics a crucial question to be answered is how distinct classical dynamical phase space features translate into the quantum picture. This problem becomes even more interesting if these phase space features occupy a much smaller volume than ℎ in a phase space spanned by two non-commuting variables such as position and momentum. The question whether phase space structures in quantum mechanics associated with sub-Planck scales have physical signatures has recently evoked a lot of discussion. Here we will show that sub-Planck classical dynamical phase space structures, for example regions of regular motion, can give rise to states whose phase space representation is of size ℎ or larger. This is illustrated using period-1 regions of regular motion (modes of oscillatory motion of a particle in a modulated well) whose volume is distinctly smaller than Planck's constant. They are magnified in the quantum picture and appear as states whose phase space representation is of size h or larger. Cold atoms provide an ideal test bed to probe such fundamental aspects of quantum and classical dynamics. In the experiment a Bose-Einstein condensate is loaded into a far detuned optical lattice. The lattice depth is modulated resulting in the emergence of regions of regular motion surrounded by chaotic motion in the phase space spanned by position and momentum of the atoms along the standing wave. Sub-Planck scaled phase space features in the classical phase space are magnified and appear as distinct broad peaks in the atomic momentum distribution. The corresponding quantum analysis shows states of size Ti which can be associated with much smaller classical dynamical phase space features. This effect may considered as the dynamical equivalent of the Goldstone and Jaffe theorem which predicts the existence of at least one bound state at a bend in a two or three dimensional spatial potential

Positivity properties of phase-plane distribution functions

NARCIS (Netherlands)

Janssen, A.J.E.M.

1984-01-01

The aim of this paper is to compare the members of Cohen's class of phase-plane distributions with respect to positivity properties. It is known that certain averages (which are in a sense compatible with Heisenberg's uncertainty principle) of the Wigner distribution over the phase-plane yield

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2011-01-01

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

Functional Wigner representation of quantum dynamics of Bose-Einstein condensate

Energy Technology Data Exchange (ETDEWEB)

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

2013-04-15

We develop a method of simulating the full quantum field dynamics of multi-mode multi-component Bose-Einstein condensates in a trap. We use the truncated Wigner representation to obtain a probabilistic theory that can be sampled. This method produces c-number stochastic equations which may be solved using conventional stochastic methods. The technique is valid for large mode occupation numbers. We give a detailed derivation of methods of functional Wigner representation appropriate for quantum fields. Our approach describes spatial evolution of spinor components and properly accounts for nonlinear losses. Such techniques are applicable to calculating the leading quantum corrections, including effects such as quantum squeezing, entanglement, EPR correlations, and interactions with engineered nonlinear reservoirs. By using a consistent expansion in the inverse density, we are able to explain an inconsistency in the nonlinear loss equations found by earlier authors.

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

Energy Technology Data Exchange (ETDEWEB)

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

2006-12-28

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

Classical mechanics in non-commutative phase space

International Nuclear Information System (INIS)

Wei Gaofeng; Long Chaoyun; Long Zhengwen; Qin Shuijie

2008-01-01

In this paper the laws of motion of classical particles have been investigated in a non-commutative phase space. The corresponding non-commutative relations contain not only spatial non-commutativity but also momentum non-commutativity. First, new Poisson brackets have been defined in non-commutative phase space. They contain corrections due to the non-commutativity of coordinates and momenta. On the basis of this new Poisson brackets, a new modified second law of Newton has been obtained. For two cases, the free particle and the harmonic oscillator, the equations of motion are derived on basis of the modified second law of Newton and the linear transformation (Phys. Rev. D, 2005, 72: 025010). The consistency between both methods is demonstrated. It is shown that a free particle in commutative space is not a free particle with zero-acceleration in the non-commutative phase space, but it remains a free particle with zero-acceleration in non-commutative space if only the coordinates are non-commutative. (authors)

Sympathetic Wigner-function tomography of a dark trapped ion

DEFF Research Database (Denmark)

Mirkhalaf, Safoura; Mølmer, Klaus

2012-01-01

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

Ray tracing the Wigner distribution function for optical simulations

NARCIS (Netherlands)

Mout, B.M.; Wick, Michael; Bociort, F.; Petschulat, Joerg; Urbach, Paul

2018-01-01

We study a simulation method that uses the Wigner distribution function to incorporate wave optical effects in an established framework based on geometrical optics, i.e., a ray tracing engine. We use the method to calculate point spread functions and show that it is accurate for paraxial systems

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

Science.gov (United States)

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

2018-06-01

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

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

KAUST Repository

Chen, Jyun-Hong

2018-03-12

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

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)

Nonlinear transport of dynamic system phase space

International Nuclear Information System (INIS)

Xie Xi; Xia Jiawen

1993-01-01

The inverse transform of any order solution of the differential equation of general nonlinear dynamic systems is derived, realizing theoretically the nonlinear transport for the phase space of nonlinear dynamic systems. The result is applicable to general nonlinear dynamic systems, with the transport of accelerator beam phase space as a typical example

Real-space Berry phases: Skyrmion soccer (invited)

Science.gov (United States)

Everschor-Sitte, Karin; Sitte, Matthias

2014-05-01

Berry phases occur when a system adiabatically evolves along a closed curve in parameter space. This tutorial-like article focuses on Berry phases accumulated in real space. In particular, we consider the situation where an electron traverses a smooth magnetic structure, while its magnetic moment adjusts to the local magnetization direction. Mapping the adiabatic physics to an effective problem in terms of emergent fields reveals that certain magnetic textures, skyrmions, are tailormade to study these Berry phase effects.

Real-space Berry phases: Skyrmion soccer (invited)

Energy Technology Data Exchange (ETDEWEB)

Everschor-Sitte, Karin, E-mail: karin@physics.utexas.edu; Sitte, Matthias [The University of Texas at Austin, Department of Physics, 2515 Speedway, Austin, Texas 78712 (United States)

2014-05-07

Berry phases occur when a system adiabatically evolves along a closed curve in parameter space. This tutorial-like article focuses on Berry phases accumulated in real space. In particular, we consider the situation where an electron traverses a smooth magnetic structure, while its magnetic moment adjusts to the local magnetization direction. Mapping the adiabatic physics to an effective problem in terms of emergent fields reveals that certain magnetic textures, skyrmions, are tailormade to study these Berry phase effects.

Real-space Berry phases: Skyrmion soccer (invited)

International Nuclear Information System (INIS)

Everschor-Sitte, Karin; Sitte, Matthias

2014-01-01

Berry phases occur when a system adiabatically evolves along a closed curve in parameter space. This tutorial-like article focuses on Berry phases accumulated in real space. In particular, we consider the situation where an electron traverses a smooth magnetic structure, while its magnetic moment adjusts to the local magnetization direction. Mapping the adiabatic physics to an effective problem in terms of emergent fields reveals that certain magnetic textures, skyrmions, are tailormade to study these Berry phase effects

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

Study on a phase space representation of quantum theory

International Nuclear Information System (INIS)

Ranaivoson, R.T.R; Raoelina Andriambololona; Hanitriarivo, R.; Raboanary, R.

2013-01-01

A study on a method for the establishment of a phase space representation of quantum theory is presented. The approach utilizes the properties of Gaussian distribution, the properties of Hermite polynomials, Fourier analysis and the current formulation of quantum mechanics which is based on the use of Hilbert space and linear operators theory. Phase space representation of quantum states and wave functions in phase space are introduced using properties of a set of functions called harmonic Gaussian functions. Then, new operators called dispersion operators are defined and identified as the operators which admit as eigenstates the basis states of the phase space representation. Generalization of the approach for multidimensional cases is shown. Examples of applications are given.

Miniature Active Space Radiation Dosimeter, Phase II

Data.gov (United States)

National Aeronautics and Space Administration — Space Micro will extend our Phase I R&D to develop a family of miniature, active space radiation dosimeters/particle counters, with a focus on biological/manned...

From stochastic phase-space evolution to brownian motion in collective space

Energy Technology Data Exchange (ETDEWEB)

Benhassine, B. (Lab. de Physique Nucleaire/ CNRS et Univ. de Nantes, 44 Nantes (France)); Farine, M. (Lab. de Physique Nucleaire/ CNRS et Univ. de Nantes, 44 Nantes (France) Ecole Navale, Lamveoc-Loulmic, 29 Brest-Naval (France)); Hernandez, E.S. (Dept. de Fisica - Facultad de Ciencias Exactas y Naturales, Univ. de Buenos Aires (Argentina)); Idier, D. (Lab. de Physique Nucleaire/ CNRS et Univ. de Nantes, 44 Nantes (France)); Remaud, B. (Lab. de Physique Nucleaire/ CNRS et Univ. de Nantes, 44 Nantes (France)); Sebille, F. (Lab. de Physique Nucleaire/ CNRS et Univ. de Nantes, 44 Nantes (France))

1994-01-24

Within the framework of stochastic transport equations in phase space, we study the dynamics of fluctuations on collective variables in homogeneous fermion systems. The transport coefficients are formally deduced in the relaxation-time approximation and a general method to compute dynamically the dispersions of collective observables is proposed as a set of coupled equations: respectively, the BUU/Landau-Vlasov equation for the average phase-space trajectories and the equations for the averages and dispersions of the observables. Independently, we derive the general covariance matrix of phase-space fluctuations and then by projection, the dispersion on collective variables at equilibrium. Detailed numerical applications of the formalism are given; they show that the dynamics of fluctuations can be extracted from noisy numerical simulations and that the leading parameter for collective fluctuations is the excitation energy, whatever is its degree of thermalization. (orig.)

From stochastic phase-space evolution to brownian motion in collective space

International Nuclear Information System (INIS)

Benhassine, B.; Farine, M.; Hernandez, E.S.; Idier, D.; Remaud, B.; Sebille, F.

1994-01-01

Within the framework of stochastic transport equations in phase space, we study the dynamics of fluctuations on collective variables in homogeneous fermion systems. The transport coefficients are formally deduced in the relaxation-time approximation and a general method to compute dynamically the dispersions of collective observables is proposed as a set of coupled equations: respectively, the BUU/Landau-Vlasov equation for the average phase-space trajectories and the equations for the averages and dispersions of the observables. Independently, we derive the general covariance matrix of phase-space fluctuations and then by projection, the dispersion on collective variables at equilibrium. Detailed numerical applications of the formalism are given; they show that the dynamics of fluctuations can be extracted from noisy numerical simulations and that the leading parameter for collective fluctuations is the excitation energy, whatever is its degree of thermalization. (orig.)

Phase space descriptions for simplicial 4D geometries

International Nuclear Information System (INIS)

Dittrich, Bianca; Ryan, James P

2011-01-01

Starting from the canonical phase space for discretized (4D) BF theory, we implement a canonical version of the simplicity constraints and construct phase spaces for simplicial geometries. Our construction allows us to study the connection between different versions of Regge calculus and approaches using connection variables, such as loop quantum gravity. We find that on a fixed triangulation the (gauge invariant) phase space associated with loop quantum gravity is genuinely larger than the one for length and even area Regge calculus. Rather, it corresponds to the phase space of area-angle Regge calculus, as defined in [1] (prior to the imposition of gluing constraints, which ensure the metricity of the triangulation). Finally, we show that for a subclass of triangulations one can construct first-class Hamiltonian and diffeomorphism constraints leading to flat 4D spacetimes.

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.

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.

Discrete Wigner function and quantum-state tomography

Science.gov (United States)

Leonhardt, Ulf

1996-05-01

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

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

International Nuclear Information System (INIS)

Bonzom, Valentin; Fleury, Pierre

2012-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2015-12-15

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

Phase space density representations in fluid dynamics

International Nuclear Information System (INIS)

Ramshaw, J.D.

1989-01-01

Phase space density representations of inviscid fluid dynamics were recently discussed by Abarbanel and Rouhi. Here it is shown that such representations may be simply derived and interpreted by means of the Liouville equation corresponding to the dynamical system of ordinary differential equations that describes fluid particle trajectories. The Hamiltonian and Poisson bracket for the phase space density then emerge as immediate consequences of the corresponding structure of the dynamics. For barotropic fluids, this approach leads by direct construction to the formulation presented by Abarbanel and Rouhi. Extensions of this formulation to inhomogeneous incompressible fluids and to fluids in which the state equation involves an additional transported scalar variable are constructed by augmenting the single-particle dynamics and phase space to include the relevant additional variable

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.

Beam phase space and emittance

International Nuclear Information System (INIS)

Buon, J.

1990-12-01

The classical and elementary results for canonical phase space, the Liouville theorem and the beam emittance are reviewed. Then, the importance of phase portraits to obtain a geometrical description of motion is emphasized, with examples in accelerator physics. Finally, a statistical point of view is used to define beam emittance, to study its law of approximate conservation and to treat two particular examples

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)

Grassmann phase space theory for fermions

Energy Technology Data Exchange (ETDEWEB)

Dalton, Bryan J. [Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne, Victoria, 3122 (Australia); Jeffers, John [Department of Physics, University of Strathclyde, Glasgow, G4 ONG (United Kingdom); Barnett, Stephen M. [School of Physics and Astronomy, University of Glasgow, Glasgow, G12 8QQ (United Kingdom)

2017-06-15

A phase space theory for fermions has been developed using Grassmann phase space variables which can be used in numerical calculations for cold Fermi gases and for large fermion numbers. Numerical calculations are feasible because Grassmann stochastic variables at later times are related linearly to such variables at earlier times via c-number stochastic quantities. A Grassmann field version has been developed making large fermion number applications possible. Applications are shown for few mode and field theory cases. (copyright 2016 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)

The Quantum Space Phase Transitions for Particles and Force Fields

Directory of Open Access Journals (Sweden)

Chung D.-Y.

2006-07-01

Full Text Available We introduce a phenomenological formalism in which the space structure is treated in terms of attachment space and detachment space. Attachment space attaches to an object, while detachment space detaches from the object. The combination of these spaces results in three quantum space phases: binary partition space, miscible space and binary lattice space. Binary lattice space consists of repetitive units of alternative attachment space and detachment space. In miscible space, attachment space is miscible to detachment space, and there is no separation between attachment space and detachment spaces. In binary partition space, detachment space and attachment space are in two separat continuous regions. The transition from wavefunction to the collapse of wavefuction under interference becomes the quantum space phase transition from binary lattice space to miscible space. At extremely conditions, the gauge boson force field undergoes a quantum space phase transition to a "hedge boson force field", consisting of a "vacuum" core surrounded by a hedge boson shell, like a bubble with boundary.

Exact phase boundaries and topological phase transitions of the X Y Z spin chain

Science.gov (United States)

Jafari, S. A.

2017-07-01

Within the block spin renormalization group, we give a very simple derivation of the exact phase boundaries of the X Y Z spin chain. First, we identify the Ising order along x ̂ or y ̂ as attractive renormalization group fixed points of the Kitaev chain. Then, in a global phase space composed of the anisotropy λ of the X Y interaction and the coupling Δ of the Δ σzσz interaction, we find that the above fixed points remain attractive in the two-dimesional parameter space. We therefore classify the gapped phases of the X Y Z spin chain as: (1) either attracted to the Ising limit of the Kitaev-chain, which in turn is characterized by winding number ±1 , depending on whether the Ising order parameter is along x ̂ or y ̂ directions; or (2) attracted to the charge density wave (CDW) phases of the underlying Jordan-Wigner fermions, which is characterized by zero winding number. We therefore establish that the exact phase boundaries of the X Y Z model in Baxter's solution indeed correspond to topological phase transitions. The topological nature of the phase transitions of the X Y Z model justifies why our analytical solution of the three-site problem that is at the core of the present renormalization group treatment is able to produce the exact phase boundaries of Baxter's solution. We argue that the distribution of the winding numbers between the three Ising phases is a matter of choice of the coordinate system, and therefore the CDW-Ising phase is entitled to host appropriate form of zero modes. We further observe that in the Kitaev-chain the renormalization group flow can be cast into a geometric progression of a properly identified parameter. We show that this new parameter is actually the size of the (Majorana) zero modes.

Q-boson interferometry and generalized Wigner function

International Nuclear Information System (INIS)

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

2004-01-01

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

Wigner distribution function and its application to first-order optics

NARCIS (Netherlands)

Bastiaans, M.J.

1979-01-01

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

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....

Source reconstruction using phase space beam summation technique

International Nuclear Information System (INIS)

Graubart, Gideon.

1990-10-01

In this work, the phase-space beam summation technique (PSBS), is applied to back propagation and inverse source problems. The PSBS expresses the field as a superposition of shifted and tilted beams. This phase space spectrum of beams is matched to the source distribution via an amplitude function which expresses the local spectrum of the source function in terms of a local Fourier transform. In this work, the emphasis is on the phase space processing of the data, on the information content of this data and on the back propagation scheme. More work is still required to combine this back propagation approach in a full, multi experiment inverse scattering scheme. It is shown that the phase space distribution of the data, computed via the local spectrum transform, is localized along lines that define the local arrival direction of the wave data. We explore how the choice of the beam width affects the compactification of this distribution, and derive criteria for choosing a window that optimizes this distribution. It should be emphasized that compact distribution implies fewer beams in the back propagation scheme and therefore higher numerical efficiency and better physical insight. Furthermore it is shown how the local information property of the phase space representation can be used to improve the performance of this simple back propagation problem, in particular with regard to axial resolution; the distance to the source can be determined by back propagating only the large angle phase space beams that focus on the source. The information concerning transverse distribution of the source, on the other hand, is contained in the axial phase space region and can therefore be determined by the corresponding back propagating beams. Because of the global nature of the plane waves propagators the conventional plane wave back propagation scheme does not have the same 'focusing' property, and therefore suffers from lack of information localization and axial resolution. The

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

Science.gov (United States)

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

2017-06-07

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

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

Science.gov (United States)

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

2017-06-01

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

Quantum mechanics and dynamics in phase space

International Nuclear Information System (INIS)

Zlatev, I.S.

1979-01-01

Attention is paid to formal similarity of quantum mechanics and classical statistical physics. It is supposed that quantum mechanics can be reformulated by means of the quasiprobabilistic distributions (QPD). The procedure of finding a possible dynamics of representative points in a phase space is described. This procedure would lead to an equation of the Liouville type for the given QPD. It is shown that there is always a dynamics for which the phase volume is preserved and there is another dynamics for which the equations of motion are ''canonical''. It follows from the paper that in terms of the QPD the quantum mechanics is analogous to the classical statistical mechanics and it can be interpreted as statistics of phase points, their motion obeying the canonical equations. The difference consists in the fact that in the classical statistical physics constructed is statistics of points in a phase space which depict real, existing, observable states of the system under consideration. In the quantum mechanics constructed is statistics of points in a phase space which correspond to the ''substrate'' of quantum-mechanical objects which have no any physical sense and cannot be observed separately

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

DEFF Research Database (Denmark)

Dahl, Jens Peder; Schleich, W. P.

2009-01-01

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

Eugene P. Wigner – in the light of unexpected events

Directory of Open Access Journals (Sweden)

Koblinger L.

2014-01-01

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

Overview of Phase Space Manipulations of Relativistic Electron Beams

Energy Technology Data Exchange (ETDEWEB)

Xiang, Dao; /SLAC

2012-08-31

Phase space manipulation is a process to rearrange beam's distribution in 6-D phase space. In this paper, we give an overview of the techniques for tailoring beam distribution in 2D, 4D, and 6D phase space to meet the requirements of various applications. These techniques become a new focus of accelerator physics R&D and very likely these advanced concepts will open up new opportunities in advanced accelerators and the science enabled by them.

Overview of Phase Space Manipulations of Relativistic Electron Beams

International Nuclear Information System (INIS)

Xiang, Dao

2012-01-01

Phase space manipulation is a process to rearrange beam's distribution in 6-D phase space. In this paper, we give an overview of the techniques for tailoring beam distribution in 2D, 4D, and 6D phase space to meet the requirements of various applications. These techniques become a new focus of accelerator physics R and D and very likely these advanced concepts will open up new opportunities in advanced accelerators and the science enabled by them.

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.

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

Phase space model for transmission of light beam

International Nuclear Information System (INIS)

Fu Shinian

1989-01-01

Based on Fermat's principle of ray optics, the Hamiltonian of an optical ray is derived by comparison with classical mechanics. A phase space model of light beam is proposed, assuming that the light beam, regarded as a group of rays, can be described by an ellipse in the μ-phase space. Therefore, the transmission of light beam is represented by the phase space matrix transformation. By means of this non-wave formulation, the same results are obtained as those from wave equation such as Kogelnik's ABCD law. As an example of the application on this model, the matching problem of optical cavity is solved

Intelligent Monte Carlo phase-space division and importance estimation

International Nuclear Information System (INIS)

Booth, T.E.

1989-01-01

Two years ago, a quasi-deterministic method (QD) for obtaining the Monte Carlo importance function was reported. Since then, a number of very complex problems have been solved with the aid of QD. Not only does QD estimate the importance far faster than the (weight window) generator currently in MCNP, QD requires almost no user intervention in contrast to the generator. However, both the generator and QD require the user to divide the phase-space into importance regions. That is, both methods will estimate the importance of a phase-space region, but the user must define the regions. In practice this is tedious and time consuming, and many users are not particularly good at defining sensible importance regions. To make full use of the fat that QD is capable of getting good importance estimates in tens of thousands of phase-space regions relatively easily, some automatic method for dividing the phase space will be useful and perhaps essential. This paper describes recent progress toward an automatic and intelligent phase-space divider

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

Relativistic implications of the quantum phase

International Nuclear Information System (INIS)

Low, Stephen G

2012-01-01

The quantum phase leads to projective representations of symmetry groups in quantum mechanics. The projective representations are equivalent to the unitary representations of the central extension of the group. A celebrated example is Wigner's formulation of special relativistic quantum mechanics as the projective representations of the inhomogeneous Lorentz group. However, Wigner's formulation makes no mention of the Weyl-Heisenberg group and the hermitian representation of its algebra that are the Heisenberg commutation relations fundamental to quantum physics. We put aside the relativistic symmetry and show that the maximal quantum symmetry that leaves the Heisenberg commutation relations invariant is the projective representations of the conformally scaled inhomogeneous symplectic group. The Weyl-Heisenberg group and noncommutative structure arises directly because the quantum phase requires projective representations. We then consider the relativistic implications of the quantum phase that lead to the Born line element and the projective representations of an inhomogeneous unitary group that defines a noninertial quantum theory. (Understanding noninertial quantum mechanics is a prelude to understanding quantum gravity.) The remarkable properties of this symmetry and its limits are studied.

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

Foundations of phase-space quantum mechanics

International Nuclear Information System (INIS)

Guz, W.

1984-01-01

In the present paper a general concept of a phase-space representation of the ordinary Hilbert-space quantum theory is formulated, and then, by using some elementary facts of functional analysis, several equivalent forms of that concept are analyzed. Several important physical examples are presented in Section 3 of the paper. (author)

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

Stochastic inflation: Quantum phase-space approach

International Nuclear Information System (INIS)

Habib, S.

1992-01-01

In this paper a quantum-mechanical phase-space picture is constructed for coarse-grained free quantum fields in an inflationary universe. The appropriate stochastic quantum Liouville equation is derived. Explicit solutions for the phase-space quantum distribution function are found for the cases of power-law and exponential expansions. The expectation values of dynamical variables with respect to these solutions are compared to the corresponding cutoff regularized field-theoretic results (we do not restrict ourselves only to left-angle Φ 2 right-angle). Fair agreement is found provided the coarse-graining scale is kept within certain limits. By focusing on the full phase-space distribution function rather than a reduced distribution it is shown that the thermodynamic interpretation of the stochastic formalism faces several difficulties (e.g., there is no fluctuation-dissipation theorem). The coarse graining does not guarantee an automatic classical limit as quantum correlations turn out to be crucial in order to get results consistent with standard quantum field theory. Therefore, the method does not by itself constitute an explanation of the quantum to classical transition in the early Universe. In particular, we argue that the stochastic equations do not lead to decoherence

Phase-space dynamics of Bianchi IX cosmological models

International Nuclear Information System (INIS)

Soares, I.D.

1985-01-01

The complex phase-space dynamical behaviour of a class of Biachi IX cosmological models is discussed, as the chaotic gravitational collapse due Poincare's homoclinic phenomena, and the n-furcation of periodic orbits and tori in the phase space of the models. Poincare maps which show this behaviour are constructed merically and applications are discussed. (Author) [pt

Kinetic theory in maximal-acceleration invariant phase space

International Nuclear Information System (INIS)

Brandt, H.E.

1989-01-01

A vanishing directional derivative of a scalar field along particle trajectories in maximal acceleration invariant phase space is identical in form to the ordinary covariant Vlasov equation in curved spacetime in the presence of both gravitational and nongravitational forces. A natural foundation is thereby provided for a covariant kinetic theory of particles in maximal-acceleration invariant phase space. (orig.)

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.

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

Resonance controlled transport in phase space

Science.gov (United States)

Leoncini, Xavier; Vasiliev, Alexei; Artemyev, Anton

2018-02-01

We consider the mechanism of controlling particle transport in phase space by means of resonances in an adiabatic setting. Using a model problem describing nonlinear wave-particle interaction, we show that captures into resonances can be used to control transport in momentum space as well as in physical space. We design the model system to provide creation of a narrow peak in the distribution function, thus producing effective cooling of a sub-ensemble of the particles.

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.

Coordinate, Momentum and Dispersion operators in Phase space representation

International Nuclear Information System (INIS)

Rakotoson, H.; Raoelina Andriambololona; Ranaivoson, R.T.R.; Raboanary, R.

2017-07-01

The aim of this paper is to present a study on the representations of coordinate, momentum and dispersion operators in the framework of a phase space representation of quantum mechanics that we have introduced and studied in previous works. We begin in the introduction section with a recall about the concept of representation of operators on wave function spaces. Then, we show that in the case of the phase space representation the coordinate and momentum operators can be represented either with differential operators or with matrices. The explicit expressions of both the differential operators and matrices representations are established. Multidimensional generalization of the obtained results are performed and phase space representation of dispersion operators are given.

Grassmann phase space theory and the Jaynes–Cummings model

International Nuclear Information System (INIS)

Dalton, B.J.; Garraway, B.M.; Jeffers, J.; Barnett, S.M.

2013-01-01

The Jaynes–Cummings model of a two-level atom in a single mode cavity is of fundamental importance both in quantum optics and in quantum physics generally, involving the interaction of two simple quantum systems—one fermionic system (the TLA), the other bosonic (the cavity mode). Depending on the initial conditions a variety of interesting effects occur, ranging from ongoing oscillations of the atomic population difference at the Rabi frequency when the atom is excited and the cavity is in an n-photon Fock state, to collapses and revivals of these oscillations starting with the atom unexcited and the cavity mode in a coherent state. The observation of revivals for Rydberg atoms in a high-Q microwave cavity is key experimental evidence for quantisation of the EM field. Theoretical treatments of the Jaynes–Cummings model based on expanding the state vector in terms of products of atomic and n-photon states and deriving coupled equations for the amplitudes are a well-known and simple method for determining the effects. In quantum optics however, the behaviour of the bosonic quantum EM field is often treated using phase space methods, where the bosonic mode annihilation and creation operators are represented by c-number phase space variables, with the density operator represented by a distribution function of these variables. Fokker–Planck equations for the distribution function are obtained, and either used directly to determine quantities of experimental interest or used to develop c-number Langevin equations for stochastic versions of the phase space variables from which experimental quantities are obtained as stochastic averages. Phase space methods have also been developed to include atomic systems, with the atomic spin operators being represented by c-number phase space variables, and distribution functions involving these variables and those for any bosonic modes being shown to satisfy Fokker–Planck equations from which c-number Langevin equations are

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.

An extensive phase space for the potential martian biosphere.

Science.gov (United States)

Jones, Eriita G; Lineweaver, Charles H; Clarke, Jonathan D

2011-12-01

We present a comprehensive model of martian pressure-temperature (P-T) phase space and compare it with that of Earth. Martian P-T conditions compatible with liquid water extend to a depth of ∼310 km. We use our phase space model of Mars and of terrestrial life to estimate the depths and extent of the water on Mars that is habitable for terrestrial life. We find an extensive overlap between inhabited terrestrial phase space and martian phase space. The lower martian surface temperatures and shallower martian geotherm suggest that, if there is a hot deep biosphere on Mars, it could extend 7 times deeper than the ∼5 km depth of the hot deep terrestrial biosphere in the crust inhabited by hyperthermophilic chemolithotrophs. This corresponds to ∼3.2% of the volume of present-day Mars being potentially habitable for terrestrial-like life.

Semiclassical evolution of dissipative Markovian systems

International Nuclear Information System (INIS)

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

2009-01-01

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

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.

Microcanonical rates, gap times, and phase space dividing surfaces

NARCIS (Netherlands)

Ezra, Gregory S.; Waalkens, Holger; Wiggins, Stephen

2009-01-01

The general approach to classical unimolecular reaction rates due to Thiele is revisited in light of recent advances in the phase space formulation of transition state theory for multidimensional systems. Key concepts, such as the phase space dividing surface separating reactants from products, the

Phase space quark counting rule

International Nuclear Information System (INIS)

Wei-gin, C.; Lo, S.

1980-01-01

A simple quark counting rule based on phase space consideration suggested before is used to fit all 39 recent experimental data points on inclusive reactions. Parameter free relations are found to agree with experiments. Excellent detail fits are obtained for 11 inclusive reactions

Explaining Gibbsean phase space to second year students

International Nuclear Information System (INIS)

Vesely, Franz J

2005-01-01

A new approach to teaching introductory statistical physics is presented. We recommend making extensive use of the fact that even systems with a very few degrees of freedom may display chaotic behaviour. This permits a didactic 'bottom-up' approach, starting out with toy systems whose phase space may be depicted on a screen or blackboard, then proceeding to ever higher dimensions in Gibbsean phase space

On the characterization of infinitesimal symmetries of the relativistic phase space

International Nuclear Information System (INIS)

Janyška, Josef; Vitolo, Raffaele

2012-01-01

The phase space of relativistic particle mechanics is defined as the first jet space of motions regarded as time-like one-dimensional submanifolds of spacetime. A Lorentzian metric and an electromagnetic 2-form define naturally a generalized contact structure on the odd-dimensional phase space. In the paper, infinitesimal symmetries of the phase structures are characterized. More precisely, it is proved that all phase infinitesimal symmetries are special Hamiltonian lifts of distinguished conserved quantities on the phase space. It is proved that generators of infinitesimal symmetries constitute a Lie algebra with respect to a special bracket. A momentum map for groups of symmetries of the geometric structures is provided. (paper)

Alternating phase focussing including space charge

International Nuclear Information System (INIS)

Cheng, W.H.; Gluckstern, R.L.

1992-01-01

Longitudinal stability can be obtained in a non-relativistic drift tube accelerator by traversing each gap as the rf accelerating field rises. However, the rising accelerating field leads to a transverse defocusing force which is usually overcome by magnetic focussing inside the drift tubes. The radio frequency quadrupole is one way of providing simultaneous longitudinal and transverse focusing without the use of magnets. One can also avoid the use of magnets by traversing alternate gaps between drift tubes as the field is rising and falling, thus providing an alternation of focussing and defocusing forces in both the longitudinal and transverse directions. The stable longitudinal phase space area is quite small, but recent efforts suggest that alternating phase focussing (APF) may permit low velocity acceleration of currents in the 100-300 ma range. This paper presents a study of the parameter space and a test of crude analytic predictions by adapting the code PARMILA, which includes space charge, to APF. 6 refs., 3 figs

Eugene Wigner – A Gedanken Pioneer of the Second Quantum Revolution

Directory of Open Access Journals (Sweden)

Zeilinger Anton

2014-01-01

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

Ray tracing the Wigner distribution function for optical simulations

Science.gov (United States)

Mout, Marco; Wick, Michael; Bociort, Florian; Petschulat, Joerg; Urbach, Paul

2018-01-01

We study a simulation method that uses the Wigner distribution function to incorporate wave optical effects in an established framework based on geometrical optics, i.e., a ray tracing engine. We use the method to calculate point spread functions and show that it is accurate for paraxial systems but produces unphysical results in the presence of aberrations. The cause of these anomalies is explained using an analytical model.

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

International Nuclear Information System (INIS)

Yu Liang

2011-01-01

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

Phase-space quark counting rule

Energy Technology Data Exchange (ETDEWEB)

Wei-Gin, Chao; Lo, Shui-Yin [Academia Sinica, Beijing (China). Inst. of High Energy Physics

1981-05-21

A simple quark counting rule based on the phase-space consideration suggested before is used to fit all 39 recent experimental data points on inclusive reactions. Parameter-free relations are found to agree with experiments. Excellent detail fits are obtained for 11 inclusive reactions.

From stochastic phase space evolution to Brownian motion in collective space

International Nuclear Information System (INIS)

Benhassine, B.; Farine, M.; Hernandez, E.S.; Idier, D.; Remaud, B.; Sebille, F.

1993-01-01

Within the framework of stochastic transport equations in phase space, the dynamics of fluctuations on collective variables in homogeneous fermion systems is studied. The transport coefficients are formally deduced in the relaxation time approximation and a general method to compute dynamically the dispersions of collective observables is proposed as a set of coupled equations. Independently, the general covariance matrix of phase space fluctuations and the dispersion on collective variables at equilibrium are derived. Detailed numerical applications show that dynamics of fluctuations can be extracted from noisy numerical simulations and that the leading parameter for collective fluctuations is the excitation energy whatever is its degree of thermalization. (authors). 16 refs., 12 figs

Beam envelope profile of non-centrosymmetric polygonal phase space

International Nuclear Information System (INIS)

Chen Yinbao; Xie Xi

1984-01-01

The general theory of beam envelope profile of non-centrosymmetric polygonal phase space is developed. By means of this theory the beam envelope profile of non-centrosymmetric polygonal phase space can be calculated directly. An example is carried out in detail to show the practical application of the theory

Beam phase space and emittance

International Nuclear Information System (INIS)

Buon, J.

1992-02-01

The classical and elementary results for canonical phase space, the Liouville theorem and the beam emittance are reviewed. Then, the importance of phase portraits to obtain a geometrical description of motion is emphasized, with examples in accelerator physics. Finally, a statistical point of view is used to define beam emittance, to study its law of approximate conservation, with three particular examples, and to introduce a beam envelope-ellipse and the β-function, emphasing the statistical features of its properties. (author) 14 refs.; 11 figs

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.

Incorporating space charge in the transverse phase-space matching and tomography at PITZ

Energy Technology Data Exchange (ETDEWEB)

Kourkafas, Georgios

2015-11-15

The ever-expanding achievements in the field of particle accelerators push their specifications to very demanding levels. The performance of many modern applications depends on their ability to be operated with high bunch charges confined in small volumes. However, the consequence of increased intensity is strong space-charge forces, which perplex the beam manipulation and undermine the beam quality. As a result, reliable methods are needed to control and measure the accelerated particles under these extraordinary conditions. The phase space tomography is a diagnostic technique which can reveal details of the transverse beam parameters for a wide range of intensities and energies, with minimal influence from the machine instabilities, in a quasi non-destructive way. The accuracy of this method relies on the precise knowledge and control of the particle dynamics under the influence of space charge in different stages of the measurement. On the one hand, the matching of the beam to the measurement's design transverse parameters requires a procedure which efficiently compensates the effects of space charge. Depending on the structure of the magnetic lattice, different aspects of these effects prevail, therefore different strategies have to be developed. On the other hand, the impact of the space-charge forces on the phase-space transformations during the data acquisition has to be included in the model which is used for the tomographic reconstruction. The aim of this thesis is to provide and test time-efficient solutions for the incorporation of space charge in the transverse beam matching and phase space tomography.

Incorporating space charge in the transverse phase-space matching and tomography at PITZ

International Nuclear Information System (INIS)

Kourkafas, Georgios

2015-11-01

The ever-expanding achievements in the field of particle accelerators push their specifications to very demanding levels. The performance of many modern applications depends on their ability to be operated with high bunch charges confined in small volumes. However, the consequence of increased intensity is strong space-charge forces, which perplex the beam manipulation and undermine the beam quality. As a result, reliable methods are needed to control and measure the accelerated particles under these extraordinary conditions. The phase space tomography is a diagnostic technique which can reveal details of the transverse beam parameters for a wide range of intensities and energies, with minimal influence from the machine instabilities, in a quasi non-destructive way. The accuracy of this method relies on the precise knowledge and control of the particle dynamics under the influence of space charge in different stages of the measurement. On the one hand, the matching of the beam to the measurement's design transverse parameters requires a procedure which efficiently compensates the effects of space charge. Depending on the structure of the magnetic lattice, different aspects of these effects prevail, therefore different strategies have to be developed. On the other hand, the impact of the space-charge forces on the phase-space transformations during the data acquisition has to be included in the model which is used for the tomographic reconstruction. The aim of this thesis is to provide and test time-efficient solutions for the incorporation of space charge in the transverse beam matching and phase space tomography.

Remarks on the formulation of quantum mechanics on noncommutative phase spaces

International Nuclear Information System (INIS)

Muthukumar, Balasundaram

2007-01-01

We consider the probabilistic description of nonrelativistic, spinless one-particle classical mechanics, and immerse the particle in a deformed noncommutative phase space in which position coordinates do not commute among themselves and also with canonically conjugate momenta. With a postulated normalized distribution function in the quantum domain, the square of the Dirac delta density distribution in the classical case is properly realised in noncommutative phase space and it serves as the quantum condition. With only these inputs, we pull out the entire formalisms of noncommutative quantum mechanics in phase space and in Hilbert space, and elegantly establish the link between classical and quantum formalisms and between Hilbert space and phase space formalisms of noncommutative quantum mechanics. Also, we show that the distribution function in this case possesses 'twisted' Galilean symmetry

Quantum de Finetti theorem in phase-space representation

International Nuclear Information System (INIS)

Leverrier, Anthony; Cerf, Nicolas J.

2009-01-01

The quantum versions of de Finetti's theorem derived so far express the convergence of n-partite symmetric states, i.e., states that are invariant under permutations of their n parties, toward probabilistic mixtures of independent and identically distributed (IID) states of the form σ xn . Unfortunately, these theorems only hold in finite-dimensional Hilbert spaces, and their direct generalization to infinite-dimensional Hilbert spaces is known to fail. Here, we address this problem by considering invariance under orthogonal transformations in phase space instead of permutations in state space, which leads to a quantum de Finetti theorem particularly relevant to continuous-variable systems. Specifically, an n-mode bosonic state that is invariant with respect to this continuous symmetry in phase space is proven to converge toward a probabilistic mixture of IID Gaussian states (actually, n identical thermal states).

Evolution of Quantum Phase Space Distribution: a Trajectory-Density Approach

International Nuclear Information System (INIS)

Xue-Feng, Zhang; Yu-Jun, Zheng

2009-01-01

The trajectory-density method of a quantum system is developed by using local Koopman and Frobenius–Perron operators. We propose a new scheme of approximation from two sets of trajectory-density mixed equations. By examining the local generation and termination of trajectories, we show how they can be adopted to the propagation of negative values of the Wigner function even if it starts off positive everywhere

Correction of aberrations in beams filling elliptical phase-space areas

International Nuclear Information System (INIS)

Wollnik, H.

1988-01-01

For the optimization of an optical system it is advantageous to amend the system by a virtual object lens so that the calculation always starts from an upright phase-space distribution. Furthermore, in case of a beam filling an elliptical phase-space volume, the most extreme rays of a beam, filling a parallelogram-like phase-space volume, do not exist, so that the corresponding sum of aberrations is smaller. For an optimization thus corresponding attenuation factors should be taken into accout

Controlling quantum interference in phase space with amplitude

OpenAIRE

Xue, Yinghong; Li, Tingyu; Kasai, Katsuyuki; Okada-Shudo, Yoshiko; Watanabe, Masayoshi; Zhang, Yun

2017-01-01

We experimentally show a quantum interference in phase space by interrogating photon number probabilities (n?=?2, 3, and 4) of a displaced squeezed state, which is generated by an optical parametric amplifier and whose displacement is controlled by amplitude of injected coherent light. It is found that the probabilities exhibit oscillations of interference effect depending upon the amplitude of the controlling light field. This phenomenon is attributed to quantum interference in phase space a...

Group theoretical construction of planar noncommutative phase spaces

Energy Technology Data Exchange (ETDEWEB)

Ngendakumana, Ancille, E-mail: nancille@yahoo.fr; Todjihoundé, Leonard, E-mail: leonardt@imsp.uac.org [Institut de Mathématiques et des Sciences Physiques (IMSP), Porto-Novo (Benin); Nzotungicimpaye, Joachim, E-mail: kimpaye@kie.ac.rw [Kigali Institute of Education (KIE), Kigali (Rwanda)

2014-01-15

Noncommutative phase spaces are generated and classified in the framework of centrally extended anisotropic planar kinematical Lie groups as well as in the framework of noncentrally abelian extended planar absolute time Lie groups. Through these constructions the coordinates of the phase spaces do not commute due to the presence of naturally introduced fields giving rise to minimal couplings. By symplectic realizations methods, physical interpretations of generators coming from the obtained structures are given.

Group theoretical construction of planar noncommutative phase spaces

International Nuclear Information System (INIS)

Ngendakumana, Ancille; Todjihoundé, Leonard; Nzotungicimpaye, Joachim

2014-01-01

Noncommutative phase spaces are generated and classified in the framework of centrally extended anisotropic planar kinematical Lie groups as well as in the framework of noncentrally abelian extended planar absolute time Lie groups. Through these constructions the coordinates of the phase spaces do not commute due to the presence of naturally introduced fields giving rise to minimal couplings. By symplectic realizations methods, physical interpretations of generators coming from the obtained structures are given

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.

Grassmann phase space methods for fermions. II. Field theory

Energy Technology Data Exchange (ETDEWEB)

Dalton, B.J., E-mail: bdalton@swin.edu.au [Centre for Quantum and Optical Science, Swinburne University of Technology, Melbourne, Victoria 3122 (Australia); Jeffers, J. [Department of Physics, University of Strathclyde, Glasgow G4ONG (United Kingdom); Barnett, S.M. [School of Physics and Astronomy, University of Glasgow, Glasgow G12 8QQ (United Kingdom)

2017-02-15

In both quantum optics and cold atom physics, the behaviour of bosonic photons and atoms is often treated using phase space methods, where mode annihilation and creation operators are represented by c-number phase space variables, with the density operator equivalent to a distribution function of these variables. The anti-commutation rules for fermion annihilation, creation operators suggests the possibility of using anti-commuting Grassmann variables to represent these operators. However, in spite of the seminal work by Cahill and Glauber and a few applications, the use of Grassmann phase space methods in quantum-atom optics to treat fermionic systems is rather rare, though fermion coherent states using Grassmann variables are widely used in particle physics. This paper presents a phase space theory for fermion systems based on distribution functionals, which replace the density operator and involve Grassmann fields representing anti-commuting fermion field annihilation, creation operators. It is an extension of a previous phase space theory paper for fermions (Paper I) based on separate modes, in which the density operator is replaced by a distribution function depending on Grassmann phase space variables which represent the mode annihilation and creation operators. This further development of the theory is important for the situation when large numbers of fermions are involved, resulting in too many modes to treat separately. Here Grassmann fields, distribution functionals, functional Fokker–Planck equations and Ito stochastic field equations are involved. Typical applications to a trapped Fermi gas of interacting spin 1/2 fermionic atoms and to multi-component Fermi gases with non-zero range interactions are presented, showing that the Ito stochastic field equations are local in these cases. For the spin 1/2 case we also show how simple solutions can be obtained both for the untrapped case and for an optical lattice trapping potential.

Grassmann phase space methods for fermions. II. Field theory

International Nuclear Information System (INIS)

Dalton, B.J.; Jeffers, J.; Barnett, S.M.

2017-01-01

In both quantum optics and cold atom physics, the behaviour of bosonic photons and atoms is often treated using phase space methods, where mode annihilation and creation operators are represented by c-number phase space variables, with the density operator equivalent to a distribution function of these variables. The anti-commutation rules for fermion annihilation, creation operators suggests the possibility of using anti-commuting Grassmann variables to represent these operators. However, in spite of the seminal work by Cahill and Glauber and a few applications, the use of Grassmann phase space methods in quantum-atom optics to treat fermionic systems is rather rare, though fermion coherent states using Grassmann variables are widely used in particle physics. This paper presents a phase space theory for fermion systems based on distribution functionals, which replace the density operator and involve Grassmann fields representing anti-commuting fermion field annihilation, creation operators. It is an extension of a previous phase space theory paper for fermions (Paper I) based on separate modes, in which the density operator is replaced by a distribution function depending on Grassmann phase space variables which represent the mode annihilation and creation operators. This further development of the theory is important for the situation when large numbers of fermions are involved, resulting in too many modes to treat separately. Here Grassmann fields, distribution functionals, functional Fokker–Planck equations and Ito stochastic field equations are involved. Typical applications to a trapped Fermi gas of interacting spin 1/2 fermionic atoms and to multi-component Fermi gases with non-zero range interactions are presented, showing that the Ito stochastic field equations are local in these cases. For the spin 1/2 case we also show how simple solutions can be obtained both for the untrapped case and for an optical lattice trapping potential.

On the minimum uncertainty of space-time geodesics

International Nuclear Information System (INIS)

Diosi, L.; Lukacs, B.

1989-10-01

Although various attempts for systematic quantization of the space-time geometry ('gravitation') have appeared, none of them is considered fully consistent or final. Inspired by a construction of Wigner, the quantum relativistic limitations of measuring the metric tensor of a certain space-time were calculated. The result is suggested to be estimate for fluctuations of g ab whose rigorous determination will be a subject of a future relativistic quantum gravity. (author) 11 refs

Physical Fock space of tensionless strings

CERN Document Server

Antoniadis, Ignatios; Antoniadis, Ignatios; Savvidy, George

2004-01-01

We study the physical Fock space of the tensionless string theory with perimeter action which has pure massless spectrum. The states are classified by the Wigner's little group for massless particles. The ground state contains infinite many massless fields of fixed helicity, the excitation levels realize CSR representations. We demonstrate that the first and the second excitation levels are physical null states.

Semiclassical expansions of the nuclear relativistic Hartree-Fock theory

International Nuclear Information System (INIS)

Weigel, M.K.; Haddad, S.

1991-01-01

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

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

International Nuclear Information System (INIS)

Jacobsen, Sol H; Jarvis, P D

2008-01-01

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

Wigner function and tomogram of the excited squeezed vacuum state

International Nuclear Information System (INIS)

Meng Xiangguo; Wang Jisuo; Fan Hongyi

2007-01-01

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

Wigner function and tomogram of the excited squeezed vacuum state

Energy Technology Data Exchange (ETDEWEB)

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

2007-01-29

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

Ring-shaped functions and Wigner 6j-symbols

International Nuclear Information System (INIS)

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

2006-01-01

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

Optical Coherence Tomography: Modeling and Applications

DEFF Research Database (Denmark)

Thrane, Lars

this system. A demonstration of the imaging capabilities of the OCT system is given. Moreover, a novel truereflection OCT imaging algorithm, based on the new OCT model presented in this thesis, is demonstrated. Finally, a theoretical analysis of the Wigner phase-space distribution function for the OCT...... geometry, i.e., reflection geometry, is developed. As in the new OCT model, multiple scattered photons has been taken into account together with multiple scattering effects. As an important result, a novel method of creating images based on measurements of the momentum width of the Wigner phase...

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

Identifying Phase Space Boundaries with Voronoi Tessellations

CERN Document Server

Debnath, Dipsikha; Kilic, Can; Kim, Doojin; Matchev, Konstantin T.; Yang, Yuan-Pao

2016-11-24

Determining the masses of new physics particles appearing in decay chains is an important and longstanding problem in high energy phenomenology. Recently it has been shown that these mass measurements can be improved by utilizing the boundary of the allowed region in the fully differentiable phase space in its full dimensionality. Here we show that the practical challenge of identifying this boundary can be solved using techniques based on the geometric properties of the cells resulting from Voronoi tessellations of the relevant data. The robust detection of such phase space boundaries in the data could also be used to corroborate a new physics discovery based on a cut-and-count analysis.

Phase-space exploration in nuclear giant resonance decay

International Nuclear Information System (INIS)

Drozdz, S.; Nishizaki, S.; Wambach, J.; Speth, J.

1995-01-01

The rate of phase-space exploration in the decay of isovector and isoscalar giant quadrupole resonances in 40 Ca is analyzed. The study is based on the time dependence of the survival probability and of the spectrum of generalized entropies evaluated in the space of one-particle--one-hole (1p-1h) and 2p-2h states. Three different cases for the level distribution of 2p-2h background states, corresponding to (a) high degeneracy, (b) classically regular motion, and (c) classically chaotic motion, are studied. In the latter case the isovector excitation evolves almost statistically while the isoscalar excitation remains largely localized, even though it penetrates the whole available phase space

Phase-space formalism: Operational calculus and solution of evolution equations in phase-space

International Nuclear Information System (INIS)

Dattoli, G.; Torre, A.

1995-05-01

Phase-space formulation of physical problems offers conceptual and practical advantages. A class of evolution type equations, describing the time behaviour of a physical system, using an operational formalism useful to handle time ordering problems has been described. The methods proposed generalize the algebraic ordering techniques developed to deal with the ordinary Schroedinger equation, and how they are taylored suited to treat evolution problems both in classical and quantum dynamics has been studied

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

About the phase space of SL(3) black holes

Energy Technology Data Exchange (ETDEWEB)

Cabo-Bizet, Alejandro [SISSA and INFN, Via Bonomea 265, 34128 Trieste (Italy); Giraldo-Rivera, V.I. [SISSA and INFN, Via Bonomea 265, 34128 Trieste (Italy); ICTP, Strada Costiera 11, 34014 Trieste (Italy)

2015-03-17

In this note we address some issues of recent interest, related to the asymptotic symmetry algebra of higher spin black holes in sl(3,ℝ)×sl(3,ℝ) Chern Simons (CS) formulation. We compute the fixed time Dirac bracket algebra that acts on two different phase spaces. Both of these spaces contain black holes as zero modes. The result for one of these phase spaces is explicitly shown to be isomorphic to W{sub 3}{sup (2)}×W{sub 3}{sup (2)} in first order perturbations.

Efficient characterization of phase space mapping in axially symmetric optical systems

Science.gov (United States)

Barbero, Sergio; Portilla, Javier

2018-01-01

Phase space mapping, typically between an object and image plane, characterizes an optical system within a geometrical optics framework. We propose a novel conceptual frame to characterize the phase mapping in axially symmetric optical systems for arbitrary object locations, not restricted to a specific object plane. The idea is based on decomposing the phase mapping into a set of bivariate equations corresponding to different values of the radial coordinate on a specific object surface (most likely the entrance pupil). These equations are then approximated through bivariate Chebyshev interpolation at Chebyshev nodes, which guarantees uniform convergence. Additionally, we propose the use of a new concept (effective object phase space), defined as the set of points of the phase space at the first optical element (typically the entrance pupil) that are effectively mapped onto the image surface. The effective object phase space provides, by means of an inclusion test, a way to avoid tracing rays that do not reach the image surface.

Phase-space description of plasma waves. Linear and nonlinear theory

International Nuclear Information System (INIS)

Biro, T.

1992-11-01

We develop an (r,k) phase space description of waves in plasmas by introducing Gaussian window functions to separate short scale oscillations from long scale modulations of the wave fields and variations in the plasma parameters. To obtain a wave equation that unambiguously separates conservative dynamics from dissipation also in an inhomogeneous and time varying background plasma, we first discuss the proper form of the current response function. On the analogy of the particle distribution function f(v,r,t), we introduce a wave density N(k,r,t) on phase space. This function is proven to satisfy a simple continuity equation. Dissipation is also included, and this allows us to describe the damping or growth of wave density' along rays. Problems involving geometric optics of continuous media often appear simpler when viewed in phase space, since the flow of N in phase space is incompressible. Within the phase space representation, we obtain a very general formula for the second order nonlinear current in terms of the vector potential. This formula is a convenient starting point for studies of coherent as well as turbulent nonlinear processes. We derive kinetic equations for weakly inhomogeneous and turbulent plasma, including the effects of inhomogeneous turbulence, wave convection and refraction. (author)

Hamiltonian flow over saddles for exploring molecular phase space structures

Science.gov (United States)

Farantos, Stavros C.

2018-03-01

Despite using potential energy surfaces, multivariable functions on molecular configuration space, to comprehend chemical dynamics for decades, the real happenings in molecules occur in phase space, in which the states of a classical dynamical system are completely determined by the coordinates and their conjugate momenta. Theoretical and numerical results are presented, employing alanine dipeptide as a model system, to support the view that geometrical structures in phase space dictate the dynamics of molecules, the fingerprints of which are traced by following the Hamiltonian flow above saddles. By properly selecting initial conditions in alanine dipeptide, we have found internally free rotor trajectories the existence of which can only be justified in a phase space perspective. This article is part of the theme issue `Modern theoretical chemistry'.

Taming the escape dynamics of nonadiabatic time-periodically driven quantum dissipative system within the frame of Wigner formalism

Energy Technology Data Exchange (ETDEWEB)

Shit, Anindita [Department of Chemistry, Bengal Engineering and Science University, Shibpur, Howrah 711103 (India); Chattopadhyay, Sudip, E-mail: sudip_chattopadhyay@rediffmail.com [Department of Chemistry, Bengal Engineering and Science University, Shibpur, Howrah 711103 (India); Ray Chaudhuri, Jyotipratim, E-mail: jprc_8@yahoo.com [Department of Physics, Katwa College, Katwa, Burdwan 713130 (India)

2014-03-18

Highlights: • Nonadiabatic dynamics of quantum particle under the impact of high-frequency force. • Formulation of time-independent dynamics via Floquet and Kapitza schemes. • Manipulation of external force parameters allows us to control the escape rate. • Increase of (amplitudes/frequency) causes the system to decay faster, in general. • Crossover temperature increases in the presence of the field. - Abstract: Escape under the action of the external modulation constitutes a nontrivial generalization of an conventional Kramers rate because the system is away from thermal equilibrium. A derivation of this result from the point of view of Langevin dynamics in the frame of Floquet theorem in conjunction with the Kapitza–Landau time window (that leads to an attractive description of the time-dependent quantum dynamics in terms of time-independent one) has been provided. The quantum escape rate in the intermediate-to-high and very-high damping regime so obtained analytically using the phase space formalism associated with the Wigner distribution and path-integral formalism bears a quantum correction that depends strongly on the barrier height. It is shown that an increase of (amplitude/frequency) ratio causes the system to decay faster, in general. The crossover temperature between tunneling and thermal activation increases in the presence of field so that quantum effects in the escape are relevant at higher temperatures.

Wave packet dynamics and photofragmentation in time-dependent quadratic potentials

DEFF Research Database (Denmark)

Møller, Klaus Braagaard; Henriksen, Niels Engholm

1996-01-01

We study the dynamics of generalized harmonic oscillator states in time-dependent quadratic potentials and derive analytical expressions for the momentum space and the Wigner phase space representation of these wave packets. Using these results we consider a model for the rotational excitation...

Relativistic phase space: dimensional recurrences

International Nuclear Information System (INIS)

Delbourgo, R; Roberts, M L

2003-01-01

We derive recurrence relations between phase space expressions in different dimensions by confining some of the coordinates to tori or spheres of radius R and taking the limit as R→∞. These relations take the form of mass integrals, associated with extraneous momenta (relative to the lower dimension), and produce the result in the higher dimension

Phase space and jet definitions in soft-collinear effective theory

International Nuclear Information System (INIS)

Cheung, William Man-Yin; Luke, Michael; Zuberi, Saba

2009-01-01

We discuss consistent power counting for integrating soft and collinear degrees of freedom over arbitrary regions of phase space in the soft-collinear effective theory, and illustrate our results at one-loop with several jet algorithms: JADE, Sterman-Weinberg and k perpendicular . Consistently applying soft-collinear effective theory power counting in phase space, along with nontrivial zero-bin subtractions, prevents double counting of final states. The resulting phase space integrals over soft and collinear regions are individually ultraviolet divergent, but the phase space ultraviolet divergences cancel in the sum. Whether the soft and collinear contributions are individually infrared safe depends on the jet definition. We show that while this is true at one-loop for JADE and Sterman-Weinberg, the k perpendicular algorithm does not factorize into individually infrared safe soft and collinear pieces in dimensional regularization. We point out that this statement depends on the ultraviolet regulator, and that in a cutoff scheme the soft functions are infrared safe.

Hydrogen atom in phase space

International Nuclear Information System (INIS)

Chetouani, L.; Hammann, T.F.

1987-01-01

The Hamiltonian of the three-dimensional hydrogen atom is reduced, in parabolic coordinates, to the Hamiltonians of two bidimensional harmonic oscillators, by doing several space-time transformations,separating the movement along the three parabolic directions (ξ,eta,phi), and introducing two auxiliary angular variables psi and psi', 0≤psi, psi'≤2π. The Green's function is developed into partial Green's functions, and expressed in terms of two Green's functions that describe the movements along both the ξ and eta axes. Introducing auxiliary Hamiltonians allows one to calculate the Green's function in the configurational space, via the phase-space evolution function of the two-dimensional harmonic oscillator. The auxiliary variables psi and psi' are eliminated by projection. The thus-obtained Green's function, save for a multiplicating factor, coincides with that calculated following the path-integral formalism

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.)

The Quantum Space Phase Transitions for Particles and Force Fields

OpenAIRE

Chung D.-Y.; Krasnoholovets V.

2006-01-01

We introduce a phenomenological formalism in which the space structure is treated in terms of attachment space and detachment space. Attachment space attaches to an object, while detachment space detaches from the object. The combination of these spaces results in three quantum space phases: binary partition space, miscible space and binary lattice space. Binary lattice space consists of repetitive units of alternative attachment space and detachment spac...

Phase transitions in de Sitter space

Directory of Open Access Journals (Sweden)

Alexander Vilenkin

1983-10-01

Full Text Available An effective potential in de Sitter space is calculated for a model of two interacting scalar fields in one-loop approximation and in a self-consistent approximation which takes into account an infinite set of diagrams. Various approaches to renormalization in de Sitter space are discussed. The results are applied to analyze the phase transition in the Hawking-Moss version of the inflationary universe scenario. Requiring that inflation is sufficiently large, we derive constraints on the parameters of the model.

Generally covariant theories: the Noether obstruction for realizing certain space-time diffeomorphisms in phase space

International Nuclear Information System (INIS)

Pons, Josep M

2003-01-01

Relying on known results of the Noether theory of symmetries extended to constrained systems, it is shown that there exists an obstruction that prevents certain tangent-space diffeomorphisms being projectable to phase space, for generally covariant theories. This main result throws new light on the old fact that the algebra of gauge generators in the phase space of general relativity, or other generally covariant theories, only closes as a soft algebra and not as a Lie algebra. The deep relationship between these two issues is clarified. In particular, we see that the second one may be understood as a side effect of the procedure to solve the first. It is explicitly shown how the adoption of specific metric-dependent diffeomorphisms, as a way to achieve projectability, causes the algebra of gauge generators (constraints) in phase space not to be a Lie algebra -with structure constants - but a soft algebra - with structure functions

Identifying phase-space boundaries with Voronoi tessellations

International Nuclear Information System (INIS)

Debnath, Dipsikha; Matchev, Konstantin T.; Gainer, James S.; Kilic, Can; Yang, Yuan-Pao; Kim, Doojin

2016-01-01

Determining the masses of new physics particles appearing in decay chains is an important and longstanding problem in high energy phenomenology. Recently it has been shown that these mass measurements can be improved by utilizing the boundary of the allowed region in the fully differentiable phase space in its full dimensionality. Here we show that the practical challenge of identifying this boundary can be solved using techniques based on the geometric properties of the cells resulting from Voronoi tessellations of the relevant data. The robust detection of such phase-space boundaries in the data could also be used to corroborate a new physics discovery based on a cut-and-count analysis. (orig.)

Identifying phase-space boundaries with Voronoi tessellations

Energy Technology Data Exchange (ETDEWEB)

Debnath, Dipsikha; Matchev, Konstantin T. [University of Florida, Physics Department, Gainesville, FL (United States); Gainer, James S. [University of Hawaii, Department of Physics and Astronomy, Honolulu, HI (United States); Kilic, Can; Yang, Yuan-Pao [The University of Texas at Austin, Theory Group, Department of Physics and Texas Cosmology Center, Austin, TX (United States); Kim, Doojin [University of Florida, Physics Department, Gainesville, FL (United States); CERN, Theory Division, Geneva 23 (Switzerland)

2016-11-15

Determining the masses of new physics particles appearing in decay chains is an important and longstanding problem in high energy phenomenology. Recently it has been shown that these mass measurements can be improved by utilizing the boundary of the allowed region in the fully differentiable phase space in its full dimensionality. Here we show that the practical challenge of identifying this boundary can be solved using techniques based on the geometric properties of the cells resulting from Voronoi tessellations of the relevant data. The robust detection of such phase-space boundaries in the data could also be used to corroborate a new physics discovery based on a cut-and-count analysis. (orig.)

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

Science.gov (United States)

Knighton, Talbot

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

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

Fourier duality as a quantization principle

International Nuclear Information System (INIS)

Aldrovandi, R.; Saeger, L.A.

1996-08-01

The Weyl-Wigner prescription for quantization on Euclidean phase spaces makes essential use of Fourier duality. The extension of this property to more general phase spaces requires the use of Kac algebras, which provide the necessary background for the implementation of Fourier duality on general locally groups. Kac algebras - and the duality they incorporate are consequently examined as candidates for a general quantization framework extending the usual formalism. Using as a test case the simplest non-trivial phase space, the half-plane, it is shown how the structures present in the complete-plane case must be modified. Traces, for example, must be replaced by their noncommutative generalizations - weights - and the correspondence embodied in the Weyl-Wigner formalism is no more complete. Provided the underlying algebraic structure is suitably adapted to each case, Fourier duality is shown to be indeed a very powerful guide to the quantization of general physical systems. (author). 30 refs

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

Cryptographic analysis on the key space of optical phase encryption algorithm based on the design of discrete random phase mask

Science.gov (United States)

Lin, Chao; Shen, Xueju; Li, Zengyan

2013-07-01

The key space of phase encryption algorithm using discrete random phase mask is investigated by numerical simulation in this paper. Random phase mask with finite and discrete phase levels is considered as the core component in most practical optical encryption architectures. The key space analysis is based on the design criteria of discrete random phase mask. The role of random amplitude mask and random phase mask in optical encryption system is identified from the perspective of confusion and diffusion. The properties of discrete random phase mask in a practical double random phase encoding scheme working in both amplitude encoding (AE) and phase encoding (PE) modes are comparably analyzed. The key space of random phase encryption algorithm is evaluated considering both the encryption quality and the brute-force attack resistibility. A method for enlarging the key space of phase encryption algorithm is also proposed to enhance the security of optical phase encryption techniques.

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

Science.gov (United States)

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

2014-07-01

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

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).

Implementing phase-covariant cloning in circuit quantum electrodynamics

Energy Technology Data Exchange (ETDEWEB)

Zhu, Meng-Zheng [School of Physics and Material Science, Anhui University, Hefei 230039 (China); School of Physics and Electronic Information, Huaibei Normal University, Huaibei 235000 (China); Ye, Liu, E-mail: yeliu@ahu.edu.cn [School of Physics and Material Science, Anhui University, Hefei 230039 (China)

2016-10-15

An efficient scheme is proposed to implement phase-covariant quantum cloning by using a superconducting transmon qubit coupled to a microwave cavity resonator in the strong dispersive limit of circuit quantum electrodynamics (QED). By solving the master equation numerically, we plot the Wigner function and Poisson distribution of the cavity mode after each operation in the cloning transformation sequence according to two logic circuits proposed. The visualizations of the quasi-probability distribution in phase-space for the cavity mode and the occupation probability distribution in the Fock basis enable us to penetrate the evolution process of cavity mode during the phase-covariant cloning (PCC) transformation. With the help of numerical simulation method, we find out that the present cloning machine is not the isotropic model because its output fidelity depends on the polar angle and the azimuthal angle of the initial input state on the Bloch sphere. The fidelity for the actual output clone of the present scheme is slightly smaller than one in the theoretical case. The simulation results are consistent with the theoretical ones. This further corroborates our scheme based on circuit QED can implement efficiently PCC transformation.

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.

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.