Retrieval of phase-derivative discontinuities in digital speckle pattern interferometry fringes using the Wigner-Ville distribution

NASA Astrophysics Data System (ADS)

Federico, Alejandro; Kaufmann, Guillermo H.

2004-08-01

We evaluate the application of the Wigner-Ville distribution (WVD) to measure phase gradient maps in digital speckle pattern interferometry (DSPI), when the generated correlation fringes present phase discontinuities. The performance of the WVD method is evaluated using computer-simulated fringes. The influence of the filtering process to smooth DSPI fringes and additional drawbacks that emerge when this method is applied are discussed. A comparison with the conventional method based on the continuous wavelet transform in the stationary phase approximation is also presented.

Salient target detection based on pseudo-Wigner-Ville distribution and Rényi entropy.

PubMed

Xu, Yuannan; Zhao, Yuan; Jin, Chenfei; Qu, Zengfeng; Liu, Liping; Sun, Xiudong

2010-02-15

We present what we believe to be a novel method based on pseudo-Wigner-Ville distribution (PWVD) and Rényi entropy for salient targets detection. In the foundation of studying the statistical property of Rényi entropy via PWVD, the residual entropy-based saliency map of an input image can be obtained. From the saliency map, target detection is completed by the simple and convenient threshold segmentation. Experimental results demonstrate the proposed method can detect targets effectively in complex ground scenes.

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

PubMed

Ginzburg, D; Mann, A

2014-03-10

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

Improved accuracy in Wigner-Ville distribution-based sizing of rod-shaped particle using flip and replication technique

NASA Astrophysics Data System (ADS)

Chuamchaitrakool, Porntip; Widjaja, Joewono; Yoshimura, Hiroyuki

2018-01-01

A method for improving accuracy in Wigner-Ville distribution (WVD)-based particle size measurements from inline holograms using flip and replication technique (FRT) is proposed. The FRT extends the length of hologram signals being analyzed, yielding better spatial-frequency resolution of the WVD output. Experimental results verify reduction in measurement error as the length of the hologram signals increases. The proposed method is suitable for particle sizing from holograms recorded using small-sized image sensors.

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

DTIC Science & Technology

1992-06-01

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

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

DTIC Science & Technology

2014-03-27

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

Higher-order stochastic differential equations and the positive Wigner function

NASA Astrophysics Data System (ADS)

Drummond, P. D.

2017-12-01

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

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

NASA Technical Reports Server (NTRS)

Isar, Aurelian

1995-01-01

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

Autonomous Non-Linear Classification of LPI Radar Signal Modulations

DTIC Science & Technology

2007-09-01

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

Chirplet Wigner-Ville distribution for time-frequency representation and its application

NASA Astrophysics Data System (ADS)

Chen, G.; Chen, J.; Dong, G. M.

2013-12-01

This paper presents a Chirplet Wigner-Ville Distribution (CWVD) that is free for cross-term that usually occurs in Wigner-Ville distribution (WVD). By transforming the signal with frequency rotating operators, several mono-frequency signals without intermittent are obtained, WVD is applied to the rotated signals that is cross-term free, then some frequency shift operators corresponding to the rotating operator are utilized to relocate the signal‧s instantaneous frequencies (IFs). The operators‧ parameters come from the estimation of the IFs which are approached with a polynomial functions or spline functions. What is more, by analysis of error, the main factors for the performance of the novel method have been discovered and an effective signal extending method based on the IFs estimation has been developed to improve the energy concentration of WVD. The excellent performance of the novel method was manifested by applying it to estimate the IFs of some numerical signals and the echolocation signal emitted by the Large Brown Bat.

Radar Imaging Using The Wigner-Ville Distribution

NASA Astrophysics Data System (ADS)

Boashash, Boualem; Kenny, Owen P.; Whitehouse, Harper J.

1989-12-01

The need for analysis of time-varying signals has led to the formulation of a class of joint time-frequency distributions (TFDs). One of these TFDs, the Wigner-Ville distribution (WVD), has useful properties which can be applied to radar imaging. This paper first discusses the radar equation in terms of the time-frequency representation of the signal received from a radar system. It then presents a method of tomographic reconstruction for time-frequency images to estimate the scattering function of the aircraft. An optical archi-tecture is then discussed for the real-time implementation of the analysis method based on the WVD.

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

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

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

2010-06-20

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

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

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

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

2011-09-15

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

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

PubMed

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

2008-07-01

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

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

PubMed

Texier, Christophe; Majumdar, Satya N

2013-06-21

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

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

DTIC Science & Technology

2008-03-01

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

Signal Processing Applications Of Wigner-Ville Analysis

NASA Astrophysics Data System (ADS)

Whitehouse, H. J.; Boashash, B.

1986-04-01

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

Sampling in the light of Wigner distribution.

PubMed

Stern, Adrian; Javidi, Bahram

2004-03-01

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

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

DTIC Science & Technology

1989-10-18

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

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

DTIC Science & Technology

2010-11-10

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

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

NASA Astrophysics Data System (ADS)

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

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

Two Dimensional Processing Of Speech And Ecg Signals Using The Wigner-Ville Distribution

NASA Astrophysics Data System (ADS)

Boashash, Boualem; Abeysekera, Saman S.

1986-12-01

The Wigner-Ville Distribution (WVD) has been shown to be a valuable tool for the analysis of non-stationary signals such as speech and Electrocardiogram (ECG) data. The one-dimensional real data are first transformed into a complex analytic signal using the Hilbert Transform and then a 2-dimensional image is formed using the Wigner-Ville Transform. For speech signals, a contour plot is determined and used as a basic feature. for a pattern recognition algorithm. This method is compared with the classical Short Time Fourier Transform (STFT) and is shown, to be able to recognize isolated words better in a noisy environment. The same method together with the concept of instantaneous frequency of the signal is applied to the analysis of ECG signals. This technique allows one to classify diseased heart-beat signals. Examples are shown.

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

DTIC Science & Technology

1992-09-01

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

Wigner-Ville distribution and Gabor transform in Doppler ultrasound signal processing.

PubMed

Ghofrani, S; Ayatollahi, A; Shamsollahi, M B

2003-01-01

Time-frequency distributions have been used extensively for nonstationary signal analysis, they describe how the frequency content of a signal is changing in time. The Wigner-Ville distribution (WVD) is the best known. The draw back of WVD is cross-term artifacts. An alternative to the WVD is Gabor transform (GT), a signal decomposition method, which displays the time-frequency energy of a signal on a joint t-f plane without generating considerable cross-terms. In this paper the WVD and GT of ultrasound echo signals are computed analytically.

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

NASA Astrophysics Data System (ADS)

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

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

Detection and Parameter Estimation of Chirped Radar Signals.

DTIC Science & Technology

2000-01-10

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

STAP for SAR

DTIC Science & Technology

2003-04-01

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

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

DTIC Science & Technology

1992-10-30

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

Self spectrum window method in wigner-ville distribution.

PubMed

Liu, Zhongguo; Liu, Changchun; Liu, Boqiang; Lv, Yangsheng; Lei, Yinsheng; Yu, Mengsun

2005-01-01

Wigner-Ville distribution (WVD) is an important type of time-frequency analysis in biomedical signal processing. The cross-term interference in WVD has a disadvantageous influence on its application. In this research, the Self Spectrum Window (SSW) method was put forward to suppress the cross-term interference, based on the fact that the cross-term and auto-WVD- terms in integral kernel function are orthogonal. With the Self Spectrum Window (SSW) algorithm, a real auto-WVD function was used as a template to cross-correlate with the integral kernel function, and the Short Time Fourier Transform (STFT) spectrum of the signal was used as window function to process the WVD in time-frequency plane. The SSW method was confirmed by computer simulation with good analysis results. Satisfactory time- frequency distribution was obtained.

Ultrasound shear wave simulation based on nonlinear wave propagation and Wigner-Ville Distribution analysis

NASA Astrophysics Data System (ADS)

Bidari, Pooya Sobhe; Alirezaie, Javad; Tavakkoli, Jahan

2017-03-01

This paper presents a method for modeling and simulation of shear wave generation from a nonlinear Acoustic Radiation Force Impulse (ARFI) that is considered as a distributed force applied at the focal region of a HIFU transducer radiating in nonlinear regime. The shear wave propagation is simulated by solving the Navier's equation from the distributed nonlinear ARFI as the source of the shear wave. Then, the Wigner-Ville Distribution (WVD) as a time-frequency analysis method is used to detect the shear wave at different local points in the region of interest. The WVD results in an estimation of the shear wave time of arrival, its mean frequency and local attenuation which can be utilized to estimate medium's shear modulus and shear viscosity using the Voigt model.

Code Optimization for the Choi-Williams Distribution for ELINT Applications

DTIC Science & Technology

2009-12-01

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

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

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

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

2014-09-15

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

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

DTIC Science & Technology

2008-05-01

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

Wigner distributions for an electron

NASA Astrophysics Data System (ADS)

Kumar, Narinder; Mondal, Chandan

2018-06-01

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

Bilinear Time-frequency Analysis for Lamb Wave Signal Detected by Electromagnetic Acoustic Transducer

NASA Astrophysics Data System (ADS)

Sun, Wenxiu; Liu, Guoqiang; Xia, Hui; Xia, Zhengwu

2018-03-01

Accurate acquisition of the detection signal travel time plays a very important role in cross-hole tomography. The experimental platform of aluminum plate under the perpendicular magnetic field is established and the bilinear time-frequency analysis methods, Wigner-Ville Distribution (WVD) and the pseudo-Wigner-Ville distribution (PWVD), are applied to analyse the Lamb wave signals detected by electromagnetic acoustic transducer (EMAT). By extracting the same frequency component of the time-frequency spectrum as the excitation frequency, the travel time information can be obtained. In comparison with traditional linear time-frequency analysis method such as short-time Fourier transform (STFT), the bilinear time-frequency analysis method PWVD is more appropriate in extracting travel time and recognizing patterns of Lamb wave.

Simulation of wave packet tunneling of interacting identical particles

NASA Astrophysics Data System (ADS)

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

2003-02-01

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

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

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

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

2003-09-01

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

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

DTIC Science & Technology

2005-06-01

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

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

PubMed

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

1997-09-01

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

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

PubMed

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.

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

PubMed

Kaprálová-Ždánská, Petra Ruth

2011-05-28

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

Simple procedure for phase-space measurement and entanglement validation

NASA Astrophysics Data System (ADS)

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

2017-08-01

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

Particle tracking by using single coefficient of Wigner-Ville distribution

NASA Astrophysics Data System (ADS)

Widjaja, J.; Dawprateep, S.; Chuamchaitrakool, P.; Meemon, P.

2016-11-01

A new method for extracting information from particle holograms by using a single coefficient of Wigner-Ville distribution (WVD) is proposed to obviate drawbacks of conventional numerical reconstructions. Our previous study found that analysis of the holograms by using the WVD gives output coefficients which are mainly confined along a diagonal direction intercepted at the origin of the WVD plane. The slope of this diagonal direction is inversely proportional to the particle position. One of these coefficients always has minimum amplitude, regardless of the particle position. By detecting position of the coefficient with minimum amplitude in the WVD plane, the particle position can be accurately measured. The proposed method is verified through computer simulations.

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

NASA Astrophysics Data System (ADS)

Wu, Xiaoyang; Liu, Tianyou

2009-07-01

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

Entropy and wigner functions

PubMed

Manfredi; Feix

2000-10-01

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

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

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

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

2014-02-01

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

The Wigner distribution and 2D classical maps

NASA Astrophysics Data System (ADS)

Sakhr, Jamal

2017-07-01

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

The use of the Wigner Distribution to analyze structural impulse responses

NASA Technical Reports Server (NTRS)

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

1990-01-01

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

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

PubMed

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

1994-09-10

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

Analysis of Digital Communication Signals and Extraction of Parameters.

DTIC Science & Technology

1994-12-01

Fast Fourier Transform (FFT). The correlation methods utilize modified time-frequency distributions , where one of these is based on the Wigner - Ville ... Distribution ( WVD ). Gaussian white noise is added to the signal to simulate various signal-to-noise ratios (SNRs).

Time-Frequency Analysis And Pattern Recognition Using Singular Value Decomposition Of The Wigner-Ville Distribution

NASA Astrophysics Data System (ADS)

Boashash, Boualem; Lovell, Brian; White, Langford

1988-01-01

Time-Frequency analysis based on the Wigner-Ville Distribution (WVD) is shown to be optimal for a class of signals where the variation of instantaneous frequency is the dominant characteristic. Spectral resolution and instantaneous frequency tracking is substantially improved by using a Modified WVD (MWVD) based on an Autoregressive spectral estimator. Enhanced signal-to-noise ratio may be achieved by using 2D windowing in the Time-Frequency domain. The WVD provides a tool for deriving descriptors of signals which highlight their FM characteristics. These descriptors may be used for pattern recognition and data clustering using the methods presented in this paper.

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

NASA Technical Reports Server (NTRS)

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

1993-01-01

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

Study on time-frequency analysis method of very fast transient overvoltage

NASA Astrophysics Data System (ADS)

Li, Shuai; Liu, Shiming; Huang, Qiyan; Fu, Chuanshun

2018-04-01

The operation of the disconnector in the gas insulated substation (GIS) may produce very fast transient overvoltage (VFTO), which has the characteristics of short rise time, short duration, high amplitude and rich frequency components. VFTO can cause damage to GIS and secondary equipment, and the frequency components contained in the VFTO can cause resonance overvoltage inside the transformer, so it is necessary to study the spectral characteristics of the VFTO. From the perspective of signal processing, VFTO is a kind of non-stationary signal, the traditional Fourier transform is difficult to describe its frequency which changes with time, so it is necessary to use time-frequency analysis to analyze VFTO spectral characteristics. In this paper, we analyze the performance of short time Fourier transform (STFT), Wigner-Ville distribution (WVD), pseudo Wigner-Ville distribution (PWVD) and smooth pseudo Wigner-Ville distribution (SPWVD). The results show that SPWVD transform is the best. The time-frequency aggregation of SPWVD is higher than STFT, and it does not have cross-interference terms, which can meet the requirements of VFTO spectrum analysis.

Gear Fatigue Crack Diagnosis by Vibration Analysis Using Embedded Modeling

DTIC Science & Technology

2001-04-05

gave references on Wigner - Ville Distribution ( WVD ) and some statistical based methods including FM4, NA4 and NB4. There are limitations for vibration...Embedded Modeling DISTRIBUTION : Approved for public release, distribution unlimited This paper is part of the following report: TITLE: New Frontiers in

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

PubMed

Sels, Dries; Brosens, Fons

2013-10-01

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

Wigner Distribution for Angle Coordinates in Quantum Mechanics.

ERIC Educational Resources Information Center

Mukunda, N.

1979-01-01

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

Detection and Estimation of Multi-Pulse LFMCW Radar Signals

DTIC Science & Technology

2010-01-01

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

On the Wigner law in dilute random matrices

NASA Astrophysics Data System (ADS)

Khorunzhy, A.; Rodgers, G. J.

1998-12-01

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

Time-varying higher order spectra

NASA Astrophysics Data System (ADS)

Boashash, Boualem; O'Shea, Peter

1991-12-01

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

Ladar imaging detection of salient map based on PWVD and Rényi entropy

NASA Astrophysics Data System (ADS)

Xu, Yuannan; Zhao, Yuan; Deng, Rong; Dong, Yanbing

2013-10-01

Spatial-frequency information of a given image can be extracted by associating the grey-level spatial data with one of the well-known spatial/spatial-frequency distributions. The Wigner-Ville distribution (WVD) has a good characteristic that the images can be represented in spatial/spatial-frequency domains. For intensity and range images of ladar, through the pseudo Wigner-Ville distribution (PWVD) using one or two dimension window, the statistical property of Rényi entropy is studied. We also analyzed the change of Rényi entropy's statistical property in the ladar intensity and range images when the man-made objects appear. From this foundation, a novel method for generating saliency map based on PWVD and Rényi entropy is proposed. After that, target detection is completed when the saliency map is segmented using a simple and convenient threshold method. For the ladar intensity and range images, experimental results show the proposed method can effectively detect the military vehicles from complex earth background with low false alarm.

Denoised Wigner distribution deconvolution via low-rank matrix completion

DOE PAGES

Lee, Justin; Barbastathis, George

2016-08-23

Wigner distribution deconvolution (WDD) is a decades-old method for recovering phase from intensity measurements. Although the technique offers an elegant linear solution to the quadratic phase retrieval problem, it has seen limited adoption due to its high computational/memory requirements and the fact that the technique often exhibits high noise sensitivity. Here, we propose a method for noise suppression in WDD via low-rank noisy matrix completion. Our technique exploits the redundancy of an object’s phase space to denoise its WDD reconstruction. We show in model calculations that our technique outperforms other WDD algorithms as well as modern iterative methods for phasemore » retrieval such as ptychography. Here, our results suggest that a class of phase retrieval techniques relying on regularized direct inversion of ptychographic datasets (instead of iterative reconstruction techniques) can provide accurate quantitative phase information in the presence of high levels of noise.« less

Denoised Wigner distribution deconvolution via low-rank matrix completion

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

Lee, Justin; Barbastathis, George

Wigner distribution deconvolution (WDD) is a decades-old method for recovering phase from intensity measurements. Although the technique offers an elegant linear solution to the quadratic phase retrieval problem, it has seen limited adoption due to its high computational/memory requirements and the fact that the technique often exhibits high noise sensitivity. Here, we propose a method for noise suppression in WDD via low-rank noisy matrix completion. Our technique exploits the redundancy of an object’s phase space to denoise its WDD reconstruction. We show in model calculations that our technique outperforms other WDD algorithms as well as modern iterative methods for phasemore » retrieval such as ptychography. Here, our results suggest that a class of phase retrieval techniques relying on regularized direct inversion of ptychographic datasets (instead of iterative reconstruction techniques) can provide accurate quantitative phase information in the presence of high levels of noise.« less

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

PubMed

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

2000-12-01

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

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

NASA Astrophysics Data System (ADS)

Kocia, Lucas; Love, Peter

2017-12-01

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

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

NASA Astrophysics Data System (ADS)

Yu, Zhisong; Ren, Guihua; Yu, Ziyang; Wei, Chenhuinan; Fan, Hongyi

2018-06-01

For developing quantum mechanics theory in phase space, we explore how the Wigner operator {Δ } (α ,α ^{\\ast } )≡ {1}/{π } :e^{-2(α ^{\\ast } -α ^{\\dag })(α -α )}:, when viewed as a quasi-density operator correponding to the Wigner quasiprobability distribution, evolves in a damping channel. with the damping constant κ. We derive that it evolves into 1/T + 1:\\exp 2/T + 1[-(α^{\\ast} e^{-κ t}-a^{\\dag} )(α e^{-κ t}-a)]: where T ≡ 1 - e - 2 κ t . This in turn helps to directly obtain the final state ρ( t) out of the dessipative channel from the initial classical function corresponding to initial ρ(0). Throught the work, the method of integration within ordered product (IWOP) of operators is employed.

Three Dimensional Imaging of the Nucleon

NASA Astrophysics Data System (ADS)

More, Jai; Mukherjee, Asmita; Nair, Sreeraj

2018-05-01

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

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

NASA Astrophysics Data System (ADS)

Widjaja, Joewono; Dawprateep, Saowaros; Chuamchaitrakool, Porntip

2017-07-01

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

Positive Wigner functions render classical simulation of quantum computation efficient.

PubMed

Mari, A; Eisert, J

2012-12-07

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

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

NASA Technical Reports Server (NTRS)

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

1992-01-01

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

A mathematical solution for the parameters of three interfering resonances

NASA Astrophysics Data System (ADS)

Han, X.; Shen, C. P.

2018-04-01

The multiple-solution problem in determining the parameters of three interfering resonances from a fit to an experimentally measured distribution is considered from a mathematical viewpoint. It is shown that there are four numerical solutions for a fit with three coherent Breit-Wigner functions. Although explicit analytical formulae cannot be derived in this case, we provide some constraint equations between the four solutions. For the cases of nonrelativistic and relativistic Breit-Wigner forms of amplitude functions, a numerical method is provided to derive the other solutions from that already obtained, based on the obtained constraint equations. In real experimental measurements with more complicated amplitude forms similar to Breit-Wigner functions, the same method can be deduced and performed to get numerical solutions. The good agreement between the solutions found using this mathematical method and those directly from the fit verifies the correctness of the constraint equations and mathematical methodology used. Supported by National Natural Science Foundation of China (NSFC) (11575017, 11761141009), the Ministry of Science and Technology of China (2015CB856701) and the CAS Center for Excellence in Particle Physics (CCEPP)

A Wigner Monte Carlo approach to density functional theory

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

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

2014-08-01

In order to simulate quantum N-body systems, stationary and time-dependent density functional theories rely on the capacity of calculating the single-electron wave-functions of a system from which one obtains the total electron density (Kohn–Sham systems). In this paper, we introduce the use of the Wigner Monte Carlo method in ab-initio calculations. This approach allows time-dependent simulations of chemical systems in the presence of reflective and absorbing boundary conditions. It also enables an intuitive comprehension of chemical systems in terms of the Wigner formalism based on the concept of phase-space. Finally, being based on a Monte Carlo method, it scales verymore » well on parallel machines paving the way towards the time-dependent simulation of very complex molecules. A validation is performed by studying the electron distribution of three different systems, a Lithium atom, a Boron atom and a hydrogenic molecule. For the sake of simplicity, we start from initial conditions not too far from equilibrium and show that the systems reach a stationary regime, as expected (despite no restriction is imposed in the choice of the initial conditions). We also show a good agreement with the standard density functional theory for the hydrogenic molecule. These results demonstrate that the combination of the Wigner Monte Carlo method and Kohn–Sham systems provides a reliable computational tool which could, eventually, be applied to more sophisticated problems.« less

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

PubMed

de Gosson, Maurice A; de Gosson, Serge M

2012-01-09

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

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

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

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

2015-01-01

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

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

NASA Astrophysics Data System (ADS)

Ikegami, Hiroki; Akimoto, Hikota; Kono, Kimitoshi

2015-05-01

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

Wigner Function Reconstruction in Levitated Optomechanics

NASA Astrophysics Data System (ADS)

Rashid, Muddassar; Toroš, Marko; Ulbricht, Hendrik

2017-10-01

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

Time-frequency distributions for propulsion-system diagnostics

NASA Astrophysics Data System (ADS)

Griffin, Michael E.; Tulpule, Sharayu

1991-12-01

The Wigner distribution and its smoothed versions, i.e., Choi-Williams and Gaussian kernels, are evaluated for propulsion system diagnostics. The approach is intended for off-line kernel design by using the ambiguity domain to select the appropriate Gaussian kernel. The features produced by the Wigner distribution and its smoothed versions correlate remarkably well with documented failure indications. The selection of the kernel on the other hand is very subjective for our unstructured data.

Peculiarities of the momentum distribution functions of strongly correlated charged fermions

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

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

PubMed

Koda, Shin-ichi

2015-12-28

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

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

PubMed

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.

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

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

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

2014-12-15

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

A Wigner-based ray-tracing method for imaging simulations

NASA Astrophysics Data System (ADS)

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

2015-09-01

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 spectrum can be easily obtained from the WDF and the WDF remains constant along the paths of paraxial geometrical rays. In this study we use these properties by implementing a numerical Wigner-Based Ray-Tracing method (WBRT) to simulate diffraction effects at apertures in free-space and in imaging systems. Both paraxial and non-paraxial systems are considered and the results are compared with numerical implementations of the Rayleigh-Sommerfeld and Fresnel diffraction integrals to investigate the limits of the applicability of this approach. The results of the different methods are in good agreement when simulating free-space diffraction or calculating point spread functions (PSFs) for aberration-free imaging systems, even at numerical apertures exceeding the paraxial regime. For imaging systems with aberrations, the PSFs of WBRT diverge from the results using diffraction integrals. For larger aberrations WBRT predicts negative intensities, suggesting that this model is unable to deal with aberrations.

Positive phase space distributions and uncertainty relations

NASA Technical Reports Server (NTRS)

Kruger, Jan

1993-01-01

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

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

DTIC Science & Technology

2013-03-22

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

[A new method to extract time-frequency characteristics of hypertension pathological signal based on pseudo Wigner-Ville distribution].

PubMed

Zhang, Xun; Zhang, Miaomiao; Du, Panpan

2012-02-01

Hypertension, as one of diseases with the highest incidence in the world at present, is an important cause of stroke, coronary heart disease, renal insufficiency and other serious diseases. Based on pseudo Wigner-Ville distribution, this paper makes an analysis on the relevant pulse characteristics by measuring time range of the energy concentration circle. In view of the present situation, that is, about half of the high-normal blood pressure persons are likely to develop hypertension, we explored the pulse characteristics to find the pathological changes in subjects with prehypertension, in order to solve the problems that there are no obvious clinical significant features in prehypertension. The results showed that the duration of high energy circle in signal with hypertension pathological changes was shorter than the duration of healthy signal. Hence, healthy signal and hypertension pathological signal can be effectively distinguished by this method, and this provides a new basis to identify the lesion signal when blood pressure is in critical period.

Super-Resolution of Multi-Pixel and Sub-Pixel Images for the SDI

DTIC Science & Technology

1993-06-08

where the phase of the transmitted signal is not needed. The Wigner - Ville distribution ( WVD ) of a real signal s(t), associated with the complex...B. Boashash, 0. P. Kenny and H. J. Whitehouse, "Radar imaging using the Wigner - Ville distribution ", in Real-Time Signal Processing, J. P. Letellier...analytic signal z(t), is a time- frequency distribution defined as-’- 00 W(tf) Z (~t + ) t- -)exp(-i2nft) . (45) Note that the WVD is the double Fourier

Distribution of nuclei in equilibrium stellar matter from the free-energy density in a Wigner-Seitz cell

NASA Astrophysics Data System (ADS)

Grams, G.; Giraud, S.; Fantina, A. F.; Gulminelli, F.

2018-03-01

The aim of the present study is to calculate the nuclear distribution associated at finite temperature to any given equation of state of stellar matter based on the Wigner-Seitz approximation, for direct applications in core-collapse simulations. The Gibbs free energy of the different configurations is explicitly calculated, with special care devoted to the calculation of rearrangement terms, ensuring thermodynamic consistency. The formalism is illustrated with two different applications. First, we work out the nuclear statistical equilibrium cluster distribution for the Lattimer and Swesty equation of state, widely employed in supernova simulations. Secondly, we explore the effect of including shell structure, and consider realistic nuclear mass tables from the Brussels-Montreal Hartree-Fock-Bogoliubov model (specifically, HFB-24). We show that the whole collapse trajectory is dominated by magic nuclei, with extremely spread and even bimodal distributions of the cluster probability around magic numbers, demonstrating the importance of cluster distributions with realistic mass models in core-collapse simulations. Simple analytical expressions are given, allowing further applications of the method to any relativistic or nonrelativistic subsaturation equation of state.

Battle Damage Assessment Using Inverse Synthetic Aperture Radar (ISAR)

DTIC Science & Technology

2004-12-01

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

Extracting Micro-Doppler Radar Signatures from Rotating Targets Using Fourier-Bessel Transform and Time-Frequency Analysis

DTIC Science & Technology

2014-10-16

Time-Frequency analysis, Short-Time Fourier Transform, Wigner Ville Distribution, Fourier Bessel Transform, Fractional Fourier Transform. I...INTRODUCTION Most widely used time-frequency transforms are short-time Fourier Transform (STFT) and Wigner Ville distribution (WVD). In STFT, time and...frequency resolutions are limited by the size of window function used in calculating STFT. For mono-component signals, WVD gives the best time and frequency

Vibration Signature Analysis of a Faulted Gear Transmission System

NASA Technical Reports Server (NTRS)

Choy, F. K.; Huang, S.; Zakrajsek, J. J.; Handschuh, R. F.; Townsend, D. P.

1994-01-01

A comprehensive procedure in predicting faults in gear transmission systems under normal operating conditions is presented. Experimental data was obtained from a spiral bevel gear fatigue test rig at NASA Lewis Research Center. Time synchronous averaged vibration data was recorded throughout the test as the fault progressed from a small single pit to severe pitting over several teeth, and finally tooth fracture. A numerical procedure based on the Winger-Ville distribution was used to examine the time averaged vibration data. Results from the Wigner-Ville procedure are compared to results from a variety of signal analysis techniques which include time domain analysis methods and frequency analysis methods. Using photographs of the gear tooth at various stages of damage, the limitations and accuracy of the various techniques are compared and discussed. Conclusions are drawn from the comparison of the different approaches as well as the applicability of the Wigner-Ville method in predicting gear faults.

Wigner functions for evanescent waves.

PubMed

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.

Path integral approach to the Wigner representation of canonical density operators for discrete systems coupled to harmonic baths.

PubMed

Montoya-Castillo, Andrés; Reichman, David R

2017-01-14

We derive a semi-analytical form for the Wigner transform for the canonical density operator of a discrete system coupled to a harmonic bath based on the path integral expansion of the Boltzmann factor. The introduction of this simple and controllable approach allows for the exact rendering of the canonical distribution and permits systematic convergence of static properties with respect to the number of path integral steps. In addition, the expressions derived here provide an exact and facile interface with quasi- and semi-classical dynamical methods, which enables the direct calculation of equilibrium time correlation functions within a wide array of approaches. We demonstrate that the present method represents a practical path for the calculation of thermodynamic data for the spin-boson and related systems. We illustrate the power of the present approach by detailing the improvement of the quality of Ehrenfest theory for the correlation function C zz (t)=Re⟨σ z (0)σ z (t)⟩ for the spin-boson model with systematic convergence to the exact sampling function. Importantly, the numerically exact nature of the scheme presented here and its compatibility with semiclassical methods allows for the systematic testing of commonly used approximations for the Wigner-transformed canonical density.

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

DTIC Science & Technology

1993-09-01

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

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

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

Gaunaurd, G.; Strifors, H.C.

1996-09-01

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

Group Velocity Dispersion Curves from Wigner-Ville Distributions

NASA Astrophysics Data System (ADS)

Lloyd, Simon; Bokelmann, Goetz; Sucic, Victor

2013-04-01

With the widespread adoption of ambient noise tomography, and the increasing number of local earthquakes recorded worldwide due to dense seismic networks and many very dense temporary experiments, we consider it worthwhile to evaluate alternative Methods to measure surface wave group velocity dispersions curves. Moreover, the increased computing power of even a simple desktop computer makes it feasible to routinely use methods other than the typically employed multiple filtering technique (MFT). To that end we perform tests with synthetic and observed seismograms using the Wigner-Ville distribution (WVD) frequency time analysis, and compare dispersion curves measured with WVD and MFT with each other. Initial results suggest WVD to be at least as good as MFT at measuring dispersion, albeit at a greater computational expense. We therefore need to investigate if, and under which circumstances, WVD yields better dispersion curves than MFT, before considering routinely applying the method. As both MFT and WVD generally work well for teleseismic events and at longer periods, we explore how well the WVD method performs at shorter periods and for local events with smaller epicentral distances. Such dispersion information could potentially be beneficial for improving velocity structure resolution within the crust.

Analysis of cardiac signals using spatial filling index and time-frequency domain

PubMed Central

Faust, Oliver; Acharya U, Rajendra; Krishnan, SM; Min, Lim Choo

2004-01-01

Background Analysis of heart rate variation (HRV) has become a popular noninvasive tool for assessing the activities of the autonomic nervous system (ANS). HRV analysis is based on the concept that fast fluctuations may specifically reflect changes of sympathetic and vagal activity. It shows that the structure generating the signal is not simply linear, but also involves nonlinear contributions. These signals are essentially non-stationary; may contain indicators of current disease, or even warnings about impending diseases. The indicators may be present at all times or may occur at random in the time scale. However, to study and pinpoint abnormalities in voluminous data collected over several hours is strenuous and time consuming. Methods This paper presents the spatial filling index and time-frequency analysis of heart rate variability signal for disease identification. Renyi's entropy is evaluated for the signal in the Wigner-Ville and Continuous Wavelet Transformation (CWT) domain. Results This Renyi's entropy gives lower 'p' value for scalogram than Wigner-Ville distribution and also, the contours of scalogram visually show the features of the diseases. And in the time-frequency analysis, the Renyi's entropy gives better result for scalogram than the Wigner-Ville distribution. Conclusion Spatial filling index and Renyi's entropy has distinct regions for various diseases with an accuracy of more than 95%. PMID:15361254

Measurement of complete and continuous Wigner functions for discrete atomic systems

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

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

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

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

2015-11-01

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

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

PubMed

Sun, Dong; Zhao, Daomu

2005-08-01

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

Time-Frequency Based Instantaneous Frequency Estimation of Sparse Signals from an Incomplete Set of Samples

DTIC Science & Technology

2014-06-17

100 0 2 4 Wigner distribution 0 50 100 0 0.5 1 Auto-correlation function 0 50 100 0 2 4 L- Wigner distribution 0 50 100 0 0.5 1 Auto-correlation function ...bilinear or higher order autocorrelation functions will increase the number of missing samples, the analysis shows that accurate instantaneous...frequency estimation can be achieved even if we deal with only few samples, as long as the auto-correlation function is properly chosen to coincide with

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

PubMed

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.

An Overview Of Wideband Signal Analysis Techniques

NASA Astrophysics Data System (ADS)

Speiser, Jeffrey M.; Whitehouse, Harper J.

1989-11-01

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

Analysis of frequency shifting in seismic signals using Gabor-Wigner transform

NASA Astrophysics Data System (ADS)

Kumar, Roshan; Sumathi, P.; Kumar, Ashok

2015-12-01

A hybrid time-frequency method known as Gabor-Wigner transform (GWT) is introduced in this paper for examining the time-frequency patterns of earthquake damaged buildings. GWT is developed by combining the Gabor transform (GT) and Wigner-Ville distribution (WVD). GT and WVD have been used separately on synthetic and recorded earthquake data to identify frequency shifting due to earthquake damages, but GT is prone to windowing effect and WVD involves ambiguity function. Hence to obtain better clarity and to remove the cross terms (frequency interference), GT and WVD are judiciously combined and the resultant GWT used to identify frequency shifting. Synthetic seismic response of an instrumented building and real-time earthquake data recorded on the building were investigated using GWT. It is found that GWT offers good accuracy for even slow variations in frequency, good time-frequency resolution, and localized response. Presented results confirm the efficacy of GWT when compared with GT and WVD used separately. Simulation results were quantified by the Renyi entropy measures and GWT shown to be an adequate technique in identifying localized response for structural damage detection.

Lattice Wigner equation.

PubMed

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.

Semiclassical propagation: Hilbert space vs. Wigner representation

NASA Astrophysics Data System (ADS)

Gottwald, Fabian; Ivanov, Sergei D.

2018-03-01

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

Lattice Wigner equation

NASA Astrophysics Data System (ADS)

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.

A novel procedure for detecting and focusing moving objects with SAR based on the Wigner-Ville distribution

NASA Astrophysics Data System (ADS)

Barbarossa, S.; Farina, A.

A novel scheme for detecting moving targets with synthetic aperture radar (SAR) is presented. The proposed approach is based on the use of the Wigner-Ville distribution (WVD) for simultaneously detecting moving targets and estimating their motion kinematic parameters. The estimation plays a key role for focusing the target and correctly locating it with respect to the stationary background. The method has a number of advantages: (i) the detection is efficiently performed on the samples in the time-frequency domain, provided the WVD, without resorting to the use of a bank of filters, each one matched to possible values of the unknown target motion parameters; (ii) the estimation of the target motion parameters can be done on the same time-frequency domain by locating the line where the maximum energy of the WVD is concentrated. A validation of the approach is given by both analytical and simulation means. In addition, the estimation of the target kinematic parameters and the corresponding image focusing are also demonstrated.

A phase space approach to wave propagation with dispersion.

PubMed

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.

Reconstruction of fiber grating period profiles by use of Wigner-Ville distributions and spectrograms.

PubMed

Azaña, J; Muriel, M A

2000-12-01

The grating-period profile and length of an arbitrary fiber Bragg grating structure can be reconstructed from the structure's reflection response by use of a time-frequency signal representation based on the well-known Wigner-Ville distribution and spectrogram. We present a detailed description of this synthesis technique. By means of numerical simulations, the technique is tested with several fiber grating structures. In general, our results show good agreement between exact and reconstructed functions. The technique's advantages and limitations are discussed. We propose and demonstrate the application of the proposed synthesis technique to distributed mechanical strain or temperature sensing.

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

PubMed

Terraneo, M; Georgeot, B; Shepelyansky, D L

2005-06-01

We study the efficiency of quantum algorithms which aim at obtaining phase-space distribution functions of quantum systems. Wigner and Husimi functions are considered. Different quantum algorithms are envisioned to build these functions, and compared with the classical computation. Different procedures to extract more efficiently information from the final wave function of these algorithms are studied, including coarse-grained measurements, amplitude amplification, and measure of wavelet-transformed wave function. The algorithms are analyzed and numerically tested on a complex quantum system showing different behavior depending on parameters: namely, the kicked rotator. The results for the Wigner function show in particular that the use of the quantum wavelet transform gives a polynomial gain over classical computation. For the Husimi distribution, the gain is much larger than for the Wigner function and is larger with the help of amplitude amplification and wavelet transforms. We discuss the generalization of these results to the simulation of other quantum systems. We also apply the same set of techniques to the analysis of real images. The results show that the use of the quantum wavelet transform allows one to lower dramatically the number of measurements needed, but at the cost of a large loss of information.

[An EMD based time-frequency distribution and its application in EEG analysis].

PubMed

Li, Xiaobing; Chu, Meng; Qiu, Tianshuang; Bao, Haiping

2007-10-01

Hilbert-Huang transform (HHT) is a new time-frequency analytic method to analyze the nonlinear and the non-stationary signals. The key step of this method is the empirical mode decomposition (EMD), with which any complicated signal can be decomposed into a finite and small number of intrinsic mode functions (IMF). In this paper, a new EMD based method for suppressing the cross-term of Wigner-Ville distribution (WVD) is developed and is applied to analyze the epileptic EEG signals. The simulation data and analysis results show that the new method suppresses the cross-term of the WVD effectively with an excellent resolution.

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

PubMed

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

2009-07-14

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

Computing thermal Wigner densities with the phase integration method

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

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

2014-08-28

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

Computing thermal Wigner densities with the phase integration method.

PubMed

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

2014-08-28

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

Mean-field approximation for spacing distribution functions in classical systems

NASA Astrophysics Data System (ADS)

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

2012-01-01

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

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

PubMed

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

2014-10-01

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

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

PubMed

Tanaka, Takashi

2017-04-15

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

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

NASA Technical Reports Server (NTRS)

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

1989-01-01

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

[Evoked Potential Blind Extraction Based on Fractional Lower Order Spatial Time-Frequency Matrix].

PubMed

Long, Junbo; Wang, Haibin; Zha, Daifeng

2015-04-01

The impulsive electroencephalograph (EEG) noises in evoked potential (EP) signals is very strong, usually with a heavy tail and infinite variance characteristics like the acceleration noise impact, hypoxia and etc., as shown in other special tests. The noises can be described by a stable distribution model. In this paper, Wigner-Ville distribution (WVD) and pseudo Wigner-Ville distribution (PWVD) time-frequency distribution based on the fractional lower order moment are presented to be improved. We got fractional lower order WVD (FLO-WVD) and fractional lower order PWVD (FLO-PWVD) time-frequency distribution which could be suitable for a stable distribution process. We also proposed the fractional lower order spatial time-frequency distribution matrix (FLO-STFM) concept. Therefore, combining with time-frequency underdetermined blind source separation (TF-UBSS), we proposed a new fractional lower order spatial time-frequency underdetermined blind source separation (FLO-TF-UBSS) which can work in a stable distribution environment. We used the FLO-TF-UBSS algorithm to extract EPs. Simulations showed that the proposed method could effectively extract EPs in EEG noises, and the separated EPs and EEG signals based on FLO-TF-UBSS were almost the same as the original signal, but blind separation based on TF-UBSS had certain deviation. The correlation coefficient of the FLO-TF-UBSS algorithm was higher than the TF-UBSS algorithm when generalized signal-to-noise ratio (GSNR) changed from 10 dB to 30 dB and a varied from 1. 06 to 1. 94, and was approximately e- qual to 1. Hence, the proposed FLO-TF-UBSS method might be better than the TF-UBSS algorithm based on second order for extracting EP signal under an EEG noise environment.

Moments of the Wigner function and Renyi entropies at freeze-out

NASA Astrophysics Data System (ADS)

Bialas, A.; Czyz, W.; Zalewski, K.

2006-03-01

The relation between Renyi entropies and moments of the Wigner function, representing the quantum mechanical description of the M-particle semi-inclusive distribution at freeze-out, is investigated. It is shown that in the limit of infinite volume of the system, the classical and quantum descriptions are equivalent. Finite volume corrections are derived and shown to be small for systems encountered in relativistic heavy ion collisions.

Phase-space methods for the spin dynamics in condensed matter systems

PubMed Central

Hurst, Jérôme; Manfredi, Giovanni

2017-01-01

Using the phase-space formulation of quantum mechanics, we derive a four-component Wigner equation for a system composed of spin- fermions (typically, electrons) including the Zeeman effect and the spin–orbit coupling. This Wigner equation is coupled to the appropriate Maxwell equations to form a self-consistent mean-field model. A set of semiclassical Vlasov equations with spin effects is obtained by expanding the full quantum model to first order in the Planck constant. The corresponding hydrodynamic equations are derived by taking velocity moments of the phase-space distribution function. A simple closure relation is proposed to obtain a closed set of hydrodynamic equations. This article is part of the themed issue ‘Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces’. PMID:28320903

Analyzing capture zone distributions (CZD) in growth: Theory and applications

NASA Astrophysics Data System (ADS)

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

2014-09-01

We have argued that the capture-zone distribution (CZD) in submonolayer growth can be well described by the generalized Wigner distribution (GWD) P(s) =asβ exp(-bs2), where s is the CZ area divided by its average value. This approach offers arguably the most robust (least sensitive to mass transport) method to find the critical nucleus size i, since β ≈ i + 2. Various analytical and numerical investigations, which we discuss, show that the simple GWD expression is inadequate in the tails of the distribution, it does account well for the central regime 0.5 < s < 2, where the data is sufficiently large to be reliably accessible experimentally. We summarize and catalog the many experiments in which this method has been applied.

Analytical and Experimental Vibration Analysis of a Faulty Gear System.

DTIC Science & Technology

1994-10-01

Wigner - Ville Distribution ( WVD ) was used to give a comprehensive comparison of the predicted and...experimental results. The WVD method applied to the experimental results were also compared to other fault detection techniques to verify the WVD’s ability to...of the damaged test gear and the predicted vibration from the model with simulated gear tooth pitting damage. Results also verified that the WVD method can successfully detect and locate gear tooth wear and pitting damage.

Radar signal analysis of ballistic missile with micro-motion based on time-frequency distribution

NASA Astrophysics Data System (ADS)

Wang, Jianming; Liu, Lihua; Yu, Hua

2015-12-01

The micro-motion of ballistic missile targets induces micro-Doppler modulation on the radar return signal, which is a unique feature for the warhead discrimination during flight. In order to extract the micro-Doppler feature of ballistic missile targets, time-frequency analysis is employed to process the micro-Doppler modulated time-varying radar signal. The images of time-frequency distribution (TFD) reveal the micro-Doppler modulation characteristic very well. However, there are many existing time-frequency analysis methods to generate the time-frequency distribution images, including the short-time Fourier transform (STFT), Wigner distribution (WD) and Cohen class distribution, etc. Under the background of ballistic missile defence, the paper aims at working out an effective time-frequency analysis method for ballistic missile warhead discrimination from the decoys.

Seismic spectral decomposition and analysis based on Wigner-Ville distribution for sandstone reservoir characterization in West Sichuan depression

NASA Astrophysics Data System (ADS)

Wu, Xiaoyang; Liu, Tianyou

2010-06-01

Reflections from a hydrocarbon-saturated zone are generally expected to have a tendency to be low frequency. Previous work has shown the application of seismic spectral decomposition for low-frequency shadow detection. In this paper, we further analyse the characteristics of spectral amplitude in fractured sandstone reservoirs with different fluid saturations using the Wigner-Ville distribution (WVD)-based method. We give a description of the geometric structure of cross-terms due to the bilinear nature of WVD and eliminate cross-terms using smoothed pseudo-WVD (SPWVD) with time- and frequency-independent Gaussian kernels as smoothing windows. SPWVD is finally applied to seismic data from West Sichuan depression. We focus our study on the comparison of SPWVD spectral amplitudes resulting from different fluid contents. It shows that prolific gas reservoirs feature higher peak spectral amplitude at higher peak frequency, which attenuate faster than low-quality gas reservoirs and dry or wet reservoirs. This can be regarded as a spectral attenuation signature for future exploration in the study area.

Symplectic evolution of Wigner functions in Markovian open systems.

PubMed

Brodier, O; Almeida, A M Ozorio de

2004-01-01

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

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

PubMed

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

2012-01-01

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

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

NASA Astrophysics Data System (ADS)

Chatterjee, Arpita

2018-02-01

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

Use of the Wigner-Ville distribution in interpreting and identifying ULF waves in triaxial magnetic records

NASA Astrophysics Data System (ADS)

Chi, P. J.; Russell, C. T.

2008-01-01

Magnetospheric ultra-low-frequency (ULF) waves (f = 1 mHz to 1 Hz) exhibit highly time-dependent characteristics due to the dynamic properties of these waves and, for observations in space, the spacecraft motion. These time-dependent features may not be properly resolved by conventional Fourier techniques. In this study we examine how the Wigner-Ville distribution (WVD) can be used to analyze ULF waves. We find that this approach has unique advantages over the conventional Fourier spectrograms and wavelet scalograms. In particular, for Pc1 wave packets, field line/cavity mode resonances in the Pc 3-4 band, and Pi2 pulsations, the start and end times of each wave packet can be well identified and the frequency better defined. In addition, we demonstrate that the Wigner-Ville distribution can be used to calculate the polarization of wave signals in triaxial magnetic field data in a way analogous to Fourier analysis. Motivated by the large amount of ULF wave observations, we have also developed a WVD-based algorithm to identify ULF waves as a way to facilitate the rapid processing of the data collected by satellite missions and the vast network of ground magnetometers.

Statistical analysis of excitation energies in actinide and rare-earth nuclei

NASA Astrophysics Data System (ADS)

Levon, A. I.; Magner, A. G.; Radionov, S. V.

2018-04-01

Statistical analysis of distributions of the collective states in actinide and rare-earth nuclei is performed in terms of the nearest-neighbor spacing distribution (NNSD). Several approximations, such as the linear approach to the level repulsion density and that suggested by Brody to the NNSDs were applied for the analysis. We found an intermediate character of the experimental spectra between the order and the chaos for a number of rare-earth and actinide nuclei. The spectra are closer to the Wigner distribution for energies limited by 3 MeV, and to the Poisson distribution for data including higher excitation energies and higher spins. The latter result is in agreement with the theoretical calculations. These features are confirmed by the cumulative distributions, where the Wigner contribution dominates at smaller spacings while the Poisson one is more important at larger spacings, and our linear approach improves the comparison with experimental data at all desired spacings.

Wigner Functions for the Bateman System on Noncommutative Phase Space

NASA Astrophysics Data System (ADS)

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

2010-09-01

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

Use of the Wigner representation in scattering problems

NASA Technical Reports Server (NTRS)

Bemler, E. A.

1975-01-01

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

Finite-mode analysis by means of intensity information in fractional optical systems.

PubMed

Alieva, Tatiana; Bastiaans, Martin J

2002-03-01

It is shown how a coherent optical signal that contains only a finite number of Hermite-Gauss modes can be reconstructed from the knowledge of its Radon-Wigner transform-associated with the intensity distribution in a fractional-Fourier-transform optical system-at only two transversal points. The proposed method can be generalized to any fractional system whose generator transform has a complete orthogonal set of eigenfunctions.

Application Of The Wigner-Ville Distribution To The Identification Of Machine Noise

NASA Astrophysics Data System (ADS)

Boashash, Boualem; O'Shea, Peter

1988-02-01

The theory of signal detection using the Wigner-Ville Distribution (WVD) and the Cross Wagner-Ville Distribution (XWVD) is reviewed, and applied to the signaturing, detection, and identification of some specific machine sounds - the individual cylinder firings of a marine engine. For this task, a 4 step procedure has been devised. The Autocorrelation Function (ACF) is first employed for ascertaining the number of engine cylinders and the firing rate of the engine. Cross-correlation techniques are then used for detecting the occurrence of cylinder firing events. This is followed by the use WVD and XWVD based analyses to produce high resolution Time-Frequency signatures, and finally 2D correlations are employed for identification of the cylinders. The proposed methodology is applied to real data.

A time-frequency approach for the analysis of normal and arrhythmia cardiac signals.

PubMed

Mahmoud, Seedahmed S; Fang, Qiang; Davidović, Dragomir M; Cosic, Irena

2006-01-01

Previously, electrocardiogram (ECG) signals have been analyzed in either a time-indexed or spectral form. The reality, is that the ECG and all other biological signals belong to the family of multicomponent nonstationary signals. Due to this reason, the use of time-frequency analysis can be unavoidable for these signals. The Husimi and Wigner distributions are normally used in quantum mechanics for phase space representations of the wavefunction. In this paper, we introduce the Husimi distribution (HD) to analyze the normal and abnormal ECG signals in time-frequency domain. The abnormal cardiac signal was taken from a patient with supraventricular arrhythmia. Simulation results show that the HD has a good performance in the analysis of the ECG signals comparing with the Wigner-Ville distribution (WVD).

Shear wave elastography using Wigner-Ville distribution: a simulated multilayer media study.

PubMed

Bidari, Pooya Sobhe; Alirezaie, Javad; Tavakkoli, Jahan

2016-08-01

Shear Wave Elastography (SWE) is a quantitative ultrasound-based imaging modality for distinguishing normal and abnormal tissue types by estimating the local viscoelastic properties of the tissue. These properties have been estimated in many studies by propagating ultrasound shear wave within the tissue and estimating parameters such as speed of wave. Vast majority of the proposed techniques are based on the cross-correlation of consecutive ultrasound images. In this study, we propose a new method of wave detection based on time-frequency (TF) analysis of the ultrasound signal. The proposed method is a modified version of the Wigner-Ville Distribution (WVD) technique. The TF components of the wave are detected in a propagating ultrasound wave within a simulated multilayer tissue and the local properties are estimated based on the detected waves. Image processing techniques such as Alternative Sequential Filters (ASF) and Circular Hough Transform (CHT) have been utilized to improve the estimation of TF components. This method has been applied to a simulated data from Wave3000™ software (CyberLogic Inc., New York, NY). This data simulates the propagation of an acoustic radiation force impulse within a two-layer tissue with slightly different viscoelastic properties between the layers. By analyzing the local TF components of the wave, we estimate the longitudinal and shear elasticities and viscosities of the media. This work shows that our proposed method is capable of distinguishing between different layers of a tissue.

Functional Wigner representation of quantum dynamics of Bose-Einstein condensate

NASA Astrophysics Data System (ADS)

Opanchuk, B.; Drummond, P. D.

2013-04-01

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

Wigner surmises and the two-dimensional homogeneous Poisson point process.

PubMed

Sakhr, Jamal; Nieminen, John M

2006-04-01

We derive a set of identities that relate the higher-order interpoint spacing statistics of the two-dimensional homogeneous Poisson point process to the Wigner surmises for the higher-order spacing distributions of eigenvalues from the three classical random matrix ensembles. We also report a remarkable identity that equates the second-nearest-neighbor spacing statistics of the points of the Poisson process and the nearest-neighbor spacing statistics of complex eigenvalues from Ginibre's ensemble of 2 x 2 complex non-Hermitian random matrices.

Wigner distribution function and kurtosis parameter of vortex beams propagating through turbulent atmosphere

NASA Astrophysics Data System (ADS)

Suo, Qiangbo; Han, Yiping; Cui, Zhiwei

2017-09-01

Based on the extended Huygens-Fresnel integral, the analytical expressions for the Wigner distribution function (WDF) and kurtosis parameter of partially coherent flat-topped vortex (PCFTV) beams propagating through atmospheric turbulence and free space are derived. The WDF and kurtosis parameter of PCFTV beams through turbulent atmosphere are discussed with numerical examples. The numerical results show that the beam quality depends on the structure constants, the inner scale turbulence, the outer scale turbulence, the spatial correlation length, the wave length and the beam order. PCFTV beams are less affected by turbulence than partially flat-topped coherent (PCFT) beams under the same conditions, and will be useful in free-space optical communications.

Quantum theory of shuttling instability in a movable quantum dot array

NASA Astrophysics Data System (ADS)

Donarini, Andrea; Novotný, Tomás; Jauho, Antti-Pekka

2004-04-01

We study the shuttling instability in an array of three quantum dots the central one of which is movable. We extend the results by Armour and MacKinnon on this problem to a broader parameter regime. The results obtained by an efficient numerical method are interpreted directly using the Wigner distributions. We emphasize that the instability should be viewed as a crossover phenomenon rather than a clear-cut transition.

Dissipative quantum transport in silicon nanowires based on Wigner transport equation

NASA Astrophysics Data System (ADS)

Barraud, Sylvain

2011-11-01

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

Analysis of digital communication signals and extraction of parameters

NASA Astrophysics Data System (ADS)

Al-Jowder, Anwar

1994-12-01

The signal classification performance of four types of electronics support measure (ESM) communications detection systems is compared from the standpoint of the unintended receiver (interceptor). Typical digital communication signals considered include binary phase shift keying (BPSK), quadrature phase shift keying (QPSK), frequency shift keying (FSK), and on-off keying (OOK). The analysis emphasizes the use of available signal processing software. Detection methods compared include broadband energy detection, FFT-based narrowband energy detection, and two correlation methods which employ the fast Fourier transform (FFT). The correlation methods utilize modified time-frequency distributions, where one of these is based on the Wigner-Ville distribution (WVD). Gaussian white noise is added to the signal to simulate various signal-to-noise ratios (SNR's).

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

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

NASA Astrophysics Data System (ADS)

Chai, Yunzi; Zhang, Xudong

2016-10-01

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

Functional Wigner representation of quantum dynamics of Bose-Einstein condensate

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

Opanchuk, B.; Drummond, P. D.

2013-04-15

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

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

NASA Technical Reports Server (NTRS)

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

1986-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

Symplectic quantum mechanics (SQM) considers a non-commutative algebra of functions on a phase space Γ and an associated Hilbert space HΓ, to construct a unitary representation for the Galilei group. From this unitary representation the Schrödinger equation is rewritten in phase space variables and the Wigner function can be derived without the use of the Liouville-von Neumann equation. In this article the Coulomb potential in three dimensions (3D) is resolved completely by using the phase space Schrödinger equation. The Kustaanheimo-Stiefel(KS) transformation is applied and the Coulomb and harmonic oscillator potentials are connected. In this context we determine the energy levels, the amplitude of probability in phase space and correspondent Wigner quasi-distribution functions of the 3D-hydrogen atom described by Schrödinger equation in phase space.

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

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

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

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

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

DOE PAGES

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

2017-04-01

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

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

DOE PAGES

Miller, William H.; Cotton, Stephen J.

2016-08-28

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

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

PubMed

Miller, William H; Cotton, Stephen J

2016-08-28

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

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

NASA Astrophysics Data System (ADS)

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

2012-02-01

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

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

PubMed

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

NASA Astrophysics Data System (ADS)

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.

Fresnel representation of the Wigner function: an operational approach.

PubMed

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

2003-07-04

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

A signed particle formulation of non-relativistic quantum mechanics

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

Sellier, Jean Michel, E-mail: jeanmichel.sellier@parallel.bas.bg

2015-09-15

A formulation of non-relativistic quantum mechanics in terms of Newtonian particles is presented in the shape of a set of three postulates. In this new theory, quantum systems are described by ensembles of signed particles which behave as field-less classical objects which carry a negative or positive sign and interact with an external potential by means of creation and annihilation events only. This approach is shown to be a generalization of the signed particle Wigner Monte Carlo method which reconstructs the time-dependent Wigner quasi-distribution function of a system and, therefore, the corresponding Schrödinger time-dependent wave-function. Its classical limit is discussedmore » and a physical interpretation, based on experimental evidences coming from quantum tomography, is suggested. Moreover, in order to show the advantages brought by this novel formulation, a straightforward extension to relativistic effects is discussed. To conclude, quantum tunnelling numerical experiments are performed to show the validity of the suggested approach.« less

Phase retrieval in digital speckle pattern interferometry by use of a smoothed space-frequency distribution.

PubMed

Federico, Alejandro; Kaufmann, Guillermo H

2003-12-10

We evaluate the use of a smoothed space-frequency distribution (SSFD) to retrieve optical phase maps in digital speckle pattern interferometry (DSPI). The performance of this method is tested by use of computer-simulated DSPI fringes. Phase gradients are found along a pixel path from a single DSPI image, and the phase map is finally determined by integration. This technique does not need the application of a phase unwrapping algorithm or the introduction of carrier fringes in the interferometer. It is shown that a Wigner-Ville distribution with a smoothing Gaussian kernel gives more-accurate results than methods based on the continuous wavelet transform. We also discuss the influence of filtering on smoothing of the DSPI fringes and some additional limitations that emerge when this technique is applied. The performance of the SSFD method for processing experimental data is then illustrated.

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

Miller, William H., E-mail: millerwh@berkeley.edu; Cotton, Stephen J., E-mail: StephenJCotton47@gmail.com

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

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

Miller, William H.; Cotton, Stephen J.

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

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

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

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. Themore » 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.« less

Wigner functions defined with Laplace transform kernels.

PubMed

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

2011-10-24

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

Analysis Using Bi-Spectral Related Technique

DTIC Science & Technology

1993-11-17

filtering is employed as the data is processed (equation 1). Earlier results have shown that in contrast to the Wigner - Ville Distribution ( WVD ) no spectral...Technique by-o -~ Ralph Hippenstiel November 17, 1993 94 2 22 1 0 Approved for public reslease; distribution unlimited. Prepared for: Naval Command Control...Government. 12a. DISTRIBUTION /AVAILABILITY STATEMENT 12b. DISTRIBUTION ’.ODE Approved for public relkase; distribution unlimited. 13. ABSTRACT (Maximum

Further Progress Applying the Generalized Wigner Distribution to Analysis of Vicinal Surfaces

NASA Astrophysics Data System (ADS)

Einstein, T. L.; Richards, Howard L.; Cohen, S. D.

2001-03-01

Terrace width distributions (TWDs) can be well fit by the generalized Wigner distribution (GWD), generally better than by conventional Gaussians, and thus offers a convenient way to estimate the dimensionless elastic repulsion strength tildeA from σ^2, the TWD variance.(T.L. Einstein and O. Pierre-Louis, Surface Sci. 424), L299 (1999) The GWD σ^2 accurately reproduces values for the two exactly soluble cases at small tildeA and in the asymptotic limit. Taxing numerical simulations show that the GWD σ^2 interpolates well between these limits. Extensive applications have been made to experimental data, esp. on Cu.(M. Giesen and T.L. Einstein, Surface Sci. 449), 191 (2000) Recommended analysis procedures are catalogued.(H.L. Richards, S.D. Cohen, TLE, & M. Giesen, Surf Sci 453), 59 (2000) Extensions of the GWD for multistep distributions are tested, with good agreement for second-neighbor distributions, less good for third.(TLE, HLR, SDC, & OP-L, Proc ISSI-PDSC2000, cond-mat/0012xxxxx) Alternatively, step-step correlation functions, about which there is more theoretical information, should be measured.

The Wigner function in the relativistic quantum mechanics

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

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

2016-12-15

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

Radar modulation classification using time-frequency representation and nonlinear regression

NASA Astrophysics Data System (ADS)

De Luigi, Christophe; Arques, Pierre-Yves; Lopez, Jean-Marc; Moreau, Eric

1999-09-01

In naval electronic environment, pulses emitted by radars are collected by ESM receivers. For most of them the intrapulse signal is modulated by a particular law. To help the classical identification process, a classification and estimation of this modulation law is applied on the intrapulse signal measurements. To estimate with a good accuracy the time-varying frequency of a signal corrupted by an additive noise, one method has been chosen. This method consists on the Wigner distribution calculation, the instantaneous frequency is then estimated by the peak location of the distribution. Bias and variance of the estimator are performed by computed simulations. In a estimated sequence of frequencies, we assume the presence of false and good estimated ones, the hypothesis of Gaussian distribution is made on the errors. A robust non linear regression method, based on the Levenberg-Marquardt algorithm, is thus applied on these estimated frequencies using a Maximum Likelihood Estimator. The performances of the method are tested by using varied modulation laws and different signal to noise ratios.

Entanglement with negative Wigner function of three thousand atoms heralded by one photon

NASA Astrophysics Data System (ADS)

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

2016-06-01

Quantum-mechanically correlated (entangled) states of many particles are of interest in quantum information, quantum computing and quantum metrology. Metrologically useful entangled states of large atomic ensembles have been experimentally realized [1, 2, 3, 4, 5, 6, 7, 8, 9, 10], but these states display Gaussian spin distribution functions with a non-negative Wigner function. Non-Gaussian entangled states have been produced in small ensembles of ions [11, 12], and very recently in large atomic ensembles [13, 14, 15]. Here, we generate entanglement in a large atomic ensemble via the interaction with a very weak laser pulse; remarkably, the detection of a single photon prepares several thousand atoms in an entangled state. We reconstruct a negative-valued Wigner function, an important hallmark of nonclassicality, and verify an entanglement depth (minimum number of mutually entangled atoms) of 2910 ± 190 out of 3100 atoms. Attaining such a negative Wigner function and the mutual entanglement of virtually all atoms is unprecedented for an ensemble containing more than a few particles. While the achieved purity of the state is slightly below the threshold for entanglement-induced metrological gain, further technical improvement should allow the generation of states that surpass this threshold, and of more complex Schrödinger cat states for quantum metrology and information processing.

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

The Kirillov picture for the Wigner particle

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Analysis of the time-varying energy of brain responses to an oddball paradigm using short-term smoothed Wigner-Ville distribution.

PubMed

Tağluk, M E; Cakmak, E D; Karakaş, S

2005-04-30

Cognitive brain responses to external stimuli, as measured by event related potentials (ERPs), have been analyzed from a variety of perspectives to investigate brain dynamics. Here, the brain responses of healthy subjects to auditory oddball paradigms, standard and deviant stimuli, recorded on an Fz electrode site were studied using a short-term version of the smoothed Wigner-Ville distribution (STSW) method. A smoothing kernel was designed to preserve the auto energy of the signal with maximum time and frequency resolutions. Analysis was conducted mainly on the time-frequency distributions (TFDs) of sweeps recorded during successive trials including the TFD of averaged single sweeps as the evoked time-frequency (ETF) brain response and the average of TFDs of single sweeps as the time-frequency (TF) brain response. Also the power entropy and the phase angles of the signal at frequency f and time t locked to the stimulus onset were studied across single trials as the TF power-locked and the TF phase-locked brain responses, respectively. TFDs represented in this way demonstrated the ERP spectro-temporal characteristics from multiple perspectives. The time-varying energy of the individual components manifested interesting TF structures in the form of amplitude modulated (AM) and frequency modulated (FM) energy bursts. The TF power-locked and phase-locked brain responses provoked ERP energies in a manner modulated by cognitive functions, an observation requiring further investigation. These results may lead to a better understanding of integrative brain dynamics.

Semiclassical propagation of Wigner functions.

PubMed

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.

Quantum tomography of a molecular bond in ice.

PubMed

Goldschleger, I U; Golschleger, I U; van Staveren, M N; Apkarian, V Ara

2013-07-21

We present the moving picture of a molecular bond, in phase-space, in real-time, at resolution limited by quantum uncertainty. The images are tomographically reconstructed Wigner distribution functions (WDF) obtained from four-wave mixing measurements on Br2-doped ice. The WDF completely characterizes the dissipative quantum evolution of the system, which despite coupling to the environment retains quantum coherence, as evidenced by its persistent negative Wigner hole. The spectral decomposition of the WDF allows a direct visualization of wavefunctions and spatiotemporal coherences of the system and the system-bath interaction. The measurements vividly illustrate nonclassical wave mechanics in a many-body system, in ordinary condensed matter.

Proton spin structure from measurable parton distributions.

PubMed

Ji, Xiangdong; Xiong, Xiaonu; Yuan, Feng

2012-10-12

We present a systematic study of the proton spin structure in terms of measurable parton distributions. For a transversely polarized proton, we derive a polarization sum rule from the leading generalized parton distributions appearing in hard exclusive processes. For a longitudinally polarized proton, we obtain a helicity decomposition from well-known quark and gluon helicity distributions and orbital angular-momentum contributions. The latter are shown to be related to measurable subleading generalized parton distributions and quantum-phase space Wigner distributions.

Detection and imaging of moving objects with SAR by a joint space-time-frequency processing

NASA Astrophysics Data System (ADS)

Barbarossa, Sergio; Farina, Alfonso

This paper proposes a joint spacetime-frequency processing scheme for the detection and imaging of moving targets by Synthetic Aperture Radars (SAR). The method is based on the availability of an array antenna. The signals received by the array elements are combined, in a spacetime processor, to cancel the clutter. Then, they are analyzed in the time-frequency domain, by computing their Wigner-Ville Distribution (WVD), in order to estimate the instantaneous frequency, to be used for the successive phase compensation, necessary to produce a high resolution image.

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

NASA Astrophysics Data System (ADS)

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

2013-03-01

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

Professor Louis Michel (1923-1999)

NASA Astrophysics Data System (ADS)

Zak, J.

2001-04-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

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

PubMed

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

2006-04-01

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

Eugene P. Wigner - in the light of unexpected events

NASA Astrophysics Data System (ADS)

Koblinger, L.

2014-09-01

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

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

NASA Astrophysics Data System (ADS)

Alexanian, Moorad

2018-01-01

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

Anomalous current from the covariant Wigner function

NASA Astrophysics Data System (ADS)

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.

The Bravyi-Kitaev transformation for quantum computation of electronic structure

NASA Astrophysics Data System (ADS)

Seeley, Jacob T.; Richard, Martin J.; Love, Peter J.

2012-12-01

Quantum simulation is an important application of future quantum computers with applications in quantum chemistry, condensed matter, and beyond. Quantum simulation of fermionic systems presents a specific challenge. The Jordan-Wigner transformation allows for representation of a fermionic operator by O(n) qubit operations. Here, we develop an alternative method of simulating fermions with qubits, first proposed by Bravyi and Kitaev [Ann. Phys. 298, 210 (2002), 10.1006/aphy.2002.6254; e-print arXiv:quant-ph/0003137v2], that reduces the simulation cost to O(log n) qubit operations for one fermionic operation. We apply this new Bravyi-Kitaev transformation to the task of simulating quantum chemical Hamiltonians, and give a detailed example for the simplest possible case of molecular hydrogen in a minimal basis. We show that the quantum circuit for simulating a single Trotter time step of the Bravyi-Kitaev derived Hamiltonian for H2 requires fewer gate applications than the equivalent circuit derived from the Jordan-Wigner transformation. Since the scaling of the Bravyi-Kitaev method is asymptotically better than the Jordan-Wigner method, this result for molecular hydrogen in a minimal basis demonstrates the superior efficiency of the Bravyi-Kitaev method for all quantum computations of electronic structure.

Wavelets and Affine Distributions: A Time-Frequency Perspective

DTIC Science & Technology

2005-01-07

Ville Distribution ( WVD ) • Prominent member of the AC: the WVD • Properties of the WVD : – Covariant to TF scaling and time shift (of course) – Covariant...QTFRs • Wigner - Ville distribution and affine smoothing • Doppler tolerance and hyperbolic impulses • Hyperbolic TF localization and Bertrand P0...satisfy hyperbolic TF localization property: • Not satisfied by WVD ! 25 – 49 –WAMA-04 Cargèse, France The Bertrand P0 distribution • The hyperbolic

Fault diagnosis for diesel valve trains based on time frequency images

NASA Astrophysics Data System (ADS)

Wang, Chengdong; Zhang, Youyun; Zhong, Zhenyuan

2008-11-01

In this paper, the Wigner-Ville distributions (WVD) of vibration acceleration signals which were acquired from the cylinder head in eight different states of valve train were calculated and displayed in grey images; and the probabilistic neural networks (PNN) were directly used to classify the time-frequency images after the images were normalized. By this way, the fault diagnosis of valve train was transferred to the classification of time-frequency images. As there is no need to extract further fault features (such as eigenvalues or symptom parameters) from time-frequency distributions before classification, the fault diagnosis process is highly simplified. The experimental results show that the faults of diesel valve trains can be classified accurately by the proposed methods.

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

NASA Astrophysics Data System (ADS)

Tang, Guixin; Eggert, Sebastian; Pelster, Axel

2015-12-01

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

A phase space approach to imaging from limited data

NASA Astrophysics Data System (ADS)

Testorf, Markus E.

2015-09-01

The optical instrument function is used as the basis to develop optical system theory for imaging applications. The detection of optical signals is conveniently described as the overlap integral of the Wigner distribution functions of instrument and optical signal. Based on this framework various optical imaging systems, including plenoptic cameras, phase-retrieval algorithms, and Shack-Hartman sensors are shown to acquire information about a domain in phase-space, with finite extension and finite resolution. It is demonstrated how phase space optics can be used both to analyze imaging systems, as well as for designing methods for image reconstruction.

Optical Parametric Amplification of Single Photon: Statistical Properties and Quantum Interference

NASA Astrophysics Data System (ADS)

Xu, Xue-Xiang; Yuan, Hong-Chun

2014-05-01

By using phase space method, we theoretically investigate the quantum statistical properties and quantum interference of optical parametric amplification of single photon. The statistical properties, such as the Wigner function (WF), average photon number, photon number distribution and parity, are derived analytically for the fields of the two output ports. The results indicate that the fields in the output ports are multiphoton states rather than single photon state due to the amplification of the optical parametric amplifiers (OPA). In addition, the phase sensitivity is also examined by using the detection scheme of parity measurement.

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

NASA Astrophysics Data System (ADS)

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

2015-11-01

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

Properties of two-mode squeezed number states

NASA Technical Reports Server (NTRS)

Chizhov, Alexei V.; Murzakhmetov, B. K.

1994-01-01

Photon statistics and phase properties of two-mode squeezed number states are studied. It is shown that photon number distribution and Pegg-Barnett phase distribution for such states have similar (N + 1)-peak structure for nonzero value of the difference in the number of photons between modes. Exact analytical formulas for phase distributions based on different phase approaches are derived. The Pegg-Barnett phase distribution and the phase quasiprobability distribution associated with the Wigner function are close to each other, while the phase quasiprobability distribution associated with the Q function carries less phase information.

FAST TRACK COMMUNICATION: Semiclassical Klein Kramers and Smoluchowski equations for the Brownian motion of a particle in an external potential

NASA Astrophysics Data System (ADS)

Coffey, W. T.; Kalmykov, Yu P.; Titov, S. V.; Mulligan, B. P.

2007-01-01

The quantum Brownian motion of a particle in an external potential V(x) is treated using the master equation for the Wigner distribution function W(x, p, t) in phase space (x, p). A heuristic method of determination of diffusion coefficients in the master equation is proposed. The time evolution equation so obtained contains explicit quantum correction terms up to o(planck4) and in the classical limit, planck → 0, reduces to the Klein-Kramers equation. For a quantum oscillator, the method yields an evolution equation for W(x, p, t) coinciding with that of Agarwal (1971 Phys. Rev. A 4 739). In the non-inertial regime, by applying the Brinkman expansion of the momentum distribution in Weber functions (Brinkman 1956 Physica 22 29), the corresponding semiclassical Smoluchowski equation is derived.

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

NASA Astrophysics Data System (ADS)

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

2006-04-01

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

Motion estimation of magnetic resonance cardiac images using the Wigner-Ville and hough transforms

NASA Astrophysics Data System (ADS)

Carranza, N.; Cristóbal, G.; Bayerl, P.; Neumann, H.

2007-12-01

Myocardial motion analysis and quantification is of utmost importance for analyzing contractile heart abnormalities and it can be a symptom of a coronary artery disease. A fundamental problem in processing sequences of images is the computation of the optical flow, which is an approximation of the real image motion. This paper presents a new algorithm for optical flow estimation based on a spatiotemporal-frequency (STF) approach. More specifically it relies on the computation of the Wigner-Ville distribution (WVD) and the Hough Transform (HT) of the motion sequences. The latter is a well-known line and shape detection method that is highly robust against incomplete data and noise. The rationale of using the HT in this context is that it provides a value of the displacement field from the STF representation. In addition, a probabilistic approach based on Gaussian mixtures has been implemented in order to improve the accuracy of the motion detection. Experimental results in the case of synthetic sequences are compared with an implementation of the variational technique for local and global motion estimation, where it is shown that the results are accurate and robust to noise degradations. Results obtained with real cardiac magnetic resonance images are presented.

Breit-Wigner Approximation and the Distributionof Resonances

NASA Astrophysics Data System (ADS)

Petkov, Vesselin; Zworski, Maciej

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

Wigner analysis of three dimensional pupil with finite lateral aperture

PubMed Central

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

2015-01-01

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

Control of Wigner localization and electron cavity effects in near-field emission spectra of In(Ga)P/GaInP quantum-dot structures

NASA Astrophysics Data System (ADS)

Mintairov, A. M.; Kapaldo, J.; Merz, J. L.; Rouvimov, S.; Lebedev, D. V.; Kalyuzhnyy, N. A.; Mintairov, S. A.; Belyaev, K. G.; Rakhlin, M. V.; Toropov, A. A.; Brunkov, P. N.; Vlasov, A. S.; Zadiranov, Yu. M.; Blundell, S. A.; Mozharov, A. M.; Mukhin, I.; Yakimov, M.; Oktyabrsky, S.; Shelaev, A. V.; Bykov, V. A.

2018-05-01

Structural and emission properties of few-electron In(Ga)P/GaInP quantum dots (QDs) representing natural Wigner molecules (WM) and whispering gallery mode (WGM) electron (e ) cavities have been investigated. QD structures were grown using self-organized metal-organic vapor phase epitaxy and deposition from ˜3 to 7 monolayers of InP at 700 °C. Using atomic force microscopy, transmission electron microscopy, near-field scanning optical microscopy (NSOM), and μ -photoluminescence (μ -PL) spectra we obtained In(Ga)P/GaInP QDs having lateral size 80-180 nm, height 5-30 nm, Ga content 0.0-0.4, density 2 -10 μm-2 , and electron population up to 20 and demonstrated control of their density and size distribution. Using high-spatial-resolution low-temperature PL spectra, NSOM imaging, and calculations of charge density distributions we observed Wigner localization and e -cavity effects for a series of dots having quantum confinement ℏ ω0=0.5 -6 meV . We used these data together with time-resolved PL measurements to clarify the effect of Coulomb interaction and WM formation on emission spectra of few-electron QDs. We present direct observation of 2 e , 6 e , and 9 e WMs; 2 e and 4 e WGMs; and Fabry-Perot e modes and establish conditions of e -WGM-cavity formation in these QDs.

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

NASA Astrophysics Data System (ADS)

Hoai, Nguyen Thi Xuan; Duc, Truong Minh

2016-01-01

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

Entanglement of 3000 atoms by detecting one photon

NASA Astrophysics Data System (ADS)

Vuletic, Vladan

2016-05-01

Quantum-mechanically correlated (entangled) states of many particles are of interest in quantum information, quantum computing and quantum metrology. In particular, entangled states of many particles can be used to overcome limits on measurements performed with ensembles of independent atoms (standard quantum limit). Metrologically useful entangled states of large atomic ensembles (spin squeezed states) have been experimentally realized. These states display Gaussian spin distribution functions with a non-negative Wigner quasiprobability distribution function. We report the generation of 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, and verify an entanglement depth (the minimum number of mutually entangled atoms) that comprises 90% of the atomic ensemble containing 3100 atoms. Further technical improvement should allow the generation of more complex Schrödinger cat states, and of states the overcome the standard quantum limit.

Unifying distribution functions: some lesser known distributions.

PubMed

Moya-Cessa, J R; Moya-Cessa, H; Berriel-Valdos, L R; Aguilar-Loreto, O; Barberis-Blostein, P

2008-08-01

We show that there is a way to unify distribution functions that describe simultaneously a classical signal in space and (spatial) frequency and position and momentum for a quantum system. Probably the most well known of them is the Wigner distribution function. We show how to unify functions of the Cohen class, Rihaczek's complex energy function, and Husimi and Glauber-Sudarshan distribution functions. We do this by showing how they may be obtained from ordered forms of creation and annihilation operators and by obtaining them in terms of expectation values in different eigenbases.

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

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

Dorda, Antonius, E-mail: dorda@tugraz.at; Schürrer, Ferdinand, E-mail: ferdinand.schuerrer@tugraz.at

2015-03-01

We present a novel numerical scheme for the deterministic solution of the Wigner transport equation, especially suited to deal with situations in which strong quantum effects are present. The unique feature of the algorithm is the expansion of the Wigner function in local basis functions, similar to finite element or finite volume methods. This procedure yields a discretization of the pseudo-differential operator that conserves the particle density on arbitrarily chosen grids. The high flexibility in refining the grid spacing together with the weighted essentially non-oscillatory (WENO) scheme for the advection term allows for an accurate and well-resolved simulation of themore » phase space dynamics. A resonant tunneling diode is considered as test case and a detailed convergence study is given by comparing the results to a non-equilibrium Green's functions calculation. The impact of the considered domain size and of the grid spacing is analyzed. The obtained convergence of the results towards a quasi-exact agreement of the steady state Wigner and Green's functions computations demonstrates the accuracy of the scheme, as well as the high flexibility to adjust to different physical situations.« less

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

PubMed

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

2004-01-01

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

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

PubMed Central

Dorda, Antonius; Schürrer, Ferdinand

2015-01-01

We present a novel numerical scheme for the deterministic solution of the Wigner transport equation, especially suited to deal with situations in which strong quantum effects are present. The unique feature of the algorithm is the expansion of the Wigner function in local basis functions, similar to finite element or finite volume methods. This procedure yields a discretization of the pseudo-differential operator that conserves the particle density on arbitrarily chosen grids. The high flexibility in refining the grid spacing together with the weighted essentially non-oscillatory (WENO) scheme for the advection term allows for an accurate and well-resolved simulation of the phase space dynamics. A resonant tunneling diode is considered as test case and a detailed convergence study is given by comparing the results to a non-equilibrium Green's functions calculation. The impact of the considered domain size and of the grid spacing is analyzed. The obtained convergence of the results towards a quasi-exact agreement of the steady state Wigner and Green's functions computations demonstrates the accuracy of the scheme, as well as the high flexibility to adjust to different physical situations. PMID:25892748

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

PubMed

Dorda, Antonius; Schürrer, Ferdinand

2015-03-01

We present a novel numerical scheme for the deterministic solution of the Wigner transport equation, especially suited to deal with situations in which strong quantum effects are present. The unique feature of the algorithm is the expansion of the Wigner function in local basis functions, similar to finite element or finite volume methods. This procedure yields a discretization of the pseudo-differential operator that conserves the particle density on arbitrarily chosen grids. The high flexibility in refining the grid spacing together with the weighted essentially non-oscillatory (WENO) scheme for the advection term allows for an accurate and well-resolved simulation of the phase space dynamics. A resonant tunneling diode is considered as test case and a detailed convergence study is given by comparing the results to a non-equilibrium Green's functions calculation. The impact of the considered domain size and of the grid spacing is analyzed. The obtained convergence of the results towards a quasi-exact agreement of the steady state Wigner and Green's functions computations demonstrates the accuracy of the scheme, as well as the high flexibility to adjust to different physical situations.

The Application of Auto-Disturbance Rejection Control Optimized by Least Squares Support Vector Machines Method and Time-Frequency Representation in Voltage Source Converter-High Voltage Direct Current System.

PubMed

Liu, Ying-Pei; Liang, Hai-Ping; Gao, Zhong-Ke

2015-01-01

In order to improve the performance of voltage source converter-high voltage direct current (VSC-HVDC) system, we propose an improved auto-disturbance rejection control (ADRC) method based on least squares support vector machines (LSSVM) in the rectifier side. Firstly, we deduce the high frequency transient mathematical model of VSC-HVDC system. Then we investigate the ADRC and LSSVM principles. We ignore the tracking differentiator in the ADRC controller aiming to improve the system dynamic response speed. On this basis, we derive the mathematical model of ADRC controller optimized by LSSVM for direct current voltage loop. Finally we carry out simulations to verify the feasibility and effectiveness of our proposed control method. In addition, we employ the time-frequency representation methods, i.e., Wigner-Ville distribution (WVD) and adaptive optimal kernel (AOK) time-frequency representation, to demonstrate our proposed method performs better than the traditional method from the perspective of energy distribution in time and frequency plane.

The Application of Auto-Disturbance Rejection Control Optimized by Least Squares Support Vector Machines Method and Time-Frequency Representation in Voltage Source Converter-High Voltage Direct Current System

PubMed Central

Gao, Zhong-Ke

2015-01-01

In order to improve the performance of voltage source converter-high voltage direct current (VSC-HVDC) system, we propose an improved auto-disturbance rejection control (ADRC) method based on least squares support vector machines (LSSVM) in the rectifier side. Firstly, we deduce the high frequency transient mathematical model of VSC-HVDC system. Then we investigate the ADRC and LSSVM principles. We ignore the tracking differentiator in the ADRC controller aiming to improve the system dynamic response speed. On this basis, we derive the mathematical model of ADRC controller optimized by LSSVM for direct current voltage loop. Finally we carry out simulations to verify the feasibility and effectiveness of our proposed control method. In addition, we employ the time-frequency representation methods, i.e., Wigner-Ville distribution (WVD) and adaptive optimal kernel (AOK) time-frequency representation, to demonstrate our proposed method performs better than the traditional method from the perspective of energy distribution in time and frequency plane. PMID:26098556

Wigner functions for fermions in strong magnetic fields

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

Time-frequency signal analysis and synthesis - The choice of a method and its application

NASA Astrophysics Data System (ADS)

Boashash, Boualem

In this paper, the problem of choosing a method for time-frequency signal analysis is discussed. It is shown that a natural approach leads to the introduction of the concepts of the analytic signal and instantaneous frequency. The Wigner-Ville Distribution (WVD) is a method of analysis based upon these concepts and it is shown that an accurate Time-Frequency representation of a signal can be obtained by using the WVD for the analysis of a class of signals referred to as 'asymptotic'. For this class of signals, the instantaneous frequency describes an important physical parameter characteristic of the process under investigation. The WVD procedure for signal analysis and synthesis is outlined and its properties are reviewed for deterministic and random signals.

Time-Frequency Signal Analysis And Synthesis The Choice Of A Method And Its Application

NASA Astrophysics Data System (ADS)

Boashash, Boualem

1988-02-01

In this paper, the problem of choosing a method for time-frequency signal analysis is discussed. It is shown that a natural approach leads to the introduction of the concepts of the analytic signal and in-stantaneous frequency. The Wigner-Ville Distribution (WVD) is a method of analysis based upon these concepts and it is shown that an accurate Time-Frequency representation of a signal can be obtained by using the WVD for the analysis of a class of signals referred to as "asymptotic". For this class of signals, the instantaneous frequency describes an important physical parameter characteristic of the process under investigation. The WVD procedure for signal analysis and synthesis is outlined and its properties are reviewed for deterministic and random signals.

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

PubMed

Liu, Jian; Miller, William H

2007-06-21

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

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

NASA Astrophysics Data System (ADS)

Gelfert, Axel

2014-05-01

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

Towards a wave theory of charged beam transport: A collection of thoughts

NASA Technical Reports Server (NTRS)

Dattoli, G.; Mari, C.; Torre, A.

1992-01-01

We formulate in a rigorous way a wave theory of charged beam linear transport. The Wigner distribution function is introduced and provides the link with classical mechanics. Finally, the von Neumann equation is shown to coincide with the Liouville equation for the nonlinear transport.

Quantum-field-theoretical approach to phase–space techniques: Symmetric Wick theorem and multitime Wigner representation

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

Plimak, L.I., E-mail: Lev.Plimak@mbi-berlin.de; Olsen, M.K.

2014-12-15

In this work we present the formal background used to develop the methods used in earlier works to extend the truncated Wigner representation of quantum and atom optics in order to address multi-time problems. Analogs of Wick’s theorem for the Weyl ordering are verified. Using the Bose–Hubbard chain as an example, we show how these may be applied to constructing a mapping of the system in question to phase space. Regularisation issues and the reordering problem for the Heisenberg operators are addressed.

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

PubMed

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

2016-04-01

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

Quantum melting of a two-dimensional Wigner crystal

NASA Astrophysics Data System (ADS)

Dolgopolov, V. T.

2017-10-01

The paper reviews theoretical predictions about the behavior of two-dimensional low-density electron systems at nearly absolute zero temperatures, including the formation of an electron (Wigner) crystal, crystal melting at a critical electron density, and transitions between crystal modifications in more complex (for example, two-layer) systems. The paper presents experimental results obtained from real two-dimensional systems in which the nonconducting (solid) state of the electronic system with indications of collective localization is actually realized. Experimental methods for detecting a quantum liquid-solid phase interface are discussed.

Incomplete Detection of Nonclassical Phase-Space Distributions

NASA Astrophysics Data System (ADS)

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.

Wigner functions on non-standard symplectic vector spaces

NASA Astrophysics Data System (ADS)

Dias, Nuno Costa; Prata, João Nuno

2018-01-01

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

Waveform Retrieval and Phase Identification for Seismic Data from the CASS Experiment

NASA Astrophysics Data System (ADS)

Li, Zhiwei; You, Qingyu; Ni, Sidao; Hao, Tianyao; Wang, Hongti; Zhuang, Cantao

2013-05-01

The little destruction to the deployment site and high repeatability of the Controlled Accurate Seismic Source (CASS) shows its potential for investigating seismic wave velocities in the Earth's crust. However, the difficulty in retrieving impulsive seismic waveforms from the CASS data and identifying the seismic phases substantially prevents its wide applications. For example, identification of the seismic phases and accurate measurement of travel times are essential for resolving the spatial distribution of seismic velocities in the crust. Until now, it still remains a challenging task to estimate the accurate travel times of different seismic phases from the CASS data which features extended wave trains, unlike processing of the waveforms from impulsive events such as earthquakes or explosive sources. In this study, we introduce a time-frequency analysis method to process the CASS data, and try to retrieve the seismic waveforms and identify the major seismic phases traveling through the crust. We adopt the Wigner-Ville Distribution (WVD) approach which has been used in signal detection and parameter estimation for linear frequency modulation (LFM) signals, and proves to feature the best time-frequency convergence capability. The Wigner-Hough transform (WHT) is applied to retrieve the impulsive waveforms from multi-component LFM signals, which comprise seismic phases with different arrival times. We processed the seismic data of the 40-ton CASS in the field experiment around the Xinfengjiang reservoir with the WVD and WHT methods. The results demonstrate that these methods are effective in waveform retrieval and phase identification, especially for high frequency seismic phases such as PmP and SmS with strong amplitudes in large epicenter distance of 80-120 km. Further studies are still needed to improve the accuracy on travel time estimation, so as to further promote applicability of the CASS for and imaging the seismic velocity structure.

The joint time-frequency spectrogram structure of heptanes boilover noise

NASA Astrophysics Data System (ADS)

Xu, Qiang

2006-04-01

An experiment was conducted to study the noise characteristics in the boilover phenomena. The boilover occurs in the combustion of a liquid fuel floating on water. It will cause a sharp increase in burning rate and external radiation. Explosive burning of the fuel would cause potential safety consequence. Combustion noise accompanies the development of fire and displays different characteristics in typical period. These characteristics can be used to predict the start time of boilover. The acoustic signal in boilover procedure during the combustion of heptanes-water mixture is obtained in a set of experiments. Joint time-frequency analysis (JTFA) method is applied in the treatment of noise data. Several JTFA algorithms were used in the evaluation. These algorithms include Gabor, adaptive spectrogram, cone shape distribution, choi-williams distribution, Wigner-Ville Distribution, and Short Time Fourier Transform with different windows such as rectangular, Blackman, Hamming and Hanning. Time-frequency distribution patterns of the combustion noise are obtained, and they are compared with others from jet flow and small plastic bubble blow up.

Wigner Functions for Arbitrary Quantum Systems.

PubMed

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

2016-10-28

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

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

NASA Technical Reports Server (NTRS)

Farley, John W.

1989-01-01

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

Contextuality and Wigner-function negativity in qubit quantum computation

NASA Astrophysics Data System (ADS)

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

2017-05-01

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

Monte Carlo sampling of Wigner functions and surface hopping quantum dynamics

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

Kube, Susanna; Lasser, Caroline; Weber, Marcus

2009-04-01

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

Generalized Reduction Formula for Discrete Wigner Functions of Multiqubit Systems

NASA Astrophysics Data System (ADS)

Srinivasan, K.; Raghavan, G.

2018-03-01

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

Sequential fuzzy diagnosis method for motor roller bearing in variable operating conditions based on vibration analysis.

PubMed

Li, Ke; Ping, Xueliang; Wang, Huaqing; Chen, Peng; Cao, Yi

2013-06-21

A novel intelligent fault diagnosis method for motor roller bearings which operate under unsteady rotating speed and load is proposed in this paper. The pseudo Wigner-Ville distribution (PWVD) and the relative crossing information (RCI) methods are used for extracting the feature spectra from the non-stationary vibration signal measured for condition diagnosis. The RCI is used to automatically extract the feature spectrum from the time-frequency distribution of the vibration signal. The extracted feature spectrum is instantaneous, and not correlated with the rotation speed and load. By using the ant colony optimization (ACO) clustering algorithm, the synthesizing symptom parameters (SSP) for condition diagnosis are obtained. The experimental results shows that the diagnostic sensitivity of the SSP is higher than original symptom parameter (SP), and the SSP can sensitively reflect the characteristics of the feature spectrum for precise condition diagnosis. Finally, a fuzzy diagnosis method based on sequential inference and possibility theory is also proposed, by which the conditions of the machine can be identified sequentially as well.

Sequential Fuzzy Diagnosis Method for Motor Roller Bearing in Variable Operating Conditions Based on Vibration Analysis

PubMed Central

Li, Ke; Ping, Xueliang; Wang, Huaqing; Chen, Peng; Cao, Yi

2013-01-01

A novel intelligent fault diagnosis method for motor roller bearings which operate under unsteady rotating speed and load is proposed in this paper. The pseudo Wigner-Ville distribution (PWVD) and the relative crossing information (RCI) methods are used for extracting the feature spectra from the non-stationary vibration signal measured for condition diagnosis. The RCI is used to automatically extract the feature spectrum from the time-frequency distribution of the vibration signal. The extracted feature spectrum is instantaneous, and not correlated with the rotation speed and load. By using the ant colony optimization (ACO) clustering algorithm, the synthesizing symptom parameters (SSP) for condition diagnosis are obtained. The experimental results shows that the diagnostic sensitivity of the SSP is higher than original symptom parameter (SP), and the SSP can sensitively reflect the characteristics of the feature spectrum for precise condition diagnosis. Finally, a fuzzy diagnosis method based on sequential inference and possibility theory is also proposed, by which the conditions of the machine can be identified sequentially as well. PMID:23793021

Markov chain Monte Carlo estimation of quantum states

NASA Astrophysics Data System (ADS)

Diguglielmo, James; Messenger, Chris; Fiurášek, Jaromír; Hage, Boris; Samblowski, Aiko; Schmidt, Tabea; Schnabel, Roman

2009-03-01

We apply a Bayesian data analysis scheme known as the Markov chain Monte Carlo to the tomographic reconstruction of quantum states. This method yields a vector, known as the Markov chain, which contains the full statistical information concerning all reconstruction parameters including their statistical correlations with no a priori assumptions as to the form of the distribution from which it has been obtained. From this vector we can derive, e.g., the marginal distributions and uncertainties of all model parameters, and also of other quantities such as the purity of the reconstructed state. We demonstrate the utility of this scheme by reconstructing the Wigner function of phase-diffused squeezed states. These states possess non-Gaussian statistics and therefore represent a nontrivial case of tomographic reconstruction. We compare our results to those obtained through pure maximum-likelihood and Fisher information approaches.

Quantum mechanics on phase space and the Coulomb potential

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

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

NASA Astrophysics Data System (ADS)

Siyouri, Fatima-Zahra

2017-12-01

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

Wigner functions from the two-dimensional wavelet group.

PubMed

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.

LASER APPLICATIONS AND OTHER TOPICS IN QUANTUM ELECTRONICS: Application of the Wigner function and matrix optics to describe variations in the shape of ultrashort laser pulses propagating through linear optical systems

NASA Astrophysics Data System (ADS)

Gitin, Andrey V.

2006-04-01

The transformation of the shape of ultrashort laser pulses (USPs) in time can be described similarly to the process of image formation in space. It is shown that the wave description of imaging is simplified by using the Wigner function, this description in the quadratic approximation being identical to the use of the ABCD matrices. The transformation of USPs propagating through linear optical systems was described and these systems were classified by the methods of matrix optics.

Reproducing Quantum Probability Distributions at the Speed of Classical Dynamics: A New Approach for Developing Force-Field Functors.

PubMed

Sundar, Vikram; Gelbwaser-Klimovsky, David; Aspuru-Guzik, Alán

2018-04-05

Modeling nuclear quantum effects is required for accurate molecular dynamics (MD) simulations of molecules. The community has paid special attention to water and other biomolecules that show hydrogen bonding. Standard methods of modeling nuclear quantum effects like Ring Polymer Molecular Dynamics (RPMD) are computationally costlier than running classical trajectories. A force-field functor (FFF) is an alternative method that computes an effective force field that replicates quantum properties of the original force field. In this work, we propose an efficient method of computing FFF using the Wigner-Kirkwood expansion. As a test case, we calculate a range of thermodynamic properties of Neon, obtaining the same level of accuracy as RPMD, but with the shorter runtime of classical simulations. By modifying existing MD programs, the proposed method could be used in the future to increase the efficiency and accuracy of MD simulations involving water and proteins.

Elliptic flow in small systems due to elliptic gluon distributions?

DOE PAGES

Hagiwara, Yoshikazu; Hatta, Yoshitaka; Xiao, Bo-Wen; ...

2017-05-31

We investigate the contributions from the so-called elliptic gluon Wigner distributions to the rapidity and azimuthal correlations of particles produced in high energy pp and pA collisions by applying the double parton scattering mechanism. We compute the ‘elliptic flow’ parameter v 2 as a function of the transverse momentum and rapidity, and find qualitative agreement with experimental observations. This shall encourage further developments with more rigorous studies of the elliptic gluon distributions and their applications in hard scattering processes in pp and pA collisions.

Elliptic flow in small systems due to elliptic gluon distributions?

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

Hagiwara, Yoshikazu; Hatta, Yoshitaka; Xiao, Bo-Wen

We investigate the contributions from the so-called elliptic gluon Wigner distributions to the rapidity and azimuthal correlations of particles produced in high energy pp and pA collisions by applying the double parton scattering mechanism. We compute the ‘elliptic flow’ parameter v 2 as a function of the transverse momentum and rapidity, and find qualitative agreement with experimental observations. This shall encourage further developments with more rigorous studies of the elliptic gluon distributions and their applications in hard scattering processes in pp and pA collisions.

Nonlinear Computerized Methodology. A. Angle of Arrival Estimation. B. Data Modeling and Identification

DTIC Science & Technology

1991-06-10

essentially In the Wianer- Ville distribution ( WVD ). A preliminary analysis indicates that the simple operation of autoconvolution can enhance spectral...many troublesome cases as a supplement to MUSIC (and its adaptations) and as a simple alternative (or representation of) the Wigner - Ville ... WVD is a time-frequency distribution which provides an unbiased spectrum estimate by W(t,W) = f H,(u) X (t - u/2) X (t + u/2) e -iwu du , where the

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

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

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

Bialas, A.; Czyz, W.; Zalewski, K.

The relation between Renyi entropies and moments of the Wigner function, representing the quantum mechanical description of the M-particle semi-inclusive distribution at freeze-out, is investigated. It is shown that in the limit of infinite volume of the system, the classical and quantum descriptions are equivalent. Finite volume corrections are derived and shown to be small for systems encountered in relativistic heavy ion collisions.

A short walk in quantum probability

NASA Astrophysics Data System (ADS)

Hudson, Robin

2018-04-01

This is a personal survey of aspects of quantum probability related to the Heisenberg commutation relation for canonical pairs. Using the failure, in general, of non-negativity of the Wigner distribution for canonical pairs to motivate a more satisfactory quantum notion of joint distribution, we visit a central limit theorem for such pairs and a resulting family of quantum planar Brownian motions which deform the classical planar Brownian motion, together with a corresponding family of quantum stochastic areas. This article is part of the themed issue `Hilbert's sixth problem'.

Phase Properties of Photon-Added Coherent States for Nonharmonic Oscillators in a Nonlinear Kerr Medium

NASA Astrophysics Data System (ADS)

Jahanbakhsh, F.; Honarasa, G.

2018-04-01

The potential of nonharmonic systems has several applications in the field of quantum physics. The photon-added coherent states for annharmonic oscillators in a nonlinear Kerr medium can be used to describe some quantum systems. In this paper, the phase properties of these states including number-phase Wigner distribution function, Pegg-Barnett phase distribution function, number-phase squeezing and number-phase entropic uncertainty relations are investigated. It is found that these states can be considered as the nonclassical states.

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

NASA Astrophysics Data System (ADS)

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

2013-10-01

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

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

NASA Astrophysics Data System (ADS)

Reil, Frank; Thomas, John E.

2002-05-01

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

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

PubMed

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.

Generation of highly pure Schrödinger's cat states and real-time quadrature measurements via optical filtering

NASA Astrophysics Data System (ADS)

Asavanant, Warit; Nakashima, Kota; Shiozawa, Yu; Yoshikawa, Jun-Ichi; Furusawa, Akira

2017-12-01

Until now, Schr\\"odinger's cat states are generated by subtracting single photons from the whole bandwidth of squeezed vacua. However, it was pointed out recently that the achievable purities are limited in such method (J. Yoshikawa, W. Asavanant, and A. Furusawa, arXiv:1707.08146 [quant-ph] (2017)). In this paper, we used our new photon subtraction method with a narrowband filtering cavity and generated a highly pure Schr\\"odinger's cat state with the value of $-0.184$ at the origin of the Wigner function. To our knowledge, this is the highest value ever reported without any loss corrections. The temporal mode also becomes exponentially rising in our method, which allows us to make a real-time quadrature measurement on Schr\\"odinger's cat states, and we obtained the value of $-0.162$ at the origin of the Wigner function.

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

NASA Astrophysics Data System (ADS)

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

2018-07-01

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

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

NASA Technical Reports Server (NTRS)

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

1988-01-01

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

Classical versus quantum dynamical chaos: Sensitivity to external perturbations, stability and reversibility

NASA Astrophysics Data System (ADS)

Sokolov, Valentin V.; Zhirov, Oleg V.; Kharkov, Yaroslav A.

The extraordinary complexity of classical trajectories of typical nonlinear systems that manifest stochastic behavior is intimately connected with exponential sensitivity to small variations of initial conditions and/or weak external perturbations. In rigorous terms, such classical systems are characterized by positive algorithmic complexity described by the Lyapunov exponent or, alternatively, by the Kolmogorov-Sinai entropy. The said implies that, in spite of the fact that, formally, any however complex trajectory of a perfectly isolated (closed) system is unique and differentiable for any certain initial conditions and the motion is perfectly reversible, it is impractical to treat that sort of classical systems as closed ones. Inevitably, arbitrary weak influence of an environment crucially impacts the dynamics. This influence, that can be considered as a noise, rapidly effaces the memory of initial conditions and turns the motion into an irreversible random process. In striking contrast, the quantum mechanics of the classically chaotic systems exhibit much weaker sensitivity and strong memory of the initial state. Qualitatively, this crucial difference could be expected in view of a much simpler structure of quantum states as compared to the extraordinary complexity of random and unpredictable classical trajectories. However the very notion of trajectories is absent in quantum mechanics so that the concept of exponential instability seems to be irrelevant in this case. The problem of a quantitative measure of complexity of a quantum state of motion, that is a very important and nontrivial issue of the theory of quantum dynamical chaos, is the one of our concern. With such a measure in hand, we quantitatively analyze the stability and reversibility of quantum dynamics in the presence of external noise. To solve this problem we point out that individual classical trajectories are of minor interest if the motion is chaotic. Properties of all of them are alike in this case and rather the behavior of their manifolds carries really valuable information. Therefore the phase-space methods and, correspondingly, the Liouville form of the classical mechanics become the most adequate. It is very important that, opposite to the classical trajectories, the classical phase space distribution and the Liouville equation have direct quantum analogs. Hence, the analogy and difference of classical and quantum dynamics can be traced by comparing the classical (W(c)(I,θ;t)) and quantum (Wigner function W(I,θ;t)) phase space distributions both expressed in identical phase-space variables but ruled by different(!) linear equations. The paramount property of the classical dynamical chaos is the exponentially fast structuring of the system's phase space on finer and finer scales. On the contrary, degree of structuring of the corresponding Wigner function is restricted by the quantization of the phase space. This makes Wigner function more coarse and relatively "simple" as compared to its classical counterpart. Fourier analysis affords quite suitable ground for analyzing complexity of a phase space distribution, that is equally valid in classical and quantum cases. We demonstrate that the typical number of Fourier harmonics is indeed a relevant measure of complexity of states of motion in both classical as well as quantum cases. This allowed us to investigate in detail and introduce a quantitative measure of sensitivity to an external noisy environment and formulate the conditions under which the quantum motion remains reversible. It turns out that while the mean number of harmonics of the classical phase-space distribution of a non-integrable system grows with time exponentially during the whole time of the motion, the time of exponential upgrowth of this number in the case of the corresponding quantum Wigner function is restricted only to the Ehrenfest interval 0 < t < tE - just the interval within which the Wigner function still satisfies the classical Liouville equation. We showed that the number of harmonics increases beyond this interval algebraically. This fact gains a crucial importance when the Ehrenfest time is so short that the exponential regime has no time to show up. Under this condition the quantum motion turns out to be quite stable and reversible.

TEMPEST II--A NEUTRON THERMALIZATION CODE

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

Shudde, R.H.; Dyer, J.

The TEMPEST II neutron thermalization code in Fortran for IBM 709 or 7090 calculates thermal neutron flux spectra based upon the Wigner-Wilkins equation, the Wilkins equation, or the Maxwellian distribution. When a neutron spectrum is obtained, TEMPEST II provides microscopic and macroscopic cross section averages over that spectrum. Equations used by the code and sample input and output data are given. (auth)

New Interpretation of the Wigner Function

NASA Technical Reports Server (NTRS)

Daboul, Jamil

1996-01-01

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

Comparison of time-frequency distribution techniques for analysis of spinal somatosensory evoked potential.

PubMed

Hu, Y; Luk, K D; Lu, W W; Holmes, A; Leong, J C

2001-05-01

Spinal somatosensory evoked potential (SSEP) has been employed to monitor the integrity of the spinal cord during surgery. To detect both temporal and spectral changes in SSEP waveforms, an investigation of the application of time-frequency analysis (TFA) techniques was conducted. SSEP signals from 30 scoliosis patients were analysed using different techniques; short time Fourier transform (STFT), Wigner-Ville distribution (WVD), Choi-Williams distribution (CWD), cone-shaped distribution (CSD) and adaptive spectrogram (ADS). The time-frequency distributions (TFD) computed using these methods were assessed and compared with each other. WVD, ADS, CSD and CWD showed better resolution than STFT. Comparing normalised peak widths, CSD showed the sharpest peak width (0.13+/-0.1) in the frequency dimension, and a mean peak width of 0.70+/-0.12 in the time dimension. Both WVD and CWD produced cross-term interference, distorting the TFA distribution, but this was not seen with CSD and ADS. CSD appeared to give a lower mean peak power bias (10.3%+/-6.2%) than ADS (41.8%+/-19.6%). Application of the CSD algorithm showed both good resolution and accurate spectrograms, and is therefore recommended as the most appropriate TFA technique for the analysis of SSEP signals.

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

PubMed Central

Yan, Yong-sheng; Poon, Carmen CY; Zhang, Yuan-ting

2005-01-01

Background The pulse oximeter, a medical device capable of measuring blood oxygen saturation (SpO2), has been shown to be a valuable device for monitoring patients in critical conditions. In order to incorporate the technique into a wearable device which can be used in ambulatory settings, the influence of motion artifacts on the estimated SpO2 must be reduced. This study investigates the use of the smoothed psuedo Wigner-Ville distribution (SPWVD) for the reduction of motion artifacts affecting pulse oximetry. Methods The SPWVD approach is compared with two techniques currently used in this field, i.e. the weighted moving average (WMA) and the fast Fourier transform (FFT) approaches. SpO2 and pulse rate were estimated from a photoplethysmographic (PPG) signal recorded when subject is in a resting position as well as in the act of performing four types of motions: horizontal and vertical movements of the hand, and bending and pressing motions of the finger. For each condition, 24 sets of PPG signals collected from 6 subjects, each of 30 seconds, were studied with reference to the PPG signal recorded simultaneously from the subject's other hand, which was stationary at all times. Results and Discussion The SPWVD approach shows significant improvement (p < 0.05), as compared to traditional approaches, when subjects bend their finger or press their finger against the sensor. In addition, the SPWVD approach also reduces the mean absolute pulse rate error significantly (p < 0.05) from 16.4 bpm and 11.2 bpm for the WMA and FFT approaches, respectively, to 5.62 bpm. Conclusion The results suggested that the SPWVD approach could potentially be used to reduce motion artifact on wearable pulse oximeters. PMID:15737241

Fractional Wigner Crystal in the Helical Luttinger Liquid.

PubMed

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.

Supersymmetric symplectic quantum mechanics

NASA Astrophysics Data System (ADS)

de Menezes, Miralvo B.; Fernandes, M. C. B.; Martins, Maria das Graças R.; Santana, A. E.; Vianna, J. D. M.

2018-02-01

Symplectic Quantum Mechanics SQM considers a non-commutative algebra of functions on a phase space Γ and an associated Hilbert space HΓ to construct a unitary representation for the Galilei group. From this unitary representation the Schrödinger equation is rewritten in phase space variables and the Wigner function can be derived without the use of the Liouville-von Neumann equation. In this article we extend the methods of supersymmetric quantum mechanics SUSYQM to SQM. With the purpose of applications in quantum systems, the factorization method of the quantum mechanical formalism is then set within supersymmetric SQM. A hierarchy of simpler hamiltonians is generated leading to new computation tools for solving the eigenvalue problem in SQM. We illustrate the results by computing the states and spectra of the problem of a charged particle in a homogeneous magnetic field as well as the corresponding Wigner function.

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

NASA Astrophysics Data System (ADS)

Colmenares, Pedro J.

2018-05-01

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

Quantum to classical transition in the Hořava-Lifshitz quantum cosmology

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

Simulation of Devices with Molecular Potentials

DTIC Science & Technology

2013-12-22

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

Modified interferometric imaging condition for reverse-time migration

NASA Astrophysics Data System (ADS)

Guo, Xue-Bao; Liu, Hong; Shi, Ying

2018-01-01

For reverse-time migration, high-resolution imaging mainly depends on the accuracy of the velocity model and the imaging condition. In practice, however, the small-scale components of the velocity model cannot be estimated by tomographical methods; therefore, the wavefields are not accurately reconstructed from the background velocity, and the imaging process will generate artefacts. Some of the noise is due to cross-correlation of unrelated seismic events. Interferometric imaging condition suppresses imaging noise very effectively, especially the unknown random disturbance of the small-scale part. The conventional interferometric imaging condition is extended in this study to obtain a new imaging condition based on the pseudo-Wigner distribution function (WDF). Numerical examples show that the modified interferometric imaging condition improves imaging precision.

Deformation quantization of fermi fields

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

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

2008-04-15

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

A short walk in quantum probability.

PubMed

Hudson, Robin

2018-04-28

This is a personal survey of aspects of quantum probability related to the Heisenberg commutation relation for canonical pairs. Using the failure, in general, of non-negativity of the Wigner distribution for canonical pairs to motivate a more satisfactory quantum notion of joint distribution, we visit a central limit theorem for such pairs and a resulting family of quantum planar Brownian motions which deform the classical planar Brownian motion, together with a corresponding family of quantum stochastic areas.This article is part of the themed issue 'Hilbert's sixth problem'. © 2018 The Author(s).

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

Hatta, Yoshitaka; Xiao, Bo-Wen; Yuan, Feng

We present a full evaluation of the deeply virtual Compton scattering cross section in the dipole framework in the small-x region. The result features the cosφ and cos2φ azimuthal angular correlations, which have been missing in previous studies based on the dipole model. In particular, the cos2φ term is generated by the elliptic gluon Wigner distribution of which the measurement at the planned electron-ion collider provides important information about the gluon tomography at small x. Here, we also show the consistency with the standard collinear factorization approach based on the quark and gluon generalized parton distributions.

Coherent distributions for the rigid rotator

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

Grigorescu, Marius

2016-06-15

Coherent solutions of the classical Liouville equation for the rigid rotator are presented as positive phase-space distributions localized on the Lagrangian submanifolds of Hamilton-Jacobi theory. These solutions become Wigner-type quasiprobability distributions by a formal discretization of the left-invariant vector fields from their Fourier transform in angular momentum. The results are consistent with the usual quantization of the anisotropic rotator, but the expected value of the Hamiltonian contains a finite “zero point” energy term. It is shown that during the time when a quasiprobability distribution evolves according to the Liouville equation, the related quantum wave function should satisfy the time-dependent Schrödingermore » equation.« less

Cyclostationarity approach for monitoring chatter and tool wear in high speed milling

NASA Astrophysics Data System (ADS)

Lamraoui, M.; Thomas, M.; El Badaoui, M.

2014-02-01

Detection of chatter and tool wear is crucial in the machining process and their monitoring is a key issue, for: (1) insuring better surface quality, (2) increasing productivity and (3) protecting both machines and safe workpiece. This paper presents an investigation of chatter and tool wear using the cyclostationary method to process the vibrations signals acquired from high speed milling. Experimental cutting tests were achieved on slot milling operation of aluminum alloy. The experimental set-up is designed for acquisition of accelerometer signals and encoding information picked up from an encoder. The encoder signal is used for re-sampling accelerometers signals in angular domain using a specific algorithm that was developed in LASPI laboratory. The use of cyclostationary on accelerometer signals has been applied for monitoring chatter and tool wear in high speed milling. The cyclostationarity appears on average properties (first order) of signals, on the energetic properties (second order) and it generates spectral lines at cyclic frequencies in spectral correlation. Angular power and kurtosis are used to analyze chatter phenomena. The formation of chatter is characterized by unstable, chaotic motion of the tool and strong anomalous fluctuations of cutting forces. Results show that stable machining generates only very few cyclostationary components of second order while chatter is strongly correlated to cyclostationary components of second order. By machining in the unstable region, chatter results in flat angular kurtosis and flat angular power, such as a pseudo (white) random signal with flat spectrum. Results reveal that spectral correlation and Wigner Ville spectrum or integrated Wigner Ville issued from second-order cyclostationary are an efficient parameter for the early diagnosis of faults in high speed machining, such as chatter, tool wear and bearings, compared to traditional stationary methods. Wigner Ville representation of the residual signal shows that the energy corresponding to the tooth passing decreases when chatter phenomenon occurs. The effect of the tool wear and the number of broken teeth on the excitation of structure resonances appears in Wigner Ville presentation.

Understanding squeezing of quantum states with the Wigner function

NASA Technical Reports Server (NTRS)

Royer, Antoine

1994-01-01

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

On use of characteristic wavelengths of track irregularities to predict track portions with deteriorated wheel/rail forces

NASA Astrophysics Data System (ADS)

Xu, Lei; Zhai, Wanming; Chen, Zhaowei

2018-05-01

The dynamic performance of the railway vehicles and the guiding tracks is mainly governed by the wheel-rail interactions, particularly in cases of track irregularities. In this work, a united model was developed to investigate the track portions subject to violent wheel/rail forces triggered by track irregularities at middle-low frequencies. In the modeling procedures, a time-frequency unification method combining wavelet transform and Wigner-Ville distribution for characterizing time-frequency characteristics of track irregularities and a three-dimensional nonlinear model for describing vehicle-track interaction signatures were developed and coupled, based on which the method for predicting track portions subject to deteriorated wheel/rail forces was proposed. The theoretical models developed in this paper were comprehensively validated by numerical investigations. The significance of this present study mainly lies on offering a new path to establish correlation and realize mutual prediction between track irregularity and railway system dynamics.

Fusion of multi-spectral and panchromatic images based on 2D-PWVD and SSIM

NASA Astrophysics Data System (ADS)

Tan, Dongjie; Liu, Yi; Hou, Ruonan; Xue, Bindang

2016-03-01

A combined method using 2D pseudo Wigner-Ville distribution (2D-PWVD) and structural similarity(SSIM) index is proposed for fusion of low resolution multi-spectral (MS) image and high resolution panchromatic (PAN) image. First, the intensity component of multi-spectral image is extracted with generalized IHS transform. Then, the spectrum diagrams of the intensity components of multi-spectral image and panchromatic image are obtained with 2D-PWVD. Different fusion rules are designed for different frequency information of the spectrum diagrams. SSIM index is used to evaluate the high frequency information of the spectrum diagrams for assigning the weights in the fusion processing adaptively. After the new spectrum diagram is achieved according to the fusion rule, the final fusion image can be obtained by inverse 2D-PWVD and inverse GIHS transform. Experimental results show that, the proposed method can obtain high quality fusion images.

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

NASA Astrophysics Data System (ADS)

Liu, Jianfei; Wei, Ying; Zeng, Xiangye; Lu, Jia; Zhang, Shuangxi; Wang, Mengjun

2018-03-01

A joint timing and frequency synchronization method has been proposed for coherent optical orthogonal frequency-division multiplexing (CO-OFDM) system in this paper. The timing offset (TO), integer frequency offset (FO) and the fractional FO can be realized by only one training symbol, which consists of two linear frequency modulation (LFM) signals with opposite chirp rates. By detecting the peak of LFM signals after Radon-Wigner transform (RWT), the TO and the integer FO can be estimated at the same time, moreover, the fractional FO can be acquired correspondingly through the self-correlation characteristic of the same training symbol. Simulation results show that the proposed method can give a more accurate TO estimation than the existing methods, especially at poor OSNR conditions; for the FO estimation, both the fractional and the integer FO can be estimated through the proposed training symbol with no extra overhead, a more accurate estimation and a large FO estimation range of [ - 5 GHz, 5GHz] can be acquired.

Analysis of the circumferential acoustic waves backscattered by a tube using the time-frequency representation of Wigner-Ville

NASA Astrophysics Data System (ADS)

Latif, R.; Aassif, E.; Maze, G.; Decultot, D.; Moudden, A.; Faiz, B.

2000-01-01

This paper presents a study of the group velocity dispersion of some circumferential waves propagating around an elastic tube. The dispersive character of the circumferential waves is theoretically known, but the experimental measurement of the group velocity in a dispersive medium is still a complex operation. We have determined the characteristics of the circumferential wave dispersion for aluminium and steel tubes using a time-frequency representation. Among these time-frequency techniques, the Wigner-Ville distribution (WVD) is used here for its interesting properties in terms of acoustic applications. The WVD is applied to the analysis of the dispersion of S0 symmetric and A1 antisymmetric circumferential waves propagating around a tube with a radii ratio equal to 0.95 (internal radius:external radius). This allowed us to determine their group velocities and reduced cutoff frequencies. The results obtained are in good agreement with the calculated values using the proper modes theory.

First Observation of the {Lambda}(1405) Line Shape in Electroproduction

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

Lu, Haiyun; Schumacher, Reinhard A.

2013-10-01

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

Dissipative transport in superlattices within the Wigner function formalism

DOE PAGES

Jonasson, O.; Knezevic, I.

2015-07-30

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

Solitons in a one-dimensional Wigner crystal

DOE PAGES

Pustilnik, M.; Matveev, K. A.

2015-04-16

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

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

Zhu, Meng-Zheng; School of Physics and Electronic Information, Huaibei Normal University, Huaibei 235000; Ye, Liu, E-mail: yeliu@ahu.edu.cn

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)more » 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.« less

The application of the Wigner Distribution to wave type identification in finite length beams

NASA Technical Reports Server (NTRS)

Wahl, T. J.; Bolton, J. Stuart

1994-01-01

The object of the research described in this paper was to develop a means of identifying the wave-types propagating between two points in a finite length beam. It is known that different structural wave-types possess different dispersion relations: i.e., that their group speeds and the frequency dependence of their group speeds differ. As a result of those distinct dispersion relationships, different wave-types may be associated with characteristic features when structural responses are examined in the time frequency domain. Previously, the time-frequency character of analytically generated structural responses of both single element and multi-element structures were examined by using the Wigner Distribution (WD) along with filtering techniques that were designed to detect the wave-types present in the responses. In the work to be described here, the measure time-frequency response of finite length beam is examined using the WD and filtering procedures. This paper is organized as follows. First the concept of time-frequency analysis of structural responses is explained. The WD is then introduced along with a description of the implementation of a discrete version. The time-frequency filtering techniques are then presented and explained. The results of applying the WD and the filtering techniques to the analysis of a transient response is then presented.

Wigner in Hungary

NASA Astrophysics Data System (ADS)

Marx, George

2002-04-01

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

Evolution of a hybrid micro-macro entangled state of the qubit-oscillator system via the generalized rotating wave approximation

NASA Astrophysics Data System (ADS)

Chakrabarti, R.; Yogesh, V.

2016-04-01

We study the evolution of the hybrid entangled states in a bipartite (ultra) strongly coupled qubit-oscillator system. Using the generalized rotating wave approximation the reduced density matrices of the qubit and the oscillator are obtained. The reduced density matrix of the oscillator yields the phase space quasi probability distributions such as the diagonal P-representation, the Wigner W-distribution and the Husimi Q-function. In the strong coupling regime the Q-function evolves to uniformly separated macroscopically distinct Gaussian peaks representing ‘kitten’ states at certain specified times that depend on multiple time scales present in the interacting system. The ultrastrong coupling strength of the interaction triggers appearance of a large number of modes that quickly develop a randomization of their phase relationships. A stochastic averaging of the dynamical quantities sets in, and leads to the decoherence of the system. The delocalization in the phase space of the oscillator is studied by using the Wehrl entropy. The negativity of the W-distribution reflects the departure of the oscillator from the classical states, and allows us to study the underlying differences between various information-theoretic measures such as the Wehrl entropy and the Wigner entropy. Other features of nonclassicality such as the existence of the squeezed states and appearance of negative values of the Mandel parameter are realized during the course of evolution of the bipartite system. In the parametric regime studied here these properties do not survive in the time-averaged limit.

Feedback-induced bistability of an optically levitated nanoparticle: A Fokker-Planck treatment

NASA Astrophysics Data System (ADS)

Ge, Wenchao; Rodenburg, Brandon; Bhattacharya, M.

2016-08-01

Optically levitated nanoparticles have recently emerged as versatile platforms for investigating macroscopic quantum mechanics and enabling ultrasensitive metrology. In this paper we theoretically consider two damping regimes of an optically levitated nanoparticle cooled by cavityless parametric feedback. Our treatment is based on a generalized Fokker-Planck equation derived from the quantum master equation presented recently and shown to agree very well with experiment [B. Rodenburg, L. P. Neukirch, A. N. Vamivakas, and M. Bhattacharya, Quantum model of cooling and force sensing with an optically trapped nanoparticle, Optica 3, 318 (2016), 10.1364/OPTICA.3.000318]. For low damping, we find that the resulting Wigner function yields the single-peaked oscillator position distribution and recovers the appropriate energy distribution derived earlier using a classical theory and verified experimentally [J. Gieseler, R. Quidant, C. Dellago, and L. Novotny, Dynamic relaxation of a levitated nanoparticle from a non-equilibrium steady state, Nat. Nano. 9, 358 (2014), 10.1038/nnano.2014.40]. For high damping, in contrast, we predict a double-peaked position distribution, which we trace to an underlying bistability induced by feedback. Unlike in cavity-based optomechanics, stochastic processes play a major role in determining the bistable behavior. To support our conclusions, we present analytical expressions as well as numerical simulations using the truncated Wigner function approach. Our work opens up the prospect of developing bistability-based devices, characterization of phase-space dynamics, and investigation of the quantum-classical transition using levitated nanoparticles.

Physical scales in the Wigner-Boltzmann equation

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

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

2013-01-15

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

Eugene Wigner and Fundamental Symmetry Principles

Science.gov Websites

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

Time-frequency analysis of backscattered signals from diffuse radar targets

NASA Astrophysics Data System (ADS)

Kenny, O. P.; Boashash, B.

1993-06-01

The need for analysis of time-varying signals has led to the formulation of a class of joint time-frequency distributions (TFDs). One of these TFDs, the Wigner-Ville distribution (WVD), has useful properties which can be applied to radar imaging. The authors discuss time-frequency representation of the backscattered signal from a diffuse radar target. It is then shown that for point scatterers which are statistically dependent or for which the reflectivity coefficient has a nonzero mean value, reconstruction using time of flight positron emission tomography on time-frequency images is effective for estimating the scattering function of the target.

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

NASA Astrophysics Data System (ADS)

Carré, Frank

2014-09-01

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

Equivalence between contextuality and negativity of the Wigner function for qudits

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

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

NASA Astrophysics Data System (ADS)

Stolz, Michael

2018-02-01

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

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

PubMed Central

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

2013-01-01

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

Two elementary proofs of the Wigner theorem on symmetry in quantum mechanics

NASA Astrophysics Data System (ADS)

Simon, R.; Mukunda, N.; Chaturvedi, S.; Srinivasan, V.

2008-11-01

In quantum theory, symmetry has to be defined necessarily in terms of the family of unit rays, the state space. The theorem of Wigner asserts that a symmetry so defined at the level of rays can always be lifted into a linear unitary or an antilinear antiunitary operator acting on the underlying Hilbert space. We present two proofs of this theorem which are both elementary and economical. Central to our proofs is the recognition that a given Wigner symmetry can, by post-multiplication by a unitary symmetry, be taken into either the identity or complex conjugation. Our analysis often focuses on the behaviour of certain two-dimensional subspaces of the Hilbert space under the action of a given Wigner symmetry, but the relevance of this behaviour to the larger picture of the whole Hilbert space is made transparent at every stage.

Some rules for polydimensional squeezing

NASA Technical Reports Server (NTRS)

Manko, Vladimir I.

1994-01-01

The review of the following results is presented: For mixed state light of N-mode electromagnetic field described by Wigner function which has generic Gaussian form, the photon distribution function is obtained and expressed explicitly in terms of Hermite polynomials of 2N-variables. The momenta of this distribution are calculated and expressed as functions of matrix invariants of the dispersion matrix. The role of new uncertainty relation depending on photon state mixing parameter is elucidated. New sum rules for Hermite polynomials of several variables are found. The photon statistics of polymode even and odd coherent light and squeezed polymode Schroedinger cat light is given explicitly. Photon distribution for polymode squeezed number states expressed in terms of multivariable Hermite polynomials is discussed.

Genuine Quantum Signatures in Synchronization of Anharmonic Self-Oscillators.

PubMed

Lörch, Niels; Amitai, Ehud; Nunnenkamp, Andreas; Bruder, Christoph

2016-08-12

We study the synchronization of a Van der Pol self-oscillator with Kerr anharmonicity to an external drive. We demonstrate that the anharmonic, discrete energy spectrum of the quantum oscillator leads to multiple resonances in both phase locking and frequency entrainment not present in the corresponding classical system. Strong driving close to these resonances leads to nonclassical steady-state Wigner distributions. Experimental realizations of these genuine quantum signatures can be implemented with current technology.

Quantum Statistics of the Toda Oscillator in the Wigner Function Formalism

NASA Astrophysics Data System (ADS)

Vojta, Günter; Vojta, Matthias

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

Product of Ginibre matrices: Fuss-Catalan and Raney distributions

NASA Astrophysics Data System (ADS)

Penson, Karol A.; Życzkowski, Karol

2011-06-01

Squared singular values of a product of s square random Ginibre matrices are asymptotically characterized by probability distributions Ps(x), such that their moments are equal to the Fuss-Catalan numbers of order s. We find a representation of the Fuss-Catalan distributions Ps(x) in terms of a combination of s hypergeometric functions of the type sFs-1. The explicit formula derived here is exact for an arbitrary positive integer s, and for s=1 it reduces to the Marchenko-Pastur distribution. Using similar techniques, involving the Mellin transform and the Meijer G function, we find exact expressions for the Raney probability distributions, the moments of which are given by a two-parameter generalization of the Fuss-Catalan numbers. These distributions can also be considered as a two-parameter generalization of the Wigner semicircle law.

Product of Ginibre matrices: Fuss-Catalan and Raney distributions.

PubMed

Penson, Karol A; Zyczkowski, Karol

2011-06-01

Squared singular values of a product of s square random Ginibre matrices are asymptotically characterized by probability distributions P(s)(x), such that their moments are equal to the Fuss-Catalan numbers of order s. We find a representation of the Fuss-Catalan distributions P(s)(x) in terms of a combination of s hypergeometric functions of the type (s)F(s-1). The explicit formula derived here is exact for an arbitrary positive integer s, and for s=1 it reduces to the Marchenko-Pastur distribution. Using similar techniques, involving the Mellin transform and the Meijer G function, we find exact expressions for the Raney probability distributions, the moments of which are given by a two-parameter generalization of the Fuss-Catalan numbers. These distributions can also be considered as a two-parameter generalization of the Wigner semicircle law.

Seismic signal time-frequency analysis based on multi-directional window using greedy strategy

NASA Astrophysics Data System (ADS)

Chen, Yingpin; Peng, Zhenming; Cheng, Zhuyuan; Tian, Lin

2017-08-01

Wigner-Ville distribution (WVD) is an important time-frequency analysis technology with a high energy distribution in seismic signal processing. However, it is interfered by many cross terms. To suppress the cross terms of the WVD and keep the concentration of its high energy distribution, an adaptive multi-directional filtering window in the ambiguity domain is proposed. This begins with the relationship of the Cohen distribution and the Gabor transform combining the greedy strategy and the rotational invariance property of the fractional Fourier transform in order to propose the multi-directional window, which extends the one-dimensional, one directional, optimal window function of the optimal fractional Gabor transform (OFrGT) to a two-dimensional, multi-directional window in the ambiguity domain. In this way, the multi-directional window matches the main auto terms of the WVD more precisely. Using the greedy strategy, the proposed window takes into account the optimal and other suboptimal directions, which also solves the problem of the OFrGT, called the local concentration phenomenon, when encountering a multi-component signal. Experiments on different types of both the signal models and the real seismic signals reveal that the proposed window can overcome the drawbacks of the WVD and the OFrGT mentioned above. Finally, the proposed method is applied to a seismic signal's spectral decomposition. The results show that the proposed method can explore the space distribution of a reservoir more precisely.

Time-frequency characterisation of paediatric heart sounds

NASA Astrophysics Data System (ADS)

Leung, Terence Sze-Tat

1998-08-01

The operation of the heart can be monitored by the sounds it emits. Structural defects or malfunction of the heart valves will cause additional abnormal sounds such as murmurs and ejection clicks. This thesis aims to characterise the heart sounds of three groups of children who either have an Atrial Septal Defect (ASD), a Ventricular Septal Defect (VSD), or are normal. Two aspects of heart sounds have been specifically investigated; the time-frequency analysis of systolic murmurs and the identification of splitting patterns in the second heart sound. The analysis is based on 42 paediatric heart sound recordings. Murmurs are sounds generated by turbulent flow of blood in the heart. They can be found in patients with both pathological and non-pathological conditions. The acoustic quality of the murmurs generated in each heart condition are different. The first aspect of this work is to characterise the three types of murmurs in the time- frequency domain. Modern time-frequency methods including, the Wigner-Ville Distribution, Smoothed Pseudo Wigner-Ville Distribution, Choi-Williams Distribution and spectrogram have been applied to characterise the murmurs. It was found that the three classes of murmurs exhibited different signatures in their time-frequency representations. By performing Discriminant Analysis, it was shown that spectral features extracted from the time- frequency representations can be used to distinguish between the three classes. The second aspect of the research is to identify splitting patterns in the second heart sound, which consists of two acoustic components due to the closure of the aortic valve and pulmonary valve. The aortic valve usually closes before the pulmonary valve, introducing a time delay known as 'split'. The split normally varies in duration over the respiratory cycle. In certain pathologies such as the ASD, the split becomes fixed over the respiration cycle. A technique based on adaptive signal decomposition is developed to measure the split and hence to identify the splitting pattern as either 'variable' or 'fixed'. This work has successfully characterised the murmurs and splitting patterns in the three groups of patients. Features extracted can be used for diagnostic purposes.

Scars of the Wigner Function.

PubMed

Toscano; de Aguiar MA; Ozorio De Almeida AM

2001-01-01

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

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

NASA Astrophysics Data System (ADS)

Jha, Stefania

2011-09-01

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

Wigner expansions for partition functions of nonrelativistic and relativistic oscillator systems

NASA Technical Reports Server (NTRS)

Zylka, Christian; Vojta, Guenter

1993-01-01

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

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

NASA Astrophysics Data System (ADS)

Arnold, Thorsten; Siegmund, Marc; Pankratov, Oleg

2011-08-01

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

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

PubMed

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

2014-02-28

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

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

PubMed

Arnold, Thorsten; Siegmund, Marc; Pankratov, Oleg

2011-08-24

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

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

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

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

2014-02-28

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

First-principles study of the structural and elastic properties of AuxV1-x and AuxNb1-x alloys

NASA Astrophysics Data System (ADS)

Al-Zoubi, N.

2018-04-01

Ab initio total energy calculations, based on the Exact Muffin-Tin Orbitals (EMTO) method in combination with the coherent potential approximation (CPA), are used to calculate the total energy of AuxV1-x and AuxNb1-x random alloys along the Bain path that connects the body-centred cubic (bcc) and face-centred cubic (fcc) structures as a function of composition x (0 ≤ x ≤ 1). The equilibrium Wigner-Seitz radius and the elastic properties of both systems are determined as a function of composition. Our theoretical prediction in case of pure elements (x = 0 or x = 1) are in good agreement with the available experimental data. For the Au-V system, the equilibrium Wigner-Seitz radius increase as x increases, while for the Au-Nb system, the equilibrium Wigner-Seitz radius is almost constant. The bulk modulus B and C44 for both alloys exhibit nearly parabolic trend. On the other hand, the tetragonal shear elastic constant C‧ decreases as x increases and correlates reasonably well with the structural energy difference between fcc and bcc structures. Our results offer a consistent starting point for further theoretical and experimental studies of the elastic and micromechanical properties of Au-V and Au-Nb systems.

Determination of knock characteristics in spark ignition engines: an approach based on ensemble empirical mode decomposition

NASA Astrophysics Data System (ADS)

Li, Ning; Yang, Jianguo; Zhou, Rui; Liang, Caiping

2016-04-01

Knock is one of the major constraints to improve the performance and thermal efficiency of spark ignition (SI) engines. It can also result in severe permanent engine damage under certain operating conditions. Based on the ensemble empirical mode decomposition (EEMD), this paper proposes a new approach to determine the knock characteristics in SI engines. By adding a uniformly distributed and finite white Gaussian noise, the EEMD can preserve signal continuity in different scales and therefore alleviates the mode-mixing problem occurring in the classic empirical mode decomposition (EMD). The feasibilities of applying the EEMD to detect the knock signatures of a test SI engine via the pressure signal measured from combustion chamber and the vibration signal measured from cylinder head are investigated. Experimental results show that the EEMD-based method is able to detect the knock signatures from both the pressure signal and vibration signal, even in initial stage of knock. Finally, by comparing the application results with those obtained by short-time Fourier transform (STFT), Wigner-Ville distribution (WVD) and discrete wavelet transform (DWT), the superiority of the EEMD method in determining knock characteristics is demonstrated.

Blind source separation based on time-frequency morphological characteristics for rigid acoustic scattering by underwater objects

NASA Astrophysics Data System (ADS)

Yang, Yang; Li, Xiukun

2016-06-01

Separation of the components of rigid acoustic scattering by underwater objects is essential in obtaining the structural characteristics of such objects. To overcome the problem of rigid structures appearing to have the same spectral structure in the time domain, time-frequency Blind Source Separation (BSS) can be used in combination with image morphology to separate the rigid scattering components of different objects. Based on a highlight model, the separation of the rigid scattering structure of objects with time-frequency distribution is deduced. Using a morphological filter, different characteristics in a Wigner-Ville Distribution (WVD) observed for single auto term and cross terms can be simplified to remove any cross-term interference. By selecting time and frequency points of the auto terms signal, the accuracy of BSS can be improved. An experimental simulation has been used, with changes in the pulse width of the transmitted signal, the relative amplitude and the time delay parameter, in order to analyzing the feasibility of this new method. Simulation results show that the new method is not only able to separate rigid scattering components, but can also separate the components when elastic scattering and rigid scattering exist at the same time. Experimental results confirm that the new method can be used in separating the rigid scattering structure of underwater objects.

Time-frequency approach to underdetermined blind source separation.

PubMed

Xie, Shengli; Yang, Liu; Yang, Jun-Mei; Zhou, Guoxu; Xiang, Yong

2012-02-01

This paper presents a new time-frequency (TF) underdetermined blind source separation approach based on Wigner-Ville distribution (WVD) and Khatri-Rao product to separate N non-stationary sources from M(M <; N) mixtures. First, an improved method is proposed for estimating the mixing matrix, where the negative value of the auto WVD of the sources is fully considered. Then after extracting all the auto-term TF points, the auto WVD value of the sources at every auto-term TF point can be found out exactly with the proposed approach no matter how many active sources there are as long as N ≤ 2M-1. Further discussion about the extraction of auto-term TF points is made and finally the numerical simulation results are presented to show the superiority of the proposed algorithm by comparing it with the existing ones.

Image Quality Assessment Using the Joint Spatial/Spatial-Frequency Representation

NASA Astrophysics Data System (ADS)

Beghdadi, Azeddine; Iordache, Răzvan

2006-12-01

This paper demonstrates the usefulness of spatial/spatial-frequency representations in image quality assessment by introducing a new image dissimilarity measure based on 2D Wigner-Ville distribution (WVD). The properties of 2D WVD are shortly reviewed, and the important issue of choosing the analytic image is emphasized. The WVD-based measure is shown to be correlated with subjective human evaluation, which is the premise towards an image quality assessor developed on this principle.

Exact solution of equations for proton localization in neutron star matter

NASA Astrophysics Data System (ADS)

Kubis, Sebastian; Wójcik, Włodzimierz

2015-11-01

The rigorous treatment of proton localization phenomenon in asymmetric nuclear matter is presented. The solution of proton wave function and neutron background distribution is found by the use of the extended Thomas-Fermi approach. The minimum of energy is obtained in the Wigner-Seitz approximation of a spherically symmetric cell. The analysis of four different nuclear models suggests that the proton localization is likely to take place in the interior of a neutron star.

The eigenvalue problem in phase space.

PubMed

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.

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

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

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

2015-04-07

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

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

NASA Astrophysics Data System (ADS)

Mohamed, Abdel-Baset A.

2017-10-01

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

Unraveling hadron structure with generalized parton distributions

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

Andrei Belitsky; Anatoly Radyushkin

2004-10-01

The recently introduced generalized parton distributions have emerged as a universal tool to describe hadrons in terms of quark and gluonic degrees of freedom. They combine the features of form factors, parton densities and distribution amplitudes - the functions used for a long time in studies of hadronic structure. Generalized parton distributions are analogous to the phase-space Wigner quasi-probability function of non-relativistic quantum mechanics which encodes full information on a quantum-mechanical system. We give an extensive review of main achievements in the development of this formalism. We discuss physical interpretation and basic properties of generalized parton distributions, their modeling andmore » QCD evolution in the leading and next-to-leading orders. We describe how these functions enter a wide class of exclusive reactions, such as electro- and photo-production of photons, lepton pairs, or mesons.« less

Multi-scale and Multi-physics Numerical Methods for Modeling Transport in Mesoscopic Systems

DTIC Science & Technology

2014-10-13

function and wide band Fast multipole methods for Hankel waves. (2) a new linear scaling discontinuous Galerkin density functional theory, which provide a...inflow boundary condition for Wigner quantum transport equations. Also, a book titled "Computational Methods for Electromagnetic Phenomena...equationsin layered media with FMM for Bessel functions , Science China Mathematics, (12 2013): 2561. doi: TOTAL: 6 Number of Papers published in peer

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

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

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

2014-07-01

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

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

NASA Astrophysics Data System (ADS)

Kakofengitis, Dimitris; Steuernagel, Ole

2017-09-01

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

Enhanced production of ψ (2 S ) mesons in heavy ion collisions

NASA Astrophysics Data System (ADS)

Cho, Sungtae

2015-05-01

I study the production of a ψ (2 S ) meson in heavy ion collisions. I evaluate Wigner functions for the ψ (2 S ) meson using both Gaussian and Coulomb wave functions, and investigate the wave function dependence in the ψ (2 S ) meson production by recombination of charm and anticharm quarks. The enhanced transverse momentum distribution of ψ (2 S ) mesons compared to that of J /ψ mesons, originated from wave function distributions of the ψ (2 S ) and J /ψ meson in momentum space, provides a plausible explanation for the recent measurement of the nuclear modification factor ratio between the ψ (2 S ) and J /ψ meson.

Gluon tomography from deeply virtual Compton scattering at small x

DOE PAGES

Hatta, Yoshitaka; Xiao, Bo-Wen; Yuan, Feng

2017-06-29

We present a full evaluation of the deeply virtual Compton scattering cross section in the dipole framework in the small-x region. The result features the cosφ and cos2φ azimuthal angular correlations, which have been missing in previous studies based on the dipole model. In particular, the cos2φ term is generated by the elliptic gluon Wigner distribution of which the measurement at the planned electron-ion collider provides important information about the gluon tomography at small x. Here, we also show the consistency with the standard collinear factorization approach based on the quark and gluon generalized parton distributions.

Development of a Model Based Technique for Gear Diagnostics using the Wigner-Ville method

NASA Technical Reports Server (NTRS)

Choy, F.; Xu, A.; Polyshchuk, V.

1997-01-01

Imperfections in gear tooth geometry often result from errors in the manufacturing process or excessive material wear during operation. Such faults in the gear tooth geometry can result in large vibrations in the transmission system, and, in some cases, may lead to early failure of the gear transmission system. This report presents the study of the effects of imperfection in gear tooth geometry on the dynamic characteristics of a gear transmission system. The faults in the gear tooth geometry are modeled numerically as the deviation of the tooth profile from its original involute geometry. The changes in gear mesh stiffness due to various profile and pattern variations are evaluated numerically. The resulting changes in the mesh stiffness are incorporated into a computer code to simulate the dynamics of the gear transmission system. A parametric study is performed to examine the sensitivity of gear tooth geometry imperfections on the vibration of a gear transmission system. The parameters variations in this study consist of the magnitude of the imperfection, the pattern of the profile variation, and the total number of teeth affected. Numerical results from the dynamic simulations are examined in both the time and the frequency domains. A joint time-frequency analysis procedure using the Wigner-Ville Distribution is also introduced to identify the location of the damaged tooth from the vibration signature. Numerical simulations of the system dynamics with gear faults were compared to experimental results. An optimal tracker was introduced to quantify the level of damage in the gear mesh system. Conclusions are drawn from the results of this numerical study.

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

PubMed Central

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

2015-01-01

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

Proposal for chiral-boson search at LHC via their unique new signature

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

Chizhov, M. V.; Bednyakov, V. A.; Budagov, J. A.

The resonance production of new chiral spin-1 bosons and their detection through the Drell-Yan process at the CERN LHC is considered. Quantitative evaluations of various differential cross sections of the chiral-boson production are made within the CalcHEP package. The new neutral chiral bosons can be observed as a Breit-Wigner resonance peak in the invariant-dilepton-mass distribution, as usual. However, unique new signatures of the chiral bosons exist. First, there is no Jacobian peak in the lepton transverse-momentum distribution. Second, the lepton angular distribution in the Collins-Soper frame for the high on-peak invariant masses of the lepton pairs has a peculiar 'swallowtail'more » shape.« less

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

NASA Technical Reports Server (NTRS)

Dattoli, G.; Torre, Amalia

1994-01-01

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

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

NASA Astrophysics Data System (ADS)

Subotnik, Joseph E.; Shenvi, Neil

2011-06-01

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

Adaptive Window Zero-Crossing-Based Instantaneous Frequency Estimation

NASA Astrophysics Data System (ADS)

Sekhar, S. Chandra; Sreenivas, TV

2004-12-01

We address the problem of estimating instantaneous frequency (IF) of a real-valued constant amplitude time-varying sinusoid. Estimation of polynomial IF is formulated using the zero-crossings of the signal. We propose an algorithm to estimate nonpolynomial IF by local approximation using a low-order polynomial, over a short segment of the signal. This involves the choice of window length to minimize the mean square error (MSE). The optimal window length found by directly minimizing the MSE is a function of the higher-order derivatives of the IF which are not available a priori. However, an optimum solution is formulated using an adaptive window technique based on the concept of intersection of confidence intervals. The adaptive algorithm enables minimum MSE-IF (MMSE-IF) estimation without requiring a priori information about the IF. Simulation results show that the adaptive window zero-crossing-based IF estimation method is superior to fixed window methods and is also better than adaptive spectrogram and adaptive Wigner-Ville distribution (WVD)-based IF estimators for different signal-to-noise ratio (SNR).

Automatic classification of sleep stages based on the time-frequency image of EEG signals.

PubMed

Bajaj, Varun; Pachori, Ram Bilas

2013-12-01

In this paper, a new method for automatic sleep stage classification based on time-frequency image (TFI) of electroencephalogram (EEG) signals is proposed. Automatic classification of sleep stages is an important part for diagnosis and treatment of sleep disorders. The smoothed pseudo Wigner-Ville distribution (SPWVD) based time-frequency representation (TFR) of EEG signal has been used to obtain the time-frequency image (TFI). The segmentation of TFI has been performed based on the frequency-bands of the rhythms of EEG signals. The features derived from the histogram of segmented TFI have been used as an input feature set to multiclass least squares support vector machines (MC-LS-SVM) together with the radial basis function (RBF), Mexican hat wavelet, and Morlet wavelet kernel functions for automatic classification of sleep stages from EEG signals. The experimental results are presented to show the effectiveness of the proposed method for classification of sleep stages from EEG signals. Copyright © 2013 Elsevier Ireland Ltd. All rights reserved.

Mathematics as an Instigator of Scientific Revolutions

ERIC Educational Resources Information Center

Brush, Stephen G.

2015-01-01

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

Eugene Wigner - A Gedanken Pioneer of the Second Quantum Revolution

NASA Astrophysics Data System (ADS)

Zeilinger, Anton

2014-09-01

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

Quantum cryptography with entangled photons

PubMed

Jennewein; Simon; Weihs; Weinfurter; Zeilinger

2000-05-15

By realizing a quantum cryptography system based on polarization entangled photon pairs we establish highly secure keys, because a single photon source is approximated and the inherent randomness of quantum measurements is exploited. We implement a novel key distribution scheme using Wigner's inequality to test the security of the quantum channel, and, alternatively, realize a variant of the BB84 protocol. Our system has two completely independent users separated by 360 m, and generates raw keys at rates of 400-800 bits/s with bit error rates around 3%.

Propagation properties of a partially coherent radially polarized beam in atmospheric turbulence

NASA Astrophysics Data System (ADS)

Zheng, Guo; Wang, Lin; Wang, Jue; Zhou, Muchun; Song, Minmin

2018-07-01

Based on the extended Huygens-Fresnel integral, second-order moments of the Wigner distribution function of a partially coherent radially polarized beam propagating through atmospheric turbulence are derived. Besides, propagation properties such as the mean-squared beam width, angular width, effective radius of curvature, beam propagation factor and Rayleigh range can also be obtained and calculated numerically. It is shown that the propagation properties are dependent on the spatial correlation length, refraction index structure constant and propagation distance.

Ponderomotive effects in multiphoton pair production

NASA Astrophysics Data System (ADS)

Kohlfürst, Christian; Alkofer, Reinhard

2018-02-01

The Dirac-Heisenberg-Wigner formalism is employed to investigate electron-positron pair production in cylindrically symmetric but otherwise spatially inhomogeneous, oscillating electric fields. The oscillation frequencies are hereby tuned to obtain multiphoton pair production in the nonperturbative threshold regime. An effective mass, as well as a trajectory-based semiclassical analysis, is introduced in order to interpret the numerical results for the distribution functions as well as for the particle yields and spectra. The results, including the asymptotic particle spectra, display clear signatures of ponderomotive forces.

Classification of amyotrophic lateral sclerosis disease based on convolutional neural network and reinforcement sample learning algorithm.

PubMed

Sengur, Abdulkadir; Akbulut, Yaman; Guo, Yanhui; Bajaj, Varun

2017-12-01

Electromyogram (EMG) signals contain useful information of the neuromuscular diseases like amyotrophic lateral sclerosis (ALS). ALS is a well-known brain disease, which can progressively degenerate the motor neurons. In this paper, we propose a deep learning based method for efficient classification of ALS and normal EMG signals. Spectrogram, continuous wavelet transform (CWT), and smoothed pseudo Wigner-Ville distribution (SPWVD) have been employed for time-frequency (T-F) representation of EMG signals. A convolutional neural network is employed to classify these features. In it, Two convolution layers, two pooling layer, a fully connected layer and a lost function layer is considered in CNN architecture. The CNN architecture is trained with the reinforcement sample learning strategy. The efficiency of the proposed implementation is tested on publicly available EMG dataset. The dataset contains 89 ALS and 133 normal EMG signals with 24 kHz sampling frequency. Experimental results show 96.80% accuracy. The obtained results are also compared with other methods, which show the superiority of the proposed method.

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

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

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

2014-09-15

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

Dynamics of the Wigner crystal of composite particles

NASA Astrophysics Data System (ADS)

Shi, Junren; Ji, Wencheng

2018-03-01

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

Baryon transition form factors at the pole

DOE PAGES

Tiator, L.; Döring, M.; Workman, R. L.; ...

2016-12-21

Electromagnetic resonance properties are uniquely defined at the pole and do not depend on the separation of the resonance from background or the decay channel. Photon-nucleon branching ratios are nowadays often quoted at the pole, and we generalize the considerations to the case of virtual photons. In this paper, we derive and compare relations for nucleon to baryon transition form factors both for the Breit-Wigner and the pole positions. Using the MAID2007 and SAID SM08 partial wave analyses of pion electroproduction data, we compare themore » $$G_M$$, $$G_E$$, and $$G_C$$ form factors for the $$\\Delta(1232)$$ resonance excitation at the Breit-Wigner resonance and pole positions up to $Q^2=5$ GeV$^2$. We also explore the $E/M$ and $S/M$ ratios as functions of $Q^2$. Finally, for pole and residue extraction, we apply the Laurent + Pietarinen method.« less

Baryon transition form factors at the pole

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

Tiator, L.; Döring, M.; Workman, R. L.

Electromagnetic resonance properties are uniquely defined at the pole and do not depend on the separation of the resonance from background or the decay channel. Photon-nucleon branching ratios are nowadays often quoted at the pole, and we generalize the considerations to the case of virtual photons. In this paper, we derive and compare relations for nucleon to baryon transition form factors both for the Breit-Wigner and the pole positions. Using the MAID2007 and SAID SM08 partial wave analyses of pion electroproduction data, we compare themore » $$G_M$$, $$G_E$$, and $$G_C$$ form factors for the $$\\Delta(1232)$$ resonance excitation at the Breit-Wigner resonance and pole positions up to $Q^2=5$ GeV$^2$. We also explore the $E/M$ and $S/M$ ratios as functions of $Q^2$. Finally, for pole and residue extraction, we apply the Laurent + Pietarinen method.« less

ππ P-wave resonant scattering from lattice QCD

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

A novel conductivity mechanism of highly disordered carbon systems based on an investigation of graph zeta function

NASA Astrophysics Data System (ADS)

Matsutani, Shigeki; Sato, Iwao

2017-09-01

In the previous report (Matsutani and Suzuki, 2000 [21]), by proposing the mechanism under which electric conductivity is caused by the activational hopping conduction with the Wigner surmise of the level statistics, the temperature-dependent of electronic conductivity of a highly disordered carbon system was evaluated including apparent metal-insulator transition. Since the system consists of small pieces of graphite, it was assumed that the reason why the level statistics appears is due to the behavior of the quantum chaos in each granular graphite. In this article, we revise the assumption and show another origin of the Wigner surmise, which is more natural for the carbon system based on a recent investigation of graph zeta function in graph theory. Our method can be applied to the statistical treatment of the electronic properties of the randomized molecular system in general.

Moving target parameter estimation of SAR after two looks cancellation

NASA Astrophysics Data System (ADS)

Gan, Rongbing; Wang, Jianguo; Gao, Xiang

2005-11-01

Moving target detection of synthetic aperture radar (SAR) by two looks cancellation is studied. First, two looks are got by the first and second half of the synthetic aperture. After two looks cancellation, the moving targets are reserved and stationary targets are removed. After that, a Constant False Alarm Rate (CFAR) detector detects moving targets. The ground range velocity and cross-range velocity of moving target can be got by the position shift between the two looks. We developed a method to estimate the cross-range shift due to slant range moving. we estimate cross-range shift by Doppler frequency center. Wigner-Ville Distribution (WVD) is used to estimate the Doppler frequency center (DFC). Because the range position and cross range before correction is known, estimation of DFC is much easier and efficient. Finally experiments results show that our algorithms have good performance. With the algorithms we can estimate the moving target parameter accurately.

Hybrid methods for witnessing entanglement in a microscopic-macroscopic system

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

Spagnolo, Nicolo; Consorzio Nazionale Interuniversitario per le Scienze Fisiche della Materia, Piazzale Aldo Moro 5, I-00185 Roma; Vitelli, Chiara

2011-09-15

We propose a hybrid approach to the experimental assessment of the genuine quantum features of a general system consisting of microscopic and macroscopic parts. We infer entanglement by combining dichotomic measurements on a bidimensional system and phase-space inference through the Wigner distribution associated with the macroscopic component of the state. As a benchmark, we investigate the feasibility of our proposal in a bipartite-entangled state composed of a single-photon and a multiphoton field. Our analysis shows that, under ideal conditions, maximal violation of a Clauser-Horne-Shimony-Holt-based inequality is achievable regardless of the number of photons in the macroscopic part of the state.more » The difficulty in observing entanglement when losses and detection inefficiency are included can be overcome by using a hybrid entanglement witness that allows efficient correction for losses in the few-photon regime.« less

Dynamical Evolution of Properties for Atom and Field in the Process of Two-Photon Absorption and Emission Between Atomic Levels

NASA Astrophysics Data System (ADS)

Wang, Jian-ming; Xu, Xue-xiang

2018-04-01

Using dressed state method, we cleverly solve the dynamics of atom-field interaction in the process of two-photon absorption and emission between atomic levels. Here we suppose that the atom is initially in the ground state and the optical field is initially in Fock state, coherent state or thermal state, respectively. The properties of the atom, including the population in excited state and ground state, the atom inversion, and the properties for optical field, including the photon number distribution, the mean photon number, the second-order correlation function and the Wigner function, are discussed in detail. We derive their analytical expressions and then make numerical analysis for them. In contrast with Jaynes-Cummings model, some similar results, such as quantum Rabi oscillation, revival and collapse, are also exhibit in our considered model. Besides, some novel nonclassical states are generated.

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

DTIC Science & Technology

2013-11-26

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

Discrimination of isotrigon textures using the Rényi entropy of Allan variances.

PubMed

Gabarda, Salvador; Cristóbal, Gabriel

2008-09-01

We present a computational algorithm for isotrigon texture discrimination. The aim of this method consists in discriminating isotrigon textures against a binary random background. The extension of the method to the problem of multitexture discrimination is considered as well. The method relies on the fact that the information content of time or space-frequency representations of signals, including images, can be readily analyzed by means of generalized entropy measures. In such a scenario, the Rényi entropy appears as an effective tool, given that Rényi measures can be used to provide information about a local neighborhood within an image. Localization is essential for comparing images on a pixel-by-pixel basis. Discrimination is performed through a local Rényi entropy measurement applied on a spatially oriented 1-D pseudo-Wigner distribution (PWD) of the test image. The PWD is normalized so that it may be interpreted as a probability distribution. Prior to the calculation of the texture's PWD, a preprocessing filtering step replaces the original texture with its localized spatially oriented Allan variances. The anisotropic structure of the textures, as revealed by the Allan variances, turns out to be crucial later to attain a high discrimination by the extraction of Rényi entropy measures. The method has been empirically evaluated with a family of isotrigon textures embedded in a binary random background. The extension to the case of multiple isotrigon mosaics has also been considered. Discrimination results are compared with other existing methods.

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Hunting the Gluon Orbital Angular Momentum at the Electron-Ion Collider.

PubMed

Ji, Xiangdong; Yuan, Feng; Zhao, Yong

2017-05-12

Applying the connection between the parton Wigner distribution and orbital angular momentum (OAM), we investigate the probe of the gluon OAM in hard scattering processes at the planned electron-ion collider. We show that the single longitudinal target-spin asymmetry in the hard diffractive dijet production is very sensitive to the gluon OAM distribution. The associated spin asymmetry leads to a characteristic azimuthal angular correlation of sin(ϕ_{q}-ϕ_{Δ}), where ϕ_{Δ} and ϕ_{q} are the azimuthal angles of the proton momentum transfer and the relative transverse momentum between the quark-antiquark pair. This study may motivate a first measurement of the gluon OAM in the proton spin sum rule.

An Efficient Implementation For Real Time Applications Of The Wigner-Ville Distribution

NASA Astrophysics Data System (ADS)

Boashash, Boualem; Black, Peter; Whitehouse, Harper J.

1986-03-01

The Wigner-Ville Distribution (WVD) is a valuable tool for time-frequency signal analysis. In order to implement the WVD in real time an efficient algorithm and architecture have been developed which may be implemented with commercial components. This algorithm successively computes the analytic signal corresponding to the input signal, forms a weighted kernel function and analyses the kernel via a Discrete Fourier Transform (DFT). To evaluate the analytic signal required by the algorithm it is shown that the time domain definition implemented as a finite impulse response (FIR) filter is practical and more efficient than the frequency domain definition of the analytic signal. The windowed resolution of the WVD in the frequency domain is shown to be similar to the resolution of a windowed Fourier Transform. A real time signal processsor has been designed for evaluation of the WVD analysis system. The system is easily paralleled and can be configured to meet a variety of frequency and time resolutions. The arithmetic unit is based on a pair of high speed VLSI floating-point multiplier and adder chips. Dual operand buses and an independent result bus maximize data transfer rates. The system is horizontally microprogrammed and utilizes a full instruction pipeline. Each microinstruction specifies two operand addresses, a result location, the type of arithmetic and the memory configuration. input and output is via shared memory blocks with front-end processors to handle data transfers during the non access periods of the analyzer.

A New Reassigned Spectrogram Method in Interference Detection for GNSS Receivers.

PubMed

Sun, Kewen; Jin, Tian; Yang, Dongkai

2015-09-02

Interference detection is very important for Global Navigation Satellite System (GNSS) receivers. Current work on interference detection in GNSS receivers has mainly focused on time-frequency (TF) analysis techniques, such as spectrogram and Wigner-Ville distribution (WVD), where the spectrogram approach presents the TF resolution trade-off problem, since the analysis window is used, and the WVD method suffers from the very serious cross-term problem, due to its quadratic TF distribution nature. In order to solve the cross-term problem and to preserve good TF resolution in the TF plane at the same time, in this paper, a new TF distribution by using a reassigned spectrogram has been proposed in interference detection for GNSS receivers. This proposed reassigned spectrogram method efficiently combines the elimination of the cross-term provided by the spectrogram itself according to its inherent nature and the improvement of the TF aggregation property achieved by the reassignment method. Moreover, a notch filter has been adopted in interference mitigation for GNSS receivers, where receiver operating characteristics (ROCs) are used as metrics for the characterization of interference mitigation performance. The proposed interference detection method by using a reassigned spectrogram is evaluated by experiments on GPS L1 signals in the disturbing scenarios in comparison to the state-of-the-art TF analysis approaches. The analysis results show that the proposed interference detection technique effectively overcomes the cross-term problem and also keeps good TF localization properties, which has been proven to be valid and effective to enhance the interference Sensors 2015, 15 22168 detection performance; in addition, the adoption of the notch filter in interference mitigation has shown a significant acquisition performance improvement in terms of ROC curves for GNSS receivers in jamming environments.

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

ERIC Educational Resources Information Center

Gelfert, Axel

2014-01-01

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

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

ERIC Educational Resources Information Center

O'Donnell, Kane; Visser, Matt

2011-01-01

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

Entanglement and Wigner Function Negativity of Multimode Non-Gaussian States

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

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

PubMed

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

2017-11-03

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

Lessons on electronic decoherence in molecules from exact modeling

NASA Astrophysics Data System (ADS)

Hu, Wenxiang; Gu, Bing; Franco, Ignacio

2018-04-01

Electronic decoherence processes in molecules and materials are usually thought and modeled via schemes for the system-bath evolution in which the bath is treated either implicitly or approximately. Here we present computations of the electronic decoherence dynamics of a model many-body molecular system described by the Su-Schrieffer-Heeger Hamiltonian with Hubbard electron-electron interactions using an exact method in which both electronic and nuclear degrees of freedom are taken into account explicitly and fully quantum mechanically. To represent the electron-nuclear Hamiltonian in matrix form and propagate the dynamics, the computations employ the Jordan-Wigner transformation for the fermionic creation/annihilation operators and the discrete variable representation for the nuclear operators. The simulations offer a standard for electronic decoherence that can be used to test approximations. They also provide a useful platform to answer fundamental questions about electronic decoherence that cannot be addressed through approximate or implicit schemes. Specifically, through simulations, we isolate basic mechanisms for electronic coherence loss and demonstrate that electronic decoherence is possible even for one-dimensional nuclear bath. Furthermore, we show that (i) decreasing the mass of the bath generally leads to faster electronic decoherence; (ii) electron-electron interactions strongly affect the electronic decoherence when the electron-nuclear dynamics is not pure-dephasing; (iii) classical bath models with initial conditions sampled from the Wigner distribution accurately capture the short-time electronic decoherence dynamics; (iv) model separable initial superpositions often used to understand decoherence after photoexcitation are only relevant in experiments that employ delta-like laser pulses to initiate the dynamics. These insights can be employed to interpret and properly model coherence phenomena in molecules.

Real-time and imaginary-time quantum hierarchal Fokker-Planck equations

NASA Astrophysics Data System (ADS)

Tanimura, Yoshitaka

2015-04-01

We consider a quantum mechanical system represented in phase space (referred to hereafter as "Wigner space"), coupled to a harmonic oscillator bath. We derive quantum hierarchal Fokker-Planck (QHFP) equations not only in real time but also in imaginary time, which represents an inverse temperature. This is an extension of a previous work, in which we studied a spin-boson system, to a Brownian system. It is shown that the QHFP in real time obtained from a correlated thermal equilibrium state of the total system possesses the same form as those obtained from a factorized initial state. A modified terminator for the hierarchal equations of motion is introduced to treat the non-Markovian case more efficiently. Using the imaginary-time QHFP, numerous thermodynamic quantities, including the free energy, entropy, internal energy, heat capacity, and susceptibility, can be evaluated for any potential. These equations allow us to treat non-Markovian, non-perturbative system-bath interactions at finite temperature. Through numerical integration of the real-time QHFP for a harmonic system, we obtain the equilibrium distributions, the auto-correlation function, and the first- and second-order response functions. These results are compared with analytically exact results for the same quantities. This provides a critical test of the formalism for a non-factorized thermal state and elucidates the roles of fluctuation, dissipation, non-Markovian effects, and system-bath coherence. Employing numerical solutions of the imaginary-time QHFP, we demonstrate the capability of this method to obtain thermodynamic quantities for any potential surface. It is shown that both types of QHFP equations can produce numerical results of any desired accuracy. The FORTRAN source codes that we developed, which allow for the treatment of Wigner space dynamics with any potential form (TanimuranFP15 and ImTanimuranFP15), are provided as the supplementary material.

Salecker-Wigner-Peres clock, Feynman paths, and a tunneling time that should not exist

NASA Astrophysics Data System (ADS)

Sokolovski, D.

2017-08-01

The Salecker-Wigner-Peres (SWP) clock is often used to determine the duration a quantum particle is supposed to spend in a specified region of space Ω . By construction, the result is a real positive number, and the method seems to avoid the difficulty of introducing complex time parameters, which arises in the Feynman paths approach. However, it tells little about the particle's motion. We investigate this matter further, and show that the SWP clock, like any other Larmor clock, correlates the rotation of its angular momentum with the durations τ , which the Feynman paths spend in Ω , thereby destroying interference between different durations. An inaccurate weakly coupled clock leaves the interference almost intact, and the need to resolve the resulting "which way?" problem is one of the main difficulties at the center of the "tunnelling time" controversy. In the absence of a probability distribution for the values of τ , the SWP results are expressed in terms of moduli of the "complex times," given by the weighted sums of the corresponding probability amplitudes. It is shown that overinterpretation of these results, by treating the SWP times as physical time intervals, leads to paradoxes and should be avoided. We also analyze various settings of the SWP clock, different calibration procedures, and the relation between the SWP results and the quantum dwell time. The cases of stationary tunneling and tunnel ionization are considered in some detail. Although our detailed analysis addresses only one particular definition of the duration of a tunneling process, it also points towards the impossibility of uniting various time parameters, which may occur in quantum theory, within the concept of a single tunnelling time.

Vital sign sensing method based on EMD in terahertz band

NASA Astrophysics Data System (ADS)

Xu, Zhengwu; Liu, Tong

2014-12-01

Non-contact respiration and heartbeat rates detection could be applied to find survivors trapped in the disaster or the remote monitoring of the respiration and heartbeat of a patient. This study presents an improved algorithm that extracts the respiration and heartbeat rates of humans by utilizing the terahertz radar, which further lessens the effects of noise, suppresses the cross-term, and enhances the detection accuracy. A human target echo model for the terahertz radar is first presented. Combining the over-sampling method, low-pass filter, and Empirical Mode Decomposition improves the signal-to-noise ratio. The smoothed pseudo Wigner-Ville distribution time-frequency technique and the centroid of the spectrogram are used to estimate the instantaneous velocity of the target's cardiopulmonary motion. The down-sampling method is adopted to prevent serious distortion. Finally, a second time-frequency analysis is applied to the centroid curve to extract the respiration and heartbeat rates of the individual. Simulation results show that compared with the previously presented vital sign sensing method, the improved algorithm enhances the signal-to-noise ratio to 1 dB with a detection accuracy of 80%. The improved algorithm is an effective approach for the detection of respiration and heartbeat signal in a complicated environment.

Study of transionospheric signal scintillation: Quasi- particle approach

NASA Astrophysics Data System (ADS)

Lyle, Ruthie D.

1998-07-01

A quasi-particle approach is applied to study amplitude scintillation of transionospheric signals caused by Bottomside Sinusoidal (BSS) irregularities. The quasi- particle method exploits wave-particle duality, viewing the wave as a distribution of quasi-particles. This is accomplished by transforming the autocorrelation of the wave function into a Wigner distribution function, which serves as a distribution of quasi-particles in the (/vec r,/ /vec k) phase space. The quasi-particle distribution at any instant of time represents the instantaneous state of the wave. Scattering of the signal by the ionospheric irregularities is equivalent to the evolution of the quasi-particle distribution, due to the collision of the quasi-particles with objects arising from the presence of the BSS irregularities. Subsequently, the perturbed quasi-particle distribution facilitates the computation of average space time propagation properties of the wave. Thus, the scintillation index S4 is determined. Incorporation of essential BSS features in the analysis is accomplished by analytically modeling the power spectrum of the BSS irregularities measured in-situ by the low orbiting Atmosphere-E (AE - E) Satellite. The effect of BSS irregularities on transionospheric signals has been studied. The numerical results agree well with multi-satellite scintillation observations made at Huancayo Peru in close time correspondence with BSS irregularities observed by the AE - E satellite over a few nights (December 8-11, 1979). During this period, the severity of the scintillation varied from moderate to intense, S4 = 0.1-0.8.

Developments in Characterizing Capture Zone Distributions in Island Growth

NASA Astrophysics Data System (ADS)

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

2013-03-01

The utility of using the distribution of capture zones (CZD) to characterize epitaxial growth continues to mount. For non-Poisson deposition (i.e. when island nucleation is not fully random) the areas of these Voronoi cells (proximity polygons) can be well described by the generalized Wigner distribution (GWD), particularly in the central region around the mean area. We discuss several recent applications to experimental systems, showing how this perspective leads to insights about the critical nucleus size. In contrast, several studies have shown that the GWD may not describe the numerical data from painstaking simulations in both tails. We discuss some refinements that have been proposed. Finally, we comment on applications to social phenomena such as area distributions of secondary administrative units (like counties) and of Voronoi cells around Metro stops. Work at UMD supported by NSF-MRSEC Grant DMR 05-20471 and NSF CHE 07-49949

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Instanton approach to large N Harish-Chandra-Itzykson-Zuber integrals.

PubMed

Bun, J; Bouchaud, J P; Majumdar, S N; Potters, M

2014-08-15

We reconsider the large N asymptotics of Harish-Chandra-Itzykson-Zuber integrals. We provide, using Dyson's Brownian motion and the method of instantons, an alternative, transparent derivation of the Matytsin formalism for the unitary case. Our method is easily generalized to the orthogonal and symplectic ensembles. We obtain an explicit solution of Matytsin's equations in the case of Wigner matrices, as well as a general expansion method in the dilute limit, when the spectrum of eigenvalues spreads over very wide regions.

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

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

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

2008-01-15

Basic Breit-Wigner features of the S{sub 11}(1535), S{sub 11}(1650), and P{sub 11}(1710) nucleon resonances are evaluated in a model-independent way on the basis of the results obtained previously from a partial-wave analysis of eta-meson photoproduction on protons.

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

PubMed

Karlovets, Dmitry V; Serbo, Valeriy G

2017-10-27

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

Beam-width spreading of vortex beams in free space

NASA Astrophysics Data System (ADS)

Wang, Weiwei; Li, Jinhong; Duan, Meiling

2018-01-01

Based on the extended Huygens-Fresnel principle and the definition of second-order moments of the Wigner distribution function, the analytical expression for the beam-width spreading of Gaussian Schell-model (GSM) vortex beams in free space are derived, and used to study the influence of beam parameters on the beam-width spreading of GSM vortex beams. With the increment of the propagation distance, the beam-width spreading of GSM vortex beams will increase; the bigger the topological charge, spatial correlation length, wavelength and waist width are, the smaller the beam-width spreading is.

The Gamow-state description of the decay energy spectrum of neutron-unbound 25O

NASA Astrophysics Data System (ADS)

Id Betan, R. M.; de la Madrid, R.

2018-02-01

We show the feasibility of calculating the decay energy spectrum of neutron emitting nuclei within the Gamow-state description of resonances by obtaining the decay energy spectrum of 25O. We model this nucleus as a valence neutron interacting with an 24O inert core, and we obtain the resulting resonant energies, widths and decay energy spectra for the ground and first excited states. We also discuss the similarities and differences between the decay energy spectrum of a Gamow state and the Breit-Wigner distribution with energy-dependent width.

Joint measurement of complementary observables in moment tomography

NASA Astrophysics Data System (ADS)

Teo, Yong Siah; Müller, Christian R.; Jeong, Hyunseok; Hradil, Zdeněk; Řeháček, Jaroslav; Sánchez-Soto, Luis L.

Wigner and Husimi quasi-distributions, owing to their functional regularity, give the two archetypal and equivalent representations of all observable-parameters in continuous-variable quantum information. Balanced homodyning (HOM) and heterodyning (HET) that correspond to their associated sampling procedures, on the other hand, fare very differently concerning their state or parameter reconstruction accuracies. We present a general theory of a now-known fact that HET can be tomographically more powerful than balanced homodyning to many interesting classes of single-mode quantum states, and discuss the treatment for two-mode sources.

Quantum corrections of the truncated Wigner approximation applied to an exciton transport model.

PubMed

Ivanov, Anton; Breuer, Heinz-Peter

2017-04-01

We modify the path integral representation of exciton transport in open quantum systems such that an exact description of the quantum fluctuations around the classical evolution of the system is possible. As a consequence, the time evolution of the system observables is obtained by calculating the average of a stochastic difference equation which is weighted with a product of pseudoprobability density functions. From the exact equation of motion one can clearly identify the terms that are also present if we apply the truncated Wigner approximation. This description of the problem is used as a basis for the derivation of a new approximation, whose validity goes beyond the truncated Wigner approximation. To demonstrate this we apply the formalism to a donor-acceptor transport model.

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

PubMed

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

2011-12-01

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

Multiplexed phase-space imaging for 3D fluorescence microscopy.

PubMed

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.

Thomas precession, Wigner rotations and gauge transformations

NASA Technical Reports Server (NTRS)

Han, D.; Kim, Y. S.; Son, D.

1987-01-01

The exact Lorentz kinematics of the Thomas precession is discussed in terms of Wigner's O(3)-like little group which describes rotations in the Lorentz frame in which the particle is at rest. A Lorentz-covariant form for the Thomas factor is derived. It is shown that this factor is a Lorentz-boosted rotation matrix, which becomes a gauge transformation in the infinite-momentum or zero-mass limit.

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

NASA Astrophysics Data System (ADS)

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.

Revealing nonclassicality beyond Gaussian states via a single marginal distribution

PubMed Central

Park, Jiyong; Lu, Yao; Lee, Jaehak; Shen, Yangchao; Zhang, Kuan; Zhang, Shuaining; Zubairy, Muhammad Suhail; Kim, Kihwan; Nha, Hyunchul

2017-01-01

A standard method to obtain information on a quantum state is to measure marginal distributions along many different axes in phase space, which forms a basis of quantum-state tomography. We theoretically propose and experimentally demonstrate a general framework to manifest nonclassicality by observing a single marginal distribution only, which provides a unique insight into nonclassicality and a practical applicability to various quantum systems. Our approach maps the 1D marginal distribution into a factorized 2D distribution by multiplying the measured distribution or the vacuum-state distribution along an orthogonal axis. The resulting fictitious Wigner function becomes unphysical only for a nonclassical state; thus the negativity of the corresponding density operator provides evidence of nonclassicality. Furthermore, the negativity measured this way yields a lower bound for entanglement potential—a measure of entanglement generated using a nonclassical state with a beam-splitter setting that is a prototypical model to produce continuous-variable (CV) entangled states. Our approach detects both Gaussian and non-Gaussian nonclassical states in a reliable and efficient manner. Remarkably, it works regardless of measurement axis for all non-Gaussian states in finite-dimensional Fock space of any size, also extending to infinite-dimensional states of experimental relevance for CV quantum informatics. We experimentally illustrate the power of our criterion for motional states of a trapped ion, confirming their nonclassicality in a measurement-axis–independent manner. We also address an extension of our approach combined with phase-shift operations, which leads to a stronger test of nonclassicality, that is, detection of genuine non-Gaussianity under a CV measurement. PMID:28077456

Revealing nonclassicality beyond Gaussian states via a single marginal distribution.

PubMed

Park, Jiyong; Lu, Yao; Lee, Jaehak; Shen, Yangchao; Zhang, Kuan; Zhang, Shuaining; Zubairy, Muhammad Suhail; Kim, Kihwan; Nha, Hyunchul

2017-01-31

A standard method to obtain information on a quantum state is to measure marginal distributions along many different axes in phase space, which forms a basis of quantum-state tomography. We theoretically propose and experimentally demonstrate a general framework to manifest nonclassicality by observing a single marginal distribution only, which provides a unique insight into nonclassicality and a practical applicability to various quantum systems. Our approach maps the 1D marginal distribution into a factorized 2D distribution by multiplying the measured distribution or the vacuum-state distribution along an orthogonal axis. The resulting fictitious Wigner function becomes unphysical only for a nonclassical state; thus the negativity of the corresponding density operator provides evidence of nonclassicality. Furthermore, the negativity measured this way yields a lower bound for entanglement potential-a measure of entanglement generated using a nonclassical state with a beam-splitter setting that is a prototypical model to produce continuous-variable (CV) entangled states. Our approach detects both Gaussian and non-Gaussian nonclassical states in a reliable and efficient manner. Remarkably, it works regardless of measurement axis for all non-Gaussian states in finite-dimensional Fock space of any size, also extending to infinite-dimensional states of experimental relevance for CV quantum informatics. We experimentally illustrate the power of our criterion for motional states of a trapped ion, confirming their nonclassicality in a measurement-axis-independent manner. We also address an extension of our approach combined with phase-shift operations, which leads to a stronger test of nonclassicality, that is, detection of genuine non-Gaussianity under a CV measurement.

Applications of Doppler optical coherence tomography

NASA Astrophysics Data System (ADS)

Xu, Zhiqiang

A major development in biomedical imaging in the last decade has been optical coherence tomography (OCT). This technique enables microscale resolution, depth resolved imaging of the detailed morphology of transparent and nontransparent biological tissue in a noncontact and quasi-noninvasive way. In the first part of this dissertation, we will describe the development and the performance of our home-made OCT systems working with different wavelength regions based on free-space and optical fiber Michelson interferometers. The second part will focus on Doppler OCT (DOCT), an important extension of OCT, which enables the simultaneous evaluation of the structural information and of the fluid flow distribution at a localized position beneath the sample surface. Much effort has been spent during the past few years in our laboratory aimed at providing more accurate velocity measurements with an extended dynamic range. We also applied our technique in different research areas such as microfluidics and hemodynamics. Investigations on the optical properties of the biological tissues (such as absorption and scattering) corresponding to different center wavelengths, have been performed in our laboratory. We used a 10 femtosecond Ti:sapphire laser centered at about 810 nm associated with a free-space Michelson interferometer. The infrared sources were centered at about 1310 and 1560 nm with all-fiber interferometers. Comparative studies using three different sources for several in vitro biological tissues based on a graphical method illustrated how the optical properties affect the quality of the OCT images in terms of the penetration depth and backscattering intensity. We have shown the advantage of working with 810-nm emission wavelength for good backscattering amplitude and contrast, while sources emitting at 1570 nm give good penetration depth. The 1330-nm sources provide a good compromise between the two. Therefore, the choice of the source will ultimately determine the longitudinal resolution and the imaging depth for OCT imaging. Doppler OCT is becoming an increasingly popular field of investigation within optical coherence tomography with potentially important applications in cardiovascular and microfluidic research. We have spent some of the effort on searching for accurate and efficient methods for processing the experimental data. We applied the pseudo Wigner time-frequency distribution method to the data processing of Doppler OCT and compared its performance to that of the short-time Fourier transform method, the Hilbert-based phase-resolved method and the autocorrelation method. We concluded that the pseudo Wigner-distribution signal processing method is overall more precise than other often-used methods in Doppler OCT for the analysis of cross-sectional velocity distributions, especially in the high velocity regime. We also discovered the advantage of using the time-domain instead of the frequency domain for Doppler OCT for some applications where precise Doppler-speed metrology is essential. Based on the fact that the obtained local OCT interference signal is almost a single periodic waveform, we have developed a novel, simple and less time-consuming processing method based on the zero-crossing points in an OCT signal for the measurement of the Doppler frequency in a laminar flow. This method was compared to other processing approaches currently used in Doppler OCT. The results show that in the case of laminar flow, the zero-crossing method gives the more precise results, especially in the higher velocity regime with a substantial economy in processing time and an increase in dynamic range which can reach 70 dB. This feature becomes a major advantage in metrology if one wants to measure velocities over several orders of magnitude. We have applied this technique to some real flow models and the preliminary results on flow velocity distributions obtained in the case of a microfluidic circuit and in that of a phantom of a blood vessel stenosis and bifurcation will be described in this thesis. We also proposed the method to successfully obtain the 2D velocity vector map in the phantom models by overlapping the Doppler OCT scalar velocity distributions of different incident angles. This quantitative knowledge of blood velocity profiles in the vessels can provide very important information in studying some cardiovascular diseases such as atherosclerosis. (Abstract shortened by UMI.)

Time-frequency representations of the sternocleidomastoid muscle electromyographic signal recorded with concentric ring electrodes.

PubMed

Estrada, Luis; Torres, Abel; Garcia-Casado, Javier; Sarlabous, Leonardo; Prats-Boluda, Gema; Jane, Raimon

2016-08-01

The use of non-invasive methods for the study of respiratory muscle signals can provide clinical information for the evaluation of the respiratory muscle function. The aim of this study was to evaluate time-frequency characteristics of the electrical activity of the sternocleidomastoid muscle recorded superficially by means of concentric ring electrodes (CREs) in a bipolar configuration. The CREs enhance the spatial resolution, attenuate interferences, as the cardiac activity, and also simplify the orientation problem associated to the electrode location. Five healthy subjects underwent a respiratory load test in which an inspiratory load was imposed during the inspiratory phase. During the test, the electromyographic signal of the sternocleidomastoid muscle (EMGsc) and the inspiratory mouth pressure (Pmouth) were acquired. Time-frequency characteristics of the EMGsc signal were analyzed by means of eight time-frequency representations (TFRs): the spectrogram (SPEC), the Morlet scalogram (SCAL), the Wigner-Ville distribution (WVD), the Choi-Williams distribution (CHWD), two generalized exponential distributions (GED1 and GED2), the Born-Jordan distribution (BJD) and the Cone-Kernel distribution (CKD). The instantaneous central frequency of the EMGsc showed an increasing behavior during the inspiratory cycle and with the increase of the inspiratory load. The bilinear TFRs (WVD, CHWD, GEDs and BJD) were less sensitive to cardiac activity interference than classical TFRs (SPEC and SCAL). The GED2 was the TFR that shown the best results for the characterization of the instantaneous central frequency of the EMGsc.

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

PubMed

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

2018-05-10

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

Application of the Pseudo Wigner-Ville Distribution to the Measurement of the Dispersion of Lamb Modes in Graphite/Epoxy Plates

NASA Technical Reports Server (NTRS)

Prosser, W. H.; Seale, M. D.; Smith, B. T.

1997-01-01

Acoustic waves propagate in thin plates as guided or Lamb modes. The velocities of these modes are dispersive in that they depend not only on the material elastic properties and density, but also on the frequency. Accurate characterization of Lamb wave dispersion is important in many acoustic based nondestructive evaluation techniques. It is necessary for ultrasonic measurements in thin plates to determine elastic properties and for flaw detection and localization. In acoustic emission (AE) testing, if not taken into account, highly dispersive Lamb mode propagation can lead to large errors in source location. In this study, the pseudo Wigner-Ville distribution (PWVD) was used for measurement of group velocity dispersion of Lamb waves in a unidirectional graphite/epoxy (AS4/3502) laminate. The PWVD is one of a number of transforms which provide a time-frequency representation of a digitized time series. Broad band acoustic waves were generated by a pencil lead fracture (Hsu-Neilsen source) and were detected with broad band ultrasonic transducers. The arrival times for the lowest order symmetric (S(sub 0)) and antisymmetric (A(sub 0)) Lamb modes were determined from measurements of the time at which the respective peak amplitudes occurred in the PWVD. Measurements were made at several source-to-detector distances and a least squares fit used to calculate the velocity. Results are presented for propagation along, and perpendicular to, the fiber direction. Theoretical dispersion curves were also calculated and a comparison between theory and experiment demonstrates good agreement.

Extended Salecker-Wigner formula for optimal accuracy in reading a clock via a massive signal particle

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

Kudaka, Shoju; Matsumoto, Shuichi

2007-07-15

In order to acquire an extended Salecker-Wigner formula from which to derive the optimal accuracy in reading a clock with a massive particle as the signal, von Neumann's classical measurement is employed, by which simultaneously both position and momentum of the signal particle can be measured approximately. By an appropriate selection of wave function for the initial state of the composite system (a clock and a signal particle), the formula is derived accurately. Valid ranges of the running time of a clock with a given optimal accuracy are also given. The extended formula means that contrary to the Salecker-Wigner formulamore » there exists the possibility of a higher accuracy of time measurement, even if the mass of the clock is very small.« less

Generalized Weyl-Wigner map and Vey quantum mechanics

NASA Astrophysics Data System (ADS)

Dias, Nuno Costa; Prata, João Nuno

2001-12-01

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

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

NASA Astrophysics Data System (ADS)

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

2014-07-01

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

Assessing Multiple Methods for Determining Active Source Travel Times in a Dense Array

NASA Astrophysics Data System (ADS)

Parker, L.; Zeng, X.; Thurber, C. H.; Team, P.

2016-12-01

238 three-component nodal seismometers were deployed at the Brady Hot Springs geothermal field in Nevada to characterize changes in the subsurface as a result of changes in pumping conditions. The array consisted of a 500 meter by 1600 meter irregular grid with 50 meter spacing centered in an approximately rectangular 1200 meter by 1600 meter grid with 200 meter spacing. A large vibroseis truck (T-Rex) was deployed as an active seismic source at 216 locations. Over the course of 15 days, the truck occupied each location up to four times. At each location a swept-frequency source between 5 and 80 Hz over 20 seconds was produced using three vibration modes: longitudinal S-wave, transverse S-wave, and P-wave. Seismic wave arrivals were identified using three methods: cross-correlation, deconvolution, and Wigner-Ville distribution (WVD) plus the Hough Transform (HT). Surface wave arrivals were clear for all three modes of vibration using all three methods. Preliminary tomographic models will be presented, using the arrivals of the identified phases. This analysis is part of the PoroTomo project: Poroelastic Tomography by Adjoint Inverse Modeling of Data from Seismology, Geodesy, and Hydrology; http://geoscience.wisc.edu/feigl/porotomo.

Detailed Vibration Analysis of Pinion Gear with Time-Frequency Methods

NASA Technical Reports Server (NTRS)

Mosher, Marianne; Pryor, Anna H.; Lewicki, David G.

2003-01-01

In this paper, the authors show a detailed analysis of the vibration signal from the destructive testing of a spiral bevel gear and pinion pair containing seeded faults. The vibration signal is analyzed in the time domain, frequency domain and with four time-frequency transforms: the Short Time Frequency Transform (STFT), the Wigner-Ville Distribution with the Choi-Williams kernel (WV-CW), the Continuous Wavelet' Transform (CWT) and the Discrete Wavelet Transform (DWT). Vibration data of bevel gear tooth fatigue cracks, under a variety of operating load levels and damage conditions, are analyzed using these methods. A new metric for automatic anomaly detection is developed and can be produced from any systematic numerical representation of the vibration signals. This new metric reveals indications of gear damage with all of the time-frequency transforms, as well as time and frequency representations, on this data set. Analysis with the CWT detects changes in the signal at low torque levels not found with the other transforms. The WV-CW and CWT use considerably more resources than the STFT and the DWT. More testing of the new metric is needed to determine its value for automatic anomaly detection and to develop fault detection methods for the metric.

Kaon condensation in dense matter

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

Carlson, J.; Heiselberg, H.; Pandharipande, V. R.

The kaon energy in neutron matter is calculated analytically with the Klein-Gordon equation, by making a Wigner-Seitz cell approximation and employing a K{sup -}N square well potential. The transition from the low density Lenz potential, proportional to scattering length, to the high density Hartree potential is found to begin at fairly low densities. Exact nonrelativistic calculations of the kaon energy in a simple cubic crystal of neutrons are used to test the Wigner-Seitz and the Ericson-Ericson approximation methods. In this case the frequently used Erickson-Erickson approximation is found to be fairly accurate up to twice nuclear matter density. All themore » calculations indicate that by {approx}4 times nuclear matter density the Hartree limit is reached. We also show that in the Hartree limit the energy of zero momentum kaons does not have relativistic energy dependent factors present in the low density expansions. The results indicate that the density for kaon condensation is higher than previously estimated.« less

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

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

PubMed

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

2015-06-28

We develop two classes of quasi-classical dynamics that are shown to conserve the initial quantum ensemble when used in combination with the Feynman-Kleinert approximation of the density operator. These dynamics are used to improve the Feynman-Kleinert implementation of the classical Wigner approximation for the evaluation of quantum time correlation functions known as Feynman-Kleinert linearized path-integral. As shown, both classes of dynamics are able to recover the exact classical and high temperature limits of the quantum time correlation function, while a subset is able to recover the exact harmonic limit. A comparison of the approximate quantum time correlation functions obtained from both classes of dynamics is made with the exact results for the challenging model problems of the quartic and double-well potentials. It is found that these dynamics provide a great improvement over the classical Wigner approximation, in which purely classical dynamics are used. In a special case, our first method becomes identical to centroid molecular dynamics.

Evidence of two-stage melting of Wigner solids

NASA Astrophysics Data System (ADS)

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.

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

NASA Technical Reports Server (NTRS)

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

1993-01-01

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

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

PubMed

Luzanov, A V

2008-09-07

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

Continuous-variable teleportation of a negative Wigner function

NASA Astrophysics Data System (ADS)

Mišta, Ladislav, Jr.; Filip, Radim; Furusawa, Akira

2010-07-01

Teleportation is a basic primitive for quantum communication and quantum computing. We address the problem of continuous-variable (unconditional and conditional) teleportation of a pure single-photon state and a mixed attenuated single-photon state generally in a nonunity-gain regime. Our figure of merit is the maximum negativity of the Wigner function, which demonstrates a highly nonclassical feature of the teleported state. We find that the negativity of the Wigner function of the single-photon state can be unconditionally teleported for an arbitrarily weak squeezed state used to create the entangled state shared in teleportation. In contrast, for the attenuated single-photon state there is a strict threshold squeezing one has to surpass to successfully teleport the negativity of its Wigner function. The conditional teleportation allows one to approach perfect transmission of the single photon for an arbitrarily low squeezing at a cost of decrease of the success rate. In contrast, for the attenuated single photon state, conditional teleportation cannot overcome the squeezing threshold of the unconditional teleportation and it approaches negativity of the input state only if the squeezing increases simultaneously. However, as soon as the threshold squeezing is surpassed, conditional teleportation still pronouncedly outperforms the unconditional one. The main consequences for quantum communication and quantum computing with continuous variables are discussed.

Continuous-variable teleportation of a negative Wigner function

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

Mista, Ladislav Jr.; Filip, Radim; Furusawa, Akira

2010-07-15

Teleportation is a basic primitive for quantum communication and quantum computing. We address the problem of continuous-variable (unconditional and conditional) teleportation of a pure single-photon state and a mixed attenuated single-photon state generally in a nonunity-gain regime. Our figure of merit is the maximum negativity of the Wigner function, which demonstrates a highly nonclassical feature of the teleported state. We find that the negativity of the Wigner function of the single-photon state can be unconditionally teleported for an arbitrarily weak squeezed state used to create the entangled state shared in teleportation. In contrast, for the attenuated single-photon state there ismore » a strict threshold squeezing one has to surpass to successfully teleport the negativity of its Wigner function. The conditional teleportation allows one to approach perfect transmission of the single photon for an arbitrarily low squeezing at a cost of decrease of the success rate. In contrast, for the attenuated single photon state, conditional teleportation cannot overcome the squeezing threshold of the unconditional teleportation and it approaches negativity of the input state only if the squeezing increases simultaneously. However, as soon as the threshold squeezing is surpassed, conditional teleportation still pronouncedly outperforms the unconditional one. The main consequences for quantum communication and quantum computing with continuous variables are discussed.« less

Pinning mode of integer quantum Hall Wigner crystal of skyrmions

NASA Astrophysics Data System (ADS)

Zhu, Han; Sambandamurthy, G.; Chen, Y. P.; Jiang, P.-H.; Engel, L. W.; Tsui, D. C.; Pfeiffer, L. N.; West, K. W.

2009-03-01

Just away from integer Landau level (LL) filling factors ν, the dilute quasi-particles/holes at the partially filled LL form an integer-quantum-Hall Wigner crystal, which exhibits microwave pinning mode resonances [1]. Due to electron-electron interaction, it was predicted that the elementary excitation around ν= 1 is not a single spin flip, but a larger-scale spin texture, known as a skyrmion [2]. We have compared the pinning mode resonances [1] of integer quantum Hall Wigner crystals formed in the partly filled LL just away from ν= 1 and ν= 2, in the presence of an in-plane magnetic field. As an in-plane field is applied, the peak frequencies of the resonances near ν= 1 increase, while the peak frequencies below ν= 2 show neligible dependence on in-plane field. We interpret this observation as due to a skyrmion crystal phase around ν= 1 and a single-hole Wigner crystal phase below ν= 2. The in-plane field increases the Zeeman gap and causes shrinking of the skyrmion size toward single spin flips. [1] Yong P. Chen et al., Phys. Rev. Lett. 91, 016801 (2003). [2] S. L. Sondhi et al., Phys. Rev. B 47, 16 419 (1993); L. Brey et al., Phys. Rev. Lett. 75, 2562 (1995).

Adaptive phase extraction: incorporating the Gabor transform in the matching pursuit algorithm.

PubMed

Wacker, Matthias; Witte, Herbert

2011-10-01

Short-time Fourier transform (STFT), Gabor transform (GT), wavelet transform (WT), and the Wigner-Ville distribution (WVD) are just some examples of time-frequency analysis methods which are frequently applied in biomedical signal analysis. However, all of these methods have their individual drawbacks. The STFT, GT, and WT have a time-frequency resolution that is determined by algorithm parameters and the WVD is contaminated by cross terms. In 1993, Mallat and Zhang introduced the matching pursuit (MP) algorithm that decomposes a signal into a sum of atoms and uses a cross-term free pseudo-WVD to generate a data-adaptive power distribution in the time-frequency space. Thus, it solved some of the problems of the GT and WT but lacks phase information that is crucial e.g., for synchronization analysis. We introduce a new time-frequency analysis method that combines the MP with a pseudo-GT. Therefore, the signal is decomposed into a set of Gabor atoms. Afterward, each atom is analyzed with a Gabor analysis, where the time-domain gaussian window of the analysis matches that of the specific atom envelope. A superposition of the single time-frequency planes gives the final result. This is the first time that a complete analysis of the complex time-frequency plane can be performed in a fully data-adaptive and frequency-selective manner. We demonstrate the capabilities of our approach on a simulation and on real-life magnetoencephalogram data.

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

NASA Astrophysics Data System (ADS)

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

2006-12-01

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

Stochastic analysis of surface roughness models in quantum wires

NASA Astrophysics Data System (ADS)

Nedjalkov, Mihail; Ellinghaus, Paul; Weinbub, Josef; Sadi, Toufik; Asenov, Asen; Dimov, Ivan; Selberherr, Siegfried

2018-07-01

We present a signed particle computational approach for the Wigner transport model and use it to analyze the electron state dynamics in quantum wires focusing on the effect of surface roughness. Usually surface roughness is considered as a scattering model, accounted for by the Fermi Golden Rule, which relies on approximations like statistical averaging and in the case of quantum wires incorporates quantum corrections based on the mode space approach. We provide a novel computational approach to enable physical analysis of these assumptions in terms of phase space and particles. Utilized is the signed particles model of Wigner evolution, which, besides providing a full quantum description of the electron dynamics, enables intuitive insights into the processes of tunneling, which govern the physical evolution. It is shown that the basic assumptions of the quantum-corrected scattering model correspond to the quantum behavior of the electron system. Of particular importance is the distribution of the density: Due to the quantum confinement, electrons are kept away from the walls, which is in contrast to the classical scattering model. Further quantum effects are retardation of the electron dynamics and quantum reflection. Far from equilibrium the assumption of homogeneous conditions along the wire breaks even in the case of ideal wire walls.

Time frequency analysis for automated sleep stage identification in fullterm and preterm neonates.

PubMed

Fraiwan, Luay; Lweesy, Khaldon; Khasawneh, Natheer; Fraiwan, Mohammad; Wenz, Heinrich; Dickhaus, Hartmut

2011-08-01

This work presents a new methodology for automated sleep stage identification in neonates based on the time frequency distribution of single electroencephalogram (EEG) recording and artificial neural networks (ANN). Wigner-Ville distribution (WVD), Hilbert-Hough spectrum (HHS) and continuous wavelet transform (CWT) time frequency distributions were used to represent the EEG signal from which features were extracted using time frequency entropy. The classification of features was done using feed forward back-propagation ANN. The system was trained and tested using data taken from neonates of post-conceptual age of 40 weeks for both preterm (14 recordings) and fullterm (15 recordings). The identification of sleep stages was successfully implemented and the classification based on the WVD outperformed the approaches based on CWT and HHS. The accuracy and kappa coefficient were found to be 0.84 and 0.65 respectively for the fullterm neonates' recordings and 0.74 and 0.50 respectively for preterm neonates' recordings.

Wigner time delay in photodetachment of Tm-and in photoionization of Yb: A comparative study

NASA Astrophysics Data System (ADS)

Saha, Soumyajit; Jose, Jobin; Deshmukh, Pranawa; Dolmatov, Valeriy; Kheifets, Anatoli; Manson, Steven

2017-04-01

Preliminary studies of Wigner time delay in photodetachment spectra of negative ions have been reported. Photodetachment time delay for some dipole channels of Tm- and of Cl- were calculated using relativistic random phase approximation (RRPA). Comparisons between photodetachment time delay of Cl- and photoionization time delay of Ar were made. We investigate the photodetachment time delay for all three relativistically split nd -> ɛ f channels of Tm- and for nd -> ɛ f channels of Yb (isoelectronic to Tm-) using RRPA. We study the effect of the shape resonance, brought about by the centrifugal barrier potential, on photodetachment time delay. A negative ion is a good laboratory for studying the effects of shape resonances on time delay since the phase is unaffected by the Coulomb component. Wigner time delay in photodetachment of Tm- and in photoionization of Yb: A comparative study.

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

NASA Astrophysics Data System (ADS)

Zhu, Hongxuan; Ruiz, D. E.; Dodin, I. Y.

2017-10-01

The stability of zonal flows (ZFs) is analyzed within the generalized-Hasegawa-Mima model. The necessary and sufficient condition for a ZF instability, which is also known as the tertiary instability, is identified. The qualitative physics behind the tertiary instability is explained using the recently developed Wigner-Moyal formulation and the corresponding wave kinetic equation (WKE) in the geometrical-optics (GO) limit. By analyzing the drifton phase space trajectories, we find that the corrections proposed in Ref. to the WKE are critical for capturing the spatial scales characteristic for the tertiary instability. That said, we also find that this instability itself cannot be adequately described within a GO formulation in principle. Using the Wigner-Moyal equations, which capture diffraction, we analytically derive the tertiary-instability growth rate and compare it with numerical simulations. The research was sponsored by the U.S. Department of Energy.

Backreaction effects on nonequilibrium spectral function

NASA Astrophysics Data System (ADS)

Mendizabal, Sebastián; Rojas, Juan Cristobal

2017-07-01

We show how to compute the spectral function for a scalar theory in two different scenarios: one which disregards backreaction, i.e. the response of the environment to the external particle, and the other one where backreaction is considered. The calculation was performed using the Kadanoff-Baym equation through the Keldysh formalism. When backreaction is neglected, the spectral function is equal to the equilibrium one, which can be represented as a Breit-Wigner distribution. When backreaction is introduced we observed a damping in the spectral function of the thermal bath. Such behavior modifies the damping rate for particles created within the bath.

Signatures of chaos in the Brillouin zone.

PubMed

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

2017-10-01

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

Intermediate quantum maps for quantum computation

NASA Astrophysics Data System (ADS)

Giraud, O.; Georgeot, B.

2005-10-01

We study quantum maps displaying spectral statistics intermediate between Poisson and Wigner-Dyson. It is shown that they can be simulated on a quantum computer with a small number of gates, and efficiently yield information about fidelity decay or spectral statistics. We study their matrix elements and entanglement production and show that they converge with time to distributions which differ from random matrix predictions. A randomized version of these maps can be implemented even more economically and yields pseudorandom operators with original properties, enabling, for example, one to produce fractal random vectors. These algorithms are within reach of present-day quantum computers.

Measuring Gaussian quantum information and correlations using the Rényi entropy of order 2.

PubMed

Adesso, Gerardo; Girolami, Davide; Serafini, Alessio

2012-11-09

We demonstrate that the Rényi-2 entropy provides a natural measure of information for any multimode Gaussian state of quantum harmonic systems, operationally linked to the phase-space Shannon sampling entropy of the Wigner distribution of the state. We prove that, in the Gaussian scenario, such an entropy satisfies the strong subadditivity inequality, a key requirement for quantum information theory. This allows us to define and analyze measures of Gaussian entanglement and more general quantum correlations based on such an entropy, which are shown to satisfy relevant properties such as monogamy.

Central Limit Theorems for Linear Statistics of Heavy Tailed Random Matrices

NASA Astrophysics Data System (ADS)

Benaych-Georges, Florent; Guionnet, Alice; Male, Camille

2014-07-01

We show central limit theorems (CLT) for the linear statistics of symmetric matrices with independent heavy tailed entries, including entries in the domain of attraction of α-stable laws and entries with moments exploding with the dimension, as in the adjacency matrices of Erdös-Rényi graphs. For the second model, we also prove a central limit theorem of the moments of its empirical eigenvalues distribution. The limit laws are Gaussian, but unlike the case of standard Wigner matrices, the normalization is the one of the classical CLT for independent random variables.

Sufficient condition for a quantum state to be genuinely quantum non-Gaussian

NASA Astrophysics Data System (ADS)

Happ, L.; Efremov, M. A.; Nha, H.; Schleich, W. P.

2018-02-01

We show that the expectation value of the operator \\hat{{ \\mathcal O }}\\equiv \\exp (-c{\\hat{x}}2)+\\exp (-c{\\hat{p}}2) defined by the position and momentum operators \\hat{x} and \\hat{p} with a positive parameter c can serve as a tool to identify quantum non-Gaussian states, that is states that cannot be represented as a mixture of Gaussian states. Our condition can be readily tested employing a highly efficient homodyne detection which unlike quantum-state tomography requires the measurements of only two orthogonal quadratures. We demonstrate that our method is even able to detect quantum non-Gaussian states with positive–definite Wigner functions. This situation cannot be addressed in terms of the negativity of the phase-space distribution. Moreover, we demonstrate that our condition can characterize quantum non-Gaussianity for the class of superposition states consisting of a vacuum and integer multiples of four photons under more than 50 % signal attenuation.

Surface structure in simple liquid metals: An orbital-free first-principles study

NASA Astrophysics Data System (ADS)

González, D. J.; González, L. E.; Stott, M. J.

2006-07-01

Molecular dynamics simulations of the liquid-vapor interfaces in simple sp-bonded liquid metals have been performed using first-principles methods. Results are presented for liquid Li, Na, K, Rb, Cs, Mg, Ba, Al, Tl, and Si at thermodynamic conditions near their respective triple points, for samples of 2000 particles in a slab geometry. The longitudinal ionic density profiles exhibit a pronounced stratification extending several atomic diameters into the bulk, which is a feature already experimentally observed in liquid K, Ga, In, Sn, and Hg. The wavelength of the ionic oscillations shows a good scaling with the radii of the associated Wigner-Seitz spheres. The structural rearrangements at the interface are analyzed in terms of the transverse pair correlation function, the coordination number, and the bond-angle distribution between nearest neighbors. The valence electronic density profile also shows (weaker) oscillations whose phase, with respect to those of the ionic profile, changes from opposite phase in the alkalis to almost in-phase for Si.

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

PubMed

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

2010-05-01

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

Generalized quantum Fokker-Planck, diffusion, and Smoluchowski equations with true probability distribution functions.

PubMed

Banik, Suman Kumar; Bag, Bidhan Chandra; Ray, Deb Shankar

2002-05-01

Traditionally, quantum Brownian motion is described by Fokker-Planck or diffusion equations in terms of quasiprobability distribution functions, e.g., Wigner functions. These often become singular or negative in the full quantum regime. In this paper a simple approach to non-Markovian theory of quantum Brownian motion using true probability distribution functions is presented. Based on an initial coherent state representation of the bath oscillators and an equilibrium canonical distribution of the quantum mechanical mean values of their coordinates and momenta, we derive a generalized quantum Langevin equation in c numbers and show that the latter is amenable to a theoretical analysis in terms of the classical theory of non-Markovian dynamics. The corresponding Fokker-Planck, diffusion, and Smoluchowski equations are the exact quantum analogs of their classical counterparts. The present work is independent of path integral techniques. The theory as developed here is a natural extension of its classical version and is valid for arbitrary temperature and friction (the Smoluchowski equation being considered in the overdamped limit).

Uniform analytic approximation of Wigner rotation matrices

NASA Astrophysics Data System (ADS)

Hoffmann, Scott E.

2018-02-01

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

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

PubMed

Kuppermann, Aron

2011-05-14

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

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

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

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

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

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

NASA Astrophysics Data System (ADS)

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

2016-08-01

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

Multiscale Models of Melting Arctic Sea Ice

DTIC Science & Technology

2014-09-30

from weakly to highly correlated, or Poissonian toward Wigner -Dyson, as a function of system connectedness. This provides a mechanism for explaining...eluded us. Court Strong found such a method. It creates an optimal fit of a hyperbolic tangent model for the fractal dimension as a function of log A...actual melt pond images, and have made significant advances in the underlying functional and numerical analysis needed for these computations

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

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

Ligabò, Marilena, E-mail: marilena.ligabo@uniba.it

2016-08-15

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

Spectral function of few electrons in quantum wires and carbon nanotubes as a signature of Wigner localization

NASA Astrophysics Data System (ADS)

Secchi, Andrea; Rontani, Massimo

2012-03-01

We demonstrate that the profile of the space-resolved spectral function at finite temperature provides a signature of Wigner localization for electrons in quantum wires and semiconducting carbon nanotubes. Our numerical evidence is based on the exact diagonalization of the microscopic Hamiltonian of few particles interacting in gate-defined quantum dots. The minimal temperature required to suppress residual exchange effects in the spectral function image of (nanotubes) quantum wires lies in the (sub)kelvin range.

A hybrid spatiotemporal and Hough-based motion estimation approach applied to magnetic resonance cardiac images

NASA Astrophysics Data System (ADS)

Carranza, N.; Cristóbal, G.; Sroubek, F.; Ledesma-Carbayo, M. J.; Santos, A.

2006-08-01

Myocardial motion analysis and quantification is of utmost importance for analyzing contractile heart abnormalities and it can be a symptom of a coronary artery disease. A fundamental problem in processing sequences of images is the computation of the optical flow, which is an approximation to the real image motion. This paper presents a new algorithm for optical flow estimation based on a spatiotemporal-frequency (STF) approach, more specifically on the computation of the Wigner-Ville distribution (WVD) and the Hough Transform (HT) of the motion sequences. The later is a well-known line and shape detection method very robust against incomplete data and noise. The rationale of using the HT in this context is because it provides a value of the displacement field from the STF representation. In addition, a probabilistic approach based on Gaussian mixtures has been implemented in order to improve the accuracy of the motion detection. Experimental results with synthetic sequences are compared against an implementation of the variational technique for local and global motion estimation, where it is shown that the results obtained here are accurate and robust to noise degradations. Real cardiac magnetic resonance images have been tested and evaluated with the current method.

Electrostatic attraction of coupled Wigner crystals: finite temperature effects.

PubMed

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

2001-05-01

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

Semiclassical spatial correlations in chaotic wave functions.

PubMed

Toscano, Fabricio; Lewenkopf, Caio H

2002-03-01

We study the spatial autocorrelation of energy eigenfunctions psi(n)(q) corresponding to classically chaotic systems in the semiclassical regime. Our analysis is based on the Weyl-Wigner formalism for the spectral average C(epsilon)(q(+),q(-),E) of psi(n)(q(+))psi(*)(n)(q(-)), defined as the average over eigenstates within an energy window epsilon centered at E. In this framework C(epsilon) is the Fourier transform in the momentum space of the spectral Wigner function W(x,E;epsilon). Our study reveals the chord structure that C(epsilon) inherits from the spectral Wigner function showing the interplay between the size of the spectral average window, and the spatial separation scale. We discuss under which conditions is it possible to define a local system independent regime for C(epsilon). In doing so, we derive an expression that bridges the existing formulas in the literature and find expressions for C(epsilon)(q(+),q(-),E) valid for any separation size /q(+)-q(-)/.

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

NASA Astrophysics Data System (ADS)

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

2013-09-01

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

Real-time and imaginary-time quantum hierarchal Fokker-Planck equations

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

Tanimura, Yoshitaka, E-mail: tanimura@kuchem.kyoto-u.ac.jp

2015-04-14

We consider a quantum mechanical system represented in phase space (referred to hereafter as “Wigner space”), coupled to a harmonic oscillator bath. We derive quantum hierarchal Fokker-Planck (QHFP) equations not only in real time but also in imaginary time, which represents an inverse temperature. This is an extension of a previous work, in which we studied a spin-boson system, to a Brownian system. It is shown that the QHFP in real time obtained from a correlated thermal equilibrium state of the total system possesses the same form as those obtained from a factorized initial state. A modified terminator for themore » hierarchal equations of motion is introduced to treat the non-Markovian case more efficiently. Using the imaginary-time QHFP, numerous thermodynamic quantities, including the free energy, entropy, internal energy, heat capacity, and susceptibility, can be evaluated for any potential. These equations allow us to treat non-Markovian, non-perturbative system-bath interactions at finite temperature. Through numerical integration of the real-time QHFP for a harmonic system, we obtain the equilibrium distributions, the auto-correlation function, and the first- and second-order response functions. These results are compared with analytically exact results for the same quantities. This provides a critical test of the formalism for a non-factorized thermal state and elucidates the roles of fluctuation, dissipation, non-Markovian effects, and system-bath coherence. Employing numerical solutions of the imaginary-time QHFP, we demonstrate the capability of this method to obtain thermodynamic quantities for any potential surface. It is shown that both types of QHFP equations can produce numerical results of any desired accuracy. The FORTRAN source codes that we developed, which allow for the treatment of Wigner space dynamics with any potential form (TanimuranFP15 and ImTanimuranFP15), are provided as the supplementary material.« less

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

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

Dodonov, V.V., E-mail: vdodonov@fis.unb.br; Valverde, C.; Universidade Paulista, BR 153, km 7, 74845-090 Goiânia, GO

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-Hermitianmore » 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.« less

Experimental study of two-dimensional quantum Wigner solid in zero magnetic field

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

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

2014-03-31

At temperatures T → 0, strongly interacting two-dimensional (2D) electron systems manifest characteristic insulating behaviors that are key for understanding the nature of the ground state in light of the interplay between disorder and electron-electron interaction. In contrast to the hopping conductance demonstrated in the insulating side of the metal-to-insulator transition, the ultra-high quality 2D systems exhibit nonactivated T-dependence of the conductivity even for dilute carrier concentrations down to 7×10{sup 8} cm{sup −2}. The apparent metal-to-insulator transition (MIT) occurs for a large r{sub s} value around 40 for which a Wigner Crystalllization is expected. The magnetoresistance for a series ofmore » carrier densities in the vicinity of the transition exhibits a characteristic sign change in weak perpendicular magnetic field. Within the Wigner Crystallization regime (with r{sub s} > 40), we report an experimental observation of a characteristic nonlinear threshold behavior from a high-resolution dc dynamical response as an evidence for aWigner crystallization in high-purity GaAs 2D hole systems in zero magnetic field. The system under an increasing current drive exhibits voltage oscillations with negative differential resistance. They confirm the coexistence of a moving crystal along with striped edge states as observed for electrons on helium surfaces. Moreover, the threshold is well below the typical classical levels due to a different pinning and depinning mechanism that is possibly related to quantum processes.« less

Effect of Wigner energy on the symmetry energy coefficient in nuclei

NASA Astrophysics Data System (ADS)

Tian, Jun-Long; Cui, Hai-Tao; Gao, Teng; Wang, Ning

2016-09-01

The nuclear symmetry energy coefficient (including the coefficient of the I4 term) of finite nuclei is extracted by using the differences of available experimental binding energies of isobaric nuclei. It is found that the extracted symmetry energy coefficient decreases with increasing isospin asymmetry I, which is mainly caused by Wigner correction, since is the summation of the traditional symmetry energy esym and the Wigner energy eW. We obtain the optimal values J = 30.25 ± 0.10 MeV, ass = 56.18 ± 1.25 MeV, and the Wigner parameter x = 2.38 ± 0.12 through a polynomial fit to 2240 measured binding energies for nuclei with 20 ⩽ A ⩽ 261 with an rms deviation of 23.42 keV. We also find that the volume symmetry coefficient J ≃ 30 MeV is insensitive to the value x, whereas the surface symmetry coefficient ass and the coefficient are very sensitive to the value of x in the range 1 ⩽ x ⩽ 4. The contribution of the term increases rapidly with increasing isospin asymmetry I. For very neutron-rich nuclei, the contribution of the term will play an important role. Supported by National Natural Science Foundation of China (11475004, 11275052, 11305003, 11375094 and 11465005), Natural Science Foundation of He'nan Educational Committee (2011A140001 and 2011GGJS-147), Open Project Program of State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences (Y4KF041CJ1)

Relativistic equation of state at subnuclear densities in the Thomas-Fermi approximation

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

Zhang, Z. W.; Shen, H., E-mail: shennankai@gmail.com

We study the non-uniform nuclear matter using the self-consistent Thomas-Fermi approximation with a relativistic mean-field model. The non-uniform matter is assumed to be composed of a lattice of heavy nuclei surrounded by dripped nucleons. At each temperature T, proton fraction Y{sub p} , and baryon mass density ρ {sub B}, we determine the thermodynamically favored state by minimizing the free energy with respect to the radius of the Wigner-Seitz cell, while the nucleon distribution in the cell can be determined self-consistently in the Thomas-Fermi approximation. A detailed comparison is made between the present results and previous calculations in the Thomas-Fermimore » approximation with a parameterized nucleon distribution that has been adopted in the widely used Shen equation of state.« less

Lorentzian symmetry predicts universality beyond scaling laws

NASA Astrophysics Data System (ADS)

Watson, Stephen J.

2017-06-01

We present a covariant theory for the ageing characteristics of phase-ordering systems that possess dynamical symmetries beyond mere scalings. A chiral spin dynamics which conserves the spin-up (+) and spin-down (-) fractions, μ+ and μ- , serves as the emblematic paradigm of our theory. Beyond a parabolic spatio-temporal scaling, we discover a hidden Lorentzian dynamical symmetry therein, and thereby prove that the characteristic length L of spin domains grows in time t according to L = \\fracβ{\\sqrt{1 - σ^2}}t\\frac{1{2}} , where σ:= μ+ - μ- (the invariant spin-excess) and β is a universal constant. Furthermore, the normalised length distributions of the spin-up and the spin-down domains each provably adopt a coincident universal (σ-independent) time-invariant form, and this supra-universal probability distribution is empirically verified to assume a form reminiscent of the Wigner surmise.

Generation of squeezed microwave states by a dc-pumped degenerate parametric Josephson junction oscillator

NASA Astrophysics Data System (ADS)

Kaertner, Franz X.; Russer, Peter

1990-11-01

The master equation for a dc-pumped degenerate Josephson parametric amplifier is derived. It is shown that the Wigner distribution representation of this master equation can be approximated by a Fokker-Planck equation. By using this equation, the dynamical behavior of this degenerate Josephson amplifier with respect to squeezing of the radiation field is investigated. It is shown that below threshold of parametric oscillation, a squeezed vacuum state can be generated, and above threshold a second bifurcation point exists, where the device generates amplitude squeezed radiation. Basic relations between the achievable amplitude squeezing, the output power, and the operation frequency are derived.

Time-frequency filtering and synthesis from convex projections

NASA Astrophysics Data System (ADS)

White, Langford B.

1990-11-01

This paper describes the application of the theory of projections onto convex sets to time-frequency filtering and synthesis problems. We show that the class of Wigner-Ville Distributions (WVD) of L2 signals form the boundary of a closed convex subset of L2(R2). This result is obtained by considering the convex set of states on the Heisenberg group of which the ambiguity functions form the extreme points. The form of the projection onto the set of WVDs is deduced. Various linear and non-linear filtering operations are incorporated by formulation as convex projections. An example algorithm for simultaneous time-frequency filtering and synthesis is suggested.

Time-frequency analysis of human motion during rhythmic exercises.

PubMed

Omkar, S N; Vyas, Khushi; Vikranth, H N

2011-01-01

Biomechanical signals due to human movements during exercise are represented in time-frequency domain using Wigner Distribution Function (WDF). Analysis based on WDF reveals instantaneous spectral and power changes during a rhythmic exercise. Investigations were carried out on 11 healthy subjects who performed 5 cycles of sun salutation, with a body-mounted Inertial Measurement Unit (IMU) as a motion sensor. Variance of Instantaneous Frequency (I.F) and Instantaneous Power (I.P) for performance analysis of the subject is estimated using one-way ANOVA model. Results reveal that joint Time-Frequency analysis of biomechanical signals during motion facilitates a better understanding of grace and consistency during rhythmic exercise.

Discrete linear canonical transforms based on dilated Hermite functions.

PubMed

Pei, Soo-Chang; Lai, Yun-Chiu

2011-08-01

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

Cardiovascular response to acute stress in freely moving rats: time-frequency analysis.

PubMed

Loncar-Turukalo, Tatjana; Bajic, Dragana; Japundzic-Zigon, Nina

2008-01-01

Spectral analysis of cardiovascular series is an important tool for assessing the features of the autonomic control of the cardiovascular system. In this experiment Wistar rats ecquiped with intraarterial catheter for blood pressure (BP) recording were exposed to stress induced by blowing air. The problem of non stationary data was overcomed applying the Smoothed Pseudo Wigner Villle (SPWV) time-frequency distribution. Spectral analysis was done before stress, during stress, immediately after stress and later in recovery. The spectral indices were calculated for both systolic blood pressure (SBP) and pulse interval (PI) series. The time evolution of spectral indices showed perturbed sympathovagal balance.

Thermodynamic output of single-atom quantum optical amplifiers and their phase-space fingerprint

NASA Astrophysics Data System (ADS)

Perl, Y.; Band, Y. B.; Boukobza, E.

2017-05-01

We analyze a resonant single-atom two-photon quantum optical amplifier both dynamically and thermodynamically. A detailed thermodynamic analysis shows that the nonlinear amplifier is thermodynamically equivalent to the linear amplifier. However, by calculating the Wigner quasiprobability distribution for various initial field states, we show that unique quantum features in optical phase space, absent in the linear amplifier, are retained for extended times, despite the fact that dissipation tends to wash out dynamical features observed at early evolution times. These features are related to the discrete nature of the two-photon matter-field interaction and fingerprint the initial field state at thermodynamic times.

A fast complex domain-matching pursuit algorithm and its application to deep-water gas reservoir detection

NASA Astrophysics Data System (ADS)

Zeng, Jing; Huang, Handong; Li, Huijie; Miao, Yuxin; Wen, Junxiang; Zhou, Fei

2017-12-01

The main emphasis of exploration and development is shifting from simple structural reservoirs to complex reservoirs, which all have the characteristics of complex structure, thin reservoir thickness and large buried depth. Faced with these complex geological features, hydrocarbon detection technology is a direct indication of changes in hydrocarbon reservoirs and a good approach for delimiting the distribution of underground reservoirs. It is common to utilize the time-frequency (TF) features of seismic data in detecting hydrocarbon reservoirs. Therefore, we research the complex domain-matching pursuit (CDMP) method and propose some improvements. First is the introduction of a scale parameter, which corrects the defect that atomic waveforms only change with the frequency parameter. Its introduction not only decomposes seismic signal with high accuracy and high efficiency but also reduces iterations. We also integrate jumping search with ergodic search to improve computational efficiency while maintaining the reasonable accuracy. Then we combine the improved CDMP with the Wigner-Ville distribution to obtain a high-resolution TF spectrum. A one-dimensional modeling experiment has proved the validity of our method. Basing on the low-frequency domain reflection coefficient in fluid-saturated porous media, we finally get an approximation formula for the mobility attributes of reservoir fluid. This approximation formula is used as a hydrocarbon identification factor to predict deep-water gas-bearing sand of the M oil field in the South China Sea. The results are consistent with the actual well test results and our method can help inform the future exploration of deep-water gas reservoirs.

The `Miracle' of Applicability? The Curious Case of the Simple Harmonic Oscillator

NASA Astrophysics Data System (ADS)

Bangu, Sorin; Moir, Robert H. C.

2018-05-01

The paper discusses to what extent the conceptual issues involved in solving the simple harmonic oscillator model fit Wigner's famous point that the applicability of mathematics borders on the miraculous. We argue that although there is ultimately nothing mysterious here, as is to be expected, a careful demonstration that this is so involves unexpected difficulties. Consequently, through the lens of this simple case we derive some insight into what is responsible for the appearance of mystery in more sophisticated examples of the Wigner problem.

Theoretical Explanations in Mathematical Physics

NASA Astrophysics Data System (ADS)

Rivadulla, Andrés

Many physicists wonder at the usefulness of mathematics in physics. According Madrid to Einstein mathematics is admirably appropriate to the objects of reality. Wigner asserts that mathematics plays an unreasonable important role in physics. James Jeans affirms that God is a mathematician, and that the first aim of physics is to discover the laws of nature, which are written in mathematical language. Dirac suggests that God may have used very advanced mathematics in constructing the universe. And Barrow adheres himself to Wigner's claim about the unreasonable effectiveness of mathematics for the workings of the physical world.

The `Miracle' of Applicability? The Curious Case of the Simple Harmonic Oscillator

NASA Astrophysics Data System (ADS)

Bangu, Sorin; Moir, Robert H. C.

2018-03-01

The paper discusses to what extent the conceptual issues involved in solving the simple harmonic oscillator model fit Wigner's famous point that the applicability of mathematics borders on the miraculous. We argue that although there is ultimately nothing mysterious here, as is to be expected, a careful demonstration that this is so involves unexpected difficulties. Consequently, through the lens of this simple case we derive some insight into what is responsible for the appearance of mystery in more sophisticated examples of the Wigner problem.

Classical and Quantum Systems Foundations and Symmetries, Proceedings of the International Wigner Symposium Held in Goslar, Germany on July 16-20, 1991

DTIC Science & Technology

1991-07-20

problem. As he then offered me to spend a year as a postdoctoral research associate, at Princeton. close also to the group of another of Wigner’s...London, Paris. Tokyo 1988 50. Schempp. W.: Harmonic Analysis on the Heisenberg Nilpotent Lie Group , with Applications to Signal Theory. Pitman Research ...1.1 ) group . It would be very helpful if we could design experiments to test the set of 0(2,1) commutation relations involving k/ and the generators

Quantum coherence in the reflection of above barrier wavepackets

NASA Astrophysics Data System (ADS)

Petersen, Jakob; Pollak, Eli

2018-02-01

The quantum phenomenon of above barrier reflection is investigated from a time-dependent perspective using Gaussian wavepackets. The transition path time distribution, which in principle is experimentally measurable, is used to study the mean flight times ⟨t⟩R and ⟨t⟩T associated with the reflection and the transmission over the barrier paying special attention to their dependence on the width of the barrier. Both flight times, and their difference Δt, exhibit two distinct regimes depending on the ratio of the spatial width of the incident wavepacket and the length of the barrier. When the ratio is larger than unity, the reflection and transmission dynamics are coherent and dominated by the resonances above the barrier. The flight times ⟨t⟩R/T and the flight time difference Δt oscillate as a function of the barrier width (almost in phase with the transmission probability). These oscillations reflect a momentum filtering effect related to the coherent superposition of the reflected and transmitted waves. For a ratio less than unity, the barrier reflection and transmission dynamics are incoherent and the oscillations are absent. The barrier width which separates the coherent and incoherent regimes is identified analytically. The oscillatory structure of the time difference Δt as a function of the barrier width in the coherent regime is absent when considered in terms of the Wigner phase time delays for reflection and transmission. We conclude that the Wigner phase time does not correctly describe the temporal properties of above barrier reflection. We also find that the structure of the reflected and transmitted wavepackets depends on the coherence of the process. In the coherent regime, the wavepackets can have an overlapping peak structure, but the peaks are not fully resolved. In the incoherent regime, the wavepackets split in time into distinct separated Gaussian like waves, each one reflecting the number of times the wavepacket crosses the barrier region before exiting. A classical Wigner approximation, using classical trajectories which upon reaching an edge of the barrier are reflected or transmitted as if the edge was a step potential, is quantitative in the incoherent regime. The implications of the coherence observed on resonance reactive scattering are discussed.

Global EOS: exploring the 300-ms-latency region

NASA Astrophysics Data System (ADS)

Mascetti, L.; Jericho, D.; Hsu, C.-Y.

2017-10-01

EOS, the CERN open-source distributed disk storage system, provides the highperformance storage solution for HEP analysis and the back-end for various work-flows. Recently EOS became the back-end of CERNBox, the cloud synchronisation service for CERN users. EOS can be used to take advantage of wide-area distributed installations: for the last few years CERN EOS uses a common deployment across two computer centres (Geneva-Meyrin and Budapest-Wigner) about 1,000 km apart (∼20-ms latency) with about 200 PB of disk (JBOD). In late 2015, the CERN-IT Storage group and AARNET (Australia) set-up a challenging R&D project: a single EOS instance between CERN and AARNET with more than 300ms latency (16,500 km apart). This paper will report about the success in deploy and run a distributed storage system between Europe (Geneva, Budapest), Australia (Melbourne) and later in Asia (ASGC Taipei), allowing different type of data placement and data access across these four sites.

Parallels among the ``music scores'' of solar cycles, space weather and Earth's climate

NASA Astrophysics Data System (ADS)

Kolláth, Zoltán; Oláh, Katalin; van Driel-Gesztelyi, Lidia

2012-07-01

Solar variability and its effects on the physical variability of our (space) environment produces complex signals. In the indicators of solar activity at least four independent cyclic components can be identified, all of them with temporal variations in their timescales. Time-frequency distributions (see Kolláth & Oláh 2009) are perfect tools to disclose the ``music scores'' in these complex time series. Special features in the time-frequency distributions, like frequency splitting, or modulations on different timescales provide clues, which can reveal similar trends among different indices like sunspot numbers, interplanetary magnetic field strength in the Earth's neighborhood and climate data. On the pseudo-Wigner Distribution (PWD) the frequency splitting of all the three main components (the Gleissberg and Schwabe cycles, and an ~5.5 year signal originating from cycle asymmetry, i.e. the Waldmeier effect) can be identified as a ``bubble'' shaped structure after 1950. The same frequency splitting feature can also be found in the heliospheric magnetic field data and the microwave radio flux.

Time-frequency analysis of SEMG--with special consideration to the interelectrode spacing.

PubMed

Alemu, M; Kumar, Dinesh Kant; Bradley, Alan

2003-12-01

The surface electromyogram (SEMG) is a complex, nonstationary signal. The spectrum of the SEMG is dependent on the force of contraction being generated and other factors like muscle fatigue and interelectrode distance (IED). The spectrum of the signal is time variant. This paper reports the experimental research conducted to study the influence of force of muscle contraction and IED on the SEMG signal using time-frequency (T-F) analysis. Two T-F techniques have been used: Wigner-Ville distribution (WVD) and Choi-Williams distribution (CWD). The experiment was conducted with the help of ten healthy volunteers (five males and five females) who performed isometric elbow flexions of the active right arm at 20%, 50%, and 80% of their maximal voluntary contraction. The SEMG signal was recorded using surface electrodes placed at a distance of 18 and 36 mm over biceps brachii muscle. The results indicate that the two distributions were spread out across the frequency range at smaller IED. Further, regardless of the spacing, both distributions displayed increased spectral compression with time at higher contraction level.

Further Developments in Characterizing Capture Zone Distributions (CZD) in Island Growth

NASA Astrophysics Data System (ADS)

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

2014-03-01

As argued previously, analysis of the distribution of the areas of capture zones (i.e. proximity polygons [or Voronoi tesselations] with respect to island centers) is often the best way to extract the critical nucleus size in studies of epitaxial growth. For non-Poisson deposition (i.e. when island nucleation is not fully random) the areas of these Voronoi cells can be well described by the generalized Wigner distribution (GWD), particularly in the central region around the mean area where the distribution is largest. We discuss several recent applications to experimental systems, catelogued in a recent minireview,[2] showing how this perspective leads to insights about the critical nucleus size. In contrast, several (but not all) studies have shown that the GWD may not describe the numerical data from painstaking simulations in both tails.2 We discuss some refinements that have been proposed, as well as scaling forms. Finally, we comment on applications to social phenomena. Emphasis is on very recent developments. Work at UMD supported by NSF CHE 13-05892 & NSF MRSEC DMR 05-20471.

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

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

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

PubMed

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

2013-04-12

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

Bravyi-Kitaev Superfast simulation of electronic structure on a quantum computer.

PubMed

Setia, Kanav; Whitfield, James D

2018-04-28

Present quantum computers often work with distinguishable qubits as their computational units. In order to simulate indistinguishable fermionic particles, it is first required to map the fermionic state to the state of the qubits. The Bravyi-Kitaev Superfast (BKSF) algorithm can be used to accomplish this mapping. The BKSF mapping has connections to quantum error correction and opens the door to new ways of understanding fermionic simulation in a topological context. Here, we present the first detailed exposition of the BKSF algorithm for molecular simulation. We provide the BKSF transformed qubit operators and report on our implementation of the BKSF fermion-to-qubits transform in OpenFermion. In this initial study of a hydrogen molecule we have compared BKSF, Jordan-Wigner, and Bravyi-Kitaev transforms under the Trotter approximation. The gate count to implement BKSF is lower than Jordan-Wigner but higher than Bravyi-Kitaev. We considered different orderings of the exponentiated terms and found lower Trotter errors than the previously reported for Jordan-Wigner and Bravyi-Kitaev algorithms. These results open the door to the further study of the BKSF algorithm for quantum simulation.

Uncertainty principle in loop quantum cosmology by Moyal formalism

NASA Astrophysics Data System (ADS)

Perlov, Leonid

2018-03-01

In this paper, we derive the uncertainty principle for the loop quantum cosmology homogeneous and isotropic Friedmann-Lemaiter-Robertson-Walker model with the holonomy-flux algebra. The uncertainty principle is between the variables c, with the meaning of connection and μ having the meaning of the physical cell volume to the power 2/3, i.e., v2 /3 or a plaquette area. Since both μ and c are not operators, but rather the random variables, the Robertson uncertainty principle derivation that works for hermitian operators cannot be used. Instead we use the Wigner-Moyal-Groenewold phase space formalism. The Wigner-Moyal-Groenewold formalism was originally applied to the Heisenberg algebra of the quantum mechanics. One can derive it from both the canonical and path integral quantum mechanics as well as the uncertainty principle. In this paper, we apply it to the holonomy-flux algebra in the case of the homogeneous and isotropic space. Another result is the expression for the Wigner function on the space of the cylindrical wave functions defined on Rb in c variables rather than in dual space μ variables.

Gold nanoparticle-polydimethylsiloxane films reflect light internally by optical diffraction and Mie scattering

NASA Astrophysics Data System (ADS)

Dunklin, Jeremy R.; Forcherio, Gregory T.; Roper, D. Keith

2015-08-01

Optical properties of polymer films embedded with plasmonic nanoparticles (NPs) are important in many implementations. In this work, optical extinction by polydimethylsiloxane (PDMS) films containing gold (Au) NPs was enhanced at resonance compared to AuNPs in suspensions, Beer-Lambert law, or Mie theory by internal reflection due to optical diffraction in 16 nm AuNP-PDMS films and Mie scattering in 76 nm AuNP-PDMS films. Resonant extinction per AuNP for 16 nm AuNPs with negligible resonant Mie scattering was enhanced up to 1.5-fold at interparticle separation (i.e., Wigner-Seitz radii) comparable to incident wavelength. It was attributable to diffraction through apertures formed by overlapping electric fields of adjacent, resonantly excited AuNPs at Wigner-Seitz radii equal to or less than incident wavelengths. Resonant extinction per AuNP for strongly Mie scattering 76 nm AuNPs was enhanced up to 1.3-fold at Wigner-Seitz radii four or more times greater than incident wavelength. Enhanced light trapping from diffraction and/or scattering is relevant to optoelectronic, biomedical, and catalytic activity of substrates embedded with NPs.

FREQUENCY MODULATION OF DIRECTLY IMAGED EXOPLANETS: GEOMETRIC EFFECT AS A PROBE OF PLANETARY OBLIQUITY

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

Kawahara, Hajime, E-mail: kawahara@eps.s.u-tokyo.ac.jp; Research Center for the Early Universe, School of Science, The University of Tokyo, Tokyo 113-0033

2016-05-10

We consider the time–frequency analysis of a scattered light curve of a directly imaged exoplanet. We show that the geometric effect due to planetary obliquity and orbital inclination induce the frequency modulation of the apparent diurnal periodicity. We construct a model of the frequency modulation and compare it with the instantaneous frequency extracted from the pseudo-Wigner distribution of simulated light curves of a cloudless Earth. The model provides good agreement with the simulated modulation factor, even for the light curve with Gaussian noise comparable to the signal. Notably, the shape of the instantaneous frequency is sensitive to the difference betweenmore » the prograde, retrograde, and pole-on spin rotations. While our technique requires the albedo map to be static, it does not need to solve the albedo map of the planet. The time–frequency analysis is complementary to other methods which utilize the amplitude modulation. This paper demonstrates the importance of the frequency domain of the photometric variability for the characterization of directly imaged exoplanets in future research.« less

Observation of a resonancelike structure in the pi +- psi' mass distribution in exclusive B-->Kpi +- psi' decays.

PubMed

Choi, S-K; Olsen, S L; Adachi, I; Aihara, H; Aulchenko, V; Aushev, T; Aziz, T; Bakich, A M; Balagura, V; Bedny, I; Bitenc, U; Bondar, A; Bozek, A; Bracko, M; Brodzicka, J; Browder, T E; Chang, P; Chao, Y; Chen, A; Chen, K-F; Chen, W T; Cheon, B G; Chistov, R; Choi, Y; Dalseno, J; Danilov, M; Dash, M; Eidelman, S; Gabyshev, N; Golob, B; Haba, J; Hara, T; Hayasaka, K; Hayashii, H; Hazumi, M; Heffernan, D; Hoshi, Y; Hou, W-S; Hyun, H J; Iijima, T; Inami, K; Ishikawa, A; Ishino, H; Itoh, R; Iwasaki, M; Iwasaki, Y; Kah, D H; Kang, J H; Katayama, N; Kawai, H; Kawasaki, T; Kichimi, H; Kim, H O; Kim, S K; Kim, Y J; Kinoshita, K; Krizan, P; Krokovny, P; Kumar, R; Kuo, C C; Kuzmin, A; Kwon, Y-J; Lange, J S; Lee, J S; Lee, M J; Lee, S E; Lesiak, T; Limosani, A; Lin, S-W; Liu, Y; Liventsev, D; Mandl, F; Matyja, A; McOnie, S; Medvedeva, T; Mitaroff, W; Miyabayashi, K; Miyake, H; Miyata, H; Miyazaki, Y; Mizuk, R; Moloney, G R; Nakano, E; Nakao, M; Nishida, S; Nitoh, O; Nozaki, T; Ogawa, S; Ohshima, T; Okuno, S; Ozaki, H; Pakhlov, P; Pakhlova, G; Park, C W; Park, H; Peak, L S; Pestotnik, R; Piilonen, L E; Sahoo, H; Sakai, Y; Schneider, O; Schwartz, A J; Senyo, K; Shapkin, M; Shen, C P; Shibuya, H; Shwartz, B; Singh, J B; Somov, A; Stanic, S; Staric, M; Sumiyoshi, T; Suzuki, S Y; Takasaki, F; Tamai, K; Tanaka, M; Teramoto, Y; Tikhomirov, I; Uehara, S; Uglov, T; Unno, Y; Uno, S; Urquijo, P; Varner, G; Vervink, K; Villa, S; Wang, C H; Wang, M-Z; Wang, P; Wang, X L; Watanabe, Y; Wedd, R; Won, E; Yabsley, B D; Yamashita, Y; Yuan, C Z; Zhang, Z P; Zhulanov, V; Zupanc, A; Zyukova, O

2008-04-11

A distinct peak is observed in the pi +/- psi' invariant mass distribution near 4.43 GeV in B-->K pi +/- psi' decays. A fit using a Breit-Wigner resonance shape yields a peak mass and width of M=4433+/-4(stat)+/-2(syst) MeV and Gamma=45-13+18(stat)-13+30(syst) MeV. The product branching fraction is determined to be B(B 0-->K -/+Z+/-(4430)) x B(Z+/-(4430)-->pi+/-psi')=(4.1+/-1.0(stat)+/-1.4(syst)) x 10(-5), where Z+/-(4430) is used to denote the observed structure. The statistical significance of the observed peak is 6.5 sigma. These results are obtained from a 605 fb(-1) data sample that contains 657 x 10(6) BB pairs collected near the Upsilon(4S) resonance with the Belle detector at the KEKB asymmetric energy e+ e- collider.

Augmenting Phase Space Quantization to Introduce Additional Physical Effects

NASA Astrophysics Data System (ADS)

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.

Electron Waiting Times in Mesoscopic Conductors

NASA Astrophysics Data System (ADS)

Albert, Mathias; Haack, Géraldine; Flindt, Christian; Büttiker, Markus

2012-05-01

Electron transport in mesoscopic conductors has traditionally involved investigations of the mean current and the fluctuations of the current. A complementary view on charge transport is provided by the distribution of waiting times between charge carriers, but a proper theoretical framework for coherent electronic systems has so far been lacking. Here we develop a quantum theory of electron waiting times in mesoscopic conductors expressed by a compact determinant formula. We illustrate our methodology by calculating the waiting time distribution for a quantum point contact and find a crossover from Wigner-Dyson statistics at full transmission to Poisson statistics close to pinch-off. Even when the low-frequency transport is noiseless, the electrons are not equally spaced in time due to their inherent wave nature. We discuss the implications for renewal theory in mesoscopic systems and point out several analogies with level spacing statistics and random matrix theory.

Adaptive signal processing and higher order time- frequency analysis for acoustic and vibration signatures in condition monitoring

NASA Astrophysics Data System (ADS)

Lee, Sang-Kwon

This thesis is concerned with the development of a useful engineering technique to detect and analyse faults in rotating machinery. The methods developed are based on the advanced signal processing such as the adaptive signal processing and higher-order time frequency methods. The two-stage Adaptive Line Enhancer (ALE), using adaptive signal processing, has been developed for increasing the Signal to Noise Ratio of impulsive signals. The enhanced signal can then be analysed using time frequency methods to identify fault characteristics. However, if after pre-processing by the two stage ALE, the SNR of the signals is low, the residual noise often hinders clear identification of the fault characteristics in the time-frequency domain. In such cases, higher order time-frequency methods have been proposed and studied. As examples of rotating machinery, the internal combustion engine and an industrial gear box are considered in this thesis. The noise signal from an internal combustion engine and vibration signal measured on a gear box are studied in detail. Typically an impulsive signal manifests itself when the fault occurs in the machinery and is embedded in background noise, such as the fundamental frequency and its harmonic orders of the rotation speed and broadband noise. The two-stage ALE is developed for reducing this background noise. Conditions for the choice of adaptive filter parameters are studied and suitable adaptive algorithms given. The enhanced impulsive signal is analysed in the time- frequency domain using the Wigner higher order moment spectra (WHOMS) and the multi-time WHOMS (which is a dual form of the WHOMS). The WHOMS suffers from unwanted cross-terms, which increase dramatically as the order increases. Novel expressions for the cross-terms in WHOMS have been presented. The number of cross-terms can be reduced by taking the principal slice of the WHOMS. The residual cross-terms are smoothed by using a general class of kernel functions and the γ-method kernel function which is a novel development in this thesis. The WVD and the sliced WHOMS for synthesised signals and measured data from rotating machinery are analysed. The estimated ROC (Receive Operating Characteristic) curves for these methods are computed. These results lead to the conclusion that the detection performance when using the sliced WHOMS, for impulsive signals in embedded in broadband noise, is better than that of the Wigner-Ville distribution. Real data from a faulty car engine and faulty industrial gears are analysed. The car engine radiates an impulsive noise signal due to the loosening of a spark plug. The faulty industrial gear produces an impulsive vibration signal due to a spall on the tooth face in gear. The two- stage ALE and WHOMS are successfully applied to detection and analysis of these impulsive signals.

Wigner tomography of multispin quantum states

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

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

PubMed

Petruccelli, Jonathan C; Alonso, Miguel A

2007-09-01

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

Semiclassical propagator of the Wigner function.

PubMed

Dittrich, Thomas; Viviescas, Carlos; Sandoval, Luis

2006-02-24

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

Wigner molecules in carbon-nanotube quantum dots

NASA Astrophysics Data System (ADS)

Secchi, Andrea; Rontani, Massimo

2010-07-01

We demonstrate that electrons in quantum dots defined by electrostatic gates in semiconductor nanotubes freeze orderly in space realizing a “Wigner molecule.” Our exact diagonalization calculations uncover the features of the electron molecule, which may be accessed by tunneling spectroscopy—indeed some of them have already been observed by Deshpande and Bockrath [Nat. Phys. 4, 314 (2008)]10.1038/nphys895. We show that numerical results are satisfactorily reproduced by a simple ansatz vibrational wave function: electrons have localized wave functions, like nuclei in an ordinary molecule, whereas low-energy excitations are collective vibrations of electrons around their equilibrium positions.

Applications of Cosmic Muon Tracking at Shallow Depth Underground

NASA Astrophysics Data System (ADS)

Oláh, L.; Barnaföldi, G. G.; Hamar, G.; Melegh, H. G.; Surányi, G.; Varga, D.

2014-06-01

A portable cosmic muon telescope has been developed for environmental and geophysical applications, as well as cosmic background measurements for nuclear research in underground labs by the REGARD group (Wigner RCP of the HAS and Eötvös Loránd University collaboration on gaseous detector R&D). The modular, low power consuming (5 W) Close Cathode Chamber-based tracking system has 10 mrad angular resolution with its sensitive area of 0.1 m2. The angular distribution of cosmic muons has been measured at shallow depth underground (< 70 meter-rock-equivalent) in four different remote locations. Application of cosmic muon detection for the reconstruction of underground caverns and building structures are demonstrated by the measurements.

Modelling and extraction technique for micro-doppler signature of aircraft rotor blades

NASA Astrophysics Data System (ADS)

Praveen, N.; Valarmathi, J.

2017-11-01

The process of detecting and distinguishing between different aircrafts has been a major point of interest in Defence applications. Micro-Doppler effect is one such phenomenon unique for aircrafts with different rotor dynamics and design. In this paper, we focus on deducing a mathematical model for micro-Doppler signature, of aircraft rotor blades assumed to be rotating in a plane perpendicular to the flying direction, induced on the incident radar signal. Also, we use the Wigner-Ville Distribution (WVD) to extract this signature from the radar return. This mathematical model is compared with the simulation results obtained from MATLAB, to validate the results and show the accurateness of the developed model.

Wigner Distribution Function: Relation to Short-Term Spectral Estimation, Smoothing, and Performance in Noise.

DTIC Science & Technology

1988-02-16

integration rule . In particular, if we use the Trapezoidal rule and carry out the summnation over -oo, -aO, we have approximation S~~f 2A 2 exp(-14mfka...increment a and using the Trapezoidal rule : 66 ~inr J~M ’~j i ’.m -1p w A .X i 7NX~ .m-m- -_-_ I% -.M’’I j %W I W - IR 8225 -1/4 Su(t,f) (, 2) -1-i2ft...lhe STSE is given by (102) and (103). A discrete approximation, by means of the Trapezoidal rule , is furnished by t(t,f) a u exp(-i27fAk) s(kA) *(t

Fock expansion of multimode pure Gaussian states

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

Cariolaro, Gianfranco; Pierobon, Gianfranco, E-mail: gianfranco.pierobon@unipd.it

2015-12-15

The Fock expansion of multimode pure Gaussian states is derived starting from their representation as displaced and squeezed multimode vacuum states. The approach is new and appears to be simpler and more general than previous ones starting from the phase-space representation given by the characteristic or Wigner function. Fock expansion is performed in terms of easily evaluable two-variable Hermite–Kampé de Fériet polynomials. A relatively simple and compact expression for the joint statistical distribution of the photon numbers in the different modes is obtained. In particular, this result enables one to give a simple characterization of separable and entangled states, asmore » shown for two-mode and three-mode Gaussian states.« less

Quantum phase space with a basis of Wannier functions

NASA Astrophysics Data System (ADS)

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.

Geometric transformations of optical orbital angular momentum spatial modes

NASA Astrophysics Data System (ADS)

He, Rui; An, Xin

2018-02-01

With the aid of the bosonic mode conversions in two different coordinate frames, we show that (1) the coordinate eigenstate is exactly the EPR entangled state representation, and (2) the Laguerre-Gaussian (LG) mode is exactly the wave function of the common eigenvector of the orbital angular momentum and the total photon number operator. Moreover, by using the conversion of the bosonic modes, theWigner representation of the LG mode can be obtained directly. It provides an alternative to the method of Simon and Agarwal.

Construction of even and odd combinations of Morse-like coherent states

NASA Astrophysics Data System (ADS)

Récamier, José; Jáuregui, Rocio

2003-06-01

In this work we construct approximate coherent states for the Morse potential using a method inspired by the f-oscillator formalism (Man'ko et al 1996 Proc. 4th Wigner Symp. ed M Natig, Atakishiyev, T H Seligman and K B Wolf (Singapore: World Scientific) p 421). We make even and odd combinations of these states and evaluate the temporal evolution of the position operator and its dispersion as a function of time when the states evolve under a nonlinear Morse Hamiltonian.

Experimental status of the nuclear spin scissors mode

NASA Astrophysics Data System (ADS)

Balbutsev, E. B.; Molodtsova, I. V.; Schuck, P.

2018-04-01

With the Wigner function moments (WFM) method the scissors mode of the actinides and rare earth nuclei are investigated. The unexplained experimental fact that in 232Th a double hump structure is found finds a natural explanation within WFM. It is predicted that the lower peak corresponds to an isovector spin scissors mode whereas the higher-lying states corresponds to the conventional isovector orbital scissors mode. The experimental situation is scrutinized in this respect concerning practically all results of M 1 excitations.

s-Ordered Exponential of Quadratic Forms Gained via IWSOP Technique

NASA Astrophysics Data System (ADS)

Bazrafkan, M. R.; Shähandeh, F.; Nahvifard, E.

2012-11-01

Using the generalized bar{s}-ordered Wigner operator, in which bar{s} is a vector over the field of complex numbers, the technique of integration within an s-ordered product of operators (IWSOP) has been extended to multimode case. We derive the bar{s}-ordered form of the widely applicable multimode exponential of quadratic form exp\\{sum_{i,j = 1}n ai^{dag}\\varLambda_{ij}{aj}\\} , each mode being in some particular order s i , applying this method.

Quantum Brownian motion with inhomogeneous damping and diffusion

NASA Astrophysics Data System (ADS)

Massignan, Pietro; Lampo, Aniello; Wehr, Jan; Lewenstein, Maciej

2015-03-01

We analyze the microscopic model of quantum Brownian motion, describing a Brownian particle interacting with a bosonic bath through a coupling which is linear in the creation and annihilation operators of the bath, but may be a nonlinear function of the position of the particle. Physically, this corresponds to a configuration in which damping and diffusion are spatially inhomogeneous. We derive systematically the quantum master equation for the Brownian particle in the Born-Markov approximation and we discuss the appearance of additional terms, for various polynomials forms of the coupling. We discuss the cases of linear and quadratic coupling in great detail and we derive, using Wigner function techniques, the stationary solutions of the master equation for a Brownian particle in a harmonic trapping potential. We predict quite generally Gaussian stationary states, and we compute the aspect ratio and the spread of the distributions. In particular, we find that these solutions may be squeezed (superlocalized) with respect to the position of the Brownian particle. We analyze various restrictions to the validity of our theory posed by non-Markovian effects and by the Heisenberg principle. We further study the dynamical stability of the system, by applying a Gaussian approximation to the time-dependent Wigner function, and we compute the decoherence rates of coherent quantum superpositions in position space. Finally, we propose a possible experimental realization of the physics discussed here, by considering an impurity particle embedded in a degenerate quantum gas.

Bipartite qutrit local realist inequalities and the robustness of their quantum mechanical violation

NASA Astrophysics Data System (ADS)

Das, Debarshi; Datta, Shounak; Goswami, Suchetana; Majumdar, A. S.; Home, Dipankar

2017-10-01

Distinct from the type of local realist inequality (known as the Collins-Gisin-Linden-Massar-Popescu or CGLMP inequality) usually used for bipartite qutrit systems, we formulate a new set of local realist inequalities for bipartite qutrits by generalizing Wigner's argument that was originally formulated for the bipartite qubit singlet state. This treatment assumes existence of the overall joint probability distributions in the underlying stochastic hidden variable space for the measurement outcomes pertaining to the relevant trichotomic observables, satisfying the locality condition and yielding the measurable marginal probabilities. Such generalized Wigner inequalities (GWI) do not reduce to Bell-CHSH type inequalities by clubbing any two outcomes, and are violated by quantum mechanics (QM) for both the bipartite qutrit isotropic and singlet states using trichotomic observables defined by six-port beam splitter as well as by the spin-1 component observables. The efficacy of GWI is then probed in these cases by comparing the QM violation of GWI with that obtained for the CGLMP inequality. This comparison is done by incorporating white noise in the singlet and isotropic qutrit states. It is found that for the six-port beam splitter observables, QM violation of GWI is more robust than that of the CGLMP inequality for singlet qutrit states, while for isotropic qutrit states, QM violation of the CGLMP inequality is more robust. On the other hand, for the spin-1 component observables, QM violation of GWI is more robust for both the types of states considered.

Time-frequency techniques in biomedical signal analysis. a tutorial review of similarities and differences.

PubMed

Wacker, M; Witte, H

2013-01-01

This review outlines the methodological fundamentals of the most frequently used non-parametric time-frequency analysis techniques in biomedicine and their main properties, as well as providing decision aids concerning their applications. The short-term Fourier transform (STFT), the Gabor transform (GT), the S-transform (ST), the continuous Morlet wavelet transform (CMWT), and the Hilbert transform (HT) are introduced as linear transforms by using a unified concept of the time-frequency representation which is based on a standardized analytic signal. The Wigner-Ville distribution (WVD) serves as an example of the 'quadratic transforms' class. The combination of WVD and GT with the matching pursuit (MP) decomposition and that of the HT with the empirical mode decomposition (EMD) are explained; these belong to the class of signal-adaptive approaches. Similarities between linear transforms are demonstrated and differences with regard to the time-frequency resolution and interference (cross) terms are presented in detail. By means of simulated signals the effects of different time-frequency resolutions of the GT, CMWT, and WVD as well as the resolution-related properties of the interference (cross) terms are shown. The method-inherent drawbacks and their consequences for the application of the time-frequency techniques are demonstrated by instantaneous amplitude, frequency and phase measures and related time-frequency representations (spectrogram, scalogram, time-frequency distribution, phase-locking maps) of measured magnetoencephalographic (MEG) signals. The appropriate selection of a method and its parameter settings will ensure readability of the time-frequency representations and reliability of results. When the time-frequency characteristics of a signal strongly correspond with the time-frequency resolution of the analysis then a method may be considered 'optimal'. The MP-based signal-adaptive approaches are preferred as these provide an appropriate time-frequency resolution for all frequencies while simultaneously reducing interference (cross) terms.

Molecular t-matrices for Low-Energy Electron Diffraction (TMOL v1.1)

NASA Astrophysics Data System (ADS)

Blanco-Rey, Maria; de Andres, Pedro; Held, Georg; King, David A.

2004-08-01

We describe a FORTRAN-90 program that computes scattering t-matrices for a molecule. These can be used in a Low-Energy Electron Diffraction program to solve the molecular structural problem very efficiently. The intramolecular multiple scattering is computed within a Dyson-like approach, using free space Green propagators in a basis of spherical waves. The advantage of this approach is related to exploiting the chemical identity of the molecule, and to the simplicity to translate and rotate these t-matrices without performing a new multiple-scattering calculation for each configuration. FORTRAN-90 routines for rotating the resulting t-matrices using Wigner matrices are also provided. Program summaryTitle of program: TMOL Catalogue number: ADUF Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUF Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland. Computers: Alpha ev6-21264 (700 MHz) and Pentium-IV. Operating systems: Digital UNIX V5.0 and Linux (Red Hat 8.0). Programming language: FORTRAN-90/95 (Compaq True64 compiler, and Intel Fortran Compiler 7.0 for Linux). High-speed storage required for the test run: minimum 64 Mbytes, it can grow to more depending on the system considered. Disk storage required: None. No. of bits in a word: 64 and 32. No. of lines in distributed program, including test data etc.: 5404 No. of bytes in distributed program, including test data etc.: 59 856 Distribution format: tar.gz Nature of problem: We describe the FORTRAN-90 program TMOL (v1.1) for the computation of non-diagonal scattering t-matrices for molecules or any other poly-atomic sub-unit of surface structures. These matrices can be used in an standard Low-Energy Electron Diffraction program, such as LEED90 or CLEED. Method of solution: A general non-diagonal t-matrix is assumed for the atoms or more general scatterers forming the molecule. The molecular t-matrix is solved adding the possible intramolecular multiple scattering events using Green's propagator formalism. The resulting t-matrix is referred to the mass centre of the molecule and can be easily translated with these propagators and rotated applying Wigner matrices. Typical running time: Calculating the t-matrix for a single energy takes a few seconds. Time depends on the maximum angular momentum quantum number, lmax, and the number of scatterers in the molecule, N. Running time scales as lmax6 and N3. References: [1] S. Andersson, J.B. Pendry, J. Phys. C: Solid St. Phys. 13 (1980) 3547. [2] A. Gonis, W.H. Butler, Multiple Scattering in Solids, Springer-Verlag, Berlin/New York, 2000.

Time-frequency analysis of transient signals - application to cardiovascular control

NASA Astrophysics Data System (ADS)

Keselbrener, Laurence; Akselrod, Solange

A method for time-frequency decomposition (SDA) is presented for the analysis of cardiovascular signals, during steady state as well as under transient conditions. The SDA is applied to a simulated noisy non-stationary signal. It reliably discloses the time evolution of the different spectral components of the signal and does not present noise propagation as other time-frequency methods, such as Wigner-Ville distribution does. A comparison with the well-known short-time Fourier transform is also performed for non-stationary simulated signal showing that the SDA achieves a higher time-frequency resolution. Two physiological applications are then presented in which the SDA is used for the analysis of HR and BP variability, reflecting the activity of the autonomic nervous system. The power spectra of heart rate (HR) and blood pressure (BP) fluctuations during a change of posture from supine to standing are calculated. The decrease of vagal activity on standing is obvious and can be quantified from the spectrum of HR fluctuations. The increase in the LF fluctuations of both BP and HR spectra reflect the enhancement in sympathetic activity on standing. Finally, the power spectrum of fetal HR fluctuations is obtained by SDA. The respiratory peak is observed and can help in evaluating fetal well-being.

Analytical and experimental vibration analysis of a faulty gear system

NASA Astrophysics Data System (ADS)

Choy, F. K.; Braun, M. J.; Polyshchuk, V.; Zakrajsek, J. J.; Townsend, D. P.; Handschuh, R. F.

1994-10-01

A comprehensive analytical procedure was developed for predicting faults in gear transmission systems under normal operating conditions. A gear tooth fault model is developed to simulate the effects of pitting and wear on the vibration signal under normal operating conditions. The model uses changes in the gear mesh stiffness to simulate the effects of gear tooth faults. The overall dynamics of the gear transmission system is evaluated by coupling the dynamics of each individual gear-rotor system through gear mesh forces generated between each gear-rotor system and the bearing forces generated between the rotor and the gearbox structures. The predicted results were compared with experimental results obtained from a spiral bevel gear fatigue test rig at NASA Lewis Research Center. The Wigner-Ville Distribution (WVD) was used to give a comprehensive comparison of the predicted and experimental results. The WVD method applied to the experimental results were also compared to other fault detection techniques to verify the WVD's ability to detect the pitting damage, and to determine its relative performance. Overall results show good correlation between the experimental vibration data of the damaged test gear and the predicted vibration from the model with simulated gear tooth pitting damage. Results also verified that the WVD method can successfully detect and locate gear tooth wear and pitting damage.

Analytical and experimental vibration analysis of a faulty gear system

NASA Astrophysics Data System (ADS)

Choy, F. K.; Braun, M. J.; Polyshchuk, V.; Zakrajsek, J. J.; Townsend, D. P.; Handschuh, R. F.

1994-10-01

A comprehensive analytical procedure was developed for predicting faults in gear transmission systems under normal operating conditions. A gear tooth fault model is developed to simulate the effects of pitting and wear on the vibration signal under normal operating conditions. The model uses changes in the gear mesh stiffness to simulate the effects of gear tooth faults. The overall dynamics of the gear transmission system is evaluated by coupling the dynamics of each individual gear-rotor system through gear mesh forces generated between each gear-rotor system and the bearing forces generated between the rotor and the gearbox structure. The predicted results were compared with experimental results obtained from a spiral bevel gear fatigue test rig at NASA Lewis Research Center. The Wigner-Ville distribution (WVD) was used to give a comprehensive comparison of the predicted and experimental results. The WVD method applied to the experimental results were also compared to other fault detection techniques to verify the WVD's ability to detect the pitting damage, and to determine its relative performance. Overall results show good correlation between the experimental vibration data of the damaged test gear and the predicted vibration from the model with simulated gear tooth pitting damage. Results also verified that the WVD method can successfully detect and locate gear tooth wear and pitting damage.

Analytical and Experimental Vibration Analysis of a Faulty Gear System

NASA Technical Reports Server (NTRS)

Choy, F. K.; Braun, M. J.; Polyshchuk, V.; Zakrajsek, J. J.; Townsend, D. P.; Handschuh, R. F.

1994-01-01

A comprehensive analytical procedure was developed for predicting faults in gear transmission systems under normal operating conditions. A gear tooth fault model is developed to simulate the effects of pitting and wear on the vibration signal under normal operating conditions. The model uses changes in the gear mesh stiffness to simulate the effects of gear tooth faults. The overall dynamics of the gear transmission system is evaluated by coupling the dynamics of each individual gear-rotor system through gear mesh forces generated between each gear-rotor system and the bearing forces generated between the rotor and the gearbox structure. The predicted results were compared with experimental results obtained from a spiral bevel gear fatigue test rig at NASA Lewis Research Center. The Wigner-Ville distribution (WVD) was used to give a comprehensive comparison of the predicted and experimental results. The WVD method applied to the experimental results were also compared to other fault detection techniques to verify the WVD's ability to detect the pitting damage, and to determine its relative performance. Overall results show good correlation between the experimental vibration data of the damaged test gear and the predicted vibration from the model with simulated gear tooth pitting damage. Results also verified that the WVD method can successfully detect and locate gear tooth wear and pitting damage.

Fluid identification based on P-wave anisotropy dispersion gradient inversion for fractured reservoirs

NASA Astrophysics Data System (ADS)

Zhang, J. W.; Huang, H. D.; Zhu, B. H.; Liao, W.

2017-10-01

Fluid identification in fractured reservoirs is a challenging issue and has drawn increasing attentions. As aligned fractures in subsurface formations can induce anisotropy, we must choose parameters independent with azimuths to characterize fractures and fluid effects such as anisotropy parameters for fractured reservoirs. Anisotropy is often frequency dependent due to wave-induced fluid flow between pores and fractures. This property is conducive for identifying fluid type using azimuthal seismic data in fractured reservoirs. Through the numerical simulation based on Chapman model, we choose the P-wave anisotropy parameter dispersion gradient (PADG) as the new fluid factor. PADG is dependent both on average fracture radius and fluid type but independent on azimuths. When the aligned fractures in the reservoir are meter-scaled, gas-bearing layer could be accurately identified using PADG attribute. The reflection coefficient formula for horizontal transverse isotropy media by Rüger is reformulated and simplified according to frequency and the target function for inverting PADG based on frequency-dependent amplitude versus azimuth is derived. A spectral decomposition method combining Orthogonal Matching Pursuit and Wigner-Ville distribution is used to prepare the frequency-division data. Through application to synthetic data and real seismic data, the results suggest that the method is useful for gas identification in reservoirs with meter-scaled fractures using high-qualified seismic data.

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

NASA Astrophysics Data System (ADS)

Sellier, Jean Michel

2018-04-01

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

Boltzmann-conserving classical dynamics in quantum time-correlation functions: "Matsubara dynamics".

PubMed

Hele, Timothy J H; Willatt, Michael J; Muolo, Andrea; Althorpe, Stuart C

2015-04-07

We show that a single change in the derivation of the linearized semiclassical-initial value representation (LSC-IVR or "classical Wigner approximation") results in a classical dynamics which conserves the quantum Boltzmann distribution. We rederive the (standard) LSC-IVR approach by writing the (exact) quantum time-correlation function in terms of the normal modes of a free ring-polymer (i.e., a discrete imaginary-time Feynman path), taking the limit that the number of polymer beads N → ∞, such that the lowest normal-mode frequencies take their "Matsubara" values. The change we propose is to truncate the quantum Liouvillian, not explicitly in powers of ħ(2) at ħ(0) (which gives back the standard LSC-IVR approximation), but in the normal-mode derivatives corresponding to the lowest Matsubara frequencies. The resulting "Matsubara" dynamics is inherently classical (since all terms O(ħ(2)) disappear from the Matsubara Liouvillian in the limit N → ∞) and conserves the quantum Boltzmann distribution because the Matsubara Hamiltonian is symmetric with respect to imaginary-time translation. Numerical tests show that the Matsubara approximation to the quantum time-correlation function converges with respect to the number of modes and gives better agreement than LSC-IVR with the exact quantum result. Matsubara dynamics is too computationally expensive to be applied to complex systems, but its further approximation may lead to practical methods.

Investigations on neutron irradiated 3D carbon fibre reinforced carbon composite material

NASA Astrophysics Data System (ADS)

Venugopalan, Ramani; Alur, V. D.; Patra, A. K.; Acharya, R.; Srivastava, D.

2018-04-01

As against conventional graphite materials carbon-carbon (C/C) composite materials are now being contemplated as the promising candidate materials for the high temperature and fusion reactor owing to their high thermal conductivity and high thermal resistance, better mechanical/thermal properties and irradiation stability. The current need is for focused research on novel carbon materials for future new generation nuclear reactors. The advantage of carbon-carbon composite is that the microstructure and the properties can be tailor made. The present study encompasses the irradiation of 3D carbon composite prepared by reinforcement using PAN carbon fibers for nuclear application. The carbon fiber reinforced composite was subjected to neutron irradiation in the research reactor DHRUVA. The irradiated samples were characterized by Differential Scanning Calorimetry (DSC), small angle neutron scattering (SANS), XRD and Raman spectroscopy. The DSC scans were taken in argon atmosphere under a linear heating program. The scanning was carried out at temperature range from 30 °C to 700 °C at different heating rates in argon atmosphere along with reference as unirradiated carbon composite. The Wigner energy spectrum of irradiated composite showed two peaks corresponding to 200 °C and 600 °C. The stored energy data for the samples were in the range 110-170 J/g for temperature ranging from 30 °C to 700 °C. The Wigner energy spectrum of irradiated carbon composite did not indicate spontaneous temperature rise during thermal annealing. Small angle neutron scattering (SANS) experiments have been carried out to investigate neutron irradiation induced changes in porosity of the composite samples. SANS data were recorded in the scattering wave vector range of 0.17 nm-1 to 3.5 nm-1. Comparison of SANS profiles of irradiated and unirradiated samples indicates significant change in pore morphology. Pore size distributions of the samples follow power law size distribution with different exponent. Narrowing of SANS profile of the irradiated sample indicates creation of significant number of larger pores due to neutron irradiation.

From Weyl to Born-Jordan quantization: The Schrödinger representation revisited

NASA Astrophysics Data System (ADS)

de Gosson, Maurice A.

2016-03-01

The ordering problem has been one of the long standing and much discussed questions in quantum mechanics from its very beginning. Nowadays, there is more or less a consensus among physicists that the right prescription is Weyl's rule, which is closely related to the Moyal-Wigner phase space formalism. We propose in this report an alternative approach by replacing Weyl quantization with the less well-known Born-Jordan quantization. This choice is actually natural if we want the Heisenberg and Schrödinger pictures of quantum mechanics to be mathematically equivalent. It turns out that, in addition, Born-Jordan quantization can be recovered from Feynman's path integral approach provided that one used short-time propagators arising from correct formulas for the short-time action, as observed by Makri and Miller. These observations lead to a slightly different quantum mechanics, exhibiting some unexpected features, and this without affecting the main existing theory; for instance quantizations of physical Hamiltonian functions are the same as in the Weyl correspondence. The differences are in fact of a more subtle nature; for instance, the quantum observables will not correspond in a one-to-one fashion to classical ones, and the dequantization of a Born-Jordan quantum operator is less straightforward than that of the corresponding Weyl operator. The use of Born-Jordan quantization moreover solves the "angular momentum dilemma", which already puzzled L. Pauling. Born-Jordan quantization has been known for some time (but not fully exploited) by mathematicians working in time-frequency analysis and signal analysis, but ignored by physicists. One of the aims of this report is to collect and synthesize these sporadic discussions, while analyzing the conceptual differences with Weyl quantization, which is also reviewed in detail. Another striking feature is that the Born-Jordan formalism leads to a redefinition of phase space quantum mechanics, where the usual Wigner distribution has to be replaced with a new quasi-distribution reducing interference effects.

Perturbative universal state-selective correction for state-specific multi-reference coupled cluster methods

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

Brabec, Jiri; Banik, Subrata; Kowalski, Karol

2016-10-28

The implementation details of the universal state-selective (USS) multi-reference coupled cluster (MRCC) formalism with singles and doubles (USS(2)) are discussed on the example of several benchmark systems. We demonstrate that the USS(2) formalism is capable of improving accuracies of state specific multi-reference coupled-cluster (MRCC) methods based on the Brillouin-Wigner and Mukherjee’s sufficiency conditions. Additionally, it is shown that the USS(2) approach significantly alleviates problems associated with the lack of invariance of MRCC theories upon the rotation of active orbitals. We also discuss the perturbative USS(2) formulations that significantly reduce numerical overhead of the full USS(2) method.

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

NASA Astrophysics Data System (ADS)

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.

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

PubMed

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

2002-04-22

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

Path-integral approach to the Wigner-Kirkwood expansion.

PubMed

Jizba, Petr; Zatloukal, Václav

2014-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Progress in characterizing submonolayer island growth: Capture-zone distributions, growth exponents, & hot precursors

NASA Astrophysics Data System (ADS)

Einstein, Theodore L.; Pimpinelli, Alberto; González, Diego Luis; Morales-Cifuentes, Josue R.

2015-09-01

In studies of epitaxial growth, analysis of the distribution of the areas of capture zones (i.e. proximity polygons or Voronoi tessellations with respect to island centers) is often the best way to extract the critical nucleus size i. For non-random nucleation the normalized areas s of these Voronoi cells are well described by the generalized Wigner distribution (GWD) Pβ(s) = asβ exp(-bs2), particularly in the central region 0.5 < s < 2 where data are least noisy. Extensive Monte Carlo simulations reveal inadequacies of our earlier mean field analysis, suggesting β = i + 2 for diffusion-limited aggregation (DLA). Since simulations generate orders of magnitude more data than experiments, they permit close examination of the tails of the distribution, which differ from the simple GWD form. One refinement is based on a fragmentation model. We also compare island-size distributions. We compare analysis by island-size distribution and by scaling of island density with flux. Modifications appear for attach-limited aggregation (ALA). We focus on the experimental system para-hexaphenyl on amorphous mica, comparing the results of the three analysis techniques and reconciling their results via a novel model of hot precursors based on rate equations, pointing out the existence of intermediate scaling regimes between DLA and ALA.

The isotropic local Wigner-Seitz model: An accurate theoretical model for the quasi-free electron energy in fluids

NASA Astrophysics Data System (ADS)

Evans, Cherice; Findley, Gary L.

The quasi-free electron energy V0 (ρ) is important in understanding electron transport through a fluid, as well as for modeling electron attachment reactions in fluids. Our group has developed an isotropic local Wigner-Seitz model that allows one to successfully calculate the quasi-free electron energy for a variety of atomic and molecular fluids from low density to the density of the triple point liquid with only a single adjustable parameter. This model, when coupled with the quasi-free electron energy data and the thermodynamic data for the fluids, also can yield optimized intermolecular potential parameters and the zero kinetic energy electron scattering length. In this poster, we give a review of the isotropic local Wigner-Seitz model in comparison to previous theoretical models for the quasi-free electron energy. All measurements were performed at the University of Wisconsin Synchrotron Radiation Center. This work was supported by a Grants from the National Science Foundation (NSF CHE-0956719), the Petroleum Research Fund (45728-B6 and 5-24880), the Louisiana Board of Regents Support Fund (LEQSF(2006-09)-RD-A33), and the Professional Staff Congress City University of New York.

Failure of Breit-Wigner and success of dispersive descriptions of the τ- → K-ηντ decays

NASA Astrophysics Data System (ADS)

Roig, Pablo

2015-11-01

The τ- → K-ηντ decays have been studied using Chiral Perturbation Theory extended by including resonances as active fields. We have found that the treatment of final state interactions is crucial to provide a good description of the data. The Breit-Wigner approximation does not resum them and neglects the real part of the corresponding chiral loop functions, which violates analyticity and leads to a failure in the confrontation with the data. On the contrary, its resummation by means of an Omnes-like exponentiation of through a dispersive representation provides a successful explanation of the measurements. These results illustrate the fact that Breit-Wigner parametrizations of hadronic data, although simple and easy to handle, lack a link with the underlying strong interaction theory and should be avoided. As a result of our analysis we determine the properties of the K* (1410) resonance with a precision competitive to its traditional extraction using τ- → (Kπ)-ντ decays, albeit the much limited statistics accumulated for the τ- → K-ηντ channel. We also predict the soon discovery of the τ- → K-η'ντ decays.

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

NASA Astrophysics Data System (ADS)

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

2013-03-01

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

Kinetic theory molecular dynamics and hot dense matter: theoretical foundations.

PubMed

Graziani, F R; Bauer, J D; Murillo, M S

2014-09-01

Electrons are weakly coupled in hot, dense matter that is created in high-energy-density experiments. They are also mildly quantum mechanical and the ions associated with them are classical and may be strongly coupled. In addition, the dynamical evolution of plasmas under these hot, dense matter conditions involve a variety of transport and energy exchange processes. Quantum kinetic theory is an ideal tool for treating the electrons but it is not adequate for treating the ions. Molecular dynamics is perfectly suited to describe the classical, strongly coupled ions but not the electrons. We develop a method that combines a Wigner kinetic treatment of the electrons with classical molecular dynamics for the ions. We refer to this hybrid method as "kinetic theory molecular dynamics," or KTMD. The purpose of this paper is to derive KTMD from first principles and place it on a firm theoretical foundation. The framework that KTMD provides for simulating plasmas in the hot, dense regime is particularly useful since current computational methods are generally limited by their inability to treat the dynamical quantum evolution of the electronic component. Using the N-body von Neumann equation for the electron-proton plasma, three variations of KTMD are obtained. Each variant is determined by the physical state of the plasma (e.g., collisional versus collisionless). The first variant of KTMD yields a closed set of equations consisting of a mean-field quantum kinetic equation for the electron one-particle distribution function coupled to a classical Liouville equation for the protons. The latter equation includes both proton-proton Coulombic interactions and an effective electron-proton interaction that involves the convolution of the electron density with the electron-proton Coulomb potential. The mean-field approach is then extended to incorporate equilibrium electron-proton correlations through the Singwi-Tosi-Land-Sjolander (STLS) ansatz. This is the second variant of KTMD. The STLS contribution produces an effective electron-proton interaction that involves the electron-proton structure factor, thereby extending the usual mean-field theory to correlated but near equilibrium systems. Finally, a third variant of KTMD is derived. It includes dynamical electrons and their correlations coupled to a MD description for the ions. A set of coupled equations for the one-particle electron Wigner function and the electron-electron and electron-proton correlation functions are coupled to a classical Liouville equation for the protons. This latter variation has both time and momentum dependent correlations.

An interpretation model of GPR point data in tunnel geological prediction

NASA Astrophysics Data System (ADS)

He, Yu-yao; Li, Bao-qi; Guo, Yuan-shu; Wang, Teng-na; Zhu, Ya

2017-02-01

GPR (Ground Penetrating Radar) point data plays an absolutely necessary role in the tunnel geological prediction. However, the research work on the GPR point data is very little and the results does not meet the actual requirements of the project. In this paper, a GPR point data interpretation model which is based on WD (Wigner distribution) and deep CNN (convolutional neural network) is proposed. Firstly, the GPR point data is transformed by WD to get the map of time-frequency joint distribution; Secondly, the joint distribution maps are classified by deep CNN. The approximate location of geological target is determined by observing the time frequency map in parallel; Finally, the GPR point data is interpreted according to the classification results and position information from the map. The simulation results show that classification accuracy of the test dataset (include 1200 GPR point data) is 91.83% at the 200 iteration. Our model has the advantages of high accuracy and fast training speed, and can provide a scientific basis for the development of tunnel construction and excavation plan.

Evolution of arbitrary moments of radiant intensity distribution for partially coherent general beams in atmospheric turbulence

NASA Astrophysics Data System (ADS)

Dan, Youquan; Xu, Yonggen

2018-04-01

The evolution law of arbitrary order moments of the Wigner distribution function, which can be applied to the different spatial power spectra, is obtained for partially coherent general beams propagating in atmospheric turbulence using the extended Huygens-Fresnel principle. A coupling coefficient of radiant intensity distribution (RID) in turbulence is introduced. Analytical expressions of the evolution of the first five-order moments, kurtosis parameter, coupling coefficient of RID for general beams in turbulence are derived, and the formulas are applied to Airy beams. Results show that there exist two types for general beams in turbulence. A larger value of kurtosis parameter for Airy beams also reveals that coupling effect due to turbulence is stronger. Both theoretical analysis and numerical results show that the maximum value of kurtosis parameter for an Airy beam in turbulence is independent of turbulence strength parameter and is only determined by inner scale of turbulence. Relative angular spread, kurtosis and coupling coefficient are less influenced by turbulence for Airy beams with a smaller decay factor and a smaller initial width of the first lobe.

Quark orbital dynamics in the proton from lattice QCD: From Ji to Jaffe-Manohar orbital angular momentum

NASA Astrophysics Data System (ADS)

Engelhardt, M.

2017-05-01

Given a Wigner distribution simultaneously characterizing quark transverse positions and momenta in a proton, one can directly evaluate their cross product, i.e., quark orbital angular momentum. The aforementioned distribution can be obtained by generalizing the proton matrix elements of quark bilocal operators which define transverse momentum-dependent parton distributions (TMDs); the transverse momentum information is supplemented with transverse position information by introducing an additional nonzero momentum transfer. A gauge connection between the quarks must be specified in the quark bilocal operators; the staple-shaped gauge link path used in TMD calculations yields the Jaffe-Manohar definition of orbital angular momentum, whereas a straight path yields the Ji definition. An exploratory lattice calculation, performed at the pion mass mπ=518 MeV , is presented which quasicontinuously interpolates between the two definitions and demonstrates that their difference can be clearly resolved. The resulting Ji orbital angular momentum is confronted with traditional evaluations based on Ji's sum rule. Jaffe-Manohar orbital angular momentum is enhanced in magnitude compared to its Ji counterpart.

Comparison between photon annihilation-then-creation and photon creation-then-annihilation thermal states: Non-classical and non-Gaussian properties

NASA Astrophysics Data System (ADS)

Xu, Xue-Xiang; Yuan, Hong-Chun; Wang, Yan

2014-07-01

We investigate the nonclassical properties of arbitrary number photon annihilation-then-creation operation (AC) and creation-then-annihilation operation (CA) to the thermal state (TS), whose normalization factors are related to the polylogarithm function. Then we compare their quantum characters, such as photon number distribution, average photon number, Mandel Q-parameter, purity and the Wigner function. Because of the noncommutativity between the annihilation operator and the creation operator, the ACTS and the CATS have different nonclassical properties. It is found that nonclassical properties are exhibited more strongly after AC than after CA. In addition we also examine their non-Gaussianity. The result shows that the ACTS can present a slightly bigger non-Gaussianity than the CATS.

Temperature-dependent nucleation and capture-zone scaling of C 60 on silicon oxide

NASA Astrophysics Data System (ADS)

Groce, M. A.; Conrad, B. R.; Cullen, W. G.; Pimpinelli, A.; Williams, E. D.; Einstein, T. L.

2012-01-01

Submonolayer films of C 60 have been deposited on ultrathin SiO 2 films for the purpose of characterizing the initial stages of nucleation and growth as a function of temperature. Capture zones extracted from the initial film morphology were analyzed using both the gamma and generalized Wigner distributions. The calculated critical nucleus size i of the C 60 islands was observed to change over the temperature range 298 K to 483 K. All fitted values of i were found to be between 0 and 1, representing stable monomers and stable dimers, respectively. With increasing temperature of film preparation, we observed i first increasing through this range and then decreasing. We discuss possible explanations of this reentrant-like behavior.

The Bargmann-Wigner equations in spherical space

NASA Astrophysics Data System (ADS)

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

2006-01-01

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

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

PubMed

Trapani, Stefano; Navaza, Jorge

2006-07-01

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

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

PubMed

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

2005-04-01

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