Phase Probability Distribution Research Articles

A note on the Hendrickson-Lattman phase probability distribution and its equivalence to the generalized von Mises distribution.

Hendrickson & Lattman [Acta Cryst. (1970), B26, 136-143] introduced a method for representing crystallographic phase probabilities defined on the unit circle. Their approach could model the bimodal phase probability distributions that can result from experimental phase determination procedures. It also provided simple and highly effective means to combine independent sources of phase information. The present work discusses the equivalence of the Hendrickson-Lattman distribution and the generalized von Mises distribution of order two, which has been studied in the statistical literature. Recognizing this connection allows the Hendrickson-Lattman distribution to be expressed in an alternative form which is easier to interpret, as it involves the location and concentration parameters of the component von Mises distributions. It also allows clarification of the conditions for bimodality and access to a simplified analytical method for evaluating the trigonometric moments of the distribution, the first of which is required for computing the best Fourier synthesis in the presence of phase, but not amplitude, uncertainty.

Mesoscopic simulation and characterization of the morphological evolution in phase separating fluid mixtures

In this article, we use a mesoscopic model discretized with Smoothed Dissipative Particle Dynamics to study the formation of morphology behind a moving precipitation front in a phase separating fluid mixture. In contrast to previous models we include thermodynamically consistent thermal fluctuations of the mass fraction in a binary mixture. The model is validated by phase separation dynamics and probability distribution functions of the thermal fluctuations. Variation of the velocity of the precipitation front and initial composition in 2D and 3D leads to diverse morphology. We characterize these morphology using a time- and space-dependent mapping procedure using the variables of the model of Doi & Ohta to identify different orientations of the evolving porous structure.

Improving experimental phases for strong reflections prior to density modification.

Experimental phasing of diffraction data from macromolecular crystals involves deriving phase probability distributions. These distributions are often bimodal, making their weighted average, the centroid phase, improbable, so that electron-density maps computed using centroid phases are often non-interpretable. Density modification brings in information about the characteristics of electron density in protein crystals. In successful cases, this allows a choice between the modes in the phase probability distributions, and the maps can cross the borderline between non-interpretable and interpretable. Based on the suggestions by Vekhter [Vekhter (2005), Acta Cryst. D61, 899-902], the impact of identifying optimized phases for a small number of strong reflections prior to the density-modification process was investigated while using the centroid phase as a starting point for the remaining reflections. A genetic algorithm was developed that optimizes the quality of such phases using the skewness of the density map as a target function. Phases optimized in this way are then used in density modification. In most of the tests, the resulting maps were of higher quality than maps generated from the original centroid phases. In one of the test cases, the new method sufficiently improved a marginal set of experimental SAD phases to enable successful map interpretation. A computer program, SISA, has been developed to apply this method for phase improvement in macromolecular crystallography.

Wigner function of N00N state and quantum interference with N00N state as input

Using the formula of Wigner function in coherent representation, we have obtained the analytical expression for Wigner function of N00N state. Based on phase space method, we study the quantum interference with N00N state as input. We derive the analytical expression of conditional probability related with the input parameter N and phase parameter φ and analyze it numerically. It is shown that, when φ is 0 or π, the output is just N00N state. It is also shown that, for 2002 state as input, the output must be 2002 state, which is independent of phase parameters. Moreover, as the number of input photon N increases, the phase probability distributions remain to have one, two, three and four peaks and get narrower. All these results can offer theoretical reference for experiments.

Pisot [formula omitted]-coherent states quantization of the harmonic oscillator

We revisit the quantized version of the harmonic oscillator obtained through a q-dependent family of coherent states. For each q, 0<q<1, these normalized states form an overcomplete set that resolves the unity with respect to an explicit measure. We restrict our study to the case in which q−1 is a quadratic unit Pisot number, since then the q-deformed integers form Fibonacci-like sequences of integers. We then examine the main characteristics of the corresponding quantum oscillator: localization in the configuration and in the phase spaces, angle operator, probability distributions and related statistical features, time evolution and semi-classical phase space trajectories.

Pisot-Fibonacci q-coherent states

A family of q-coherent states is constructed allowing us to obtain a new quantized version of the harmonic oscillator. These q-states are normalized and form an overcomplete set resolving the unity with respect to the appropriate Jackson measure if 0 < q < 1. We only consider here those values of q such that q−1 is a Pisot number. In this case the q-deformed integers ([n]q) form Fibonacci-like sequences of integers. We study the main physical characteristics of the corresponding quantum oscillator: localization in the configuration and in the phase spaces, probability distributions and related statistical features and semi-classical phase space trajectories whose periodicity is related with the fact that q is an algebraic number.

The Wigner function and phase properties of superposition of two coherent states with the vacuum state

This paper discusses some statistical properties of the superposition of two coherent states with a vacuum state, such as sub-Poissonian photon statistics and negativity of the Wigner function. Phase probability distribution and phase variance are calculated. Special cases of the constructed superposition states are presented. The results show that depending on the vacuum state coefficient γ and the coherent state coefficient α, it can generate a variety of nonclassical states.

Anabiosis of phase distribution of a three-level atom

We study the phase probability distribution of a three-level atom interacting with a cavity field in the presence of two-photon detuning and decoherence. Anabiosis of the phase probability distribution is observed due to the presence of the Stark shift. The simulation demonstrates that there is an enhancement of the phase sensitivity as soon as the two-photon detuning is considered. The W-Wigner function is also examined and it is shown that the nonclassical effect is apparent, however, for a small value of the decoherence factor.

QUANTUM STATISTICAL PROPERTIES OF THE EVEN AND ODD NEGATIVE BINOMIAL STATES

The properties of the even and odd negative binomial states are investigated. Mainly we concentrate on the statistical properties for such states and we consider the squeezing phenomenon by examining the variation in the quadrature variances. Using the Pegg–Barnett formalism of phase operator, the phase probability distributions of the states are discussed, and also the phase and number squeezing with different parameters are studied. The numerical computation results show that the phase probability distributions for the even and odd NBSs can clearly exhibit the different features of quantum effects.

Finite-dimensional even and odd nonlinear pair coherent states and their some nonclassical properties

In this paper a new class of finite-dimensional even and odd nonlinear pair coherent states (EONLPCSs), which can be realized via operating the superposed evolution operators D±(τ) on the state |q, 0), is constructed, then their orthonormalized property, completeness relations and some nonclassical properties are discussed. It is shown that the finite-dimensional EONLPCSs possess normalization and completeness relations. Moreover, the finite-dimensional EONLPCSs exhibit remarkably different sub-Poissonian distributions and phase probability distributions for different values of parameters q,η and ζ.

Wigner Function and Phase Probability Distribution of q-Analogue of Squeezed One-Photon State

In this paper, in terms of the technique of integration within an ordered product (IWOP) of operators and the properties of the inverses of q-deformed annihilation and creation operators, normalizable q-analogue of the squeezed one-photon state, which is quite different from one introduced by Song and Fan [Int. J. Theor. Phys. 41 (2002) 695], is constructed. Moreover, the Wigner function and phase probability distribution of q-analogue of the squeezed one-photon state are examined.

Phase properties of new even and odd nonlinear coherent states

A new kind of even and odd nonlinear coherent states (EONLCSs) is introduced. Using the Pegg–Barnett formalism of phase operator we study the phase probability distributions of the new kind of EONLCSs. The numerical computation results show that the phase probability distributions for the new EONLCSs can clearly exhibit the different features of quantum interference and distinct from those of the ordinary even and odd coherent states (EOCSs) and EONLCSs. Based on the phase probability distributions we investigate the phase and number squeezing of the new EONLCSs. It is found that these states exhibit number squeezing for different ranges of the parameter | λ | .

Properties of the phase evolution of two coupled atoms Raman interacting with squeezed vacuum field

The properties of the phase evolution of two coupled atoms Raman interacting with squeezed vacuum field are studied using the Pegg-Barnett phase theory. The phase probability distribution and variance are calculated. The evolution of the phase probability distribution functions in some cases are given by curves in the polar coordinate system. The influence of Raman interaction between the coupled atoms with squeezed vacuum field, the dipole-dipole interaction between the atoms and the initial states of atoms on the phase properties are discussed.

New even and odd nonlinear coherent states and their non-classical properties

A new kind of even and odd nonlinear coherent states (EONLCS) is constructed. Using the numerical computation method, the non-classical properties such as squeezing, amplitude-squared squeezing, anti-bunching and phase probability distribution of the new EONLCS are investigated. The results show that, in the different ranges of the parameter |λ|, the new EONLCS exhibits amplitude-squared squeezing in the directions Y1 and Y2. The squeezing effect is shown in the direction X2 for new even nonlinear coherent states, and the anti-bunching effect is shown for new odd nonlinear coherent states. Moreover, we find that the new EONLCS exhibit different quntum interference properties by studying the probability distributions of the states.

Some nonclassical properties of a finite dimensional even and odd pair coherent state

The exponential form of even and odd pair coherent state (EOPCS) is constructed. The EOPCS is generalized to a finite dimensional EOPCS in the Hilbert space, and then its orthonormalized property, completeness relations and some noncalssical properties are discussed. It is shown that the finite dimensional EOPCS has normalized and completeness relations, but not orthogonal relations. By virtue of the numerical computation method, we find that, for any value of q, in different ranges of the parameter |ξ| the 5-dimensional EOPCS for the modes 1 and 2 exhibit anti-bunching effect and the photons between the two modes are always correlated. The different peak structures of the phase probability distributions for the 7-dimensional EOPCS show remarkably different quantum interference properties.

Empirical mode decomposition analysis of two different financial time series and their comparison

Analysis of financial time series with,a view to understanding its underlying characteristic features has been the recent focus of scientists and practitioners studying the financial market. One of the key attributes of a time series is its periodicity. Because of their quasi-periodic nature, the financial time series do not reveal their periodicity clearly. One of the recent developments in time signal analysis is the Hilbert–Huang empirical mode decomposition (EMD) method, which elegantly brings out the underlying periodicity of any time-series. Not many efforts have been made to utilise this technique in qualitative analysis of financial time series. In the present study, we have used the EMD technique to analyse two different financial time series, viz., the daily movement of NIFTY index value of National Stock Exchange, India, and that of Hong Kong AOI, Hong Kong Stock Exchange from July 1990 to January 2006. The returns of the two indices are shown to have strikingly similar probability distribution. The IMF phase and amplitude probability distribution of the two indices also reveal striking similarity. This indicates a remarkable similarity of trading behaviour in the two markets. Considering the geographical and political separation of the two, this indeed is an important discovery.

Manipulating the phase of a single-mode micromaser by polarized three-level atoms

We investigate the phase probability distribution (PPD) of a single-mode micromaser pumped by atoms injected in the most general case, i.e. in the superposition of the upper, intermediate and lower states by the Monte Carlo wave function approach. The phase properties of the cavity mode are greatly influenced by the relative phases and the amplitudes of the polarized atoms, and the detunings between the atom and cavity. The cavity field has a single preferred phase if the cavity is pumped by the atoms in the superposition of the upper and intermediate states or of the intermediate and lower states. However, a double-peak feature appears in the PPD of the cavity field when the cavity is pumped by the atoms in the superposition of the upper and lower states. With appropriate detunings, the double peaks become narrower and more remarkable, which shows the better defined phase of the cavity field, as compared to the resonant case. The PPD displays complicated characteristics when the cavity is pumped by the atoms in the superposition of the upper, intermediate and lower states. The phase distribution changes from a single peak to double peaks and to another single peak when we modulate the phase of the intermediate state, which has been explained in the semi-classical radiation theory.

Crystal Structure of the Yersinia enterocolitica Type III Secretion Chaperone SycT

Several Gram-negative pathogens deploy type III secretion systems (TTSSs) as molecular syringes to inject effector proteins into host cells. Prior to secretion, some of these effectors are accompanied by specific type III secretion chaperones. The Yersinia enterocolitica TTSS chaperone SycT escorts the effector YopT, a cysteine protease that inactivates the small GTPase RhoA of targeted host cells. We solved the crystal structure of SycT at 2.5 angstroms resolution. Despite limited sequence similarity among TTSS chaperones, the SycT structure revealed a global fold similar to that exhibited by other structurally solved TTSS chaperones. The dimerization domain of SycT, however, differed from that of all other known TTSS chaperone structures. Thus, the dimerization domain of TTSS chaperones does not likely serve as a general recognition pattern for downstream processing of effector/chaperone complexes. Yersinia Yop effectors are bound to their specific Syc chaperones close to the Yop N termini, distinct from their catalytic domains. Here, we showed that the catalytically inactive YopT(C139S) is reduced in its ability to bind SycT, suggesting an ancillary interaction between YopT and SycT. This interaction could maintain the protease inactive prior to secretion or could influence the secretion competence and folding of YopT.

Mutually unbiased phase states, phase uncertainties, and Gauss sums

Mutually unbiased bases (MUBs), which are such that the inner product between two vectors in different orthogonal bases is a constant equal to 1/sqrt{d), with d the dimension of the finite Hilbert space, are becoming more and more studied for applications such as quantum tomography and cryptography, and in relation to entangled states and to the Heisenberg-Weil group of quantum optics. Complete sets of MUBs of cardinality d+1 have been derived for prime power dimensions d=p^m using the tools of abstract algebra. Presumably, for non prime dimensions the cardinality is much less. Here we reinterpret MUBs as quantum phase states, i.e. as eigenvectors of Hermitean phase operators generalizing those introduced by Pegg & Barnett in 1989. We relate MUB states to additive characters of Galois fields (in odd characteristic p) and to Galois rings (in characteristic 2). Quantum Fourier transforms of the components in vectors of the bases define a more general class of MUBs with multiplicative characters and additive ones altogether. We investigate the complementary properties of the above phase operator with respect to the number operator. We also study the phase probability distribution and variance for general pure quantum electromagnetic states and find them to be related to the Gauss sums, which are sums over all elements of the field (or of the ring) of the product of multiplicative and additive characters. Finally, we relate the concepts of mutual unbiasedness and maximal entanglement. This allows to use well studied algebraic concepts as efficient tools in the study of entanglement and its information aspects

Estimating statistical properties of Eddy-current signals from steam generator tubes

We develop a model for characterizing amplitude and phase probability distributions of eddy-current signals and propose a maximum likelihood (ML) method for estimating the amplitude and phase distribution parameters from measurements corrupted by additive complex white Gaussian noise. The squared amplitudes and phases of the potential defect signals are modeled as independent, identically distributed (i.i.d.) random variables following gamma and von Mises distributions, respectively. Newton-Raphson iteration is utilized to compute the ML estimates of the unknown parameters. We also compute Crame/spl acute/r-Rao bounds (CRBs) for the unknown parameters and discuss initialization of the Newton-Raphson iteration. The proposed method is applied to analyze rotating-probe eddy-current data from steam-generator tube inspection in nuclear power plants. The obtained estimates can be utilized for maximum a posteriori (MAP) signal phase and amplitude estimation, as well as efficient feature extractors in a defect classification scheme. We present numerical examples with both real and simulated data to demonstrate the performance of the proposed methods.