Complex temporal patterns in molecular dynamics:a direct measure of the phase-space exploration by the trajectory at macroscopic time scales

Computer simulated trajectories of bulk water molecules form complex spatiotemporal structures at the picosecond time scale. This intrinsic complexity, which underlies the formation of molecular structures at longer time scales, has been quantified using a measure of statistical complexity. The method estimates the information contained in the molecular trajectory by detecting and quantifying temporal patterns present in the simulated data (velocity time series). Two types of temporal patterns are found. The first, defined by the short-time correlations corresponding to the velocity autocorrelation decay times (â‰0.1â€ps), remains asymptotically stable for time intervals longer than several tens of nanoseconds. The second is caused by previously unknown longer-time correlations (found at longer than the nanoseconds time scales) leading to a value of statistical complexity that slowly increases with time. A direct measure based on the notion of statistical complexity that describes how the trajectory explores the phase space and independent from the particular molecular signal used as the observed time series is introduced. © 2008 The American Physical Society.

Molecular phase space transport in water:non-stationary random walk model

Molecular transport in phase space is crucial for chemical reactions because it defines how pre-reactive molecular configurations are found during the time evolution of the system. Using Molecular Dynamics (MD) simulated atomistic trajectories we test the assumption of the normal diffusion in the phase space for bulk water at ambient conditions by checking the equivalence of the transport to the random walk model. Contrary to common expectations we have found that some statistical features of the transport in the phase space differ from those of the normal diffusion models. This implies a non-random character of the path search process by the reacting complexes in water solutions. Our further numerical experiments show that a significant long period of non-stationarity in the transition probabilities of the segments of molecular trajectories can account for the observed non-uniform filling of the phase space. Surprisingly, the characteristic periods in the model non-stationarity constitute hundreds of nanoseconds, that is much longer time scales compared to typical lifetime of known liquid water molecular structures (several picoseconds).

Using phase-space localized basis functions to obtain vibrational energies of molecules

For decades scientists have attempted to use ideas of classical mechanics to choose basis functions for calculating spectra. The hope is that a classically-motivated basis set will be small because it covers only the dynamically important part of phase space. One popular idea is to use phase space localized (PSL) basis functions. This thesis improves on previous efforts to use PSL functions and examines the usefulness of these improvements. Because the overlap matrix, in the matrix eigenvalue problem obtained by using PSL functions with the variational method, is not an identity, it is costly to use iterative methods to solve the matrix eigenvalue problem. We show that it is possible to circumvent the orthogonality (overlap) problem and use iterative eigensolvers. We also present an altered method of calculating the matrix elements that improves the performance of the PSL basis functions, and also a new method which more efficiently chooses which PSL functions to include. These improvements are applied to a variety of single well molecules. We conclude that for single minimum molecules, the PSL functions are inferior to other basis functions. However, the ideas developed here can be applied to other types of basis functions, and PSL functions may be useful for multi-well systems.

Bit-stream-based space vector modulators

Bit-stream-based control, which uses one bit wide signals to control power electronics applications, is a new approach for controller design in power electronic systems. This study presents a novel family of three-phase space vector modulators, which are based on the bit-stream technique and suitable for three-phase inverter systems. Each of the proposed modulators simultaneously converts a two-phase reference to the three-phase domain and reduces switching frequencies to reasonable levels. The modulators do not require carrier oscillators, trigonometric functions or, in some cases, sector detectors. A complete three-phase modulator can be implemented in as few as 102 logic elements. The performance of the proposed modulators is compared through simulation and experimental testing of a 6 kW, three-phase DC-to-AC inverter. Subject to limits on the modulation index, the proposed modulators deliver spread-spectrum output currents with total harmonic distortion comparable to a standard carrier-based space vector pulse width modulator.

A Bit-Stream based space vector modulator

Bit-Stream based control, which uses one bit wide signals to control power electronics applications, is a new approach for controller design in power electronic systems. Bit-Stream signals are inherently high frequency in nature, and as such some form of down sampling or modulating is essential to avoid excessive switching losses. This paper presents a novel three-phase space vector modulator, which is based on the Bit-Stream technique and suitable for standard three-phase inverter systems. The proposed modulator simultaneously converts a two phase reference to the three-phase domain and reduces switching frequencies to reasonable levels. The modulator consumes relatively few logic elements and does not require sector detectors, carrier oscillators or trigonometric functions. The performance of the modulator was evaluated using ModelSim. Results indicate that, subject to limits on the modulation index, the proposed modulator delivers a spread-spectrum output with total harmonic distortion comparable to standard space vector pulse width modulation techniques.

Twist phase in Gaussian-beam optics

The recently discovered twist phase is studied in the context of the full ten-parameter family of partially coherent general anisotropic Gaussian Schell-model beams. It is shown that the nonnegativity requirement on the cross-spectral density of the beam demands that the strength of the twist phase be bounded from above by the inverse of the transverse coherence area of the beam. The twist phase as a two-point function is shown to have the structure of the generalized Huygens kernel or Green's function of a first-order system. The ray-transfer matrix of this system is exhibited. Wolf-type coherent-mode decomposition of the twist phase is carried out. Imposition of the twist phase on an otherwise untwisted beam is shown to result in a linear transformation in the ray phase space of the Wigner distribution. Though this transformation preserves the four-dimensional phase-space volume, it is not symplectic and hence it can, when impressed on a Wigner distribution, push it out of the convex set of all bona fide Wigner distributions unless the original Wigner distribution was sufficiently deep into the interior of the set.

Wigner distributions for finite-state systems without redundant phase-point operators

We set up Wigner distributions for N-state quantum systems following a Dirac-inspired approach. In contrast to much of the work in this study, requiring a 2N x 2N phase space, particularly when N is even, our approach is uniformly based on an N x N phase-space grid and thereby avoids the necessity of having to invoke a `quadrupled' phase space and hence the attendant redundance. Both N odd and even cases are analysed in detail and it is found that there are striking differences between the two. While the N odd case permits full implementation of the marginal property, the even case does so only in a restricted sense. This has the consequence that in the even case one is led to several equally good definitions of the Wigner distributions as opposed to the odd case where the choice turns out to be unique.

Anomalous structural and dynamical phase transitions of soft colloidal binary mixtures

We report microscopic structural and dynamical measurements on binary mixtures of homopolymers and polymer grafted nanoparticles at high densities in good solvent. We find strong and unexpected anomalies in the structure and dynamics of these binary mixtures, including appearance of spontaneous orientational alignment, as a function of added homopolymers of different molecular weights. Our experiments point to the possibility of exploiting the phase space in density and homopolymer size, of such hybrid systems, to create new materials with novel structural and physical properties.

Anomalous phase transitions in soft colloid-polymer binary mixtures

We have shown earlier [1] that these PGNPs resemble star polymers or spherical brushes in terms of their morphology in the melt. However, these particles show dynamics in melt which is quite different from other soft colloidal particles. Since most of the work on soft colloidal particles have been performed in solutions we have now explored the phase behavior of the PGNPs in good solvent using microscopic structural and dynamical measurements on binary mixtures of homopolymers and soft colloids consisting of polymer grafted nanoparticles. We observe anomalous structural and dynamical phase transitions of these binary mixtures, including appearance of spontaneous orientational alignment and logarithmic structural relaxations, as a function of added homopolymers of different molecular weights. Our experiments points to the possibility of exploiting the phase space in density and homopolymer size, of such hybrid systems, to create new materials with unique properties.

Structural determination of a new phase of monoclinic BaTb2Mn2O7

A new phase of monoclinic BaTb2Mn2O7 with extra superlattice lines in addition to the usual orthorhombic X-ray diffraction patterns was prepared and a Rietveld refinement was applied to analyze the crystal structure using X-ray powder diffraction data at room temperature. The refined lattice parameters were a = 0.54918(8) nm, b = 2.0149(5) nm, c = 0.54922(9) nm, and beta = 90.62degrees with the space group A2/m (no. 12). The MnO6 oxygen octahedron has distortion and tilts around a-axis by about 7degrees each other in the reverse direction.

Geometric-phase backaction in a mesoscopic qubit-oscillator system

We illustrate a reverse Von Neumann measurement scheme in which a geometric phase induced on a quantum harmonic oscillator is measured using a microscopic qubit as a probe. We show how such a phase, generated by a cyclic evolution in the phase space of the harmonic oscillator, can be kicked back on the qubit, which plays the role of a quantum interferometer. We also extend our study to finite-temperature dissipative Markovian dynamics and discuss potential implementations in micro-and nanomechanical devices coupled to an effective two-level system.

Testing genuine multipartite nonlocality in phase spacea

We demonstrate genuine three-mode nonlocality based on phase-space formalism. A Svetlichny-type Bell inequality is formulated in terms of the s-parametrized quasiprobability function. We test such a tool using exemplary forms of three-mode entangled states, identifying the ideal measurement settings required for each state. We thus verify the presence of genuine three-mode nonlocality that cannot be reproduced by local or nonlocal hidden variable models between any two out of three modes. In our results, GHZ- and W-type nonlocality can be fully discriminated. We also study the behavior of genuine tripartite nonlocality under the effects of detection inefficiency and dissipation induced by local thermal environments. Our formalism can be useful to test the sharing of genuine multipartite quantum correlations among the elements of some interesting physical settings, including arrays of trapped ions and intracavity ultracold atoms. DOI: 10.1103/PhysRevA.87.022123

High-pressure phase equilibrium in the {carbon dioxide (1) + 1-chloropropane (2)} binary system

Abstract The current study reports original vapour-liquid equilibrium (VLE) for the system {CO2 (1) + 1-chloropropane (2)}. The measurements have been performed over the entire pressure-composition range for the (303.15, 313.15 and 328.15) K isotherms. The values obtained have been used for comparison of four predictive approaches, namely the equation of state (EoS) of Peng and Robinson (PR), the Soave modification of Benedict–Webb–Rubin (SBWR) EoS, the Critical Point-based Revised Perturbed-Chain Association Fluid Theory (CP-PC-SAFT) EoS, and the Conductor-like Screening Model for Real Solvents (COSMO-RS). It has been demonstrated that the three EoS under consideration yield similar and qualitatively accurate predictions of VLE, which is not the case for the COSMO-RS model examined. Although CP-PC-SAFT EoS exhibits only minor superiority in comparison with PR and SBWR EoS in predicting VLE in the system under consideration, its relative complexity can be justified when taking into account the entire thermodynamic phase space and, in particular, considering the liquid densities and sound velocities over a wider pressure-volume-temperature range.

Fock space for fermion-like lattices and the linear Glauber model

The concept of Fock space representation is developed to deal with stochastic spin lattices written in terms of fermion operators. A density operator is introduced in order to follow in parallel the developments of the case of bosons in the literature. Some general conceptual quantities for spin lattices are then derived, including the notion of generating function and path integral via Grassmann variables. The formalism is used to derive the Liouvillian of the d-dimensional Linear Glauber dynamics in the Fock-space representation. Then the time evolution equations for the magnetization and the two-point correlation function are derived in terms of the number operator. (C) 2008 Elsevier B.V. All rights reserved.