Phase Space Theory Research Articles

Wavelet Transformation and Wigner-Husimi Distribution Function

We find that the optical wavelet transformation can be used to study the Husimi distribution function in phase space theory of quantum optics. We prove that the Husimi distribution function of a quantum state |ψ〉 is just the modulus square of the wavelet transform of \(e^{-x^{2}/2}\) with ψ(x) being the mother wavelet up to a Gaussian function. Thus a convenient approach for calculating various Husimi distribution functions of miscellaneous quantum states is presented.

A Quantum Version of Wigner’s Transition State Theory

A quantum version of a recent realization of Wigner’s transition state theory in phase space is presented. The theory developed builds on a quantum normal form which locally decouples the quantum dynamics near the transition state to any desired order in \({\hbar}\). This leads to an explicit algorithm to compute cumulative quantum reaction rates and the associated Gamov–Siegert resonances with high accuracy. This algorithm is very efficient since, as opposed to other approaches, it requires no quantum time propagation.

Photochemical formation of HCO and CH3 on the ground S (A1′) state of CH3CHO

The dynamics of the photodissociation of CH(3)CHO into CH(3) + HCO products have been investigated at energies between 30,953 and 31,771 cm(-1), spanning the threshold for radical production on the triplet (T(1)) surface. A barrierless pathway to CH(3) + HCO radical products formed on the ground state (S(0)) surface was discovered and established to be an important reaction channel in acetaldehyde photodissociation throughout this wavelength range. HCO laser induced fluorescence (LIF) spectra recorded from CH(3)CHO dissociated above and below the T(1) barrier energy are quite different; HCO produced on S(0) yields a more congested LIF spectrum with sharp rotational transitions, while HCO formed on the T(1) surface displays fewer, more intense, Doppler-broadened lines. These differences have been further explored in the populations of the HCO K(a) = 1 doublets. Despite the upper and lower levels being almost isoenergetic, HCO formed on T(1) preferentially populates the upper K(c) state due to the geometry of the T(1) transition state structure. In contrast, HCO formed on S(0) produces equal population in each of the upper and lower K(a) = 1 components. Product state distributions (PSDs) showed that HCO formed on S(0) is born with an approximately statistical distribution of population in the available product states, modeled well by phase space theory. HCO formed on the T(1) surface, in contrast, has a PSD that can be characterized as arising from "impulsive" dynamics. Previous discrepancies in the height of the T(1) barrier are discussed following the observation that, once the T(1) channel is energetically accessible, there is competition between the S(0) and T(1) pathways, with the dominance of the triplet channel increasing with increasing photolysis energy.

Effects of reactant rotational excitation on H + O2→ OH + O reaction rate constant: quantum wave packet, quasi-classical trajectory and phase space theory calculations

We examine the impact of initial rotational excitation on the reactivity of the H + O(2)--> OH + O reaction. Accurate Chebyshev wave packet calculations have been carried out for the upsilon(i) = 0, j(i) = 9 initial state of O(2) and the J = 50 partial wave. In addition, we present Gaussian-weighted quasi-classical trajectory and phase space theory calculations of the integral cross section and thermal rate constant for the title reaction. These theoretical results suggest that the initial rotational excitation significantly enhances reactivity with an amount comparable to the effect of initial vibrational state excitation. The inclusion of internally excited reactants is shown to improve the agreement with experimental rate constant.

Translational, rotational and vibrational energy partitioning in the sequential loss of carbon dimers from fullerenes

The sequential thermal dissociation of up to five carbon dimers from neutral, singly and doubly charged C(60) molecules is theoretically investigated in the framework of phase space theory. Using a semiclassical treatment of vibrations and rotations, we quantify the amount of kinetic energies released in the form of translation, rotation, and vibration under realistic experimental conditions. Our results reveal that translational and vibrational energies of the dimers are nearly equilibrated after a few emissions, whereas the rotational contribution lies far below equipartition. An approximate treatment in which dimers are rotationally and vibrationally frozen essentially leads to the same conclusions.

Specific Rate Constants k(E) of the Dissociation of the Halobenzene Ions: Analysis by Statistical Unimolecular Rate Theories

Specific rate constants k(E) of the dissociation of the halobenzene ions C6H5X+ --> C6H5+ + X* (X* = Cl, Br, and I) were measured over a range of 10(3)-10(7) s-1 by threshold photoelectron-photoion coincidence (TPEPICO) spectroscopy. The experimental data were analyzed by various statistical unimolecular rate theories in order to derive the threshold energies E0. Although rigid activated complex RRKM theory fits the data in the experimentally measured energy range, it significantly underestimates E0 for chloro- and bromobenzene. Phase space theory (PST) does not fit the experimentally measured rates. A parametrized version of the variational transition state theory (VTST) as well as a simplified version of the statistical adiabatic channel model (SSACM) incorporating an energy dependent rigidity factor provide excellent fits to the experimental data and predict the correct dissociation energies. Although both approaches have just two adjustable parameters, one of which is E0, SSACM is effective and particularly simple to apply.

Topological field theory of time-reversal invariant insulators

We show that the fundamental time-reversal invariant (TRI) insulator exists in $4+1$ dimensions, where the effective-field theory is described by the $(4+1)$-dimensional Chern-Simons theory and the topological properties of the electronic structure are classified by the second Chern number. These topological properties are the natural generalizations of the time reversal-breaking quantum Hall insulator in $2+1$ dimensions. The TRI quantum spin Hall insulator in $2+1$ dimensions and the topological insulator in $3+1$ dimensions can be obtained as descendants from the fundamental TRI insulator in $4+1$ dimensions through a dimensional reduction procedure. The effective topological field theory and the ${Z}_{2}$ topological classification for the TRI insulators in $2+1$ and $3+1$ dimensions are naturally obtained from this procedure. All physically measurable topological response functions of the TRI insulators are completely described by the effective topological field theory. Our effective topological field theory predicts a number of measurable phenomena, the most striking of which is the topological magnetoelectric effect, where an electric field generates a topological contribution to the magnetization in the same direction, with a universal constant of proportionality quantized in odd multiples of the fine-structure constant $\ensuremath{\alpha}={e}^{2}∕\ensuremath{\hbar}c$. Finally, we present a general classification of all topological insulators in various dimensions and describe them in terms of a unified topological Chern-Simons field theory in phase space.

Quantum Mechanical Capture/Phase Space Theory Calculation of the Rate Constants for the Complex-Forming CH + H2 Reaction

Six-dimensional wave packet calculations on an accurate potential energy surface are used to obtain the quantum mechanical capture (QM C) probabilities for CH + H(2) corresponding to a variety of total angular momenta and internal reactant states. Rate constant calculations are made feasible by employing a Monte Carlo based sampling procedure. The QM C probabilities alone are also used to estimate the high pressure CH + H(2) rate constants corresponding to stabilization or CH(3) formation. The rate constants for CH + H(2) --> CH(2) + H reaction in the low pressure limit are obtained by combining the QM C probabilities with a phase space theory (PST) approximation for product formation from the complex. Our results are compared with the experimental results of Brownsword et al. (J. Chem. Phys. 1997, 106, 7662), as well as with purely classical PST calculations. The QM C probabilities are shown to be highly dependent on the initial rotational states of the reactants corresponding to orientational restrictions on complex formation. Consistent with this, our QM C high pressure rate constants for CH(3) formation are lower than the purely classical PST rate constants. These QM C rate constants also are in reasonable accord with experiment. A similar but somewhat more subtle picture emerges regarding the QM C/PST rate constants for CH(2) + H formation.

Collisional excitation of water in warm astrophysical media

Context: The interpretation of water line emission from infrared and submillimetre observations requires a detailed knowledge of collisional rate coefficients over a wide range of levels and temperatures. Aims: We attempt to determine rotational and rovibrational rate coefficients for H2O colliding with both H2 and electrons in warm, molecular gas. Methods: Pure rotational rates are derived by extrapolating published data using a new method partly based on the information (phase space) theory of Levine and co-workers. Ro-vibrational rates are obtained using vibrational relaxation data available in the literature and by assuming a complete decoupling of rotation and vibration. Results: Rate coefficients were obtained for the lowest 824 ro-vibrational levels of H2O in the temperature range 200-5000 K. Our data is expected to be accurate to within a factor of ~5 for the highest rates (?10-11 cm3 s-1). Smaller rates, including the ro-vibrational ones, should be generally accurate to within an order of magnitude. As a first application of this data, we show that vibrationally excited water emission observed in evolved stars is expected to be at least partly excited by means of collisions. Tables A.1-A.4 are only available in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/492/257

Semi-classical approach for Anosov diffeomorphisms and Ruelle resonances

In this paper, we show that some spectral properties of Anosov diffeomorphisms can be obtained by semi-classical analysis. In particular the Ruelle resonances which are eigenvalues of the Ruelle transfer operator acting in suitable anisotropic Sobolev spaces and which govern the decay of dynamical correlations, can be treated as the quantum resonances of open quantum systems in the Aguilar-Baslev-Combes theory or the more recent Helffer-Sjostrand phase-space theory.

Quantitative (υ, N, Ka) Product State Distributions near the Triplet Threshold for the Reaction H2CO → H + HCO Measured by Rydberg Tagging and Laser-Induced Fluorescence

In this paper, we report quantitative product state distributions for the photolysis of H2CO --> H + HCO in the triplet threshold region, specifically for several rotational states in the 2(2)4(3) and 2(3)4(1) H2CO vibrational states that lie in this region. We have combined the strengths of two complementary techniques, laser-induced fluorescence for fine resolution and H atom Rydberg tagging for the overall distribution, to quantify the upsilon, N, and Ka distributions of the HCO photofragment formed via the singlet and triplet dissociation mechanisms. Both techniques are in quantitative agreement where they overlap and provide calibration or benchmarks that permit extension of the results beyond that possible by each technique on its own. In general agreement with previous studies, broad N and Ka distributions are attributed to reaction on the S0 surface, while narrower distributions are associated with reaction on T1. The broad N and Ka distributions are modeled well by phase space theory. The narrower N and Ka distributions are in good agreement with previous quasi-classical trajectory calculations on the T1 surface. The two techniques are combined to provide quantitative vibrational populations for each initial H2CO vibrational state. For dissociation via the 2(3)4(1) state, the average product vibrational energy (15% of E(avail)) was found to be about half of the rotational energy (30% of E(avail)), independent of the initial H2CO rotational state, irrespective of the singlet or triplet mechanism. For dissociation via the 2(2)4(3) state, the rotational excitation remained about 30% of E(avail), but the vibrational excitation was reduced.

Study of the H+O2 reaction by means of quantum mechanical and statistical approaches: The dynamics on two different potential energy surfaces

The possible existence of a complex-forming pathway for the H+O(2) reaction has been investigated by means of both quantum mechanical and statistical techniques. Reaction probabilities, integral cross sections, and differential cross sections have been obtained with a statistical quantum method and the mean potential phase space theory. The statistical predictions are compared to exact results calculated by means of time dependent wave packet methods and a previously reported time independent exact quantum mechanical approach using the double many-body expansion (DMBE IV) potential energy surface (PES) [Pastrana et al., J. Phys. Chem. 94, 8073 (1990)] and the recently developed surface (denoted XXZLG) by Xu et al. [J. Chem. Phys. 122, 244305 (2005)]. The statistical approaches are found to reproduce only some of the exact total reaction probabilities for low total angular momenta obtained with the DMBE IV PES and some of the cross sections calculated at energy values close to the reaction threshold for the XXZLG surface. Serious discrepancies with the exact integral cross sections at higher energy put into question the possible statistical nature of the title reaction. However, at a collision energy of 1.6 eV, statistical rotationally resolved cross sections managed to reproduce the experimental cross sections for the H+O(2)(v=0,j=1)-->OH(v(')=1,j('))+O process reasonably well.

Calculations on the Formation Rates and Mechanisms for CnH Anions in Interstellar and Circumstellar Media

The rate coefficients for the radiative attachment reactions between the radicals CnH ( -->n = 2?8) and electrons have been calculated with the aid of quantum chemistry using a phase-space theory in which strong coupling exists among the ground and any excited anion electronic states with the same spin. The results confirm that the process increases in efficiency with the size of the radical. For -->n ? 6, the rate coefficients lie at the collisional limit, in agreement with earlier estimates. For -->n = 4,5, the new results are larger than the old estimates. The calculated rate coefficient for -->C4H + e? is now much too large to explain the current observed abundance ratio of C4H?/C4H in IRC +10216 and L1527 and its upper limit in TMC-1. It is quite possible that electronic coupling is weak, and that so-called dipole-bound and other states must act as doorways to radiative attachment. We have also calculated potential surfaces for dissociative attachment starting with the carbenes H2C2m ( -->m = 2?4) and leading to the syntheses of the anions C2mH?.

Computational modeling of beam-customization devices for heavy-charged-particle radiotherapy

A model for beam customization with collimators and a range-compensating filter based on the phase-space theory for beam transport is presented for dose distribution calculation in the treatment planning of radiotherapy with protons and heavier ions. Independent handling of pencil beams in conventional pencil-beam algorithms causes unphysical collimator-height dependence in the middle of large fields, which is resolved by the framework comprised of generation, transport, collimation, regeneration, range-compensation and edge-sharpening processes with a matrix of pencil beams. The model was verified to be consistent with measurement and analytic estimation at a submillimeter level in the penumbra of individual collimators with a combinational-collimated carbon-ion beam. The model computation is fast, accurate and readily applicable to pencil-beam algorithms in treatment planning with the capability of combinational collimation to make the best use of the beam-customization devices.

Vibrational overtone initiated unimolecular dissociation of HOCH2OOH and HOCD2OOH: Evidence for mode selective behavior

The vibrational overtone induced unimolecular dissociation of HMHP (HOCH(2)OOH) and HMHP-d(2) (HOCD(2)OOH) into OH and HOCH(2)O (HOCD(2)O) fragments is investigated in the region of the 4nu(OH) and 5nu(OH) bands. The unimolecular dissociation rates in the threshold region, corresponding to the 4nu(OH) band, exhibit measurable differences associated with excitation of the OH stretch of the alcohol versus the peroxide functional group, with the higher energy alcohol OH stretching state exhibiting a slower dissociation rate compared to the lower energy peroxide OH stretch in both HMHP and HMHP-d(2). Predictions using the Rice-Ramsperger-Kassel-Marcus theory give rates that are in reasonably good agreement with the measured dissociation rate for the alcohol OH stretch but considerably differ from the measured rates for the peroxide OH stretch in both isotopomers. The present results are interpreted as suggesting that the extent of intramolecular vibrational energy redistribution (IVR) is different for the two OH stretching states associated with the two functional groups in HMHP, with IVR being substantially less complete for the peroxide OH stretch. Analysis of the OH fragment product state distributions in conjunction with phase-space theory simulation gives a D(0) value of 38+/-0.7 kcal/mole for breaking the peroxide bond in HMHP.

A comparative study of the Si+O2→SiO+O reaction dynamics from quasiclassical trajectory and statistical based methods

The dynamics of the singlet channel of the Si+O(2)-->SiO+O reaction is investigated by means of quasiclassical trajectory (QCT) calculations and two statistical based methods, the statistical quantum method (SQM) and a semiclassical version of phase space theory (PST). The dynamics calculations have been performed on the ground (1)A(') potential energy surface of Dayou and Spielfiedel [J. Chem. Phys. 119, 4237 (2003)] for a wide range of collision energies (E(c)=5-400 meV) and initial O(2) rotational states (j=1-13). The overall dynamics is found to be highly sensitive to the selected initial conditions of the reaction, the increase in either the collisional energy or the O(2) rotational excitation giving rise to a continuous transition from a direct abstraction mechanism to an indirect insertion mechanism. The product state properties associated with a given collision energy of 135 meV and low rotational excitation of O(2) are found to be consistent with the inverted SiO vibrational state distribution observed in a recent experiment. The SQM and PST statistical approaches, especially designed to deal with complex-forming reactions, provide an accurate description of the QCT total integral cross sections and opacity functions for all cases studied. The ability of such statistical treatments in providing reliable product state properties for a reaction dominated by a competition between abstraction and insertion pathways is carefully examined, and it is shown that a valuable information can be extracted over a wide range of selected initial conditions.

Evidence for cluster shape effects on the kinetic energy spectrum in thermionic emission

Experimental kinetic energy release distributions obtained for the thermionic emission from C(n) (-) clusters, 10< or =n< or =20, exhibit significant non-Boltzmann variations. Using phase space theory, these different features are analyzed and interpreted as the consequence of contrasting shapes in the daughter clusters; linear and nonlinear isomers have clearly distinct signatures. These results provide a novel indirect structural probe for atomic clusters associated with their thermionic emission spectra.

QUANTUM PHASE SPACE THEORY BASED ON INTERMEDIATE COORDINATE-MOMENTUM REPRESENTATION

Through the Radon transformation of the normally ordered Wigner operator we introduce two mutually conjugate intermediate coordinate-momentum representations. Based on them we construct the appropriate quantum phase space theory which includes the new Wigner operator adapting to this space. We find that the new Wigner function's marginal distribution for a state |Ψ〉 is just the quantum tomogram of the state |Ψ〉.

Progress in predictability studies in China (2003–2006)

Since the last International Union of Geodesy and Geophysics General Assembly (2003), predictability studies in China have made significant progress. For dynamic forecasts, two novel approaches of conditional nonlinear optimal perturbation and nonlinear local Lyapunov exponents were proposed to cope with the predictability problems of weather and climate, which are superior to the corresponding linear theory. A possible mechanism for the “spring predictability barrier” phenomenon for the El Nino-Southern Oscillation (ENSO) was provided based on a theoretical model. To improve the forecast skill of an intermediate coupled ENSO model, a new initialization scheme was developed, and its applicability was illustrated by hindcast experiments. Using the reconstruction phase space theory and the spatio-temporal series predictive method, Chinese scientists also proposed a new approach to improve dynamical extended range (monthly) prediction and successfully applied it to the monthly-scale predictability of short-term climate variations. In statistical forecasts, it was found that the effects of sea surface temperature on precipitation in China have obvious spatial and temporal distribution features, and that summer precipitation patterns over east China are closely related to the northern atmospheric circulation. For ensemble forecasts, a new initial perturbation method was used to forecast heavy rain in Guangdong and Fujian Provinces on 8 June 1998. Additionally, the ensemble forecast approach was also used for the prediction of a tropical typhoons. A new downscaling model consisting of dynamical and statistical methods was provided to improve the prediction of the monthly mean precipitation. This new downscaling model showed a relatively higher score than the issued operational forecast.

Publisher's Note: Phase-space theory for dispersive detectors of superconducting qubits [Phys. Rev. B76, 104510 (2007)

Publisher's Note: Phase-space theory for dispersive detectors of superconducting qubits [Phys. Rev. B<b>76</b>, 104510 (2007)