Mixed Quantum/Classical Theory (MQCT) for Rotationally and Vibrationally Inelastic Scattering and Its Application to the Molecules of Astrochemical Importance

This thesis presents developments and applications of the mixed quantum/classical theory (MQCT) for inelastic scattering. In this approach, translational motion of collision partners is treated classically, while the internal degrees of freedom – rotational and/or vibrational motion – are treated quantum mechanically. Within this framework calculations of rotationally inelastic cross sections are carried out in a broad range of collision energies and results are compared against the exact full quantum data for several real systems. For CO +He, N2 + Na and H2 + He the agreement is excellent through six orders of magnitude range of cross sections values and for energies 1 \u3c E \u3c 10000 cm-1. Elastic and differential cross section for N2 + Na are described very accurately. For ro-vibrational transitions in CO + He and H2 +He MQCT reproduces full quantum results even for highly excited rotational states. For H2O + He it is found that at lower energies the typical errors for cross sections are on the order of 10%, which is acceptable. It is showed that computational cost of the fully-coupled MQCT scales as n2- 3, where n is the number of channels which is far more favorable in comparison with full quantum scaling n5-6. This enables calculations on larger molecules and at higher collision energies, than was possible using the standard approach. The largest system ever considered for rotational scattering, HCOOCH3 + He, is also treated by MQCT. At energies where quantum results are available (≤ 30 cm-1) the agreement is found very good. Then MQCT calculations for this system are extended up to E = 1000 cm-1. Finally, theoretical framework for treatment of molecule + molecule scattering is developed and applied to H2+H2 and N2+H2 systems where excellent agreement with exact quantum results is found. We also apply MQCT method to H2O + H2O rotationally inelastic scattering and obtain the first and only data for this process in a broad range of collisional energies. Success of MQCT makes this theory a practical tool for obtaining the state-to-state transition rates for astrochemical modeling and other applications

Understanding diatomic molecular dynamics triggered by a few-cycle pulse

Doctor of PhilosophyPhysicsBrett D. EsryIn strong field physics, complex atomic and molecular motions can be triggered and steered by an ultrashort strong field. With a given pulse as an carrier-envelope form, E(t) = E₀(t) cos(ωt + φ), we established our photon-phase formalism to decompose the solution of a time-dependent Schrödinger equation in terms of photons. This formalism is further implemented into a general analysis scheme that allows extract photon information direct from the numerical solution. The φ-dependence of any observables then can be understood universally as an interference effect of different photon channels. With this established, we choose the benchmark system H₂⁺ to numerically study its response to an intense few-cycle pulse. This approach helps us identify electronic, rovibrational transitions in terms of photon channels, allowing one to discuss photons in the strong field phenomena quantitatively. Furthermore, the dissociation pathways are visualized in our numerical calculations, which help predicting the outcome of dissociation. Guided by this photon picture, we explored the dissociation in a linearly polarized pulse of longer wavelengths (compared to the 800 nm of standard Ti:Saphire laser). We successfully identified strong post-pulse alignment of the dissociative fragments and found out that such alignment exists even for heavy molecules. More significant spatial asymmetry is confirmed in the longer wavelength regime, because dissociation is no longer dominated by a single photon process and hence allowed for richer interference. Besides, quantitative comparison between theory and experiment have been conducted seeking beyond the qualitative features. The discrepancy caused by different experimental inputs allows us to examine the assumptions made in the experiment. We also extend numerical studies to the dissociative ionization of H₂ by modeling the ionization

Extreme Regimes in Quantum Gravity

The thesis is divided into two parts. In the first part the low-energy limit of quantum gravity is analysed, whereas in the second we deal with the high-energy domain. In the first part, by applying the effective field theory point of view to the quantization of general relativity, detectable, though tiny, quantum effects in the position of Newtonian Lagrangian points of the Earth-Moon system are found. In order to make more realistic the quantum corrected model proposed, the full three-body problem where the Earth and the Moon interact with a generic massive body and the restricted four-body problem involving the perturbative effects produced by the gravitational presence of the Sun in the Earth-Moon system are also studied. After that, a new quantum theory having general relativity as its classical counterpart is analysed. By exploiting this framework, an innovative interesting prediction involving the position of Lagrangian points within the context of general relativity is described. Furthermore, the new pattern provides quantum corrections to the relativistic coordinates of Earth-Moon libration points of the order of few millimetres. The second part of the thesis deals with the Riemannian curvature characterizing the boosted form assumed by the Schwarzschild-de Sitter metric. The analysis of the Kretschmann invariant and the geodesic equation shows that the spacetime possesses a "scalar curvature singularity" within a 3-sphere and that it is possible to define what we here call "boosted horizon", a sort of elastic wall where all particles are surprisingly pushed away, suggesting that such "boosted geometries" are ruled by a sort of "antigravity effect". Eventually, the equivalence with the coordinate shift method is invoked in order to demonstrate that all $\delta^2$ terms appearing in the Riemann curvature tensor give vanishing contribution in distributional sense.Comment: Phd thesis in Fundamental and Applied Physics presented at University "Federico II" (Naples, Italy) on 29th April 201

Molecular Dynamics Simulation

Condensed matter systems, ranging from simple fluids and solids to complex multicomponent materials and even biological matter, are governed by well understood laws of physics, within the formal theoretical framework of quantum theory and statistical mechanics. On the relevant scales of length and time, the appropriate ‘first-principles’ description needs only the Schroedinger equation together with Gibbs averaging over the relevant statistical ensemble. However, this program cannot be carried out straightforwardly—dealing with electron correlations is still a challenge for the methods of quantum chemistry. Similarly, standard statistical mechanics makes precise explicit statements only on the properties of systems for which the many-body problem can be effectively reduced to one of independent particles or quasi-particles. [...

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described