No description available.

Strong electron correlations in electronic structure theory are purely quantum effects arising as a result of degeneracies in molecules and materials, and exhibit significantly different yet interesting characters than do weak correlations. Although weak correlations have recently been able to be described very efficiently and accurately within single particle pictures, less known are good prescriptions for treating strong correlations efficiently. Brute-force calculations of strong correlations in wave function theories tend to be very computationally-intensive, and are usually limited to small molecules for applications. Breaking symmetry in a mean-field approximation is an efficient alternative to acquire strong correlations with, in many cases, qualitatively accurate results. The symmetry broken in quantum chemistry has been traditionally of spin, in so-called unrestricted methods, which typically break spatial symmetry as a consequence, and vice versa, in most situations. In this work, we present a novel approach to accurately describing strong correlations with a mean-field cost by means of Hartree- Fock-Bogoliubov (HFB) theory. We are inspired by the number-symmetry-breaking in HFB, which, with an attractive particle interaction, accounts for strong correlations, while maintaining spin and spatial symmetry. We show that this attractive interaction must be restricted to the chemically-relevant orbitals in an active space to obtain physically meaningful results. With such constraints, our constrained pairing mean-field theory (CPMFT) can accurately describe potential energy curves of various strongly-correlated molecular systems, by cleanly separating strong and weak correlations. To achieve the correct dissociation limits in hetero-atomic molecules, we have modified our CPMFT functional by adding asymptotic constraints. We also include weak correlations by combining CPMFT with density functional theory for chemically accurate results, and reveal the connection between CPMFT and traditional unrestricted methods. The similarity between CPMFT and unrestricted methods leads us to the idea of constrained active space unrestricted mean-field approaches. Motivated by CPMFT, we partially retrieve spin-symmetry that has been fully broken in unrestricted methods. We allow symmetry breaking only in an active space. This constrained unrestricted Hartree-Fock (CUHF) is an interpolation between two extrema: the fully broken-symmetry solution and the symmetry preserved solution. This thesis defines the theory behind and reports the results of CUHF. We first show that, if an active space is chosen to include only open-shell electrons, CUHF reduces to restricted open-shell Hartree-Fock (ROHF), and such CUHF proves in many ways significantly

Few studies have been conducted to determine relationships between maternal childhood sexual abuse (CSA) history and parenting practices. Furthermore, no studies have attempted to understand how cultural coping methods dynamically impact the relationship between maternal CSA history and parenting outcomes. The purpose of this study is to understand if maternal coping mediates the relation between maternal CSA history and mother-daughter relational outcomes in a sample of African American mothers. The Strong Black Woman (SBW) Cultural Coping Scale, which consists of caretaking, affect regulation, and self-reliance factors, was used to represent maternal coping, and the Parent-Child Relationship Questionnaire (PCRQ) was used to assess warmth, personal relationship, possessiveness, and power assertion. Results showed that maternal CSA history was significantly related to SBW Cultural Coping total scores in the positive direction (i.e., mothers with CSA history reported higher scores). Mediation and indirect effects analyses revealed maternal CSA history was associated with mother-daughter possessiveness and power assertion through SBW Cultural Coping total scores. Additional analyses revealed a significant relation between maternal CSA history and subscales of the SBW, specifically caretaking and self-reliance. The meditational analyses, utilizing SBW subscale scores, revealed significant relations between maternal CSA and maternal warmth in the inverse direction via SBW caretaking, CSA and possessiveness in the positive direction via SBW self-reliance, and CSA and power assertion in the positive direction via both SBW caretaking and self-reliance factors. The results of this study highlight that specific types of trauma (i.e., CSA) can have significant implications for familial functioning within minority populations based on culturally-driven coping.

The thesis analyses the process of pair annihilation into one photon in a laser pulse. The theory of how to include pulse shapes in Strong Field QED and the resulting cross section is presented. The cross section is calculated and estimated for lasers of ELI and XFEL facilites. It is found that the effect may be experimentally verifiable at high frequency XFEL facilities for very finely tuned particle kinematics, but negligible at high intensity optical laser facilities such as ELI.

Methods of controlling molecular rotations using linearly polarized femtosecond and picosecond pulses are considered and analyzed theoretically. These laser pulses, typically in the infrared, are highly non-resonant with respect to the electronic degrees of freedom of the molecules and have intensities of &sim; 10^13 to 10^14 W/cm&sup2;. It is shown how these laser pulses can force small linear molecules to align with the direction of the electric field vector of the laser both in the presence of the laser field as well as after the application of a short laser pulse. Recent experiments on laser-induced molecular alignment are modeled and excellent agreement between experiment and theory is found. Additional methods of controlling molecular rotational dynamics are outlined. The first method considers the forced rotational acceleration of diatomic molecules, called the <i>optical centrifuge</i>. Here, the direction of polarization of a linearly polarized laser field is made to smoothly rotate faster and faster. The molecules, which tend to align with the polarization vector of the laser field, follow the rotation of the laser polarization and are accelerated to high angular momentum. The second method considers the control of field-free rotational dynamics by applying phase shifts to the molecular wave function at select times called <i>fractional revivals</i>. At these select moments, an initially localized wave function splits into several copies of the initial state. Adding phase shifts to the copies then induces interference effects which can be used to control the subsequent evolution of the rotational wave function. This same control scheme has a close link to quantum information and this connection is outlined. Finally, a recently proposed method of controlling the quantum dynamics of the classically chaotic kicked rotor system [J. Gong and P. Brumer, Phys. Rev. Lett. 86, 1741 (2001)] is analyzed from a phase space perspective. It is shown that the proposed quantum control can be linked to small islands of stability in the classical phase space. An experimentally feasible variant of this control scenario using wave packets of molecular alignment is proposed. Two applications of molecular alignment are discussed. The first application uses field-free aligned molecules as a non-linear medium for compression of a laser pulse to the 1 fs regime at optical wavelengths. At such durations, these laser pulses contain nearly a single oscillation of the electric field and represent the shortest laser pulses physically achievable for such frequencies. The second application uses molecular alignment to create a sort of gas phase "molecular crystal" which forms a basis for laser-induced electron diffraction and imaging of the aligned molecules. Here, a first laser pulse aligns the molecules in space. A second laser pulse is then used to ionize outer-shell electrons, accelerate them in the laser field, and steer them back to collide with the parent ion creating a diffraction image with sub-femtosecond and sub-Angstrom resolution.

A theorem due to Scarf in 1967 is examined in detail. Several versions of this theorem exist, some which appear at first unrelated. Two versions can be shown to be equivalent to a result due to Sperner in 1928: for a proper labelling of the vertices in a simplicial subdivision of an n-simplex, there exists at least one elementary simplex which carries all labels {0,1,..., n}. A third version is more akin to Dantzig's simplex method and is also examined. In recent years many new applications in combinatorics have been found, and we present several of them. Two applications are in the area of fair division: cake cutting and rent partitioning. Two others are graph theoretic: showing the existence of a fractional stable matching in a hypergraph and the existence of a fractional kernel in a directed graph. For these last two, we also show the second implies the first.

The adiabatic approximation is a natural approach for the description of phenomena induced by low frequency laser radiation because the ratio of the laser frequency to the characteristic frequency of an atom or a molecule is a small parameter. Since the main aim of this work is the study of ionization phenomena, the version of the adiabatic approximation that can account for the transition from a bound state to the continuum must be employed. Despite much work in this topic, a universally accepted adiabatic approach of bound-free transitions is lacking. Hence, based on Savichev's modified adiabatic approximation [Sov. Phys. JETP 73, 803 (1991)], we first of all derive the most convenient form of the adiabatic approximation for the problems at hand. Connections of the obtained result with the quasiclassical approximation and other previous investigations are discussed. Then, such an adiabatic approximation is applied to single-electron ionization and non-sequential double ionization of atoms in a strong low frequency laser field. The momentum distribution of photoelectrons induced by single-electron ionization is obtained analytically without any assumptions on the momentum of the electrons. Previous known results are derived as special cases of this general momentum distribution. The correlated momentum distribution of two-electrons due to non-sequential double ionization of atoms is calculated semi-analytically. We focus on the deeply quantum regime -- the below intensity threshold regime, where the energy of the active electron driven by the laser field is insufficient to collisionally ionize the parent ion, and the assistance of the laser field is required to create a doubly charged ion. A special attention is paid to the role of Coulomb interactions in the process. The signatures of electron-electron repulsion, electron-core attraction, and electron-laser interaction are identified. The results are compared with available experimental data. Two-electron correlated spectra of non-sequential double ionization below intensity threshold are known to exhibit back-to-back scattering of the electrons, viz., the anticorrelation of the electrons. Currently, the widely accepted interpretation of the anticorrelation is recollision-induced excitation of the ion plus subsequent field ionization of the second electron. We argue that there exists another mechanism, namely simultaneous electron emission, when the time of return of the rescattered electron is equal to the time of liberation of the bounded electron (the ion has no time for excitation), that can also explain the anticorrelation of the electrons in the deep below intensity threshold regime. Finally, we study single-electron molecular ionization. Based on the geometrical approach to tunnelling by P. D. Hislop and I. M. Sigal [Memoir. AMS 78, No. 399 (1989)], we introduce the concept of a leading tunnelling trajectory. It is then proven that leading tunnelling trajectories for single active electron models of molecular tunnelling ionization (i.e., theories where a molecular potential is modelled by a single-electron multi-centre potential) are linear in the case of short range interactions and ``almost'' linear in the case of long range interactions. The results are presented on both the formal and physically intuitive levels. Physical implications of the proven statements are discussed.

Unexpected properties of recently discovered mesons DsJ(2317) and DsJ(2460) have caused an excitement in the high energy community. These mesons are under experimental study in BaBar, Belle and CLEO. The experimental data on these mesons is quite limited at the moment, but it is expected to be improved in the following years. The unexpected properties of these mesons, such as the low mass, and small width, have caused speculations about their structure. Various models have been proposed which go beyond the simple quark-antiquark picture of the mesons, such as a meson molecule, or a four-quark state. Therefore, understanding the underlying structure of these mesons can reveal a deeper understanding of QCD. In this thesis, the strong decay of the DsJ(2317) meson, DsJ(2317)--&gt / Dspi0, is studied using three-point QCD Sum Rules method in the conventional cs framework. DsJ(2317) -&gt / Dspi0 decay violates isospin symmetry. Therefore, this decay is studied as a two stage process / an isospin conserving DsJ(2317) --&gt / Ds eta decay followed by the conversion of eta into a pi0 due to isospin violation.

Let G be a finite group and V be an orthogonal four-dimensional real representation space of G where the action of G is non-free. We give necessary and sufficient conditions for the existence of a G-equivariant vector field on the representation sphere of V in the cases G is the dihedral group, the generalized quaternion group and the semidihedral group in terms of decomposition of V into irreducible representations. In the case G is abelian, where the solution is already known, we give a more elementary solution.

No description available.