Relating thermodynamics to information theory : the equality of free energy and mutual information

In this thesis we uncover a new relation which links thermodynamics and information theory. We consider time as a channel and the detailed state of a physical system as a message. As the system evolves with time, ever present noise insures that the "message" is corrupted. Thermodynamic free energy measures the approach of the system toward equilibrium. Information theoretical mutual information measures the loss of memory of initial state. We regard the free energy and the mutual information as operators which map probability distributions over state space to real numbers. In the limit of long times, we show how the free energy operator and the mutual information operator asymptotically attain a very simple relationship to one another. This relationship is founded on the common appearance of entropy in the two operators and on an identity between internal energy and conditional entropy. The use of conditional entropy is what distinguishes our approach from previous efforts to relate thermodynamics and information theory.

The electrocatalytic and stoichiometric oxidation chemistry of binuclear ruthenium complexes incorporating the anionic tripod ligand {(η5-C5H5)Co[P(OCH3)2(=O)]3}-

The anionic tripod ligand NaLoMe (L_(oMe) - = [(η^5-C_5H_5)Co{P(O)(OCH_3)_2}_3]^-) reacts with RuO_4 in a biphasic reaction mixture of 1% H_2SO_4 and CCI_4 to afford [(L_(oMe) (HO)Ru^(IV) (µ-O)_2Ru ^(IV)(OH)(L_(oMe)] (1), which is treated with aqueous CF_3S0_3H to generate [(L_(oMe)(H_2O)Ru^(IV) (µ-O)_2R^(IV) (OH_2)(L_(oMe)][CF_3SO_3]_2 ([H_21][CF_3SO_3]_2). Addition of iodosobenzene to an acetonitrile solution of this salt yields [(L_(oMe)(O)Ru^v(µ-0)2Ru^v-(O)(_(LoMe)] (2). The dimer 1 can be reduced chemically or electrochemically to the Ru^(III)- Ru^(III) dimers [(L_(oMe)(H_20)Ru^(III) (µ-OH)_2Ru^(III) (OH_2)(L_(oMe)) ]^2+ and [(L_(oMe)) ^(III) (µ-0Hh(µ-0H2)Ru^(III) (L_(oMe)]^2+ which interconvert in aqueous media. Two electron processes dominate both the bulk chemistry and the electrochemistry of 1. Among these processes are the quasi-reversible Ru^(IV) - Ru^(IV)/Ru^(III)- Ru^(III) and Ru^(III)- Ru^(III)/ Ru^(II)- Ru^(II) reductions and a largely irreversible Ru^(V) - Ru^(V)/ Ru^(IV) - Ru^(IV)/oxidation. The dioxo dimer 2 oxidizes alcohols and aldehydes in organic media to afford 1 and the corresponding aldehydes and acids. Analogously, the Ru^(V) - Ru^(V)/ Ru^(IV)- Ru^(IV) redox wave mediates the electrooxidation of alcohols and aldehydes in aqueous buffer. In this system, substrates can be oxidized completely to CO_2. The kinetic behavior of these oxidations was examined by UV-vis and chronoamperometry, respectively, and the chemistry is typical of metal-oxo complexes, indicating that electronic coupling between two metal centers does not dramatically affect the metal-oxo chemistry. Dimer [H_21]^(2+) also reacts with alcohols, aldehydes, and triphenylphosphine in CH_3CN to afford Ru^(III)- Ru^(III) products including [(L_(oMe))CH_3CN) Ru^(III) (µ-OH)_2 Ru^(III) (NCCH_3)( L_(oMe))][CF_3SO_3]2 (characterized by X-ray crystallography) and the corresponding organic products. Reaction of 1 with formaldehyde in aqueous buffer quantitatively affords the triply bridged dimer [(L_(oMe)Ru^(III) (µ-OH)2- (µ-HCOO) Ru^(III) (L_(oMe)][CF_3SO_3] (characterized by X-ray crystallography). This reaction evidently proceeds by two parallel inner-sphere pathways, one of which is autocatalytic. Neither pathway exhibits a primary isotope effect suggesting the rate determining process could be the formation of an intermediate, perhaps a Ru^(IV) - Ru^(IV) formate adduct. The Ru^(III)- Ru^(III)formate adduct is easily oxidized to the Ru^(IV) - Ru^(IV) analog [(L_(oMe)Ru^(IV)(µ-OH)_2-(µ-HCOO) Ru^(IV) (L_(oMe)][CF_3SO_3], which, after isolation, reacts slowly with aqueous formaldehyde to generate free formate and the Ru^(III)- Ru^(III) formate adduct. These dimers function as catalysts for the electrooxidation of formaldehyde at low anodic potentials (+0.0 V versus SCE in aqueous buffer, pH 8.5) and enhance the activity of Nafion treated palladium/carbon heterogeneous fuel cell catalysts.

Nuclear weak interaction rates during stellar evolution and collapse

Nuclear weak interaction rates, including electron and positron emission rates, and continuum electron and positron capture rates , as well as the associated v and –/v energy loss rates are calculated on a detailed grid of temperature and density for the free nucleons and 226 nuclei with masses between A = 21 and 60. Gamow-Teller and Fermi discrete-state transition matrix element systematics and the Gamow-Teller T^< →/← T^> resonance transitions are discussed in depth and are implemented in the stellar rate calculations. Results of the calculations are presented on an abbreviated grid of temperature and density and comparison is made to terrestrial weak transition rates where possible. Neutron shell blocking of allowed electron capture on heavy nuclei during stellar core collapse is discussed along with several unblocking mechanisms operative at high temperature and density. The results of one-zone collapse calculations are presented which suggest that the effect of neutron shell blocking is to produce a larger core lepton fraction at neutrino trapping which leads to a larger inner-core mass and hence a stronger post-bounce shock.

Geometric quantization and foliation reduction

A standard question in the study of geometric quantization is whether symplectic reduction interacts nicely with the quantized theory, and in particular whether “quantization commutes with reduction.” Guillemin and Sternberg first proposed this question, and answered it in the affirmative for the case of a free action of a compact Lie group on a compact Kähler manifold. Subsequent work has focused mainly on extending their proof to non-free actions and non-Kähler manifolds. For realistic physical examples, however, it is desirable to have a proof which also applies to non-compact symplectic manifolds.

In this thesis we give a proof of the quantization-reduction problem for general symplectic manifolds. This is accomplished by working in a particular wavefunction representation, associated with a polarization that is in some sense compatible with reduction. While the polarized sections described by Guillemin and Sternberg are nonzero on a dense subset of the Kähler manifold, the ones considered here are distributional, having support only on regions of the phase space associated with certain quantized, or “admissible”, values of momentum.

We first propose a reduction procedure for the prequantum geometric structures that “covers” symplectic reduction, and demonstrate how both symplectic and prequantum reduction can be viewed as examples of foliation reduction. Consistency of prequantum reduction imposes the above-mentioned admissibility conditions on the quantized momenta, which can be seen as analogues of the Bohr-Wilson-Sommerfeld conditions for completely integrable systems.

We then describe our reduction-compatible polarization, and demonstrate a one-to-one correspondence between polarized sections on the unreduced and reduced spaces.

Finally, we describe a factorization of the reduced prequantum bundle, suggested by the structure of the underlying reduced symplectic manifold. This in turn induces a factorization of the space of polarized sections that agrees with its usual decomposition by irreducible representations, and so proves that quantization and reduction do indeed commute in this context.

A significant omission from the proof is the construction of an inner product on the space of polarized sections, and a discussion of its behavior under reduction. In the concluding chapter of the thesis, we suggest some ideas for future work in this direction.

Heteroepitaxy of Group IV and Group III-V semiconductor alloys for photovoltaic applications

Photovoltaic energy conversion represents a economically viable technology for realizing collection of the largest energy resource known to the Earth -- the sun. Energy conversion efficiency is the most leveraging factor in the price of energy derived from this process. This thesis focuses on two routes for high efficiency, low cost devices: first, to use Group IV semiconductor alloy wire array bottom cells and epitaxially grown Group III-V compound semiconductor alloy top cells in a tandem configuration, and second, GaP growth on planar Si for heterojunction and tandem cell applications.

Metal catalyzed vapor-liquid-solid grown microwire arrays are an intriguing alternative for wafer-free Si and SiGe materials which can be removed as flexible membranes. Selected area Cu-catalyzed vapor-liquid solid growth of SiGe microwires is achieved using chlorosilane and chlorogermane precursors. The composition can be tuned up to 12% Ge with a simultaneous decrease in the growth rate from 7 to 1 μm/min^-1. Significant changes to the morphology were observed, including tapering and faceting on the sidewalls and along the lengths of the wires. Characterization of axial and radial cross sections with transmission electron microscopy revealed no evidence of defects at facet corners and edges, and the tapering is shown to be due to in-situ removal of catalyst material during growth. X-ray diffraction and transmission electron microscopy reveal a Ge-rich crystal at the tip of the wires, strongly suggesting that the Ge incorporation is limited by the crystallization rate.

Tandem Ga_1-xIn_xP/Si microwire array solar cells are a route towards a high efficiency, low cost, flexible, wafer-free solar technology. Realizing tandem Group III-V compound semiconductor/Si wire array devices requires optimization of materials growth and device performance. GaP and Ga_1-xIn_xP layers were grown heteroepitaxially with metalorganic chemical vapor deposition on Si microwire array substrates. The layer morphology and crystalline quality have been studied with scanning electron microscopy and transmission electron microscopy, and they provide a baseline for the growth and characterization of a full device stack. Ultimately, the complexity of the substrates and the prevalence of defects resulted in material without detectable photoluminescence, unsuitable for optoelectronic applications.

Coupled full-field optical and device physics simulations of a Ga_0.51In_0.49P/Si wire array tandem are used to predict device performance. A 500 nm thick, highly doped "buffer" layer between the bottom cell and tunnel junction is assumed to harbor a high density of lattice mismatch and heteroepitaxial defects. Under simulated AM1.5G illumination, the device structure explored in this work has a simulated efficiency of 23.84% with realistic top cell SRH lifetimes and surface recombination velocities. The relative insensitivity to surface recombination is likely due to optical generation further away from the free surfaces and interfaces of the device structure.

Finally, GaP has been grown free of antiphase domains on Si (112) oriented substrates using metalorganic chemical vapor deposition. Low temperature pulsed nucleation is followed by high temperature continuous growth, yielding smooth, specular thin films. Atomic force microscopy topography mapping showed very smooth surfaces (4-6 Å RMS roughness) with small depressions in the surface. Thin films (~ 50 nm) were pseudomorphic, as confirmed by high resolution x-ray diffraction reciprocal space mapping, and 200 nm thick films showed full relaxation. Transmission electron microscopy showed no evidence of antiphase domain formation, but there is a population of microtwin and stacking fault defects.