For a significant fraction of the history of the universe, neutrinos freely fall through spacetime. While they only weakly interact with matter, neutrinos have a significant impact in astrophysics. Experimental neutrino physics and observational cosmology are amidst an interesting era, where precision measurements in both fields have significantly improved scientific understanding of the standard model of particle physics and of the universe. Experiments in neutrino physics have not only discerned that neutrinos are massive particles, but have also measured their relative masses but not their absolute masses) and the quantum mechanical mixing matrix that is a consequence of these differing mass scales. Meanwhile, precision cosmological observations have determined the energy content of the universe, which in turn has presented a self-consistent story of the history and evolution of the universe and its contents. The topics discussed in this dissertation are based upon an interplay between these two fields, at times pushing the envelope, but always focused upon the basic physical processes that affect massive neutrinos in an expanding universe. A hearty, pedagogical introduction is presented to highlight the relevant neutrino physics described in this work and an overview of cosmology, strongly biased toward the early universe, the paradigm in which much of the work in this dissertation is based. Sterile neutrinos in different regimes of mass and mixing with active neutrinos are proposed as well as asymmetries between the number density of active neutrinos and antineutrinos in the early universe. The consequences of these two propositions are discussed in terms of observables such as primordial light element abundances and the observables related to a sterile neutrino dark matter candidate. Neutrino emission from high-entropy electron-positron plasmas are introduced, and the effects of this large flux of neutrinos and antineutrinos on hot hydrogen burning are explored. Finally, the nature of the cosmic neutrino background, a relic of the hot Big Bang, is discussed as they freely fall through spacetime from weak decoupling to the present epoch.

In 1918, Einstein provided the first description of the nature of the refractive index for X-rays, showing that phase contrast effects are significant. A century later, most x-ray microscopy and nearly all medical imaging remains based on absorption contrast, even though phase contrast offers orders of magnitude improvements in contrast and reduced radiation exposure at multi-keV x-ray energies. The work presented is concerned with developing practical and quantitative methods of phase contrast for x-ray microscopy. A theoretical framework for imaging in phase contrast is put forward； this is used to obtain quantitative images in a scanning microscope using a segmented detector, and to correct for artifacts in a commercial phase contrast x-ray nano-tomography system. The principle of reciprocity between scanning and full-field microscopes is then used to arrive at a novel solution: Zernike contrast in a scanning microscope. These approaches are compared on a theoretical and experimental basis in direct connection with applications using multi-keV x-ray microscopes at the Advanced Photon Source at Argonne National Laboratory. Phase contrast provides the best means to image mass and ultrastructure of light elements that mainly constitute biological matter, while stimulated x-ray fluorescence provides high sensitivity for studies of the distribution of heavier trace elements, such as metals. These approaches are combined in a complementary way to yield quantitative maps of elemental concentration from 2D images, with elements placed in their ultrastructural context. The combination of x-ray fluorescence and phase contrast poses an ideal match for routine, high resolution tomographic imaging of biological samples in the future. The presented techniques and demonstration experiments will help pave the way for this development.

Devices that exploit laws of quantum physics offer revolutionary advances in computation and communication. However, building such devices presents an enormous challenge, since it would require technologies that go far beyond current capabilities. One of the main obstacles to building a quantum computer and devices needed for quantum communication is decoherence or noise that originates from the interaction between a quantum system and its environment, and which leads to the destruction of the fragile quantum information. Encoding into decoherence-free subspaces DFS) provides an important strategy for combating decoherence effects in quantum systems and constitutes the focus of my dissertation. The theory of DFS relies on the existence of certain symmetries in the decoherence process, which allow some states of a quantum system to be completely decoupled from the environment and thus to experience no decoherence. In this thesis I describe various approaches to DFS that are developed in the current literature. Although the general idea behind various approaches to DFS is the same, I show that different mathematical definitions of DFS actually have different physical meaning. I provide a rigorous definition of DFS for every approach, explaining its physical meaning and relation to other definitions. I also examine the theory of DFS for Markovian systems. These are systems for which the environment has no memory, i.e., any change in the environment affects the quantum system instantaneously. Examples of such systems include many systems in quantum optics that have been proposed for implementation of a quantum computer, such as atomic and molecular gases, trapped ions, and quantum dots. Here I develop a rigorous theory that provides necessary and sufficient conditions for the existence of DFS. This theory allows us to identify a special new class of DFS that was not known before. Under particular circumstances, dynamics of a quantum system can connive together with the interactions between the system and its environment in a special way to reduce decoherence. This property is used to discover new DFS that rely on rather counterintuitive phenomenon, which I call an “incoherent generation of coherences.” I also provide examples of physical systems that support such states. These DFS can be used to suppress & coherence, but may not be sufficient for performing full quantum computation. I also explore the possibility of physically generating the DFS that are useful for quantum computation. For quantum computation we need to preserve at least two quantum states to encode the quantum analogue of classical bits. Here I aim to generate DFS in a system composed from a large collection of atoms or molecules and I need to determine how one should position atoms or molecules in 3D space so that the overall system possesses a DFS with at least two states i.e., non-trivial DFS). I show that for many Markovian systems, non-trivial DFS can exist only when particles are located in exactly the same position in space. This, of course, is not possible in the real world. For these systems, I also show that states in DFS are states with infinite lifetime. However, for all practical applications we just need long-lived states. Thus in reality, we do just need to bring quantum particles close together to generate an imperfect DFS, i.e. a collection of long-lived states. This can be achieved, for example, for atoms within a single molecule.

The discovery of cosmic acceleration twelve years ago implies that our universe is dominated by dark energy, which is either a tiny cosmological constant or a mysterious fluid with large negative pressure, or that Einsteins successful theory of gravity needs to be modified at large scales/low energies. Since then, independent evidence of a number of cosmological probes has firmly established the picture of a universe where dark energy or the effective contribution from a modification of gravity) makes up about 72% of the total energy density. Whichever of the options mentioned above will turn out to be the right one, a satisfying explanation for cosmic acceleration will likely lead to important new insights in fundamental physics. The question of the physics behind cosmic acceleration is thus one of the most intriguing open questions in modern physics. In this thesis, we calculate current constraints on dark energy and study how to optimally use the cosmological tools at our disposal to learn about its nature. We will first present constraints from a host of recent data on the dark energy sound speed and equation of state for different dark energy models including early dark energy. We then study the observational properties of purely kinetic k-essence models and show how they can in principle be straightforwardly distinguished from quintessence models by their equation of state behavior. We next consider a large, representative set of dark energy and modified gravity models and show that they can be divided into a small set of observationally distinct classes. We also find that all non-early dark energy models we consider can be modeled extremely well by a simple linear equation of state form. We will then go on to discuss a number of alternative, model independent parametrizations of dark energy properties. Among other things, we find that principal component analysis is not as model-independent as one would like it to be and that assuming a fixed value for the high redshift equation of state can lead to a dangerous bias in the determination of the equation of state at low redshift. Finally, we discuss using weak gravitational lensing of cosmic microwave background CMB) anisotropies as a cosmological probe. We compare different methods for extracting cosmological information from the lensed CMB and show that CMB lensing will in the future be a useful tool for constraining dark energy and neutrino mass. Whereas marginalizing over neutrino mass can degrade dark energy constraints, CMB lensing helps to break the degeneracy between the two and restores the dark energy constraints to the level of the fixed neutrino mass case.

Since the introduction of the Schramm-Loewner-Evolution SLE) in 2000 [25]), tremendous progress has been made in rigorously understanding the scaling limits of various 2D critical statistical mechanics models in two dimensions see [22]). The starting point of understanding the scaling limit of a 2D critical lattice model is to consider the model on a bounded domain O &sub； R2 and find a suitable observable at the discrete level which satisfies some discrete analyticity or harmonicity limit and, together with establishment of suitable boundary values, leads to conformal invariance in the continuum limit. For percolation, the appropriate observable is the crossing probability – conjectured to converge to the so-called Cardys Formula in the continuum. In [7], Smirnov established conformal invariance of critical site percolation on the triangular lattice in the scaling limit) by considering a triplet of observables related to crossing probability. However, Smirnovs proof takes advantage of the complete symmetry in the case of site percolation on the triangular lattice, and the triplet observables do not easily adapt themselves to percolation on other lattices. This dissertation, representing joint work with L. Chayes and I. Binder see [4], [5], [1], [2], [3]), contains construction of a non-trivial class of models for which we establish Cardys Formula and, following the approach outlined in [8], establishes convergence to SLE6 for the law of the interface, thus establishing some limited statement of universality. In the course of and in addition to) accomplishing this, we obtain some results which may find applicability to other percolation models: 1) We show how to extract Cardys Formula given some interior analyticity statement this requires some treatment of the discretization procedure in relation to retrieval of suitable boundary values) for a general class of domains； 2) our convergence to SLE6 proof is applicable for any percolation model satisfying reasonable assumptions and for which Cardys Formula can be established； 3) we obtain some almost) uniform estimates on crossing probabilities which may lead to some statement of rate of convergence to SLE6.

Ultrarelativistic heavy-ion collisions at the Relativistic Heavy-Ion Collider RHIC) are thought to have produced a state of matter called the Quark-Gluon-Plasma QGP). The QGP forms when nuclear matter governed by Quantum Chromodynamics QCD) reaches a temperature and baryochemical potential necessary to achieve the transition of hadrons bound states of quarks and gluons) to deconfined quarks and gluons. Such conditions have been achieved at RHIC, and the resulting QGP created exhibits properties of a near perfect fluid. In particular, strong evidence shows that the QGP exhibits a very small shear viscosity to entropy density ratio eta/s, near the lower bound predicted for that quantity by Anti-deSitter space/Conformal Field Theory AdS/CFT) methods of eta/s ＝ &plank；4pkB , where h is Plancks constant and kB is Boltzmanns constant. As the produced matter expands and cools, it evolves through a phase described by a hadron gas with rapidly increasing eta/s. This thesis presents robust calculations of eta/s for hadronic and partonic media as a function of temperature using the Green-Kubo formalism. An analysis is performed for the behavior of eta/s to mimic situations of the hadronic media at RHIC evolving out of chemical equilibrium, and systematic uncertainties are assessed for our method. In addition, preliminary results are presented for the bulk viscosity to entropy density ratio zeta/s, whose behavior is not well-known in a relativistic heavy ion collisions. The diffusion coefficient for baryon number is investigated, and an algorithm is presented to improve upon the previous work of investigation of heavy quark diffusion in a thermal QGP. By combining the results of my investigations for eta/s from our microscopic transport models with what is currently known from the experimental results on elliptic flow from RHIC, I find that the trajectory of eta/s in a heavy ion collision has a rich structure, especially near the deconfinement transition temperature Tc. I have helped quantify the viscous hadronic effects to enable investigators to constrain the value of eta/s for the QGP created at RHIC.

In this work, we study invariant-class of random matrix ensembles characterized by the asymptotic logarithmic soft-confinement potential V(H) &sim； [lnH](1＋lambda) (lambda ＞ 0), named “lambda-ensembles”. The suggestion is inspired by the existing random matrix models such as the critical ensembles (lambda＝1), the free Lev&acute；y matrices (lambda &rarr； 0 limit) and the Gaussian ensembles (lambda &rarr； infinity limit) in an effort to investigate the novel universality associated with the fat-tail random matrix ensembles as well as the logarithmic soft-confinement potential within the framework of rotationally invariant random matrix theory. First of all, we show that the orthogonal polynomials with respect to the weight function exp[-(ln x)1＋lambda] belong to a novel orthogonal polynomial system, named “lambda-generalization of q-polynomials”. Second, we show that based on numerical construction of the “lambda-generalization of q-polynomials”, we can study the one-level and the two-level correlation functions as well as the level statistics of the lambda-ensembles. Third, we show that the one-level correlation (eigenvalue density) has a power-law form p(x) &prop； [ln x]lambda-1/ x and the unfolded two-level correlation function possesses the normal/anomalous structure, characteristic of the critical ensembles. We further show that the anomalous part, so-called “ghost-correlation peak” is controlled by the parameter lambda； decreasing lambda increases the anomaly. Third, we also identify the two-level kernel of the lambda-ensembles in the semi-classical regime, which can be written in a sinh-kernel form with more general argument that reduces to that of the critical ensembles for lambda ＝ 1. Forth, we show that the number variance is linear in L for all lambda and the slope (the level compressibility) is increasing as lambda decreases, which is consistent with the lambda-dependence of sum rule violation 0 &lt； X(lambda) &lt； 1. Finally, we will discuss the novel universality of the lambda-ensembles, which interpolates the Gaussian ensembles (lambda &rarr； infinity limit), the critical ensembles (lambda ＝ 1), the free Levy matrices (lambda &rarr； 0 limit).

Photoexcited iodine in rare gas systems offer a paradigm for understanding excited state condensed phase chemistry. Solvent induced nonadiabaticity plays an important role in the dynamics of these systems and modifies electronic structure by introducing off-diagonal coupling elements to our electronic Hamiltonian matrix. A semi-empirical electronic structure method, diatomics-in-molecules DIM), together with its extension designed for ionic systems, diatomics-in-ionic-systems DIIS), is applied to dynamical studies of photoexcited iodine in Ar and Xe rare gas systems. Mixed quantum-classical molecular dynamics implemented using a surface hopping algorithm is employed in a trajectory study which successfully describes the nonadiabatic nature of these systems. First we looked into the photoexcited I2 in its manifold of covalent states in solid Ar, focusing on the cage-bound but otherwise dissociative potential curves. Cage motions disturb the electronic structure and influence the coupling between electronic states to a large extent due to the large-scale intramolecular motion associated with stretching of the I2 bond resulting from double-photon excitation. Dynamical simulation with a surface hopping algorithm describes the cage-bound state photoexcitation dynamics which has only been simulated by other groups using classical methods that do not allow for nonadiabatic electronic transitions. A characteristic recursion time of the cage-bound state motion is found though our simulation which matches the experimental results, and our simulated pump-probe signals successfully reproduce the experimental spectrum. Finally we apply our potential model and surface hopping dynamical calculation method to the charge transfer complex Xe＋2I- in xenon clusters. The states of this system are accessed at much higher energy than the covalent states. Charge transfer occurs between atoms and requires a significantly more complex potential energy model for which we use an extension to the DITS method that incorporates charge-transfer-to-solvent CTTS) states. Limited experimental results are available on these systems and they have not been explored in calculations. Our studies thus provide the first microscopic insights into different possible cage exit channels that have been speculated in experimental interpretations.

The identification of suitable diatomic molecules as candidates for an electron electric dipole moment (eEDM) experiment is presented. A model is derived and developed in order to efficiently and accurately identify possible diatomic molecules. This model gives the magnitude of the effective electric field experienced by an electron at the site of one of the nuclei in the molecule. In particular, this thesis identifies several 3Delta molecules as viable candidates for the eEDM search. In addition, the relevant tools for doing precision spectroscopy on these molecules are developed. For molecular ions in rotating trapping fields, a description of geometric phases is presented that reduces to the common result in the adiabatic limit, but allows for a description of the effect of atomic and molecular structure on these phases.