Quantum Mechanical Study of Sulfuric Acid Hydration: Atmospheric Implications

The role of the binary nucleation of sulfuric acid in aerosol formation and its implications for global warming is one of the fundamental unsettled questions in atmospheric chemistry. We have investigated the thermodynamics of sulfuric acid hydration using ab initio quantum mechanical methods. For H2SO4(H2O)n where n = 1–6, we used a scheme combining molecular dynamics configurational sampling with high-level ab initio calculations to locate the global and many low lying local minima for each cluster size. For each isomer, we extrapolated the Møller–Plesset perturbation theory (MP2) energies to their complete basis set (CBS) limit and added finite temperature corrections within the rigid-rotor-harmonic-oscillator (RRHO) model using scaled harmonic vibrational frequencies. We found that ionic pair (HSO4–·H3O+)(H2O)n−1clusters are competitive with the neutral (H2SO4)(H2O)n clusters for n ≥ 3 and are more stable than neutral clusters for n ≥ 4 depending on the temperature. The Boltzmann averaged Gibbs free energies for the formation of H2SO4(H2O)n clusters are favorable in colder regions of the troposphere (T = 216.65–273.15 K) for n = 1–6, but the formation of clusters with n ≥ 5 is not favorable at higher (T > 273.15 K) temperatures. Our results suggest the critical cluster of a binary H2SO4–H2O system must contain more than one H2SO4 and are in concert with recent findings(1) that the role of binary nucleation is small at ambient conditions, but significant at colder regions of the troposphere. Overall, the results support the idea that binary nucleation of sulfuric acid and water cannot account for nucleation of sulfuric acid in the lower troposphere.

Light-cone Wilson loop in classical lattice gauge theory

The transverse broadening of an energetic jet passing through a non-Abelian plasma is believed to be described by the thermal expectation value of a light-cone Wilson loop. In this exploratory study, we measure the light-cone Wilson loop with classical lattice gauge theory simulations. We observe, as suggested by previous studies, that there are strong interactions already at short transverse distances, which may lead to more efficient jet quenching than in leading-order perturbation theory. We also verify that the asymptotics of the Wilson loop do not change qualitatively when crossing the light cone, which supports arguments in the literature that infrared contributions to jet quenching can be studied with dimensionally reduced simulations in the space-like domain. Finally we speculate on possibilities for full four-dimensional lattice studies of the same observable, perhaps by employing shifted boundary conditions in order to simulate ensembles boosted by an imaginary velocity.

Δ I = 1 / 2 rule for kaon decays derived from QCD infrared fixed point

This article gives details of our proposal to replace ordinary chiral SU(3)L×SU(3)R perturbation theory χPT3 by three-flavor chiral-scale perturbation theory χPTσ. In χPTσ, amplitudes are expanded at low energies and small u,d,s quark masses about an infrared fixed point αIR of three-flavor QCD. At αIR, the quark condensate ⟨q¯q⟩vac≠0 induces nine Nambu-Goldstone bosons: π,K,η, and a 0++ QCD dilaton σ. Physically, σ appears as the f0(500) resonance, a pole at a complex mass with real part ≲ mK. The ΔI=1/2 rule for nonleptonic K decays is then a consequence of χPTσ, with a KSσ coupling fixed by data for γγ→ππ and KS→γγ. We estimate RIR≈5 for the nonperturbative Drell-Yan ratio R=σ(e+e−→hadrons)/σ(e+e−→μ+μ−) at αIR and show that, in the many-color limit, σ/f0 becomes a narrow qq¯ state with planar-gluon corrections. Rules for the order of terms in χPTσ loop expansions are derived in Appendix A and extended in Appendix B to include inverse-power Li-Pagels singularities due to external operators. This relates to an observation that, for γγ channels, partial conservation of the dilatation current is not equivalent to σ-pole dominance.

Analysis of neuronal functions based on feynman diagrams

A method to study some neuronal functions, based on the use of the Feynman diagrams, employed in many-body theory, is reported. An equation obtained from the neuron cable theory is the basis for the method. The Green's function for this equation is obtained under some simple boundary conditions. An excitatory signal, with different conditions concerning high and pulse duration, is employed as input signal. Different responses have been obtained

Polarized interacting exciton gas in quantum wells and bulk semiconductors

We develop a theory to calculate exciton binding energies of both two- and three-dimensional spin polarized exciton gases within a mean field approach. Our method allows the analysis of recent experiments showing the importance of the polarization and intensity of the excitation light on the exciton luminescence of GaAs quantum wells. We study the breaking of the spin degeneracy observed at high exciton density (5×1010 cm2). Energy level splitting between spin +1 and spin -1 is shown to be due to many-body interexcitonic exchange while the spin relaxation time is controlled by intraexciton exchange. © 1996 The American Physical Society.

Electronic properties of transition metal atoms on Cu2N/Cu(100)

We study the nature of spin excitations of individual transition metal atoms (Ti, V, Cr, Mn, Fe, Co, and Ni) deposited on a Cu2N/Cu(100) surface using both spin-polarized density functional theory (DFT) and exact diagonalization of an Anderson model derived from DFT. We use DFT to compare the structural, electronic, and magnetic properties of different transition metal adatoms on the surface. We find that the average occupation of the transition metal d shell, main contributor to the magnetic moment, is not quantized, in contrast with the quantized spin in the model Hamiltonians that successfully describe spin excitations in this system. In order to reconcile these two pictures, we build a zero bandwidth multi-orbital Anderson Hamiltonian for the d shell of the transition metal hybridized with the p orbitals of the adjacent nitrogen atoms, by means of maximally localized Wannier function representation of the DFT Hamiltonian. The exact solutions of this model have quantized total spin, without quantized charge at the d shell. We propose that the quantized spin of the models actually belongs to many-body states with two different charge configurations in the d shell, hybridized with the p orbital of the adjacent nitrogen atoms. This scenario implies that the measured spin excitations are not fully localized at the transition metal.

Mode Localization in a Nearly Cyclic Symmetric System

Thesis (Ph.D.)--University of Washington, 2016-06

Teleportation via Multi-Qubit Channels

We investigate the problem of teleporting an unknown qubit state to a recipient via a channel of 2L qubits. In this procedure a protocol is employed whereby L Bell state measurements are made and information based on these measurements is sent via a classical channel to the recipient. Upon receiving this information the recipient determines a local gate which is used to recover the original state. We find that the 2(2L)-dimensional Hilbert space of states available for the channel admits a decomposition into four subspaces. Every state within a given subspace is a perfect channel, and each sequence of Bell measurements projects 2L qubits of the system into one of the four subspaces. As a result, only two bits of classical information need be sent to the recipient for them to determine the gate. We note some connections between these four subspaces and ground states of many-body Hamiltonian systems, and discuss the implications of these results towards understanding entanglement in multi-qubit systems.

An empirical examination of the strategic decision-making process:the relationship between context, process, and outcomes

Despite concerted academic interest in the strategic decision-making process (SDMP) since the 1980s, a coherent body of theory capable of guiding practice has not materialised. This is because many prior studies focus only on a single process characteristic, often rationality or comprehensiveness, and have paid insufficient attention to context. To further develop theory, research is required which examines: (i) the influence of context from multiple theoretical perspectives (e.g. upper echelons, environmental determinism); (ii) different process characteristics from both synoptic formal (e.g. rationality) and political incremental (e.g. politics) perspectives, and; (iii) the effects of context and process characteristics on a range of SDMP outcomes. Using data from 30 interviews and 357 questionnaires, this thesis addresses several opportunities for theory development by testing an integrative model which incorporates: (i) five SDMP characteristics representing both synoptic formal (procedural rationality, comprehensiveness, and behavioural integration) and political incremental (intuition, and political behaviour) perspectives; (ii) four SDMP outcome variables—strategic decision (SD) quality, implementation success, commitment, and SD speed, and; (iii) contextual variables from the four theoretical perspectives—upper echelons, SD-specific characteristics, environmental determinism, and firm characteristics. The present study makes several substantial and original contributions to knowledge. First, it provides empirical evidence of the contextual boundary conditions under which intuition and political behaviour positively influence SDMP outcomes. Second, it establishes the predominance of the upper echelons perspective; with TMT variables explaining significantly more variance in SDMP characteristics than SD specific characteristics, the external environment, and firm characteristics. A newly developed measure of top management team expertise also demonstrates highly significant direct and indirect effects on the SDMP. Finally, it is evident that SDMP characteristics and contextual variables influence a number of SDMP outcomes, not just overall SD quality, but also implementation success, commitment, and SD speed.

Strategic planning research:toward a theory-driven agenda

This review incorporates strategic planning research conducted over more than 30 years and ranges from the classical model of strategic planning to recent empirical work on intermediate outcomes, such as the reduction of managers’ position bias and the coordination of subunit activity. Prior reviews have not had the benefit of more socialized perspectives that developed in response to Mintzberg’s critique of planning, including research on planned emergence and strategy-as-practice approaches. To stimulate a resurgence of research interest on strategic planning, this review therefore draws on a diverse body of theory beyond the rational design and contingency approaches that characterized research in this domain until the mid-1990s. We develop a broad conceptualization of strategic planning and identify future research opportunities for improving our understanding of how strategic planning influences organizational outcomes. Our framework incorporates the role of strategic planning practitioners; the underlying routines, norms, and procedures of strategic planning (practices); and the concrete activities of planners (praxis).

Efficient computation of decoherent quantum walks through eigenvalue perturbation

A number of recent studies have investigated the introduction of decoherence in quantum walks and the resulting transition to classical random walks. Interestingly,it has been shown that algorithmic properties of quantum walks with decoherence such as the spreading rate are sometimes better than their purely quantum counterparts. Not only quantum walks with decoherence provide a generalization of quantum walks that naturally encompasses both the quantum and classical case, but they also give rise to new and different probability distribution. The application of quantum walks with decoherence to large graphs is limited by the necessity of evolving state vector whose sizes quadratic in the number of nodes of the graph, as opposed to the linear state vector of the purely quantum (or classical) case. In this technical report,we show how to use perturbation theory to reduce the computational complexity of evolving a continuous-time quantum walk subject to decoherence. More specifically, given a graph over n nodes, we show how to approximate the eigendecomposition of the n2×n2 Lindblad super-operator from the eigendecomposition of the n×n graph Hamiltonian.

Optical and Spin Properties of Defect-Bound Excitons in Semiconductors

Thesis (Ph.D.)--University of Washington, 2016-08

Continuum tensor network field states, path integral representations and spatial symmetries

A natural way to generalize tensor network variational classes to quantum field systems is via a continuous tensor contraction. This approach is first illustrated for the class of quantum field states known as continuous matrix-product states (cMPS). As a simple example of the path-integral representation we show that the state of a dynamically evolving quantum field admits a natural representation as a cMPS. A completeness argument is also provided that shows that all states in Fock space admit a cMPS representation when the number of variational parameters tends to infinity. Beyond this, we obtain a well-behaved field limit of projected entangled-pair states (PEPS) in two dimensions that provide an abstract class of quantum field states with natural symmetries. We demonstrate how symmetries of the physical field state are encoded within the dynamics of an auxiliary field system of one dimension less. In particular, the imposition of Euclidean symmetries on the physical system requires that the auxiliary system involved in the class' definition must be Lorentz-invariant. The physical field states automatically inherit entropy area laws from the PEPS class, and are fully described by the dissipative dynamics of a lower dimensional virtual field system. Our results lie at the intersection many-body physics, quantum field theory and quantum information theory, and facilitate future exchanges of ideas and insights between these disciplines.

MULTI-BAND BOSE HUBBARD MODELS AND EFFECTIVE THREE-BODY INTERACTIONS

Experiments with ultracold atoms in optical lattice have become a versatile testing ground to study diverse quantum many-body Hamiltonians. A single-band Bose-Hubbard (BH) Hamiltonian was first proposed to describe these systems in 1998 and its associated quantum phase-transition was subsequently observed in 2002. Over the years, there has been a rapid progress in experimental realizations of more complex lattice geometries, leading to more exotic BH Hamiltonians with contributions from excited bands, and modified tunneling and interaction energies. There has also been interesting theoretical insights and experimental studies on “un- conventional” Bose-Einstein condensates in optical lattices and predictions of rich orbital physics in higher bands. In this thesis, I present our results on several multi- band BH models and emergent quantum phenomena. In particular, I study optical lattices with two local minima per unit cell and show that the low energy states of a multi-band BH Hamiltonian with only pairwise interactions is equivalent to an effec- tive single-band Hamiltonian with strong three-body interactions. I also propose a second method to create three-body interactions in ultracold gases of bosonic atoms in a optical lattice. In this case, this is achieved by a careful cancellation of two contributions in the pair-wise interaction between the atoms, one proportional to the zero-energy scattering length and a second proportional to the effective range. I subsequently study the physics of Bose-Einstein condensation in the second band of a double-well 2D lattice and show that the collision aided decay rate of the con- densate to the ground band is smaller than the tunneling rate between neighboring unit cells. Finally, I propose a numerical method using the discrete variable repre- sentation for constructing real-valued Wannier functions localized in a unit cell for optical lattices. The developed numerical method is general and can be applied to a wide array of optical lattice geometries in one, two or three dimensions.

Competition between boson condensation and molecule formation in 2D Bose-Fermi mixtures with a pairing interaction

The study of ultra-cold atomic gases is one of the most active field in contemporary physics. The main motivation for the interest in this field consists in the possibility to use ultracold gases to simulate in a controlled way quantum many-body systems of relevance to other fields of physics, or to create novel quantum systems with unusual physical properties. An example of the latter are Bose-Fermi mixtures with a tunable pairing interaction between bosons and fermions. In this work, we study with many-body diagrammatic methods the properties of this kind of mixture in two spatial dimensions, extending previous work for three dimensional Bose-Fermi mixtures. At zero temperature, we focus specifically on the competition between boson condensation and the pairing of bosons and fermions into molecules. By a numerical solution of the main equations resulting by our many-body diagrammatic formalism, we calculate and present results for several thermodynamic quantities of interest. Differences and similarities between the two-dimensional and three-dimensional cases are pointed out. Finally, our new results are applied to discuss a recent proposal for creating a p-wave superfluid in Bose-Fermi mixtures with the fermionic molecules which form for sufficiently strong Bose-Fermi attraction.