On the Exact Evaluation of Certain Instances of the Potts Partition Function by Quantum Computers

We present an efficient quantum algorithm for the exact evaluation of either the fully ferromagnetic or anti-ferromagnetic q-state Potts partition function Z for a family of graphs related to irreducible cyclic codes. This problem is related to the evaluation of the Jones and Tutte polynomials. We consider the connection between the weight enumerator polynomial from coding theory and Z and exploit the fact that there exists a quantum algorithm for efficiently estimating Gauss sums in order to obtain the weight enumerator for a certain class of linear codes. In this way we demonstrate that for a certain class of sparse graphs, which we call Irreducible Cyclic Cocycle Code (ICCC_\epsilon) graphs, quantum computers provide a polynomial speed up in the difference between the number of edges and vertices of the graph, and an exponential speed up in q, over the best classical algorithms known to date

Neogene to Quaternary tectonics of the Garlock Fault and the Eastern California shear zone in the northern Mojave Desert, California

This study investigates the late Tertiary and Quaternary tectonic, structural and sedimentologic history of the central Garlock fault (GF) in Pilot Knob Valley (PKV) and southwestern Searles Valley, and its interactions with the cross-cutting Eastern California shear zone (ECSZ). The interaction of these two active, orthogonally striking strike-slip fault systems has long been somewhat of a tectonic enigma. However, this work provides considerable insight into how the kinematic and structural relationships between these structures have evolved since ~5 Ma. This in turn, furthers our understanding of how the North American-Pacific transform plate margin evolves over thousand to million-year timescales. The first contribution of this dissertation is the idea that the central GF is shown herein to have experienced large temporal variations in strain release since the late Pleistocene. A long-term, late Pleistocene slip rate of 5-7 mm/yr (e.g., McGill and Sieh, 1993) is comprises a ca. 13.2-4 ka period of low slip (4.3-5.1 mm/yr) followed by a recent, ca. 4-0 ka, period of elevated slip rate (10.2-14.3 mm/yr). Evidence for elevated slip rates in the late Holocene are from a 3.5-3.2 ka alluvial fan deposit offset 43-50 m against a shutter ridge. Two soil profile development index values and an optically stimulated luminescence age from the deposit establish robust age control. High-resolution, EarthscopeTM airborne LiDAR imagery, a boulder levee on the upstream late Holocene deposit, elevation profiles of the site and three hand-excavated trenches establish tight control on fault displacement magnitudes. Periods of elevated strain release on the GF are correlated with higher strain release rates on the San Andreas fault and shortening in the Los Angeles basin, but are anti-phased with the ECSZ (e.g., Dolan et al., 2007). A second contribution of this dissertation is the stratigraphic reorganization of late Cenozoic sedimentary rocks in PKV and Searles Valley, and the tectonic implications for the GF, Searles Valley fault and the newly identified Marine Gate fault. Here, a 1000+ m package of exposed Pliocene and Pleistocene strata have been uplifted and tilted to the northeast. Based on new age and provenance data, we adopt the name Pilot Knob Formation to describe much of these rocks north of the GF and east of the Christmas Canyon gate. The Pilot Knob Formation comprises three distinct lithologic members, from oldest to youngest, the Eagle Crags Member, Randsburg Wash Member and Slate Range Member. The Eagle Crags Member is a ~5-3.7 Ma conglomerate, sandstone, siltstone, claystone and evaporite derived from the Eagle Crags volcanic field to the south of PKV. The Randsburg Wash Member is a ~3.7-3.1 Ma siltstone, claystone and evaporite deposit that grades laterally into a sandstone and is locally interbedded with a rockfall deposit. The Slate Range Member is a ~3.1-0.3 Ma sandstone and conglomerate that grades, in the eastern study area, into a siltstone, claystone and evaporite deposit. Sediments comprising the Slate Range Member are derived from the Slate Range north of PKV. Outcrop relations within the Pilot Knob Formation reveal three stages for the post-Miocene tectonic development of PKV. An initial ~5-3.1 Ma stage characterized by an active sinistral-oblique-normal Marine Gate fault and GF, resulting in a transtensional pull-apart basin in northern PKV. A second, 3.1-1.2 Ma, stage of minimal transtension or transpression, corresponding to a cessation of sinistral slip on the Marine Gate fault at ca. 2.5 Ma, and a continuation of sinistral slip on the GF. Finally, a 1.2 Ma-present stage of significant N-S shortening across the northern PKV, as evidenced by uplifted and incised Pilot Knob Formation and younger sediments. Together, these three tectonic stages record the development and evolution of the Panamint Valley fault, located ~20 km east of PKV, since ~3.5-3 Ma. A third contribution of this dissertation involves quantifying the magnitude of modern N-S shortening in PKV and relating it to decreased slip on nearby strands of the ECSZ (e.g., Panamint Valley fault and Paradise fault zone). New detailed neotectonic mapping, EarthscopeTM airborne and ground-based LiDAR imagery, and chronology of Quaternary deposits exposed along the GF and Marine Gate fault, including (1) three 10Be terrestrial cosmogenic nuclide (TCN) depth profiles and (2) one soil description, place bounds on the vertical components of recent deformation. A ka 10Be TCN profile age for a 16-m-high terrace tread adjacent to the GF (site PKV-1) suggests a differential incision (uplift) rate of 0.40 ± 0.13 mm/yr. A ka 10Be TCN profile age from a 12.5-m-high tread located 4.5 km west on the GF (site PKV-5) suggests a differential incision (uplift) rate of 0.23 ± 0.05 mm/yr. A 25.5-m-high terrace adjacent to the southern Slate Range (site PKV-3) was dated using a soil profile development index (PDI) technique. A soil PDI age estimate of ~162 ka brackets the maximum age of uplift, and suggests a minimum uplift rate of ~0.16 mm/yr here. Using these ages and assuming dips on the GF between 90° and 80° to the north, resultant shortening magnitudes of 0-2.2 m and 0-2.8 m at sites PKV-5 and PKV-1, respectively, and 0-0.04±0.01 mm/yr at PKV-5 and 0-0.07±0.02 mm/yr at PKV-1 are estimated. At PKV-3, we estimate the dip of the newly recognized Marine Gate fault to be 70-80° to the south, resulting in 4.4-8.7 m of N-S shortening, suggesting a 0.03-0.05 mm/yr shortening rate. The shortening rate estimated at PKV-1 corresponds to 2-4% of Panamint Valley fault slip rate. Shortening at PKV-1 and PKV-3 can be summed to partially integrate 0.08-0.12 mm/yr shortening between the GF and Slate Range, or approximately 3-7% of Panamint Valley fault slip rate. The presence of numerous active reverse faults between PKV-1 and PKV-3 suggests that this is a minimum estimate. A fourth contribution of this dissertation is a 1:12,000 scale geologic map of the central GF, northern Blackwater fault, southern Searles Valley fault and the Marine Gate fault. covering approximately 280 km². Additional contributions of this work include: (1) quantification of the thermal history of the southern Slate Range through apatite and zircon (U-Th[SM])/He thermochronometry, and (2) enhancement of a Mojave-wide soil calibration tool developed and used by Eric Kirby and Eric McDonald that will be useful for future tectonic-geomorphic applications, dating climate-induced surficial processes and archeological dating

Constraints on T-Odd, P-Even Interactions from Electric Dipole Moments

We construct the relationship between nonrenormalizable,effective, time-reversal violating (TV) parity-conserving (PC) interactions of quarks and gauge bosons and various low-energy TVPC and TV parity-violating (PV) observables. Using effective field theory methods, we delineate the scenarious under which experimental limits on permanent electric dipole moments (EDM's) of the electron, neutron, and neutral atoms as well as limits on TVPC observables provide the most stringent bounds on new TVPC interactions. Under scenarios in which parity invariance is restored at short distances, the one-loop EDM of elementary fermions generate the most severe constraints. The limits derived from the atomic EDM of $^{199}$Hg are considerably weaker. When parity symmetry remains broken at short distances, direct TVPC search limits provide the least ambiguous bounds. The direct limits follow from TVPC interactions between two quarks.Comment: 43 pages, 9 figure

An improvement to multifold euclidean geometry codes

This paper presents an improvement to the multifold Euclidean geometry codes introduced by Lin (1973).The improved multifold EG codes are proved to be maximal, and therefore they are more efficient than the multifold EG codes. Relationships between the improved multifold EG codes and other known majority-logic decodable codes are proved

A Mathematica script for harmonic oscillator nuclear matrix elements arising in semileptonic electroweak interactions

Semi-leptonic electroweak interactions in nuclei - such as \beta decay, \mu capture, charged- and neutral-current neutrino reactions, and electron scattering - are described by a set of multipole operators carrying definite parity and angular momentum, obtained by projection from the underlying nuclear charge and three-current operators. If these nuclear operators are approximated by their one-body forms and expanded in the nucleon velocity through order |\vec{p}|/M, where \vec{p} and M are the nucleon momentum and mass, a set of seven multipole operators is obtained. Nuclear structure calculations are often performed in a basis of Slater determinants formed from harmonic oscillator orbitals, a choice that allows translational invariance to be preserved. Harmonic-oscillator single-particle matrix elements of the multipole operators can be evaluated analytically and expressed in terms of finite polynomials in q^2, where q is the magnitude of the three-momentum transfer. While results for such matrix elements are available in tabular form, with certain restriction on quantum numbers, the task of determining the analytic form of a response function can still be quite tedious, requiring the folding of the tabulated matrix elements with the nuclear density matrix, and subsequent algebra to evaluate products of operators. Here we provide a Mathematica script for generating these matrix elements, which will allow users to carry out all such calculations by symbolic manipulation. This will eliminate the errors that may accompany hand calculations and speed the calculation of electroweak nuclear cross sections and rates. We illustrate the use of the new script by calculating the cross sections for charged- and neutral-current neutrino scattering in ^{12}C.Comment: 15 pages, 2 tables, Mathematica notebook included in the form of figures. Mathematica package and documentation available at http://www.int.washington.edu/users/lunardi/7o.htm. Replaced version has improved graphics; text unchange

Product preserving bundle functors on fibered manifolds

summary:The complete description of all product preserving bundle functors on fibered manifolds in terms of natural transformations between product preserving bundle functors on manifolds is given

Generalized Legendre curves and Quaternionic Multiplication

This paper is devoted to abelian varieties arising from generalized Legendre curves. In particular, we consider their corresponding Galois representations, periods, and endomorphism algebras. For certain one parameter families of 2-dimensional abelian varieties of this kind, we determine when the endomorphism algebra of each fiber defined over the algebraic closure of $\Bbb Q$ contains a quaternion algebra