Yang-Baxter equation for the asymmetric eight-vertex model

In this note we study `a la Baxter [1] the possible integrable manifolds of the asymmetric eight-vertex model. As expected they occur when the Boltzmann weights are either symmetric or satisfy the free-fermion condition but our analysis clarify the reason both manifolds need to share a universal invariant. We also show that the free-fermion condition implies three distinct classes of integrable models.Comment: Latex, 12 pages, 1 figur

Selection of Optimized Retaining Wall Technique Using Self-Organizing Maps

Construction projects in urban areas tend to be associated with high-rise buildings and are of very large-scales; hence, the importance of a project’s underground construction work is significant. In this study, a rational model based on machine learning (ML) was developed. ML algorithms are programs that can learn from data and improve from experience without human intervention. In this study, self-organizing maps (SOMs) were utilized. An SOM is an alternative to existing ML methods and involves a subjective decision-making process because a developed model is used for data training to classify and effectively recognize patterns embedded in the input data space. In addition, unlike existing methods, the SOM can easily create a feature map by mapping multidimensional data to simple two-dimensional data. The objective of this study is to develop an SOM model as a decision-making approach for selecting a retaining wall technique. N-fold cross-validation was adopted to validate the accuracy of the SOM model and evaluate its reliability. The findings are useful for decision-making in selecting a retaining wall method, as demonstrated in this study. The maximum accuracy of the SOM was 81.5%, and the average accuracy was 79.8%

Monte Carlo Simulation of Lyman Alpha Scattering and Application to Damped Lyman Alpha Systems

A Monte Carlo code to solve the transfer of Lyman alpha (Lya) photons is developed, which can predict the Lya image and two-dimensional Lya spectra of a hydrogen cloud with any given geometry, Lya emissivity, neutral hydrogen density distribution, and bulk velocity field. We apply the code to several simple cases of a uniform cloud to show how the Lya image and emitted line spectrum are affected by the column density, internal velocity gradients, and emissivity distribution. We then apply the code to two models for damped Lya absorption systems: a spherical, static, isothermal cloud, and a flattened, axially symmetric, rotating cloud. If the emission is due to fluorescence of the external background radiation, the Lya image should have a core corresponding to the region where hydrogen is self-shielded. The emission line profile has the characteristic double peak with a deep central trough. We show how rotation of the cloud causes the two peaks to shift in wavelength as the slit is perpendicular to the rotation axis, and how the relative amplitude of the two peaks is changed. In reality, damped Lya systems are likely to have a clumpy gas distribution with turbulent velocity fields, which should smooth the line emission profile, but should still leave the rotation signature of the wavelength shift across the system.Comment: 19 pages, 17 eps figures. One panel is added in Fig.1 to show the recoil effect. Revisions are made in response to the referee's comments. Accepted for publication in Ap

Self-consistent non-Markovian theory of a quantum state evolution for quantum information processing

It is shown that the operator sum representation for non-Markovian dynamics and the Lindblad master equation in Markovian limit can be derived from a formal solution to quantum Liouville equation for a qubit system in the presence of decoherence processes self-consistently. Our formulation is the first principle theory based on projection-operator formalism to obtain an exact reduced density operator in time-convolutionless form starting from the quantum Liouville equation for a noisy quantum computer. The advantage of our approach is that it is general enough to describe a realistic quantum computer in the presence of decoherence provided details of the Hamiltonians are known.Comment: 5page

N=2 Supersymmetric SO(N)/Sp(N) Gauge Theories from Matrix Model

We use the matrix model to describe the N=2 SO(N)/Sp(N) supersymmetric gauge theories with massive hypermultiplets in the fundamental representation. By taking the tree level superpotential perturbation made of a polynomial of a scalar chiral multiplet, the effective action for the eigenvalues of chiral multiplet can be obtained. By varying this action with respect to an eigenvalue, a loop equation is obtained. By analyzing this equation, we derive the Seiberg-Witten curve within the context of matrix model.Comment: 14pp;v2 refs added, clarified in page 4, 6 and 11 and the sign of resolvent corrected;v3 improved in page 5 and 6 and the flavor dependent part in the integration around P added and to appear in PR

Mutual independence of critical temperature and superfluid density under pressure in optimally electron-doped superconducting LaFeAsO1−x_{1-x}Fx_{x}

The superconducting properties of LaFeAsO$_{1-x}$F$_{x}$ in conditions of optimal electron-doping are investigated upon the application of external pressure up to $\sim 23$ kbar. Measurements of muon-spin spectroscopy and dc magnetometry evidence a clear mutual independence between the critical temperature $T_{c}$ and the low-temperature saturation value for the ratio $n_{s}/m^{*}$ (superfluid density over effective band mass of Cooper pairs). Remarkably, a dramatic increase of $\sim 30$ % is reported for $n_{s}/m^{*}$ at the maximum pressure value while $T_{c}$ is substantially unaffected in the whole accessed experimental window. We argue and demonstrate that the explanation for the observed results must take the effect of non-magnetic impurities on multi-band superconductivity into account. In particular, the unique possibility to modify the ratio between intra-band and inter-bands scattering rates by acting on structural parameters while keeping the amount of chemical disorder constant is a striking result of our proposed model.Comment: 8 pages (Main text: 5 pages. Paper merged with supplemental information), 5 figure

Marginal Deformations with U(1)^3 Global Symmetry

We generate new 11-dimensional supergravity solutions from deformations based on U(1)^3 symmetries. The initial geometries are of the form AdS_4 x Y_7, where Y_7 is a 7-dimensional Sasaki-Einstein space. We consider a general family of cohomogeneity one Sasaki-Einstein spaces, as well as the recently-constructed cohomogeneity three L^{p,q,r,s} spaces. For certain cases, such as when the Sasaki-Einstein space is S^7, Q^{1,1,1} or M^{1,1,1}, the deformed gravity solutions correspond to a marginal deformation of a known dual gauge theory.Comment: 28pp; Refs. added and to appear in JHE