On the Critical Behavior of D1-brane Theories

We study renormalization-group flow patterns in theories arising on D1-branes in various supersymmetry-breaking backgrounds. We argue that the theory of N D1-branes transverse to an orbifold space can be fine-tuned to flow to the corresponding orbifold conformal field theory in the infrared, for particular values of the couplings and theta angles which we determine using the discrete symmetries of the model. By calculating various nonplanar contributions to the scalar potential in the worldvolume theory, we show that fine-tuning is in fact required at finite N, as would be generically expected. We further comment on the presence of singular conformal field theories (such as those whose target space includes a ``throat'' described by an exactly solvable CFT) in the non-supersymmetric context. Throughout the analysis two applications are considered: to gauge theory/gravity duality and to linear sigma model techniques for studying worldsheet string theory.Comment: 23 pages in harvmac big, 8 figure

Non-Gaussianity in Island Cosmology

In this paper we fully calculate the non-Gaussianity of primordial curvature perturbation of island universe by using the second order perturbation equation. We find that for the spectral index $n_s\simeq 0.96$, which is favored by current observations, the non-Gaussianity level $f_{NL}$ seen in island will generally lie between 30 $\sim$ 60, which may be tested by the coming observations. In the landscape, the island universe is one of anthropically acceptable cosmological histories. Thus the results obtained in some sense means the coming observations, especially the measurement of non-Gaussianity, will be significant to make clear how our position in the landscape is populated.Comment: 5 pages, 1 eps figure, some discussions added, published versio

Wave packet transmission of Bloch electron manipulated by magnetic field

We study the phenomenon of wave packet revivals of Bloch electrons and explore how to control them by a magnetic field for quantum information transfer. It is showed that the single electron system can be modulated into a linear dispersion regime by the "quantized" flux and then an electronic wave packet with the components localized in this regime can be transferred without spreading. This feature can be utilized to perform the high-fidelity transfer of quantum information encoded in the polarization of the spin. Beyond the linear approximation, the re-localization and self-interference occur as the novel phenomena of quantum coherence.Comment: 6 pages, 5 figures, new content adde

The Seiberg-Witten Kahler Potential as a Two-Sphere Partition Function

Recently it has been shown that the two-sphere partition function of a gauged linear sigma model of a Calabi-Yau manifold yields the exact quantum Kahler potential of the Kahler moduli space of that manifold. Since four-dimensional N=2 gauge theories can be engineered by non-compact Calabi-Yau threefolds, this implies that it is possible to obtain exact gauge theory Kahler potentials from two-sphere partition functions. In this paper, we demonstrate that the Seiberg-Witten Kahler potential can indeed be obtained as a two-sphere partition function. To be precise, we extract the quantum Kahler metric of 4D N=2 SU(2) Super-Yang-Mills theory by taking the field theory limit of the Kahler parameters of the O(-2,-2) bundle over P1 x P1. We expect this method of computing the Kahler potential to generalize to other four-dimensional N=2 gauge theories that can be geometrically engineered by toric Calabi-Yau threefolds.Comment: 12 pages + appendix; v2: minor corrections, reference adde

Exact heat kernel on a hypersphere and its applications in kernel SVM

Many contemporary statistical learning methods assume a Euclidean feature space. This paper presents a method for defining similarity based on hyperspherical geometry and shows that it often improves the performance of support vector machine compared to other competing similarity measures. Specifically, the idea of using heat diffusion on a hypersphere to measure similarity has been previously proposed, demonstrating promising results based on a heuristic heat kernel obtained from the zeroth order parametrix expansion; however, how well this heuristic kernel agrees with the exact hyperspherical heat kernel remains unknown. This paper presents a higher order parametrix expansion of the heat kernel on a unit hypersphere and discusses several problems associated with this expansion method. We then compare the heuristic kernel with an exact form of the heat kernel expressed in terms of a uniformly and absolutely convergent series in high-dimensional angular momentum eigenmodes. Being a natural measure of similarity between sample points dwelling on a hypersphere, the exact kernel often shows superior performance in kernel SVM classifications applied to text mining, tumor somatic mutation imputation, and stock market analysis

Spin-orbit coupling induced two-electron relaxation in silicon donor pairs

We unravel theoretically a key intrinsic relaxation mechanism among the low-lying singlet and triplet donor-pair states in silicon, an important element in the fast-developing field of spintronics and quantum computation. Despite the perceived weak spin-orbit coupling (SOC) in Si, we find that our discovered relaxation mechanism, combined with the electron-phonon and inter-donor interactions, dominantly drives the transitions in the two-electron states over a large range of donor coupling regime. The scaling of the relaxation rate with inter-donor exchange interaction $J$ goes from $J^5$ to $J^4$ at the low to high temperature limits. Our analytical study draws on the symmetry analysis over combined band, donor envelope and valley configurations. It uncovers naturally the dependence on the donor-alignment direction and triplet spin orientation, and especially on the dominant SOC source from donor impurities. While a magnetic field is not necessary for this relaxation, unlike in the single-donor spin relaxation, we discuss the crossover behavior with increasing Zeeman energy in order to facilitate comparison with experiments.Comment: 15 pages, 1 figure. After-publication updat