Topology protection-unprotection transition: an example from multi-terminal superconducting nanostructures

We show theoretically that in the superconducting nanostructures the gapped states of different topology are not always protected by separating gapped states. Depending on the structure design parameters, they can be either protected or not, with a protection-unprotection transition separating these two distinct situations. We build up a general theoretical description of the transition vicinity in the spirit of Landau theory. We speculate that similar protection-unprotection transitions may also occur for other realizations of topological protection in condensed matter systems

A Discrepancy-Based Design for A/B Testing Experiments

The aim of this paper is to introduce a new design of experiment method for A/B tests in order to balance the covariate information in all treatment groups. A/B tests (or "A/B/n tests") refer to the experiments and the corresponding inference on the treatment effect(s) of a two-level or multi-level controllable experimental factor. The common practice is to use a randomized design and perform hypothesis tests on the estimates. However, such estimation and inference are not always accurate when covariate imbalance exists among the treatment groups. To overcome this issue, we propose a discrepancy-based criterion and show that the design minimizing this criterion significantly improves the accuracy of the treatment effect(s) estimates. The discrepancy-based criterion is model-free and thus makes the estimation of the treatment effect(s) robust to the model assumptions. More importantly, the proposed design is applicable to both continuous and categorical response measurements. We develop two efficient algorithms to construct the designs by optimizing the criterion for both offline and online A/B tests. Through simulation study and a real example, we show that the proposed design approach achieves good covariate balance and accurate estimation.Comment: 42 Pages 10 Figure

Supercurrents in chiral channels originate from upstream information transfer: a theoretical prediction

It has been thought that the long chiral edge channels cannot support any supercurrent between the superconducting electrodes. We show theoretically that the supercurrent can be mediated by a non-local interaction that facilitates a long-distance information transfer in the direction opposite to electron flow. We compute the supercurrent for several interaction models, including that of an external circuit

Non-embeddability into a fixed sphere for a family of compact real algebraic hypersurfaces

We study the holomorphic embedding problem from a compact strongly pseudoconvex real algebraic hypersurface into a sphere of higher dimension. We construct a family of compact strongly pseudoconvex hypersurfaces $M_{\epsilon}$ in $\mathbb{C}^2,$ and prove that for any integer $N$, there is a number $\epsilon(N)$ with $0<\epsilon(N)<1$ such that for any $\epsilon$ with $0<\epsilon<\epsilon(N)$, $M_\epsilon$ can not be locally holomorphically embedded into the unit sphere $\mathbb{S}^{2N-1}$ in $\mathbb{C}^N.$Comment: 13 page

Interaction-induced supercurrent in quantum Hall setups

Recently we have proposed an unusual mechanism of superconducting current that is specific for Quantum Hall Edge channels connected to superconducting electrodes. We have shown that the supercurrent can be mediated by a nonlocal electon-electon interaction that provide an opportunity for a long-distance information transfer in the direction opposite to the electron flow. A convenient model for such interaction is that of an external circuit. The consideration has been done for the case of a single channel. In this work, we extend these results to more sophisticated setups that include the scattering between Quantum Hall channels of opposite direction and multiple superconducting contacts. For a single Quantum Hall constriction, we derive a general and comprehensive relation for the interaction- induced supercurrent in terms of scattering amplitudes and demonstrate the non-local nature of the current by considering its sensitivity to scattering. We understand the phase dependences of the supercurrents in multi-terminal setups in terms of interference of Andreev reflection processes. For more complex setups encompassing at least two constrictions we find an interplay between non-interacting and interaction-induced currents and contibutions of complex interference processes

Expansion of EYM Amplitudes in Gauge Invariant Vector Space

Motivated by the problem of expanding single-trace tree-level amplitude of Einstein-Yang-Mills theory to the BCJ basis of Yang-Mills amplitudes, we present an alternative expansion formula in the gauge invariant vector space. Starting from a generic vector space consisting of polynomials of momenta and polarization vectors, we define a new sub-space as gauge invariant vector space by imposing constraints of gauge invariant conditions. To characterize this sub-space, we compute its dimension and construct an explicit gauge invariant basis from it. We propose an expansion formula in the gauge invariant basis with expansion coefficients being linear combinations of Yang-Mills amplitude, manifesting the gauge invariance of both expansion basis and coefficients. With help of quivers, we compute the expansion coefficients via differential operators and demonstrate the general expansion algorithm by several examples.Comment: 54 pages, references added, references added. Version published in Chinese Physics

Joint Learning of Neural Networks via Iterative Reweighted Least Squares

In this paper, we introduce the problem of jointly learning feed-forward neural networks across a set of relevant but diverse datasets. Compared to learning a separate network from each dataset in isolation, joint learning enables us to extract correlated information across multiple datasets to significantly improve the quality of learned networks. We formulate this problem as joint learning of multiple copies of the same network architecture and enforce the network weights to be shared across these networks. Instead of hand-encoding the shared network layers, we solve an optimization problem to automatically determine how layers should be shared between each pair of datasets. Experimental results show that our approach outperforms baselines without joint learning and those using pretraining-and-fine-tuning. We show the effectiveness of our approach on three tasks: image classification, learning auto-encoders, and image generation

Distinguishing the right-handed up/charm quarks from top quark via discrete symmetries in the standard model extensions

We propose a class of the two Higgs doublet Standard models (SMs) with a SM singlet and a class of supersymmetric SMs with two pairs of Higgs doublets, where the right-handed up/charm quarks and the right-handed top quark have different quantum numbers under extra discrete symmetries. Thus, the right-handed up and charm quarks couple to one Higgs doublet field, while the right-handed top quark couples to another Higgs doublet. The quark CKM mixings can be generated from the down-type quark sector. As one of phenomenological consequences in our models, we explore whether one can accommodate the observed direct CP asymmetry difference in singly Cabibbo-suppressed D decays. We show that it is possible to explain the measured values of CP violation under relevant experimental constraints.Comment: 20 pages; matches published versio

Feed-down effect on Λ\Lambda spin polarization

We develop a theoretical framework to study the feed-down effect of higher-lying strange baryons on the spin polarization of the $\Lambda$ hyperon. In this framework, we consider two-body decays through strong, electromagnetic, and weak processes and derive general formulas for the angular distribution and spin polarization of the daughter particle by adopting the helicity formalism. Using the realistic experimental data as input, we explore the feed-down contribution to the global and the local $\Lambda$ polarizations and find that such a contribution suppresses the primordial $\Lambda$ polarization, which is not strong enough to resolve the discrepancy between the current theoretical and the experimental results on the azimuthal-angle dependence of $\Lambda$ polarization. Our paper may also be useful for the measurement of spin polarization of baryons heavier than $\Lambda$ (e.g., $\Xi^-$) in future experiments.Comment: 12 pages, 9 figure

E6 GUT through Effects of Dimension-5 Operators

In the effective field theory framework, quantum gravity can induce effective dimension-5 operators, which have important impacts on grand unified theories. Interestingly, one of main effects is the modification of the usual gauge coupling unification condition. We investigate the gauge coupling unification in $E_{6}$ under modified gauge coupling unification condition at scales $M_X$ in the presence of one or more dimension-5 operators. It is shown that nonsupersymmetric models of $E_6$ unification can be obtained and can easily satisfy the constraints from the proton lifetime. For constructing these models, we consider several maximal subgroups $H=SO(10)\times U(1), H=SU(3)\times SU(3)\times SU(3)$, and $H=SU(2)\times SU(6)$ of $E_{6}$ and the usual breaking chains for a specific maximal subgroup, and derive all of the Clebsch-Gordan coefficients $\Phi^{(r)}_{s,z}$ associated with $E_6$ breaking to the Standard Model, which are given in Appendix A.Comment: 20 pages, 10 tables, 8 figures, journal accepted versio