Paper-boat relaxion

A new relaxion mechanism is proposed where a small electroweak scale is preferably selected earlier than the larger one due to a potential instability, which is different from previously proposed stopping mechanisms by either Hubble friction from an increasing periodic barrier or thermal friction from gauge boson production. The sub-Planckian field excursion of an axion can be achieved without violating the bound on the $e$-folding number from a quantum gravity perspective; and our relaxion can be identified as a QCD axion, preserving the Peccei-Quinn solution to the strong $CP$ problem as well as making up all the cold dark matter in our current Universe.Comment: v1, 6 pages, 1 figure; v2, references added, minor improvement, a misused constraint corrected; v3, accepted by PRD, discussion added, title changed from "Mexican Relaxion" to meet the journal requirement; v4, final version to match the published versio

Electroweak relaxation of cosmological hierarchy

A simple model for the late-time cosmic acceleration problem is presented in the Starobinsky inflation with a negative bare cosmological constant as well as a nonminimal coupling to the Higgs boson. After electroweak symmetry breaking, the Starobinsky inflaton has been frozen until very recently, becoming a thawing quintessence, and a comparable magnitude to the observed dark energy density can be achieved without fine-tuning. Our proposal essentially reduces the cosmological constant problem into the electroweak hierarchy problem, and its late-time behaviour is also consistent with the recently proposed swampland criteria.Comment: v1, 6 pages, two columns, two figures; v2, references added, minor improvement; v3, references added, minor improvement; v4, version accepted by Phys.Rev.D with title changed into "Electroweak relaxation of cosmological hierarchy"; v5, to match the published version with title changed from "Quintessential Starobinsky inflation and swampland criteria

The harmonic map heat flow on conic manifolds

In this article, we study the the harmonic map heat flow from a manifold with conic singularities to a closed manifold. In particular, we have proved the short time existence and uniqueness of solutions as well as the existence of global solutions into manifolds with nonpositive sectional curvature. These results are established in virtue of the maximal regularity theory on manifolds with conic singularities

DTATG: An Automatic Title Generator based on Dependency Trees

We study automatic title generation for a given block of text and present a method called DTATG to generate titles. DTATG first extracts a small number of central sentences that convey the main meanings of the text and are in a suitable structure for conversion into a title. DTATG then constructs a dependency tree for each of these sentences and removes certain branches using a Dependency Tree Compression Model we devise. We also devise a title test to determine if a sentence can be used as a title. If a trimmed sentence passes the title test, then it becomes a title candidate. DTATG selects the title candidate with the highest ranking score as the final title. Our experiments showed that DTATG can generate adequate titles. We also showed that DTATG-generated titles have higher F1 scores than those generated by the previous methods.Comment: 8 pages, conference: accepted by KDIR 201

Nonlinear boundary crossing probabilities of Brownian motion with random jumps

We derive explicit formulas for probabilities of Brownian motion with jumps crossing linear or piecewise linear boundaries in any finite interval. We then use these formulas to approximate the boundary crossing probabilities for general nonlinear boundaries. The jump process can be any integer-valued process and jump sizes can have general distributions. Moreover, the jump sizes can be even correlated and/or non-identically distributed. The numerical algorithm is straightforward and easy to implement. Some numerical examples are presented

Imbert-Fedorov shift in Weyl semimetals: Dependence on monopole charge and intervalley scattering

The Imbert-Fedorov (IF) shift in optics describes the transverse shift of light beams at the reflection interface. Recently, the IF shift of Weyl fermions at the interface between Weyl semimetals (WSMs) with single monopole charge has been studied. Here, we study the IF shift at the interface between two WSMs, each of which is carrying an arbitrary integer monopole charge. We find a general relation between the monopole charges of the two WSMs and the IF shift. In particular, the IF shift is proportional to the monopole charge if both WSMs have the same one. Our results can be used to infer the topology of the materials by experimentally measuring their IF shift. Furthermore, we consider the possibility that the Weyl fermions are scattered to other Weyl cones during the reflection, which results in qualitatively different behavior of the IF shift. While we use a quantum mechanical approach to solve the problem, semiclassical equations of motion and the conservation of total angular momentum can help us intuitively interpret our results in special cases.Comment: 7 pages, 3 figures, published versio

Pseudospin Hall effect of light in photonic crystals with Weyl points

The study of spin-orbit coupling of photons has attracted much attention in recent years, and leads to many potential applications in optics. In the recently discovered metamaterial -- photonic crystals with Weyl points, the pseudospin-orbit coupling of photons bears a resemblance to the spin-orbit coupling. We study the pseudospin Hall effect of light in such metamaterials and find that during total reflection, the light beam experiences a transverse shift that is proportional to the pseudospin (or the monopole charge) of the Weyl point. As the spin Hall effect has inspired many works to explore the applications in optics, exploring the coupling between the orbital and pseudospin degrees of freedom of photons can also be fruitful in the field of optics, as well as in other fields where Weyl points can be realized.Comment: 5 page

Surface term, Virasoro algebra, and Wald entropy of black holes in higher-curvature gravity

Recently, in the Einstein gravity, Majhi and Padmanabhan proposed a straightforward and transparent way in obtaining the Bekenstein-Hawking entropy by using the approach based on the Virasoro algebra and central charge. In this work, we generalize their approach to the modified gravity with higher curvature corrections and show that their approach can successfully lead to the corresponding Wald entropy in the higher curvature gravity. Our result shows that the approach is physically general.Comment: v1: 12 pages, no figures, REVTeX 4.0; v2: no changes, this manuscript is accepted for publication in PRD; v3: English polished, match published versio

Canonical Form and Separability of PPT States on Multiple Quantum Spaces

By using the "subtracting projectors" method in proving the separability of PPT states on multiple quantum spaces, we derive a canonical form of PPT states in {\Cb}^{K_1} \otimes {\Cb}^{K_2} \otimes ... \otimes {\Cb}^{K_m} \otimes {\Cb}^N composite quantum systems with rank $N$, from which a sufficient separability condition for these states is presented.Comment: 5 page

Dark matter superfluid and DBI dark energy

It was shown recently that, without jeopardizing the success of the $\Lambda$ cold dark matter model on cosmic scales, the modified Newtonian dynamics (MOND) can be derived as an emergent phenomenon when axionlike dark matter particles condense into superfluid on the galactic scales. We propose in this paper a Dirac-Born-Infeld (DBI) scalar field conformally coupled to the matter components. To maintain the success of MOND phenomenon of dark matter superfluid on the galactic scales, the fifth force introduced by the DBI scalar should be screened on the galactic scales. It turns out that the screening effect naturally leads to a simple explanation for a longstanding puzzle that the MOND critical acceleration coincides with present Hubble scale. This galactic coincidence problem is solved, provided that the screened DBI scalar also plays the role of dark energy on the cosmic scales.Comment: v1, 4 pages, no figure; v2, 8 pages, 4 figures, numerical justifications added; v3, references added, final version to match the published versio