Min‐Sung Kim

Superconductors with the A15 structure are prototypical type-II $s$-wave superconductors which have generated considerable interest in early superconducting material history. However, the topological nature of the electronic structure remains unnoticed so far. Here, using first-principles band structure calculations based on density-functional theory, we show that the A15 superconductors (${\mathrm{Ta}}_{3}\mathrm{Sb}$, ${\mathrm{Ta}}_{3}\mathrm{Sn}$, and ${\mathrm{Ta}}_{3}\mathrm{Pb}$) have non

In this paper, an adaptive iterative learning controller (AILC) with input learning technique is presentedfor uncertain multi-input multi-output (MIMO) nonlinear systems in the normal form. The proposed AILC learnsthe internal parameter of the state equation as well as the input gain parameter, and also estimates the desired inputusing an input learning rule to track the whole history of command trajectory. The features of the proposed controlscheme can be briefly summarized as follows: 1) To th

Intriguing topological phases may appear in both insulating and semimetallic states. Topological insulators exhibit topologically nontrivial band inversion, while topological Dirac/Weyl semimetals show ``relativistic'' linear band crossings. Here, we report an unusual topological state of ${\mathrm{Pt}}_{3}\mathrm{Sn}$, where the two topological features appear simultaneously. Based on first-principles calculations, we show that ${\mathrm{Pt}}_{3}\mathrm{Sn}$ is a three-dimensional weak topologi

Using the first-principles method based on density functional theory, we investigate the electronic, mechanical, phononic, superconducting, and topological properties of the A15 superconductor Ti3Sb with/without the inclusion of spin–orbit coupling (SOC). We find that the calculated elastic constants satisfy the Born stability criteria and the ductile nature of Ti3Sb. The result of phonon calculations reveals that the Pm3¯n structure is dynamically stable. Sb atoms are dominated in the low-frequ

A bstract We propose blowup equations for 6d little string theories which generalize Nakajima-Yoshioka’s blowup equations for the 4d/5d instanton partition functions on Omega background. We find that unlike the blowup equations for standard SQFTs, we need to sum over auxiliary magnetic fluxes on the blown-up ℙ 1 for a non-dynamical 2-form gauge field which plays a role in canceling the mixed anomalies of the gauge symmetries. We demonstrate with explicit examples that the blowup equations, when

A bstract We propose two novel methods for computing the superconformal index of 5d superconformal field theories that cannot be described by conventional Lagrangian descriptions under mass deformations. The first approach involves the use of Higgs branch flows from UV Lagrangian theories, guided by transitions in 5-brane webs in Type IIB string theory. The second method employs the relationship between O7 + -plane and O7 − -plane with eight D7-branes, which applies to particular non-Lagrangian

Abstract We consider smooth locally Hamiltonian flows on compact surfaces of genus <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>g</m:mi> <m:mo>≥</m:mo> <m:mn>1</m:mn> </m:mrow> </m:math> {g\geq 1} to prove a deviation formula of Birkhoff integrals for smooth observables. Our work generalizes results of [G. Forni, Deviation of ergodic averages for area-preserving flows on surfaces of higher genus, Ann. of Math. (2) 155 2002, 1, 1–103] and [A. I. Bufetov, Limit theorems for

A bstract We explore BPS strings in supergravity theories in six-dimensions and related Swampland Conjectures. We first propose a general modular ansatz for bootstrapping elliptic genera of 2d worldvolume theories on strings in the 6d theories. By employing mirror symmetry on F-theory examples, we explicitly compute the elliptic genera and validate our ansatz. We extend this approach to investigate BPS strings and their spectrum in non-geometric 6d theories which have no known F-theory construct

Abstract In this paper we prove bounds for ergodic averages for nilflows on general higher-step nilmanifolds. Under Diophantine condition on the frequency of a toral projection of the flow, we prove that almost all orbits become equidistributed at polynomial speed. We analyze the rate of decay which is determined by the number of steps and structure of general nilpotent Lie algebras. Our main result follows from the technique of controlling scaling operators in irreducible representations and me

It is shown that a two-dimensional topological insulator can be realized and the band topology (equivalently, the edge states) may be further controlled by charge doping in an ultrathin SnTe film with a defect superstructure. Based on first-principles density functional theory (DFT), we predict that a Sn-Te bilayer, if exfoliated from three-dimensional bulk SnTe in the (1 1 1) direction, has a trivial band topology in its pristine form, but is made topologically nontrivial by introducing an appr

A bstract We investigate codimension-2 defect partition functions and quantum Seiberg-Witten curves in 5d rank-1 supersymmetric QFTs, including non-Lagrangian and Kaluza-Klein theories. Using generalized blowup equations, we compute defect partition functions in the Ω-background and show that, in the Nekrasov-Shatashvili limit, they satisfy certain difference equations that encode the quantization of classical Seiberg-Witten curves. Furthermore, we explore novel transitions in the defect partiti

The main results of this paper are to prove bounds for ergodic averages for nilflows on general higher step nilmanifolds. Under Diophantine condition on the frequency of a toral projection of the flow, we prove that almost all orbits become equidistributed at the polynomial speed. We analyze the exponent with the speed of decay which is determined by the number of steps and structure of general nilpotent Lie algebras. The main result follows from the technique over controlling scaling operators

We propose two novel methods for computing the superconformal index of 5d superconformal field theories that cannot be described by conventional Lagrangian descriptions under mass deformations. The first approach involves the use of Higgs branch flows from UV Lagrangian theories, guided by transitions in 5-brane webs in Type IIB string theory. The second method employs the relationship between O$7^+$-plane and O$7^-$-plane with eight D7-branes, which applies to particular non-Lagrangian theories

&lt;p style='text-indent:20px;'&gt;The main result of this paper is a construction of finitely additive measures for higher rank abelian actions on Heisenberg nilmanifolds. Under a full measure set of Diophantine conditions for the generators of the action, we construct &lt;i&gt;Bufetov functionals&lt;/i&gt; on rectangles on &lt;inline-formula&gt;&lt;tex-math id="M1"&gt;\begin{document}$ (2g+1) $\end{document}&lt;/tex-math&gt;&lt;/inline-formula&gt;-dimensional Heisenberg manifolds. We prove tha