Positivity and geometric function theory constraints on pion scattering

This paper presents the fascinating correspondence between the geometric function theory and the scattering amplitudes with O(N) global symmetry. A crucial ingredient to show such correspondence is a fully crossing symmetric dispersion relation in the z-variable, rather than the fixed channel dispersion relation. We have written down fully crossing symmetric dispersion relation for O(N) model in z-variable for three independent combinations of isospin amplitudes. We have presented three independent sum rules or locality constraints for the O(N) model arising from the fully crossing symmetric dispersion relations. We have derived three sets of positivity conditions. We have obtained two-sided bounds on Taylor coefficients of physical Pion amplitudes around the crossing symmetric point (for example, π+π−→ π0π0) applying the positivity conditions and the Bieberbach-Rogosinski inequalities from geometric function theory.

Racemic and Meso Crystal Structures of an Axial-Chiral Spirobi-(dinaphthoazepin)ium Salt: Emergence of an S4-Symmetric Molecule

To date, only a few instances of S4-symmetric organic molecules exist. In principle, spirobi-(dinaphthoazepin)ium cations can achieve this highly symmetric point group. Heating racemic 2,2′-bis(bromomethyl)-1,1′binaphthyl with aqueous ammonia afforded a mixture of rac- and meso-3,3′,5,5′-tetrahydro-4,4′-spirobi[dinaphtho[2,1-c:1′,2′-e]azepin]-4-ium bromide which was separated by fractional crystallisation. Both stereoisomers were characterised spectroscopically, and their crystal structures were determined and compared. The rac crystal structure differs significantly from the known enantiopure one. The meso molecules display a near-perfect S4 symmetry. Upon treatment with KOtBu, both isomers undergo Stevens rearrangement.

Strain Induced Topological Insulator Phase in CsPbBrxI3−x (x = 0, 1, 2, and 3) Perovskite: A Theoretical Study

First-principles density functional theory was used to determine the surface band structures of CsPbBrxI3−x (x = 0, 1, 2, and 3) perovskites. The equilibrium lattice constants of CsPbBrxI3−x were obtained from the minimum of the total energy as a function of the iodine concentration. We discovered that the band gaps of CsPbBrxI3−x decreased monotonically under pressure. The phase change from a normal insulator to a topological insulator was found at approximately 2–4 GPa. The Pbp- and Brs-orbitals inverted at the R symmetric point with and without spin–orbit coupling. Nontrivial Z2 topological numbers were obtained, and the surface conduction bands were demonstrated theoretically using a 1 × 1 × 10 supercell. We ascertained that CsPbBr2I has the largest electric polarization 0.025 C/m2 under a compression strain of 10%. We also observed that in the normal insulation phase, the band gap increases with a small displacement of the central Pb atom in the z-direction, but in the topological insulator phase, the band gap decreases with the movement of the Pb atom in the z-direction. Additionally, in the supercell structure, CsPbBrxI3−x is a ferroelectric topological insulator because the Pb atom leaves its own equilibrium position.

Three-loop vertex integrals at symmetric point

This paper provides details of the massless three-loop three-point integrals calculation at the symmetric point. Our work aimed to extend known two-loop results for such integrals to the three-loop level. Obtained results can find their application in regularization-invariant symmetric point momentum-subtraction (RI/SMOM) scheme QCD calculations of renormalization group functions and various composite operator matrix elements. To calculate integrals, we solve differential equations for auxiliary integrals by transforming the system to the ε-form. Calculated integrals are expressed through the basis of functions with uniform transcendental weight. We provide expansion up to the transcendental weight six for the basis functions in terms of harmonic polylogarithms with six-root of unity argument.

Thermoelectric Transport in a Double-Quantum-Dot Coupled to Majorana Zero Modes

Thermoelectric transport through a double-quantum-dot (DQD) connected to the left and right leads is theoretically investigated in the framework of non-equilibrium Green’s function technique. We consider that the dots are also coupled to Majorana zero modes (MZMs) prepared at the two ends of a topological superconductor nanowire. It is found that the sign change of thermopower, which is promising in the detection of MZMs, can be realized by tuning several system’s parameters related to the MZMs, such as the coupling strength between the dots and the MZMs, the direct coupling between the MZMs, or even the magnetic flux penetrating through the structure. The above parameters also lead to significant enhancement of the thermopower and thermoelectric figure of merit (FOM), which indicates the conversion efficiency between heat and electrical energies. We also find that in this DQD system, both the thermopower and FOM are simultaneously enhanced by the MZMs around the electron-hole symmetric point, an ideal phenomenon in applications of thermoelectric effect. In addition, the thermoelectric effect is remarkably enhanced by the direct hybridization between the MZMs, which is very different from the case in single-dot structure.

On Janowski Type Harmonic Meromorphic Functions with respect to Symmetric Point

In this paper, we define a new class of Sakaguchi type-meromorphic harmonic functions in the Janowski domain that are starlike with respect to symmetric point. Furthermore, we investigate some important geometric properties like sufficiency criteria, distortion bound, extreme point theorem, convex combination, and weighted means.

Phase Transition and Its Universality Class for a Quantum Spin Chain

We numerically diagonalize the Dimer-Trimer (DT) model Hamiltonian around the SU(3) symmetric point. As a result, we discover the phase transition at this point which belongs to the Berezinskii-Kosterlitz-Thouless (BKT)-like universality class.