The MV formalism for $${\mathrm{IBL}}_\infty $$- and $${\mathrm{BV}}_\infty $$BV∞-algebras

We develop a new formalism for the quantum master equation \(\Delta e^{S/\hbar } = 0\) and the category of \(\mathrm{IBL}_\infty \)-algebras and simplify some homotopical algebra arising in the context of oriented surfaces with boundary. We introduce and study a category of MV-algebras, which, on the one hand, contains such important categories as those of \(\mathrm{IBL}_\infty \)-algebras and \(\mathtt{L}_\infty \)-algebras and, on the other hand, is homotopically trivial, in particular allowing for a simple solution of the quantum master equation. We also present geometric interpretation of our results.     

$${\mathcal{N}=2}$$ Superconformal Algebra and the Entropy of Calabi–Yau Manifolds

We use the representation theory of \({\mathcal{N}=2}\) superconformal algebra to study the elliptic genera of Calabi–Yau (CY) D-folds. We compute the entropy of CY manifolds from the growth rate of multiplicities of the massive (non-BPS) representations in the decomposition of their elliptic genera. We find that the entropy of CY manifolds of complex dimension D behaves differently depending on whether D is even or odd. When D is odd, CY entropy coincides with the entropy of the corresponding hyperKähler (D ? 3)-folds due to a structural theorem on Jacobi forms. In particular, we find that the Calabi–Yau 3-fold has a vanishing entropy. At D > 3, using our previous results on hyperKähler manifolds, we find \({S_{CY_D}\sim 2\pi \sqrt{\frac{(D-3)^2}{2(D-1)}n}}\). When D is even, we find the behavior of CY entropy behaving as \({S_{CY_D}\sim 2 \pi\sqrt{\frac{D-1}{2}n}}\). These agree with Cardy’s formula at large D.     

$${\mathbb{Z}_N}$$ -Curves Possessing No Thomae Formulae of Bershadsky–Radul Type

A \({\mathbb{Z}_N}\) -curve is one of the form \({y^{N}=(x-\lambda_{1})^{m_{1}}\cdots(x-\lambda_{s})^{m_{s}}}\) . When N = 2 these curves are called hyperelliptic and for them Thomae proved his classical formulae linking the theta functions corresponding to their period matrices to the branching values λ₁, . . . , λ _s . In his work on Fermionic fields on \({\mathbb{Z}_N}\) -curves with arbitrary N, Bershadsky and Radul discovered the existence of generalized Thomae’s formulae for these curves which they wrote down explicitly in the case in which all rotation numbers m _i equal 1. This work was continued by several authors and new Thomae’s type formulae for \({\mathbb{Z}_N}\) -curves with other rotation numbers m _i were found. In this article we prove that for some choices of the rotation numbers the corresponding \({\mathbb{Z}_N}\) -curves do not admit such generalized Thomae’s formulae.     

Quaternionic Kähler Detour Complexes and $${\mathcal{N} = 2}$$ Supersymmetric Black Holes

We study a class of supersymmetric spinning particle models derived from the radial quantization of stationary, spherically symmetric black holes of four dimensional \({{\mathcal N} = 2}\) supergravities. By virtue of the c-map, these spinning particles move in quaternionic Kähler manifolds. Their spinning degrees of freedom describe mini-superspace-reduced supergravity fermions. We quantize these models using BRST detour complex technology. The construction of a nilpotent BRST charge is achieved by using local (worldline) supersymmetry ghosts to generate special holonomy transformations. (An interesting byproduct of the construction is a novel Dirac operator on the superghost extended Hilbert space.) The resulting quantized models are gauge invariant field theories with fields equaling sections of special quaternionic vector bundles. They underly and generalize the quaternionic version of Dolbeault cohomology discovered by Baston. In fact, Baston’s complex is related to the BPS sector of the models we write down. Our results rely on a calculus of operators on quaternionic Kähler manifolds that follows from BRST machinery, and although directly motivated by black hole physics, can be broadly applied to any model relying on quaternionic geometry.     

$\ensuremath{\mathcal{P}}$$\ensuremath{\mathcal{T}}$ Symmetry vs. Hermiticity

The relation between the P\ensuremath{\mathcal{P}} T\ensuremath{\mathcal{T}} symmetry and Hermiticity is discussed. In the finite-dimensional linear space, any Hermitian matrix is a special case of P\ensuremath{\mathcal{P}} T\ensuremath{\mathcal{T}}-symmetric matrices. Explicit results in 2×2 are shown. The early belief that the P\ensuremath{\mathcal{P}} T\ensuremath{\mathcal{T}}-symmetric quantum mechanics is a generalization of the conventional Hermitian quantum mechanics is confirmed.     

On Statistical Properties of the Gamow–Teller Strength Distribution in $${}^{\mathbf{60}}$$ Ca

Physics of Atomic Nuclei - The $$\beta$$ -decay half-life and the delayed neutron emission of $${}^{60}$$ Ca are studied within a microscopic model, which is based on the Skyrme interaction T45 to...     

Backbending Phenomena in Even–Even $${}^{\boldsymbol{162{-}172}}$$ Hf Isotopes

Physics of Atomic Nuclei - This study probes the backbending phenomena in even–even $${}^{162{-}172}$$ Hf isotopes. Experimental ground-state rotational energies up to $$J^{\pi}=36^{+}$$...     

New Expressions for the Wave Operators of Schrödinger Operators in $${\mathbb{R}^3}$$

We prove new and explicit formulas for the wave operators of Schrödinger operators in \({\mathbb{R}^3}\). These formulas put into light the very special role played by the generator of dilations and validate the topological approach of Levinson’s theorem introduced in a previous publication. Our results hold for general (not spherically symmetric) potentials decaying fast enough at infinity, without any assumption on the absence of eigenvalue or resonance at 0-energy.     

Consequences of R-parity violating interactions for anomalies in $${\bar{B}}\rightarrow D^{(*)} \tau {\bar{\nu }}$$ and $$b\rightarrow s \mu ^+\mu ^-$$b→sμ+μ-

We investigate the possibility of explaining the enhancement in semileptonic decays of \({\bar{B}} \rightarrow D^{(*)} \tau {\bar{\nu }}\), the anomalies induced by \(b\rightarrow s\mu ^+\mu ^-\) in \({\bar{B}}\rightarrow (K, K^*, \phi )\mu ^+\mu ^-\) and violation of lepton universality in \(R_K = \mathrm{Br}({\bar{B}}\rightarrow K \mu ^+\mu ^-)/\mathrm{Br}({\bar{B}}\rightarrow K e^+e^-)\) within the framework of R-parity violating MSSM. The exchange of down type right-handed squark coupled to quarks and leptons yields interactions which are similar to leptoquark induced interactions that have been proposed to explain the \({\bar{B}} \rightarrow D^{(*)} \tau {\bar{\nu }}\) by tree level interactions and \(b\rightarrow s \mu ^+\mu ^-\) anomalies by loop induced interactions, simultaneously. However, the Yukawa couplings in such theories have severe constraints from other rare processes in B and D decays. Although this interaction can provide a viable solution to the \(R(D^{(*)})\) anomaly, we show that with the severe constraint from \({\bar{B}} \rightarrow K \nu {\bar{\nu }}\), it is impossible to solve the anomalies in the \(b\rightarrow s \mu ^+\mu ^-\) process simultaneously.     

The Local Gromov–Witten Theory of $${\mathbb{C}\mathbb{P}^1}$$ and Integrable Hierarchies

In this paper we begin the study of the relationship between the local Gromov–Witten theory of Calabi–Yau rank two bundles over the projective line and the theory of integrable hierarchies. We first of all construct explicitly, in a large number of cases, the Hamiltonian dispersionless hierarchies that govern the full-descendent genus zero theory. Our main tool is the application of Dubrovin’s formalism, based on associativity equations, to the known results on the genus zero theory from local mirror symmetry and localization. The hierarchies we find are apparently new, with the exception of the resolved conifold in the equivariantly Calabi–Yau case. For this example the relevant dispersionless system turns out to be related to the long-wave limit of the Ablowitz–Ladik lattice. This identification provides us with a complete procedure to reconstruct the dispersive hierarchy which should conjecturally be related to the higher genus theory of the resolved conifold. We give a complete proof of this conjecture for genus g ≤ 1; our methods are based on establishing, analogously to the case of KdV, a “quasi-triviality” property for the Ablowitz–Ladik hierarchy at the leading order of the dispersive expansion. We furthermore provide compelling evidence in favour of the resolved conifold/Ablowitz–Ladik correspondence at higher genus by testing it successfully in the primary sector for g = 2.     

Kolmogorov’s Theory of Turbulence and Inviscid Limit of the Navier-Stokes Equations in $${\mathbb {R}^3}$$

We are concerned with the inviscid limit of the Navier-Stokes equations to the Euler equations in \mathbb R³{\mathbb {R}^3} . We first observe that a pathwise Kolmogorov hypothesis implies the uniform boundedness of the α ^th -order fractional derivatives of the velocity for some α > 0 in the space variables in L ², which is independent of the viscosity μ > 0. Then it is shown that this key observation yields the L ²-equicontinuity in the time variable and the uniform bound in L ^q , for some q > 2, of the velocity independent of μ > 0. These results lead to the strong convergence of solutions of the Navier-Stokes equations to a solution of the Euler equations in \mathbb R³{\mathbb {R}^3} . We also consider passive scalars coupled to the incompressible Navier-Stokes equations and, in this case, find the weak-star convergence for the passive scalars with a limit in the form of a Young measure (pdf depending on space and time). Not only do we offer a framework for mathematical existence theories, but also we offer a framework for the interpretation of numerical solutions through the identification of a function space in which convergence should take place, with the bounds that are independent of μ > 0, that is in the high Reynolds number limit.     

Conformal classical Yang–Baxter equation,S-equation and $${\mathcal {O}}$$O-operators

Letters in Mathematical Physics - Conformal classical Yang–Baxter equation and S-equation naturally appear in the study of Lie conformal bialgebras and left-symmetric conformal bialgebras. In...     

Vitali $$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} $$ Anatol’evich Zverev (On his 80th birthday)

Chronicle

Vitali $\overset{\lower0.5em\hbox{$\overset{\lower0.5em\hbox{ Anatol’evich Zverev (On his 80th birthday)     

Spin density matrix of the $$\omega $$ in the reaction $${\bar{p}p}\,\rightarrow \,\omega \pi ^0$$p¯p→π0

The spin density matrix of the \(\omega \) has been determined for the reaction \({\bar{p}p}\,\rightarrow \,\omega \pi ^0\) with unpolarized in-flight data measured by the Crystal Barrel LEAR experiment at CERN. The two main decay modes of the \(\omega \) into \(\pi ^0 \gamma \) and \(\pi ^+ \pi ^- \pi ^0\) have been separately analyzed for various \({\bar{p}}\)momenta between 600 and 1940 MeV/c. The results obtained with the usual method by extracting the matrix elements via the \(\omega \) decay angular distributions and with the more sophisticated method via a full partial wave analysis are in good agreement. A strong spin alignment of the \(\omega \) is clearly visible in this energy regime and all individual spin density matrix elements exhibit an oscillatory dependence on the production angle. In addition, the largest contributing orbital angular momentum of the \({\bar{p}p~}\)system has been identified for the different beam momenta. It increases from \(L^{max}_{{\bar{p}p~}}\) \(=\) 2 at 600 MeV/c to \(L^{max}_{{\bar{p}p~}}\) \(=\) 5 at 1940 MeV/c.     

A $$bb{\bar{b}}{\bar{b}}$$ di-bottomonium at the LHC?

We study the case of a di-bottomonium \(bb{\bar{b}}{\bar{b}}\) particle at the LHC. Its mass and decay width are obtained within a new model of diquark–antidiquark interactions in tetraquarks. The same model solves several open problems on the phenomenology of the experimentally better known X, Z states. We show that the \(bb\bar{b}{\bar{b}}\) tetraquark is expected approximately 100 MeV below threshold, and compare to a recent analysis by LHCb seeking it in the \(\Upsilon \mu \mu \) final state.     

On Essential Self-Adjointness for Magnetic Schrödinger and Pauli Operators on the Unit Disc in $${\mathbb {R}^2}$$

We study the question of magnetic confinement of quantum particles on the unit disk \({\mathbb {D}}\) in \({\mathbb {R}^2}\) , i.e. we wish to achieve confinement solely by means of the growth of the magnetic field \({B(\vec x)}\) near the boundary of the disk. In the spinless case, we show that \({B(\vec x)\ge \frac{\sqrt 3}{2}\cdot\frac{1}{(1-r)^2}-\frac{1}{\sqrt 3}\frac{1}{(1-r)^2\ln \frac{1}{1-r}}}\) , for \({|\vec x|}\) close to 1, insures the confinement provided we assume that the non-radially symmetric part of the magnetic field is not very singular near the boundary. Both constants \({\frac{\sqrt 3}{2}}\) and \({-\frac{1}{\sqrt 3}}\) are optimal. This answers, in this context, an open question from Colin de Verdière and Truc (Ann Inst Fourier 2011, Preprint, arXiv:0903.0803v3). We also derive growth conditions for radially symmetric magnetic fields which lead to confinement of spin 1/2 particles.     

Lifetime measurements in $$^{182}\hbox {Pt}$$ using $$\gamma $$ – $$\gamma $$ fast-timing

The European Physical Journal A - In this paper, we discuss the evolution of breakup models from fully quantum mechanical, such as the Ichimura–Austern–Vincent model to semiclassical,...     

In memory of Alekse $$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l} $$ Sergeevich Nikiforov (March 28, 1927–October 1, 2002)

Chronicle

In memory of Alekse $\overset{\lower0.5em\hbox{$\overset{\lower0.5em\hbox{ Sergeevich Nikiforov (March 28, 1927–October 1, 2002)     

In memory of Vladimir Mikha $$\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\smile}$}}{l}$$ lovich Kudryashov (December 11, 1930–February 26, 2003)

Chronicle

In memory of Vladimir Mikha $\overset{\lower0.5em\hbox{$\overset{\lower0.5em\hbox{ lovich Kudryashov (December 11, 1930–February 26, 2003)     

Exact solutions of perturbed nonlinear Schrödinger’s equation with Kerr law nonlinearity by improved $${\textbf{tan}} \left( {\frac{{\boldsymbol{\phi}} \left( {\boldsymbol{\xi}} \right)}{{\textbf{2}}}} \right)$$-expansion method

This paper carries out exact solutions of the perturbed nonlinear Schödinger’s equation withy Kerr law nonlinearity by using the improved tan\(\left( {\frac{\phi \left( \xi \right)}{2}} \right)\)-expansion method. The exact solutions contain four types: hyperbolic function solution, trigonometric function solution, exponential solution, and rational solution. The method appears to be easier and faster by means of symbolic computational system and can be applied to the other nonlinear evolution equations in mathematical physics.