$${\mathbb{Z}_N}$$ -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.     

Renormalisation of Φ4-Theory on Non-Commutative $$\mathbb{R}^{4}$$ to All Orders

We present the main ideas and techniques of the proof that the duality-covariant four-dimensional non-commutative ⁴-model is renormalisable to all orders. This includes the reformulation as a dynamical matrix model, the solution of the free theory by orthogonal polynomials as well as the renormalisation byflow equations involving power-counting theorems for ribbon graphs drawn on Riemann surfaces     

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.     

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,...     

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.     

$${\mathcal{N}=2}$$ 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.     

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.     

Kinetic freeze-out s pectra of identified particles produced in p–Pb collisions at $$\sqrt {s_{NN} }$$ = 5.02 TeV

We study the transverse momentum spectra of identified pions (π^– + π⁺), kaons ((K ^– + K ⁺), K ₀ ^s ), protons (p + p?) and lambda hyperons (Λ + Λ?) produced at mid-rapidity (0 < y _cm < 0.5) in most central (0?5)% p–Pb collisions at \(\sqrt {s_{NN} }\) = 5.02 TeV in comparison with a Unified Statistical Thermal Freeze-out Model (USTFM). The measurements for pions are reported upto p _T = 3 GeV, the kaons (K ^– + K ⁺) are reported upto p _T = 2.5 GeV, K ₀ ^s is reported upto p _T = 7 GeV, and the baryons (protons and lambda hyperons) are reported upto p _T = 3.5 GeV. A good agreement is seen between the calculated results and the experimental data points taken from the ALICE experiment. The transverse momentum spectra are found to be flatter for heavy particles than for light particles. Bulk freeze-out properties in terms of kinetic freeze-out temperature and the transverse collective flow velocity are extracted from the fits of the transverse momentum spectra of these hadrons. The effect of resonance decay contributions has also been taken care of.     

The decays of $$\bar{B}^0$$, $$\bar{B}^0_s$$B¯s0 and $$B^-$$B- into $$\eta _c$$ηc plus a scalar or vector meson

We investigate the decays of \(\bar{B}^0_s\), \(\bar{B}^0\) and \(B^-\) into \(\eta _c\) plus a scalar or vector meson in a theoretical framework by taking into account the dominant process for the weak decay of \(\bar{B}\) meson into \(\eta _c\) and a \(q\bar{q}\) pair. After hadronization of this \(q\bar{q}\) component into pairs of pseudoscalar mesons we obtain certain weights for the pseudoscalar meson-pseudoscalar meson components. In addition, the \(\bar{B}^0\) and \(\bar{B}^0_s\) decays into \(\eta _c\) and \(\rho ^0\), \(K^*\) are evaluated and compared to the \(\eta _c\) and \(\phi \) production. The calculation is based on the postulation that the scalar mesons \(f_0(500)\), \(f_0(980)\) and \(a_0(980)\) are dynamically generated states from the pseudoscalar meson-pseudoscalar meson interactions in S-wave. Up to a global normalization factor, the \(\pi \pi \), \(K \bar{K}\) and \(\pi \eta \) invariant mass distributions for the decays of \(\bar{B}^0_s \rightarrow \eta _c \pi ^+ \pi ^-\), \(\bar{B}^0_s \rightarrow \eta _c K^+ K^-\), \(\bar{B}^0 \rightarrow \eta _c \pi ^+ \pi ^-\), \(\bar{B}^0 \rightarrow \eta _c K^+ K^-\), \(\bar{B}^0 \rightarrow \eta _c \pi ^0 \eta \), \(B^- \rightarrow \eta _c K^0 K^-\) and \(B^- \rightarrow \eta _c \pi ^- \eta \) are predicted. Comparison is made with the limited experimental information available and other theoretical calcualtions. Further comparison of these results with coming LHCb measurements will be very valuable to make progress in our understanding of the nature of the low lying scalar mesons, \(f_0(500), f_0(980)\) and \(a_0(980)\).     

Uniform in N global well-posedness of the time-dependent Hartree–Fock–Bogoliubov equations in $$\mathbb {R}^{1+1}$$

We prove the global well-posedness of the time-dependent Hartree–Fock–Bogoliubov (TDHFB) equations in \(\mathbb {R}^{1+1}\) with two-body interaction potential of the form \(N^{-1}v_N(x) = N^{\beta -1} v(N^\beta x)\) where \(v\ge 0\) is a sufficiently regular radial function, i.e., \(v \in L^1(\mathbb {R})\cap C^\infty (\mathbb {R})\). In particular, using methods of dispersive PDEs similar to the ones used in Grillakis and Machedon (Commun Partial Differ Equ 42:24–67, 2017), we are able to show for any scaling parameter \(\beta >0\) the TDHFB equations are globally well-posed in some Strichartz-type spaces independent of N, cf. (Bach et al. in The time-dependent Hartree–Fock–Bogoliubov equations for Bosons, 2016. arXiv:1602.05171).     

Thermodynamics of Lema$$\hat{i}$$ tre−Tolman−Bondi Model

Here we consider our universe as inhomogeneous spherically symmetric Lema [^(i)]{\hat{i}} tre−Tolman−Bondi Model and analyze the thermodynamics of this model of the universe. The trapping horizon is calculated and is found to coincide with the apparent horizon. The Einstein field equations are shown to be equivalent with the unified first law of thermodynamics. Finally assuming the first law of thermodynamics validity of the generalized second law of thermodynamics is examined at the apparent horizon for the perfect fluid and at the event horizon for holographic dark energy.     

Prospects for constrained supersymmetry at $$\sqrt{s}={33}\,\text {TeV} $$ and $$\sqrt{s}={100}\,\text {TeV} $$ proton–proton super-colliders

Successful models of pure gravity mediation (PGM) with radiative electroweak symmetry breaking can be expressed with as few as two free parameters, which can be taken as the gravitino mass and \(\tan \beta \) . These models easily support a 125–126 GeV Higgs mass at the expense of a scalar spectrum in the multi-TeV range and a much lighter wino as the lightest supersymmetric particle. In these models, it is also quite generic that the Higgs mixing mass parameter, \(\mu \) , which is determined by the minimization of the Higgs potential is also in the multi-TeV range. For \(\mu >0\) , the thermal relic density of winos is too small to account for the dark matter. The same is true for \(\mu <0\) unless the gravitino mass is of order 500 TeV. Here, we consider the origin of a multi-TeV \(\mu \) parameter arising from the breakdown of a Peccei–Quinn (PQ) symmetry. A coupling of the PQ-symmetry breaking field, \(P\) , to the MSSM Higgs doublets, naturally leads to a value of \(\mu \sim \langle P \rangle ^2 /M_P \sim {\mathcal O}(100)\) TeV and of the order that is required in PGM models. In this case, axions make up the dark matter or some fraction of the dark matter with the remainder made up from thermal or non-thermal winos. We also provide solutions to the problem of isocurvature fluctuations with axion dark matter in this context.     

Microscopic Spin–Orbit Potential for Proton + $${}^{9}$$ Be Scattering

Physics of Atomic Nuclei - The elastic scattering differential cross-section ( $$d\sigma/d\Omega$$ ) and the vector analyzing power ( $$A_{y}$$ ) are reanalyzed simultaneously for the $$p+^{9}$$ Be...     

Vibrational states of the Pt(111)–$$ \left( {\sqrt {3} \times \sqrt {3} } \right) $$ R30°–K surface structure

Vibrational spectrum of the ordered Pt(111)–( ?3 ×?3 ) \left( {\sqrt {3} \times \sqrt {3} } \right) R30°–K surface superstructure formed on the platinum surface with adsorption of 1/3 ML potassium is calculated with the use of the interatomic interaction potentials obtained in the strong bond approximation. Relaxation of the surface, dispersion of the surface phonons, local density of vibrational states, and polarization of phonon modes of adatoms and atoms of the substrate are discussed in the work. The theoretical results obtained agree well with the available experimental data.     

One-pot synthesis of $$\upgamma $$-spiroiminolactones and $$\upgamma $$-dispiroiminolactones using $$\textit{N}{,}{} \textit{N}^{\prime }$$N,N′-disubstituted parabanic acid and thioparabanic acid derivatives

A direct entry and simple process for the synthesis of \(\upgamma \)-spiroiminolactones present in a large number of natural products has been developed. In the first step, the synthesis of parabanic acid derivatives was commenced from the reaction of \(\textit{N}{,}{} \textit{N}^{\prime }\)-disubstituted urea and thiourea with oxalyl chloride, then a three-component reaction was carried out with isocyanides, acetylenic esters, and \(\textit{N}{,}{} \textit{N}^{\prime }\)-disubstituted parabanic acid derivatives. The method allows the construction of a variety of \(\upgamma \)-spiroiminolactone structures in good to high yields starting from readily available precursors. It was found that in the case of \(\textit{N}{,}{} \textit{N}^{\prime }\)-diphenyl thioparabanic acid, additional products of \(\upgamma \)-dispiroiminolactones have been formed due to the higher electrophilicity of \(\upalpha \)-dicarbonyl groups. The structures were fully established using spectroscopic analysis NMR, IR, and Mass spectrometry. The crystal structure of \(\upgamma \)-dispiroiminolactone was confirmed from single-crystal X-ray diffraction study.     

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.     

$$\mathfrak{s}\mathfrak{u} $$ q(2)-Invariant Schrödinger Equation of the Three-Dimensional Harmonic Oscillator

We propose a q-deformation of the -invariant Schrödinger equation of a spinless particle in a central potential, which allows us not only to determine a deformed spectrum and the corresponding eigenstates, as in other approaches, but also to calculate the expectation values of some physically-relevant operators. Here we consider the case of the isotropic harmonic oscillator and of the quadrupole operator governing its interaction with an external field. We obtain the spectrum and wave functions both for and generic , and study the effects of the q-value range and of the arbitrariness in the Casimir operator choice. We then show that the quadrupole operator in l=0 states provides a good measure of the deformation influence on the wave functions and on the Hilbert space spanned by them.     

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.