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.     

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,...     

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 $$J^{\pi}=36^{+}$$...     

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.     

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.     

$${\mathbb{Z}_N}$$ -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.     

The Decrease of the ESEEM Frequency of $${\text{P}}_{700}^{ + } {\text{A}}_{1}^{ - }$$ Ion-Radical Pair in Photosystem I Embedded in Trehalose Glassy Matrix at Room Temperature can be Explained by Acceleration of Spin–Lattice Relaxation

The main observation in this work is a decrease in the modulation frequency of the primary electron spin-echo decay (ESEEM) of the \({\text{P}}_{ 7 0 0}^{ + }\) cofactor in the reaction center of Photosystem I (PS I) from cyanobacteria Synechocystis sp. PCC 6803 embedded in dry trehalose matrix as the temperature rises from 150 K to room temperature. From the previous studies of the EPR spectrum shape of this system, it is known that, in dry trehalose matrix at room temperature, the distance between \({\text{P}}_{ 7 0 0}^{ + }\) and \({\text{A}}_{ 1}^{ - }\) spins does not increase compared to the distance measured in glycerol–water solution at cryogenic temperature. From the present ESEEM study, we conclude that the decrease of modulation frequency with rising temperature in trehalose matrix can be fully attributed to the influence of accelerated spin–lattice relaxation of \({\text{A}}_{ 1}^{ - }\). Our calculations show that this requires a decrease in the spin–lattice relaxation time from 3 to 1 μs. To the best of our knowledge, this is the first time that a shift in the ESEEM frequency due to the dipole–dipole interaction between the spins is observed that is caused by spin–lattice relaxation. Based on the above-mentioned results, we formulate a model of the protective effect of trehalose matrix on the electron transfer in the reaction center of PS I that is based on different hydrogen-bond networks between trehalose, local water, and protein.     

Data on Neutron–Neutron Scattering Length from the Reaction $$\boldsymbol{n+^{2}\textrm{H}\to n+n+p}$$ at $$\boldsymbol{E_{n}=60}$$ MeV

Physics of Atomic Nuclei - The $${}^{1}S_{0}$$ neutron–neutron ( $$nn$$ ) scattering length was measured in the neutron–deuteron ( $$nd$$ ) breakup reaction at an energy of 60 MeV. The...     

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...     

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     

Implementing the Gribov–Zwanziger framework in $$\mathcal {N}=1$$ Super-Yang–Mills in the Landau gauge

This is the third of a series of papers on three-loop computation of renormalization constants for Lattice QCD. Our main points of interest are results for the regularization defined by the Iwasaki gauge action and \(n_f=4\) Wilson fermions. Our results for quark bilinears renormalized according to the RI’-MOM scheme can be compared to non-perturbative results. The latter are available for twisted mass QCD: being defined in the chiral limit, the renormalization constants must be the same. We also address more general problems. In particular, we discuss a few methodological issues connected to summing the perturbative series such as the effectiveness of boosted perturbation theory and the disentanglement of irrelevant and finite-volume contributions. Discussing these issues we consider not only the new results of this paper, but also those for the regularization defined by the tree-level Symanzik improved gauge action and \(n_f=2\) Wilson fermions, which we presented in a recent paper of ours. We finally comment on the extent to which the techniques we put at work in the NSPT context can provide a fresher look into the lattice version of the RI’-MOM scheme.     

Neutron Pairing Correlations in an {\alpha}–{n}–{n} Three-Cluster Model of the {^{6}}He Nucleus

An \({\alpha}\)–n–n three-cluster model of the \({^6}\)He nucleus is studied by solving the Faddeev equations, where the cluster potential between \({\alpha}\) and n takes into account the Pauli exclusion correction, using the Fish-Bone Optical Model (Schmid in Z Phys A 297:105, 1980). The resulting binding energy of the ground state (\({0^+}\)) is 0.831 MeV and the resonance energy of the first excited state (\({2^+}\)), 0.60–i0.012 MeV, is extracted from the three-cluster break-up threshold. These theoretical values are in reasonable agreement with the experimental data: 0.973 MeV and 0.824–i0.056 MeV, respectively. In order to investigate the structure of these states, we calculate the angle density matrix for the \({\angle n_1 \alpha n_2}\) angle in the triangle formed by the three clusters. The angle density matrix of the ground state has two peaks and the configuration of \({0^+}\) wave function corresponding to the peaks constitutes a mixture of an acute-angled triangle structure and an obtuse-angled one. This finding is consistent with the former result from a variational approach (Hagino and Sagawa in Phys Rev C 72:044321, 2005). On the other hand, in the case of \({2^+}\) state only a single peak is obtained.     

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.     

$${\mathcal{N}=2}$$ 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.     

Optical properties of $$\hbox {TlGa}(\hbox {S}_{{x}}\hbox {Se}_{1-x})_{2}$$ layered mixed crystals $$(0 \le x \le 1)$$(0≤x≤1): Absorption edge and photoluminescence study at $$T = 10\hbox { K}$$T=10K

Industrial demand for neutrons constrains careful energy measurements. Elastic scattering of monoenergetic \(\alpha \)-particles from neutron collision enables neutron energy measurement by calculating the amount of deviation from the position where collision takes place. The neutron numbers with specific energy is obtained by counting the number of \(\alpha \)-particles in the corresponding location on the charged particle detector. Monte Carlo simulation and COMSOL Multiphysics5.2 are used to account for one-to-one collision of neutrons with \(\alpha \)-particles.     

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.     

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.     

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.