The influence of the hard core on thef-sum of nuclei

Exchange forces modify thef-sum by an additional termCα.C is calculated as a function of the hard core radiusc for several types of potentials and for two densities of nuclear matter (r ₀=1·1 and 1·2 f).C is found to depend strongly onc.     

Wall Crossing as Seen by Matrix Models

The number of BPS bound states of D-branes on a Calabi-Yau manifold depends on two sets of data, the BPS charges and the stability conditions. For D0 and D2-branes bound to a single D6-brane wrapping a Calabi-Yau 3-fold X, both are naturally related to the Kähler moduli space \({{\mathcal M}(X)}\) . We construct unitary one-matrix models which count such BPS states for a class of toric Calabi-Yau manifolds at infinite ’t Hooft coupling. The matrix model for the BPS counting on X turns out to give the topological string partition function for another Calabi-Yau manifold Y, whose Kähler moduli space \({{\mathcal M}(Y)}\) contains two copies of \({{\mathcal M}(X)}\) , one related to the BPS charges and another to the stability conditions. The two sets of data are unified in \({{\mathcal M}(Y)}\) . The matrix models have a number of other interesting features. They compute spectral curves and mirror maps relevant to the remodeling conjecture. For finite ’t Hooft coupling they give rise to yet more general geometry \({\widetilde{Y}}\) containing Y.     

ASK/PSK-correspondence and the <Emphasis Type="Italic">r</Emphasis>-map

We formulate a correspondence between affine and projective special Kähler manifolds of the same dimension. As an application, we show that, under this correspondence, the affine special Kähler manifolds in the image of the rigid r-map are mapped to one-parameter deformations of projective special Kähler manifolds in the image of the supergravity r-map. The above one-parameter deformations are interpreted as perturbative \(\alpha '\)-corrections in heterotic and type II string compactifications with \(N=2\) supersymmetry. Also affine special Kähler manifolds with quadratic prepotential are mapped to one-parameter families of projective special Kähler manifolds with quadratic prepotential. We show that the completeness of the deformed supergravity r-map metric depends solely on the (well-understood) completeness of the undeformed metric and the sign of the deformation parameter.     

Massive hyper-Kähler sigma models and BPS domain walls

With the non-Abelian hyper-Kähler quotient by U(M) and SU(M) gauge groups, we give the massive hyper-Kähler sigma models that are not toric in the N=1 superfield formalism. The U(M) quotient gives N!/[M!(N-M)!] (N is the number of flavors) discrete vacua that may allow various types of domain walls, whereas the SU(M) quotient gives no discrete vacua. We derive a BPS domain-wall solution in the case of N = 2 and M = 1 in the U(M) quotient model.     

Review of searches for Higgs bosons and beyond the Standard Model Physics at the Tevatron

The energy frontier is currently at the Fermilab Tevatron accelerator, which collides protons and antiprotons at a center-of-mass energy of 1.96 TeV. The luminosity delivered to the CDF and DØ experiments has now surpassed the 4 fb^?1. This paper reviews the most recent direct searches for Higgs bosons and beyond-the-standard-model (BSM) physics at the Tevatron. The results reported correspond to an integrated luminosity of up to 2.5 fb^?1 of Run II data collected by the two Collaborations. Searches covered include the standard model (SM) Higgs boson (including sensitivity projections), the neutral Higgs bosons in the minimal supersymmetric extension of the standard model (MSSM), charged Higgs bosons and extended Higgs models, supersymmetric decays that conserve or violate R-parity, gauge-mediated supersymmetric breaking models, long-lived particles, leptoquarks, compositeness, extra gauge bosons, extra dimensions, and finally signature-based searches. Given the excellent performance of the collider and the continued productivity of the experiments, the Tevatron physics potential looks promising for discovery with the coming larger data sets. In particular, evidence for the SM Higgs boson could be obtained if its mass is light or near 160 GeV. The observed (expected) upper limits are currently a factor of 3.7 (3.3) higher than the expected SM Higgs boson cross section at m _H =115 GeV and 1.1 (1.6) at m _H =160 GeV at 95% C.L.     

Seiberg–Witten theory as a Fermi gas

We explore a new connection between Seiberg–Witten theory and quantum statistical systems by relating the dual partition function of SU(2) Super Yang–Mills theory in a self-dual \(\Omega \) background to the spectral determinant of an ideal Fermi gas. We show that the spectrum of this gas is encoded in the zeroes of the Painlevé \(\mathrm{III}_3\) \(\tau \) function. In addition, we find that the Nekrasov partition function on this background can be expressed as an O(2) matrix model. Our construction arises as a four-dimensional limit of a recently proposed conjecture relating topological strings and spectral theory. In this limit, we provide a mathematical proof of the conjecture for the local \({\mathbb P}^1 \times {\mathbb P}^1\) geometry.     

Off-Diagonal Decay of Toric Bergman Kernels

We study the off-diagonal decay of Bergman kernels \({\Pi_{h^k}(z,w)}\) and Berezin kernels \({P_{h^k}(z,w)}\) for ample invariant line bundles over compact toric projective kähler manifolds of dimension m. When the metric is real analytic, \({P_{h^k}(z,w) \simeq k^m {\rm exp} - k D(z,w)}\) where \({D(z,w)}\) is the diastasis. When the metric is only \({C^{\infty}}\) this asymptotic cannot hold for all \({(z,w)}\) since the diastasis is not even defined for all \({(z,w)}\) close to the diagonal. Our main result is that for general toric \({C^{\infty}}\) metrics, \({P_{h^k}(z,w) \simeq k^m {\rm exp} - k D(z,w)}\) as long as w lies on the \({\mathbb{R}_+^m}\)-orbit of z, and for general \({(z,w)}\), \({{\rm lim\,sup}_{k \to \infty} \frac{1}{k} {\rm log} P_{h^k}(z,w) \,\leq\, - D(z^*,w^*)}\) where \({D(z, w^*)}\) is the diastasis between z and the translate of w by \({(S^1)^m}\) to the \({\mathbb{R}_+^m}\) orbit of z. These results are complementary to Mike Christ’s negative results showing that \({P_{h^k}(z,w)}\) does not have off-diagonal exponential decay at “speed” k if \({(z,w)}\) lies on the same \({(S^1)^m}\)-orbit.     

Orbital fractional parentage coefficients for the harmonic oscillator shell model

The Hamiltonian ofn particles moving in a common harmonic oscillator potential has as its symmetry group the unitary groupU(3n) in 3n dimensions,n particle states of the harmonic oscillator shell model can be characterized as bases of irreducible representations (BIR) of the groupU(3n) and of certain subgroups of this group. Use is made of these subgroups for the factorization and calculation of 2, 3, and 4 particle fractional parentage coefficients (fpc) of the harmonic oscillator shell model. Recoupling coefficients for subgroup chains of the symmetric groupS (n) appear as factors in the fpc. These coefficients are analyzed and calculated explicitly. The 2, 3 and 4 particle fpc of the 1s 1p shell configuration are obtained as products of these recoupling coefficients with known reduced Wigner coefficients of the unitary groupU(3) in 3 dimensions. Possible applications are indicated.     

Strong homotopy Lie algebras,homotopy Poisson manifolds and Courant algebroids

We study Maurer–Cartan elements on homotopy Poisson manifolds of degree n. They unify many twisted or homotopy structures in Poisson geometry and mathematical physics, such as twisted Poisson manifolds, quasi-Poisson \(\mathfrak g\)-manifolds, and twisted Courant algebroids. Using the fact that the dual of an n-term \(L_\infty \)-algebra is a homotopy Poisson manifold of degree \(n-1\), we obtain a Courant algebroid from a 2-term \(L_\infty \)-algebra \(\mathfrak g\) via the degree 2 symplectic NQ-manifold \(T^*[2]\mathfrak g^*[1]\). By integrating the Lie quasi-bialgebroid associated to the Courant algebroid, we obtain a Lie-quasi-Poisson groupoid from a 2-term \(L_\infty \)-algebra, which is proposed to be the geometric structure on the dual of a Lie 2-algebra. These results lead to a construction of a new 2-term \(L_\infty \)-algebra from a given one, which could produce many interesting examples.     

Non-extensivity of the chemical potential of polymer melts

Following Flory’s ideality hypothesis, the chemical potential of a test chain of length n immersed into a dense solution of chemically identical polymers of length distribution P(N) is extensive in n . We argue that an additional contribution \( \delta\) \( \mu_{{{\rm c}}}^{}\)(n) ～ +1/\( \rho\) \( \sqrt{{n}}\) arises (\( \rho\) being the monomer density) for all P(N) if n ? 〈N〉 which can be traced back to the overall incompressibility of the solution leading to a long-range repulsion between monomers. Focusing on Flory-distributed melts, we obtain \( \delta\) \( \mu_{{{\rm c}}}^{}\)(n) \( \approx\) (1 - 2n/〈N〉)/\( \rho\) \( \sqrt{{n}}\) for n ? 〈N〉² , hence, \( \delta\) \( \mu_{{{\rm c}}}^{}\)(n) \( \approx\) -1/\( \rho\) \( \sqrt{{n}}\) if n is similar to the typical length of the bath 〈N〉 . Similar results are obtained for monodisperse solutions. Our perturbation calculations are checked numerically by analyzing the annealed length distribution P(N) of linear equilibrium polymers generated by Monte Carlo simulation of the bond fluctuation model. As predicted we find, e.g., the non-exponentiality parameter K _p \( \equiv\) 1 - 〈N ^p〉/p!〈N〉^p to decay as K _p \( \approx\) 1/\( \sqrt{{\langle N \rangle }}\) for all moments p of the distribution.     

Kaonic production of $ \Lambda$(1405) off deuteron target in chiral dynamics

The K^--induced production of \( \Lambda\)(1405) is investigated in K ^- d \( \rightarrow\) \( \pi\) \( \Sigma\) n reactions based on coupled-channels chiral dynamics, in order to discuss the resonance position of the \( \Lambda\)(1405) in the \( \bar{{K}}\) N channel. We find that the K ^- d \( \rightarrow\) \( \Lambda\)(1405)n process favors the production of \( \Lambda\)(1405) initiated by the \( \bar{{K}}\) N channel. The present approach indicates that the \( \Lambda\)(1405) -resonance position is 1420MeV rather than 1405MeV in the \( \pi\) \( \Sigma\) invariant-mass spectra of K ^- d \( \rightarrow\) \( \pi\) \( \Sigma\) n reactions. This is consistent with an observed spectrum of the K ^- d \( \rightarrow\) \( \pi^{{+}}_{}\) \( \Sigma^{{-}}_{}\) n with 686-844MeV/c incident K^- by bubble chamber experiments done in the 70s. Our model also reproduces the measured \( \Lambda\)(1405) production cross-section.     

Limits of Gaudin Algebras,Quantization of Bending Flows,Jucys–Murphy Elements and Gelfand–Tsetlin Bases

Gaudin algebras form a family of maximal commutative subalgebras in the tensor product of n copies of the universal enveloping algebra \({U(\mathfrak {g})}\) of a semisimple Lie algebra \({\mathfrak {g}}\). This family is parameterized by collections of pairwise distinct complex numbers z ₁, . . . , z _n . We obtain some new commutative subalgebras in \({U(\mathfrak {g})^{\otimes n}}\) as limit cases of Gaudin subalgebras. These commutative subalgebras turn to be related to the Hamiltonians of bending flows and to the Gelfand–Tsetlin bases. We use this to prove the simplicity of spectrum in the Gaudin model for some new cases.     

Der Einfluß der Umklapp-Prozesse auf den elektrischen Widerstand der Metalle bei tiefen Temperaturen

Blochs integral equation is solved under the assumption of a rigidly displaced electron distribution and thermal equilibrium of the lattice yielding the following results: If the Fermi surfaceE (t)=ξ periodically repeated in (t)-space consists of closed separate parts which are very near to each other (distanceq ^*), then transitions between two neighbouring surfaces (Umklapp-processes) give especially at rather low temperatures a large contribution to the electrical resistance. In simple cases the temperature dependence is given by ?_UP ～ Polynomial (T/Θ^*)e ^Θ*/T . Calculations were performed for alkali metals taking into account their anisotropic elastic behaviour. It was found that the contribution of the Umklapp-processes could be as high as 100 times that of the normal-processes. The agreement between theory and experiment is satisfactory excepting Li.     

Double Semions in Arbitrary Dimension

We present a generalization of the double semion topological quantum field theory to higher dimensions, as a theory of \({d-1}\) dimensional surfaces in a d dimensional ambient space. We construct a local Hamiltonian that is a sum of commuting projectors and analyze the excitations and the ground state degeneracy. Defining a consistent set of local rules requires the sign structure of the ground state wavefunction to depend not just on the number of disconnected surfaces, but also upon their higher Betti numbers through the semicharacteristic. For odd d the theory is related to the toric code by a local unitary transformation, but for even d the dimension of the space of zero energy ground states is in general different from the toric code and for even \({d > 2}\) it is also in general different from that of the twisted \({Z_2}\) Dijkgraaf–Witten model.     

Untersuchungen zur Mehrfach-Emission von Sekundärelektronen

CuBe- and NaCl-targets are bombarded by single electrons (100–600 eV). The secondary electrons accelerated by 40 kV strike the crystal of a scintillation counter, backed by a multichannel analyser. The probabilityP _n of emission ofn=0, 1, 2, 3, ... secondaries can be found from the pulse height distribution. The probability distributionP _n =f(n) shows a characteristic deviation from aPoisson's distribution. There was no evidence that there is a preference for even numbers ofn as found byBarrington andAnderson.     

Gauge Theories on ALE Space and Super Liouville Correlation Functions

We present a relation between ${\mathcal{N}=2}$ quiver gauge theories on the ALE space ${\mathcal{O}_{\mathbb{P}^1}(-2)}$ and correlators of ${\mathcal{N}=1}$ super Liouville conformal field theory, providing checks in the case of punctured spheres and tori. We derive a blow-up formula for the full Nekrasov partition function and show that, up to a U(1) factor, the ${\mathcal{N}=2^*}$ instanton partition function is given by the product of the character of ${\widehat{SU}(2)_2}$ times the super Virasoro conformal block on the torus with one puncture. Moreover, we match the perturbative gauge theory contribution with super Liouville three-point functions.     

The Structure of Radiative Tunnel Recombination Sites in Emulsion Microcrystals of AgBr(I)

To identify the structure of emissive tunnel recombination sites in the emulsion microcrystals of silver bromide AgBr(I) with iodine contaminations and to determine the role of an emulsion medium in their formation, the temperature dependence of the luminescence spectra in the range from 77 to 120 K, the kinetics of the growth of the maximum luminescence intensity value at λ ≈ 560 nm, and the luminescence flash spectrum stimulated by the infrared light are investigated. Two types of the AgBr_{1 – x}(I _x ) (x = 0.03) microcrystals—namely, obtained in an aqueous solution and on a gelatin substrate—are used in the studies. It is established that the emissive tunnel recombination sites with a luminescence maximum at λ ≈ 560 nm in AgBr_{1 – x}(I _x ) (x = 0.03) are the {(I _a ^- I _a ^- )Ag _i ⁺ } donor–acceptor complexes with the I _a ^- iodine ions located in neighbor anionic sites of the AgBr(I) crystal lattice, next to which the Ag _i ⁺ interstitial silver ion is positioned. With an increase in the temperature, the {(I _a ^- I _a ^- )Ag _i ⁺ } sites undergo structural transformation into the {(I _a ^- I _a ^- )Ag_in⁺} sites, where n = 2, 3, …. Moreover, the {(I _a ^- I _a ^- )Ag _in ⁺ } sites (n = 2) after the capture of an electron and hole also provide the tunnel recombination with a luminescence maximum at λ ≈ 720 nm. The influence of an emulsion medium consists in that gelatin interacts with the surface electron-localization sites, i.e., the interstitial silver ions Ag _in ⁺ , n = 1, 2, and forms the complexes {Ag _in ⁰ G⁺} (n = 1, 2) with them. The latter are deeper electron traps with a small capture cross section as compared to the Ag _in ⁺ sites (n = 1, 2) and that manifest themselves in that the kinetics of the luminescence growth in AgBr(I) to a stationary level at λ ≈ 560 nm is characterized by the presence of “flash firing.” At the same time, the luminescence flash stimulated by IR light, for which the Ag _in ⁺ (n = 1, 2) electron-localization sites are responsible, is absent. It is supposed that the electrons localized on the {Ag _in ⁺ G⁺} complexes (n = 2) retain the capability for emissive tunnel recombination with holes localized on paired iodine sites with a luminescence maximum at λ ≈ 750 nm.     

Exts and the AGT Relations

We prove the connection between the Nekrasov partition function of \({\mathcal{N}=2}\) super-symmetric U(2) gauge theory with adjoint matter and conformal blocks for the Virasoro algebra, as predicted by the Alday–Gaiotto–Tachikawa relations. Mathematically, this is achieved by relating the Carlsson–Okounkov Ext vector bundle on the moduli space of rank 2 sheaves with Liouville vertex operators. Our approach is geometric in nature, and uses a new method for intersection-theoretic computations of the Ext operator.     

Die absolute Intensität der durch Elektronenstoß in einer dicken Wolfram-Antikathode erzeugtenL α -Strahlung

The number\(N_{L_\alpha }^{dir} \) (produced) ofL _α -photons produced by electron-bombardment in a thick target of tungsten per incident electron has been measured absolutely with the Ross-filter method and relatively with the crystal-spectrometer method in the energyregion up to the 3.6 times theL _III-ionization energy\(E_{L_{III} } \). The result can be presented in the following empirical form:\(N_{L_\alpha }^{dir} \) (produced)=4π·?·(U ₀?1) ⁿ with ?=0.52·10^?4±5% andn=1.44±0.02\((U_0 = E_0 /E_{L_{III} }< 3.6)\). Out of this the number\(n_{L_{III} } \) ofL _III-ionizations per electron which is slowed down to the energy\(E_{L_{III} } \) within the target, has been evaluated. The computation of\(n_{L_{III} } \) out of the elementary process by usingBethe's non-relativistic formulae for totalL _III-ionization cross sectionQ _L and energy loss-dE/ds is in full agreement with experiment in the region 2<U ₀<3.6, if the constants in\(Q_{L_{III} } \) are chosen as follows:\(B = 4E_{L_{III} } , b_{L_{III} } = 0.25 \cdot 5.89\). By comparison of this result for\(b_{L_{III} } \) with the corresponding value ofb _K in the totalK-ionization cross-sectionQ _K for copper (b _K=0.35·2.26) it is concluded that\(Q_{L_{III} } \) is considerably higher than predicted by theory. The necessary correction factors as e.g. loss ofL _III-ionizations by rediffusion of electrons and portion of indirectly producedL _α -radiation-radiation are determined for tungsten quantitatively.