Commentary on “Total Hadronic Cross-Section Data and the Froissart–Martin Bound,” by Fagundes, Menon, and Silva

This commentary on the paper ??Total Hadronic Cross-Section Data and the Froissart?CMartin Bound,?? by Fagundes, Menon, and Silva (Braz. J. Phys. doi:10.1007/s13538-012-0099-5, 2012) was invited by the editors of the Brazilian Journal of Physics to appear directly after the above authors?? printed version, in the same journal issue. We here challenge the paper??s conclusions that the Froissart bound was violated. We will show that this conclusion follows from a statistical methodology that we question and will present compelling supplementary evidence that the latest ultrahigh-energy experimental pp cross-section data are consistent with a ln ² s behavior that satisfies the Froissart bound.     

Strong Enhancement of Electron–Ion Recombination Owing to Free–Bound and Bound–Bound Resonance Transitions

The effect of free–bound and bound–bound resonance nonadiabatic transitions of an electron on electron–ion recombination rates in the plasma of a Ne/Xe and Ar/Xe inert gas mixture has been studied. A kinetic model of recombination has been proposed including energy relaxation in collisions with electrons, resonant electron capture to Rydberg states through three-body collisions of Xe⁺ ions with Ne or Ar atoms and dissociative recombination of NeXe⁺ or ArXe⁺ ions, and n → n' resonance transitions. It has been shown that effective resonance processes occurring in quasimolecular systems sharply increase both the recombination coefficient and the effect of collisions with neutral particles even at quite high degrees of ionization of the plasma.     

A Rigorous Upper Bound on the Propagation Speed for the Swift–Hohenberg and Related Equations

We prove that if the initial condition of the Swift–Hohenberg equation $$\partial _t u(x,t) = (\varepsilon ^2 - (1 + \partial _x^2 )^2 ){\text{ }}u(x,t) - u^3 (x,t)$$ is bounded in modulus by Ce ^?βx as x→+∞, the solution cannot propagate to the right with a speed greater than $$\mathop {\sup }\limits_{0 < {\gamma } \leqslant \beta } {\gamma }^{ - 1} (\varepsilon ^2 + 4{\gamma }^2 + 8{\gamma }^4 ).$$ This settles a long-standing conjecture about the possible asymptotic propagation speed of the Swift–Hohenberg equation. The proof does not use the maximum principle and is simple enough to generalize easily to other equations. We illustrate this with an example of a modified Ginzburg–Landau equation, where the critical speed is not determined by the linearization alone.     

Hadronic ϕ production and the lund model for lowp T interactions

Experimental results on inclusive ? production are compared with the Lund model for lowp _T hadronic interactions. The data is based on a sample of 600,000 ? mesons in the kinematic rangep _T <1.0 (GeV/c)² and 0.0<x _F<0.4, produced in π^±,K ^±,p and \(\bar p\) Be interactions at 100 GeV/c and 120 GeV/c incident momentum. The Lund model reproduces the shapes of the longitudinal differential cross sections reasonably well, but the relative cross sections for incident, π,K andp show a discrepancy with the data.     

The Bertlmann–Martin Inequality and Spin Degrees of Freedom

The Bertlmann–Martin inequality based on the dipole sum rule is revisited taking into account the spin degrees of freedom. We consider 1 and 2 particles of spin 1/2 in a mean field, adding a spin dependent interaction. The derivation of the inequality relies on the closure relation. We discuss the effect of the Pauli principle, and the restrictions it imposes on the use of the closure relation. The problem is exemplified by a simple model based on harmonic forces. Moreover, in the 2 particle case, the model we use is separable in the relative and centre of mass coordinates. In this case, we show that for operators connecting only singlet states, their sum rule can be calculated in the usual way, i.e. via the double commutator of this operator with the Hamiltonian. An upper bound can also be obtained by using the Bertlmann–Martin technique. This is not possible for operators involving a transition between singlet and triplet states.     

Study of the asymptotic Cramér–Rao Bound for the COLD uniform linear array

In this paper, we study the Cocentered Orthogonal Loop and Dipole pairs Uniform Linear Array (COLD-ULA) which is sensitive to the source polarization in the context of the localization of time-varying narrow-band far-field sources. We derive and analyze nonmatrix expressions of the deterministic Cramér–Rao Bound (${\text{CRB}}^{\mathrm{(COLD)}}$) for the direction and the polarization parameters under the assumption that all the sources are lying in the azimuthal plane. We denote this bound by ${\text{ACRB}}^{\mathrm{(COLD)}}$, where the “A” stands for Asymptotic, meaning that the presented results are derived under the assumption that the number of sensors is sufficiently large. While, to our knowledge, closed-form (nonmatrix) expressions of the ${\text{CRB}}^{\mathrm{(COLD)}}$ for multiple time-varying polarized sources signal do not exist in the literature, we show that the ${\text{ACRB}}^{\mathrm{(COLD)}}$ takes a closed-form (nonmatrix) expression in this context and is a good approximation of the ${\text{CRB}}^{\mathrm{(COLD)}}$ even if the number of sensor is moderate (about ten), if the source signals are not spatially too close. Our approach has two important advantages: (i) the computational complexity of the proposed closed-form of the bound is very low, compared to the brute force computation of a matrix-based deterministic CRB in case of time-varying model parameters and (ii) useful informations can be deduced from the closed-form expression on the behavior of the bound. In particular, we prove that the ${\text{ACRB}}^{\mathrm{(COLD)}}$ for the direction parameter is not affected by the knowledge or the lack of it concerning the polarization parameters. Another conclusion is that with a COLD-ULA, more model parameters can be estimated than for the uniformly polarized ULA without degrading the estimation accuracy of the localization parameter. Finally, we also study the ${\text{ACRB}}^{\mathrm{(COLD)}}$ for a priori known complex amplitudes.     

The Norm Convergence of the Trotter–Kato Product Formula with Error Bound

The norm convergence of the Trotter–Kato product formula with error bound is shown for the semigroup generated by that operator sum of two nonnegative selfadjoint operators A and B which is selfadjoint.An erratum to this article can be found at     

Peculiarities of Structure and Phase Composition of Ternary NiMn–NiTi Alloys with a Quasi-Binary Cross-Section

Russian Physics Journal - The influence of a chemical composition on the phase composition, stability, and crystal structure type of the austenitic and martensitic ternary NiMn–NiTi alloys...     

Exact Bound Solution of the Klein-Gordon Equation and the Dirac Equation with Rosen-MorseⅡ Potential

In this paper, the relativistic Rosen-Morse II potential is investigated by solving the Klein-Gordon and the Dirac equations with equal attractive scalar s(r) and repulsive vector v(r) potentials. The exact energy equations of the bound state are obtained by the method of supersymmetric and shape invariance. Finally, a kind of special potential about Rosen-MorseⅡ potential is discussed.     

Decay of the Bethe–Salpeter Kernel and Bound States for Lattice Classical Ferromagnetic Spin Systems at High Temperature

We consider lattice classical ferromagnetic spin systems at high temperature (1) with nearest neighbor interactions and even single-spin distributions (ssd). Associated with each system is an imaginary time lattice quantum field theory. It is known that there is a particle of mass m–ln in the energy-momentum spectrum. If s ⁴–3s ²²<0, where s ^k is the kth moment of the ssd, and is sufficiently small, we show that in the two-particle subspace there is no mass spectrum up to 2m. For >0 we show that the only mass spectrum in (m, 2m) is a bound state of mass m _b=2m+ln(1–)+O(), where =(+2s ²²)^–1. A bound on the decay of the kernel of a Bethe–Salpeter equation is obtained and used to prove these results.     

Bound diquarks and their Bose–Einstein condensation in strongly coupled quark matter

We explore the formation of diquark bound states and their Bose–Einstein condensation (BEC) in the phase diagram of three-flavor quark matter at nonzero temperature, T, and quark chemical potential, μ  . Using a quark model with a four-fermion interaction, we identify diquark excitations as poles of the microscopically computed diquark propagator. The quark masses are obtained by solving a dynamical equation for the chiral condensate and are found to determine the stability of the diquark excitations. The stability of diquark excitations is investigated in the T–μ$T\text{–}\mu$ plane for different values of the diquark coupling strength. We find that diquark bound states appear at small quark chemical potentials and at intermediate coupling strengths. Bose–Einstein condensation of non-strange diquark states occurs when the attractive interaction between quarks is sufficiently strong.     

Bound states and resonance states of the plasma-embedded tdμ and ddμ molecular ions

We have investigated the bound states and resonance states of plasma-embedded tdμ and ddμ molecular ions using accurate correlated basis functions. The plasma effect has been taken care of by considering the Debye shielding approach of plasma modeling which admits a variety of plasma conditions. The density of resonance states are calculated using the stabilization method. The ground and excited states energies, and the S-wave resonance energies of tdμ and ddμ molecular ions immersed in plasmas are reported for various shielding parameters, along with the 1S and 2S threshold energies of the tμ and dμ atoms.     

Inverting the Nakanishi Integral Relation for a Bound State Euclidean Bethe–Salpeter Amplitude

The extraction of the weight function g of the Nakanishi integral representation of the Bethe–Salpeter amplitude is investigated. We studied the numerical inversion of the discretized Nakanishi kernel in the case of an Euclidean bound state. The discretized kernel is regularized by adding the identity operator times a small regularisation parameter \({\varepsilon}\) to avoid numerically unstabilities. We have found that the weight function g as well as the associated light-front valence wave function are unstable against variation of \({\varepsilon}\). These results suggest that the extraction of the Nakanishi weight function from an Euclidean amplitude, is an ill-defined problem. Without further assumptions on the solution or/and without developing more elaborate methods, the Nakanishi weight function, as well as the corresponding light-front valence wave function, cannot be safely determined.