Flooding of chaotic eigenstates into regular phase space islands

We introduce a criterion for the existence of regular states in systems with a mixed phase space. If this condition is not fulfilled chaotic eigenstates substantially extend into a regular island. Wave packets started in the chaotic sea progressively flood the island. The extent of flooding by eigenstates and wave packets increases logarithmically with the size of the chaotic sea and the time, respectively. This new effect is observed for the example of island chains with just ten islands.     

Electromagnetic wave propagation with negative phase velocity in regular black holes

We discuss the propagation of electromagnetic plane waves with negative phase velocity in regular black holes. For this purpose, we consider the Bardeen model as a nonlinear magnetic monopole and the Bardeen model coupled to nonlinear electrodynamics with a cosmological constant. It turns out that the region outside the event horizon of each regular black hole does not support negative phase velocity propagation, while its possibility in the region inside the event horizon is discussed.     

Upper bounds on superpartner masses from upper bounds on the Higgs boson mass

The LHC is putting bounds on the Higgs boson mass. In this Letter we use those bounds to constrain the minimal supersymmetric standard model (MSSM) parameter space using the fact that, in supersymmetry, the Higgs mass is a function of the masses of sparticles, and therefore an upper bound on the Higgs mass translates into an upper bound for the masses for superpartners. We show that, although current bounds do not constrain the MSSM parameter space from above, once the Higgs mass bound improves big regions of this parameter space will be excluded, putting upper bounds on supersymmetry (SUSY) masses. On the other hand, for the case of split-SUSY we show that, for moderate or large tanβ, the present bounds on the Higgs mass imply that the common mass for scalars cannot be greater than 10(11) GeV. We show how these bounds will evolve as LHC continues to improve the limits on the Higgs mass.     

Comments on upper bounds on the inflationary Hubble constant

This is a comment on a letter by Hawking establishing an upper bound on the value of the Hubble parameter during inflation. Here we show that his derivation of the result is based on an invalid mathematical approximation, and demonstrate that a similar bound can be obtained from the standard “slow-rollover” constraint. We also present a derivation of the same result that is completely independent of the form of the scalar field potential.     

Perturbative upper bounds for the electronic energy of diatomic molecules from level-set boundaries of nuclear charge space

Simple bounds to the electronic energy of diatomics are obtained using curvature properties in the space of nuclear charges. The bounds present the same analytic structure in terms of the internuclear separation as the exact electronic energy. They are determined from a single-atom property and can be improved using perturbative expansions of the energy. The approximate continuation of the large-R perturbation series for the electronic energy of H₂⁺ is discussed as an illustrative example.     

A new hierarchy of upper and lower bounds on expectation values

Upper and lower bounds are constructe for expectation values of functions of a real random variable with derivatives up to orderN+1 which are alternately negative and positive over the whole range of interest. The bounds are given by quadrature formulas with weights and abscissas determined by the firstN+1 moments of the underlying probability distribution. Application to a simple disordered phonon system yields sharp bounds on the specific heat.     

Bell-type inequalities and upper bounds for multiqudit states

Multiqudit systems are studied in the tomographic-probability representation of quantum states. Results of calculations for the Bell-type numbers within the framework of classical probability theory and in quantum tomography are compared. Violations of the Bell-type inequalities are shown explicitly using the method of averaging in the tomographic picture of quantum states.     

Velocity and velocity bounds in static spherically symmetric metrics

We find simple expressions for velocity of massless particles with dependence on the distance, r, in Schwarzschild coordinates. For massive particles these expressions give an upper bound for the velocity. Our results apply to static spherically symmetric metrics. We use these results to calculate the velocity for different cases: Schwarzschild, Schwarzschild-de Sitter and Reissner-Nordström with and without the cosmological constant. We emphasize the differences between the behavior of the velocity in the different metrics and find that in cases with naked singularity there always exists a region where the massless particle moves with a velocity greater than the velocity of light in vacuum. In the case of Reissner-Nordström-de Sitter we completely characterize the velocity and the metric in an algebraic way. We contrast the case of classical naked singularities with naked singularities emerging from metric inspired by noncommutative geometry where the radial velocity never exceeds one. Furthermore, we solve the Einstein equations for a constant and polytropic density profile and calculate the radial velocity of a photon moving in spaces with interior metric. The polytropic case of radial velocity displays an unexpected variation bounded by a local minimum and maximum.     

Rigorous lower and upper bounds for the slope parameter

It is proved within the framework of axiomatic field theory that the logarithmic derivative of the absorptive part of the scattering amplitude with respect to momentum transfer is bounded from above by $\text{(15}\text{log}\text{s)}\text{[4√t(2 ? √t)]}$ for a sequence of s→+∞, and from below either in the s-channel by const. × s^?5 log^?4s or in the u-channel by const. × u^?5 log^?4u for at least one sequence of s or u →+∞, respectively. In the particular case of the s?u even-symmetric amplitude, a stronger lower bound is obtained; namely, const. × s^?5 log^?4s for at least one sequence of s→+∞. Here s, t, and u are the usual Mandelstam variables, and all bounds are obtained in the forward and the unphysical regions: 0?t<4 (in units of pion mass).It is observed that the Regge amplitude β(t)s^α(t) of high-energy scattering gives the same energy dependence as the above upper bound, and, furthermore, that the slope of the Regge trajectory is bounded from above by $\text{15}\text{[4√t(2 ? √t)]}\text{for}\text{0 < t < 4}$.     

Remarks on upper bounds for correlation functions of the Ising ferromagnet

We give a sufficient condition under which a general Ising ferromagnet correlation function 〈σ_R〉 is equal to tanhβJ_R. This lemma allows us to giveI. a new simple proof of the 3rd GKS inequality and to show that the r.h.s. of this inequality is the strongest bound for correlation functions from some class of functional bounds,II. the strongest form of the Thompson “mean field” bound and of the Krinsky and Emery bound,III. a generalization of a Krinsky inequality, what results in a good estimation of the pair correlation function in the Ising model.     

Kinematics of many-particle processes in invariant variables: Physical regions, phase space and all that

The kinematics of processes involving N spinless particles, in terms of invariant variables, are studied by means of Gram determinants. It is proposed that the Gram determinant method may provide a convenient unified treatment for general kinematical purposes. Using this approach, we first obtain the necessary and sufficient conditions for describing the physical regions; their solutions produce a systematic, practical scheme for constructing the physical regions explicitly. Secondly, a simple way of obtaining relations between geometrical and invariant quantities is described; some such relations are exhibited. The application of the Gram-determinant method is illustrated mainly with a discussion on the Toller angle dependence of the reggeon-reggeon-particle vertex function; in particular, we find a certain form of such dependence, in the asymptotic Regge limit, that arises naturally from the internal consistency of multi-Reggeism. Finally, the phase-space factor for many-particle productions is discussed.     

多模光纤模式场群速与相速的关系

为了从理论上统一射线光学和导波光学关于多模光纤中各模式场传播过程中时延的论述,试从介质波导理论出发,根据模式的特征根U随光纤归一化频率R的变化关系,在弱波导近似下导出了描述模式场相速Vp与群速Vg关系的重要结果:Vp*Vg=(c/n1)2。根据这一结果可以得出结论:对于低阶模式,由于相速Vp慢,所以群速快;高阶模式其相速Vp快,所以群速慢。对于给定的光纤,利用射线光学和波导光学进行了带宽估计,2种理论计算结果的一致性,印证了上述关系的正确性。     

Lower and upper bounds on the critical temperature for anisotropic three-dimensional Ising model

The Ising model is considered on a simple cubic lattice, with a coupling constant J along one axis and coupling constants J’ along the remaining two axes. The transfer-matrix technique and an extended phenomenological renormalization group theory [18, 19] are applied to obtain two-sided bounds on the critical temperature for the model with J′/J≤1. The bounds monotonically converge with decreasing J′/J and provide improved estimates for the phase-transition temperature in anisotropic three-dimensional Ising model, as compared with those available from the literature.     

Converging upper and lower bounds for ground-state energies of atomic nuclei

The production of K⁺-mesons in proton-nucleus collisions from 1.0 to 2.3 GeV is analyzed with respect to one-step nucleon-nucleon (NN NYK⁺) and two-step -nucleon (N K⁺YN) or pion-nucleon (N K⁺Y) production channels on the basis of a coupled-channel (CBUU) transport approach including the kaon final-state-interactions (FSI). Momentum-dependent potentials for the nucleon, hyperon and kaon in the final state are included as well as K⁺ elastic rescattering in the target nucleus. The transport calculations are compared to the experimental K⁺ spectra taken at COSY-Jülich. Our systematic analysis of K⁺ spectra from ¹²C, ⁶³Cu, ¹⁰⁷Ag and ¹⁹⁷Au targets as well as their momentum differential ratios gives a repulsive K⁺ potential of 20±5 MeV at normal nuclear matter density.     

Analytic upper and lower bounds for the period of nonlinear oscillators

We show that analytic expressions for the frequency of second-order nonlinear oscillations can be obtained from dual variational principles. At each amplitude two analytic expressions can be constructed which constitute upper and lower bounds to the exact value of the frequency. The results are accurate at small and large amplitude and compare well with the perturbative approach.     

Lower and upper variational bounds in calculations of Coulomb and nuclear systems

All formulas that are necessary for deriving not only upper (E _U) but also lower (E _L) variational bounds on the energy of systems featuring a few nonrelativistic particles are obtained with trial functions in the form of expansions in multidimensional Gaussian functions or exponentials. For potentials that are used most widely, all matrix elements are expressed in terms of known functions, a circumstance that simplifies considerably relevant numerical calculations. This is so for systems featuring an arbitrary number of particles in the case of a Gaussian basis and for three-particle systems in the case of an exponential basis. Numerical results for E _U and E _L, which are characterized by record accuracies, are presented for some Coulomb and nuclear systems such as the He atom; the e ⁺ e ^? e ^?, ppμ^?, 3α, and 4α systems; and hypertritium (pnΛ). Lower bounds with exponential trial functions are obtained for the first time (the corresponding formulas are presented for the first time as well); for a Gaussian basis, lower bounds for Coulomb systems have not been known either. Given E _L and E _U, limits within which the exact value of energy, E ₀, lies can be indicated with confidence. Moreover, an analysis of the correlation between E _L and E _U with increasing number of terms in the expansion of the trial function makes it possible to improve the accuracy (at least by one order of magnitude) of the value E _∞ extrapolated to infinity. By considering specific examples, it is shown that the exponential basis is advantageous in relation to the Gaussian one.     

Sign phase transition and directed paths in random media

We consider a lattice model which corresponds to the high temperature expansions of disordered Ising and Heisenberg models and to the deeply localized regime of the disordered Anderson model. The spin correlation functions for the Ising and Heisenberg model and the amplitude of electron tunneling for the Anderson model exhibit a “sign phase transition.” At small concentration x of scatterers with a negative scattering amplitude these quantities have predictable signs while at large x their signs are unpredictable. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 4, 283–288 (25 August 1996) Published in English in the original Russian Journal. Edited by J. R. Anderson.     

Protonium decay and phase space

Nucleon-antinucleon at rest presents a variety of channels, where wide mesons often interfere, as shown by the analysis of protonium decay into three pions by the Asterix and Crystal Barrel experiments. A statistical model for emission of the narrow mesonsπ, η, η′ ω, K, ¯K is presented to account for the general profile of the reaction. It is an alternative to a model based on two-doorway state dominance proposed earlier. It allows direct prediction with phenomenological channels, but deals only with branching ratios, not with the detailed structure of the final states. The initial state interactions do not influence the bulk of predictions, although they matter for two-particle branching ratios, which are small. The model is in reasonable agreement with present experimental data and is offered as a standard for comparison with forthcoming results. Some obvious deviations claim for a dynamical explanation.