Are there sterile neutrinos in the flux of solar neutrinos on the earth?

It is shown that the future SNO and Super-Kamiokande experiments, in which high energy⁸B neutrinos will be detected through the observation of CC, NC and –e elastic scattering processes, could allow to reveal in a model independent way the presence of sterile neutrinos in the flux of solar neutrinos on the earth. Lower bounds for different averaged values of the probability of transition of solar v^e'S into sterile states and for the total flux of⁸B neutrinos are derived in terms of measurable quantities. The possibilities to reveal the presence of v and/or v in the solar neutrino flux on the earth are also considered and the case of transitions of solar v^e'S only into sterile states is discussed. Some numerical results for a simple model with v–v^s mixing are given.     

Signal of new physics and chemical composition of matter in core-crossing neutrinos

We consider the non-standard matter effect in flavor conversion of neutrinos crossing the core of the Earth. We show that oscillations of core-crossing neutrinos with E≳0.5 GeV can well be described by first order perturbation theory. We show that due to the non-standard matter effect a varying chemical composition in the Earth can modify the neutrino flavor conversion by 100%. The effects of CP violating phases in non-standard neutral current interactions are emphasized in particular.     

Can sterile neutrinos be the dark matter?

We use the Ly-alpha forest power spectrum measured by the Sloan Digital Sky Survey and high-resolution spectroscopy observations in combination with cosmic microwave background and galaxy clustering constraints to place limits on a sterile neutrino as a dark matter candidate in the warm dark matter scenario. Such a neutrino would be created in the early Universe through mixing with an active neutrino and would suppress structure on scales smaller than its free-streaming scale. We ran a series of high-resolution hydrodynamic simulations with varying neutrino masses to describe the effect of a sterile neutrino on the Ly-alpha forest power spectrum. We find that the mass limit is m(s) >13 keV at 95% C.L. (9 keV at 99.9%), which is above the upper limit allowed by x-ray constraints, excluding this candidate from being all of the dark matter in this model.     

Absence of “condensed matter effects” in the solar neutrino problem

It has been suggested by Kim, Rabinowitz, and Yoon that the solar neutrino problem can be explained by taking account of so-called condensed matter effects. We show with the aid of Liouville's theorem that the effects in question are already included in the standard treatment.     

Disturbed solution of the El Ni?no-southern oscillation sea–air delayed oscillator

A class of delayed oscillators of El Ni?o-southern oscillation (ENSO) models is considered. Using the delayed theory, the perturbed theory and other methods, the asymptotic expansions of the solutions for ENSO models are obtained and the asymptotic behaviour of solution of corresponding problem is studied.     

Analytic presentation of a solution of the Schrödinger equation

High-precision approximate analytic expressions for energies and wave functions are found for arbitrary physical potentials. The Schrödinger equation is cast into the nonlinear Riccati equation, which is solved analytically in first iteration of the quasi-linearization method (QLM). The zeroth iteration is based on general features of the exact solution near the boundaries. The approach is illustrated on the Yukawa potential. The results enable accurate analytical estimates of effects of parameter variations on physical systems.     

Unified picture for Dirac neutrinos,dark matter,dark energy and matter–antimatter asymmetry

We propose a unified scenario to generate the masses of Dirac neutrinos and cold dark matter at the TeV scale, understand the origin of dark energy and explain the matter–antimatter asymmetry of the universe. This model can lead to significant impact on the Higgs searches at LHC.     

Asymptotic solution for a class of sea-air oscillator model for El Nin^～o-southern oscillation

The El Nifio-Southern Oscillation （ENSO） is an interannual phenomenon involved in the tropical Pacific Oceanatmosphere interactions. In this paper, an asymptotic method of solving the nonlinear equation for the ENSO model is used. And based on a class of oscillator of ENSO model, the approximate solution of a corresponding problem is studied by employing the perturbation method. Firstly, an ENSO model of nonlinear time delay equation of equatorial Pacific is introduced, Secondly, by using the perturbed method, the zeroth and first order asymptotic perturbed solutions are constructed. Finally, from the comparison of the values for a figure, it is seen that the first asymptotic perturbed solution using the perturbation method has a good accuracy. And it is proved from the results that the perturbation method can be used as an analytic operation for the sea surface temperature anomaly in the equatorial Pacific of the atmosphere-ocean oscillation for the ENSO model.     

A solution spectrum of the nonlinear schrödinger equation

The soliton solutions of the form=A/coshkx and=B tanhkx of the nonlinear Schrödinger equation have been considered with respect to many problems. In this paper, it is shown that the nonlinear Schrödinger equation also possesses a solution manifold that generalizes the above soliton functions and provides a discrete spectrum of eigenfunctions and eigenvalues. With the help of a slight modification of these eigenfunctions, it is possible to extend them to the relativistic case, where they become solutions of a nonlinear Klein-Gordon equation associated with a discrete mass spectrum.     

Can sterile neutrinos be ruled out as warm dark matter candidates?

We present constraints on the mass of warm dark matter (WDM) particles from a combined analysis of the matter power spectrum inferred from the Sloan Digital Sky Survey Lyman-alpha flux power spectrum at 2.2相似文献   

On the power series solution of the Schrödinger equation

A numerical method for solving the Schrödinger equation for a one-dimensional potential expressed as a function which increases in both directions away from its minimum is proposed. The basic assumption relies on the asymptotic properties of the solution. We exemplify the method calculating energies and expectation values for the quartic anharmonic oscillator.     

Novel method for solution of coupled radial Schrödinger equations

One of the major problems in numerical solution of coupled differential equations is the maintenance of linear independence for different sets of solution vectors. A novel method for solution of radial Schrödinger equations is suggested. It consists of rearrangement of coupled equations in a way that is appropriate to avoid usual numerical instabilities associated with components of the wave function in their classically forbidden regions. Applications of the new method for nuclear structure calculations within the hyperspherical harmonics approach are given.     

Smoothness and non-smoothness of the fundamental solution of time dependent Schrödinger equations

The fundamental solutionE(t,s,x,y) of time dependent Schrödinger equationsi?u/?t=?(1/2)Δu+V(t,x)u is studied. It is shown that

?E(t,s,x,y) is smooth and bounded fort≠s if the potential is sub-quadratic in the sense thatV(t,x)=o(|x|²) at infinity;

? in one dimension, ifV(t,x)=V(x) is time independent and super-quadratic in the sense thatV(x)≧C(1+|x|)^2+ε at infinity,C>0 and ε>0, thenE(t,s,x,y) is nowhereC ¹.

The result is explained in terms of the limiting behavior as the energy tends to infinity of the corresponding classical particle.     

A solution spectrum of the nonlinear Schrödinger equation. II

It was shown in a previous communication that the nonlinear Schrödinger equation exhibits a spectrum of eigenfunctions of the form = _k,A _k (coshkx) ^–k and = _k B _k (coshkx) ^–k–1sinhkx, and the corresponding eigenvalues of the energy are related to a band structure with a characteristic energy gap as a significant feature. In the present paper, it is shown that a further spectrum exists exhibiting the general structure = _k=0 A _k(cosh kx)^–k–1/2and = _k=0 B_k(cosh kx)^–k–3/2sinhkx and yielding also a band structure. An extension of the solution spectrum to a nonlinear Klein-Gordon equation and a nonlinear Dirac equation does not imply essential difficulties, and the corresponding characteristic band structure has to be related to a mass spectrum.     

Exact solution of the discrete Schrödinger equation for ferromagnetic chains

It is shown that Bethe's exact solution for the finite Heisenberg ferromagnetic chain can be obtained via a direct Fourier transform. Unlike the Bethe ansatz approach, the latter is not confined to one space dimension and opens the possibility of obtaining exact solutions in higher dimensions.     

The periodic solution to the model for the El Nio-Southern oscillation

A class of oscillator of the El Ni?o-Southern oscillation model is considered. Using Mawhin's continuation theorem, a result on the existence of periodic solutions for ENSO model is obtained.