Regular Series


Vol. 35 (2004), No. 9, pp. 2151 – 2325


Brownian Motion: a Case of Temperature Fluctuations

abstract

A diffusion process of a Brownian particle in a medium of temperature \(T\) is re-considered. We assume that temperature of the medium fluctuates around its mean value. The velocity probability distribution is obtained. It is shown that the stationary state is not a thermodynamic equilibrium state described by the Maxwell distribution. Instead a nonequilibrium state is produced by temperature fluctuations.


Entropy for Color Superconductivity in Quark Matter

abstract

We study a known model for color superconductivity with three colors and three massless quark flavors including pairing effects. By using the Hamiltonian in the color–flavor basis we can calculate the quantum entropy. From this calculation we are able to further investigate the phases of the color superconductor, for which we find a rather sharp transition to color superconductivity above a chemical potential around \(290\;\)MeV.


Noise Reduction in Chaotic Time Series by a Local Projection with Nonlinear Constraints

abstract

On the basis of a local-projective (LP) approach we develop a method of noise reduction in time series that makes use of nonlinear constraints appearing due to the deterministic character of the underlying dynamical system. The Delaunay triangulation approach is used to find the optimal nearest neighboring points in time series. The efficiency of our method is comparable to standard LP methods but our method is more robust to the input parameter estimation. The approach has been successfully applied for separating a signal from noise in the chaotic Henon and Lorenz models as well as for noisy experimental data obtained from an electronic Chua circuit. The method works properly for a mixture of additive and dynamical noise and can be used for the noise-level detection.


Heavy Lepton Production at Linac\(\otimes \)LHC

abstract

We investigate the production, signatures and backgrounds of new heavy leptons via string inspired E\(_{6}\) model at the proposed Linac\(\otimes \)LHC. Assuming maximal mixing, the production rate is found to be 2000 events per year for masses up to 3 TeV.


Kibble–Żurek Mechanism in the Ginzburg Regime: Numerical Experiment in the Ising Model

abstract

Kibble–Żurek mechanism is a theory of defect formation in a non-equilibrium continuous phase transition. So far the theory has been successfully tested by numerical simulations and condensed matter experiments in a number of systems with small thermal fluctuations. This paper reports first numerical test of the mechanism in a system with large thermal fluctuations and strongly non-mean-field behavior: the two dimensional Ising model. The theory predicts correctly the initial density of defects that survive a quench from the disordered phase. However, before the system leaves the Ginzburg regime of large fluctuations most of these defects are annihilated and the final density is determined by the dynamics of the annihilation process only.


CJK-Improved 5 Flavour LO Parton Distributions in the Real Photon

abstract

Radiatively generated, LO quark (\(u,d,s,c,b\)) and gluon densities in the real, unpolarized photon, improved in respect to our previous paper F. Cornet, P. Jankowski, M. Krawczyk and A. Lorca, Phys. Rev. D68, 014010 (2003), are presented. We perform three global fits to the \(F_2^{\gamma }\) data, using the LO DGLAP evolution equation. We improve the treatment of the strong coupling running and use lower values of \({\mit \Lambda }_{\rm QCD}\), as we have found that the too high values adopted in the previous work caused the high \(\chi ^2\) of the fits. In addition to the modified FFNS\(_{\rm CJKL}\) model, referred to as FFNS\(_{\rm CJK}\)1 we analyse a FFNS\(_{\rm CJK}\)2 model in which we take into account the resolved-photon heavy-quark contribution. New CJK model with an improved high-\(x\) behaviour of the \(F_2^{\gamma }\left (x,Q^2\right )\) is proposed. Finally, in the case of the CJK model we abandon the valence sum rule imposed on the VMD input densities. New fits give \(\chi ^2\) per degree of freedom about 0.25 better than the old results. All features of the CJKL model, such as the realistic heavy-quark distributions, good description of the LEP data on the \(Q^2\) dependence of the \(F_2^{\gamma }\) and on \(F_{2,c}^{\gamma }\) are preserved. Moreover we present results of an analysis of the uncertainties of the CJK parton distributions due to the experimental errors. It is based on the Hessian method used for the proton and very recently applied for the photon by one of us. Parton and structure function parametrizations of the best fits in both FFNS\(_{\rm CJK}\) and CJK approaches are made accessible. For the CJK model we provide also sets of test parametrizations which allow for calculation of uncertainties of any physical value depending on the real photon parton densities.


Can One of Three Righthanded Neutrinos Be Light Enough to Produce a Small LSND Effect?

abstract

It is shown on the ground of a simple \(6\times 6\) neutrino mixing model that one of three conventional sterile (righthanded) neutrinos, if light enough, may be consistently used for explaining a small LSND effect. Then, it is still considerably heavier than the three active (lefthanded) neutrinos, so that a kind of soft seesaw mechanism can work. The usual condition that the Majorana lefthanded component of the overall \(6\times 6\) neutrino mass matrix ought to vanish, implies the smallness of active-neutrino masses versus sterile-neutrino masses, when three mixing angles between both sorts of neutrinos are small. In the presented model, the mass spectrum of active neutrinos comes out roughly degenerate, lying in the range (5–7.5)\(\times 10^{-2}\) eV, if there is a small LSND effect with the amplitude of the order \(10^{-3}\) and with the mass-squared splitting \(\sim 1~{\rm eV}^2\).


A New Proof of Existence of a Bound State in the Quantum Coulomb Field

abstract

Let \(S(x)\) be a massless scalar quantum field which lives on the three-dimensional hyperboloid \(xx= (x^0)^2-(x^1)^2-(x^2)^2-(x^3)^2=-1.\) The classical action is assumed to be \((\hbar =1=c)(8\pi e^2)^{-1}\int dx g^{ik}\partial _i S\partial _k S\), where \(e^2\) is the coupling constant, \(dx\) is the invariant measure on the de Sitter hyperboloid \(xx=-1\) and \(g_{ik}, i,k=1,2,3\), is the internal metric on this hyperboloid. Let \(u\) be a fixed four-velocity i.e. a fixed unit time-like vector. The field \(S(u)=(1/4 \pi )\int dx\delta (ux)S(x)\) is smooth enough to be exponentiated, being an average of the operator valued distribution \(S(x)\) over the entire Cauchy surface \(ux=0\). We prove that if \(0\lt e^2\lt \pi \), then the state \(|u \big \gt =\exp (-iS(u))\mid 0\big \gt \), where \(\mid 0 \big \gt \) is the Lorentz invariant vacuum state, contains a normalizable eigenstate of the Casimir operator \(C_1=-(1/2)M_{\mu \nu }M^{~\mu \nu }\); \(M_{\mu \nu }\) are generators of the proper orthochronous Lorentz group. The eigenvalue is \((e^2/\pi )(2-(e^2/\pi )).\) This theorem was first proven by the Author in 1992 in his contribution to the Czyż Festschrift, see Erratum Acta Phys. Pol. B 23, 959 (1992). In this paper a completely different proof is given: we derive the partial, differential equation satisfied by the matrix element \(\left \lt u\mid \exp (-\sigma C_1)\mid u\right \gt , \sigma \gt 0\), and show that the function \(\exp (z)\cdot (1-z)\cdot \exp [-\sigma z (2-z)], z= e^2/ \pi \), is an exact solution of this differential equation, recovering thus both the eigenvalue and the probability of occurrence of the bound state. A beautiful integral is calculated as a byproduct.


Hadronic Effective Field Theory Applied to \({\mit \Lambda }\)-Hypernuclei

abstract

In the present work, the approach of Furnstahl, Serot, and Tang (FST) is extended to the region of nonzero strangeness in application to single-particle states in single \({\mit \Lambda }\)-hypernuclei. To include \({\mit \Lambda }\)’s, an additional contribution to their effective Lagrangian is systematically constructed within the framework of FST. The relativistic Hartree (Kohn–Sham) equations are solved numerically, and least-square fits to a series of experimental levels are performed at various levels of truncation in the extended Lagrangian. The ground-state properties of any \({\mit \Lambda }\)-hypernuclei are then predicted. In addition, ground-state \({\mit \Lambda }\)-particle–nucleon–hole splittings are calculated where appropriate, and the approach is calibrated against a calculation of the \(\mathrm {s}_{1/2}\)-doublet splitting in the nucleus \(^{32}_{15}\mathrm {P}_{17}\).


Bethe Plots and Neutron Halo

abstract

The relative excess of a neutron density introduced by Bethe is applied to classify atomic nuclei with respect to a neutron halo. Calculations are based on the relativistic mean field model and are performed for 116 spherically symmetric nuclei across the periodic system of elements and for a group of deformed nuclei studied in antiproton annihilation reaction at the LEAR facility in CERN. Basic properties of the neutron excess function are discussed.


The Associated \({\mit \Sigma }\) Production and the \({\mit \Sigma }\)-Nucleus Potential

abstract

Kaon spectrum from (\(\pi ^-,K^+\)) reaction on \(^{28}\)Si target in the region of \({\mit \Sigma }\) production is analyzed in impulse approximation for different strengths of the \({\mit \Sigma }\) single particle potential. It is concluded that this potential is repulsive, and its strength is consistent with the Nijmegen model F of the hyperon–nucleon interaction.


Nuclear Resonance Scattering of Circularly Polarized SR

abstract

Results of the experiments with nuclear resonance scattering of synchrotron radiation aiming at construction of the circularly polarized beam suitable for nuclear hyperfine studies are reported. Si\((4\ 0\ 0)\) single crystal slab, 100 \({\mu }\)m thick, was used as a quarter wave plate. Observed twofold reduction of the intensity in proposed geometry is due to the Si crystal itself. Hyperfine interactions are used to probe polarization state of the synchrotron beam. Too large angular beam divergence did not allow for achieving full circular polarization of photons. Consequently, further experiments are proposed to overcame beam divergence problems. A number of calculations presented in the paper show that cheap and easily available Si plate can serve as an effective desired polarizer.


top

ver. 2024.03.17 • we use cookies and MathJax