Eine neue Methode zur Berechnung der elektrischen Leitfähigkeit von Halbleitern in starken homogenen elektrischen Feldern

The Boltzmann equation for electrons in a semiconductor is assumed to be of the form $$\frac{{\partial f}}{{\partial t}} + F \cdot \frac{{\partial f}}{{\partial k}} = \frac{{h - f}}{{\tau _0 }} + \frac{1}{{\tau \left( k \right)}} \cdot \frac{1}{{4\pi }}\int {d\Omega 'w\left( \theta \right)\left( {f\left( {k,\vartheta '} \right) - f\left( {k,\vartheta '} \right)} \right)} $$ whereh is the Maxwell-Boltzmann distribution. The energy surface structure of the lattice electronsE(k) is assumed to be spheric. The stationary solutions for strong electric fields show a concentration of electrons into the field direction (field orientation), if the elastic collision frequency is not too large. This means, at least for large energies, that nearly all electrons are in a cone with small aperture around the field direction. Every transport problem whose collision operator can be reduced to the upper form at least for large energies, can be solved by a perturbation method whose zeroth order is the ideal field orientation. The conditions for a field orientation of the electron distribution to exist will be investigated.     

Three-loop on-shell charge renormalization without integration:\Lambda _{QED}^{\overline {MS} } to four loops

Using algebraic methods, we find the three-loop relation between the bare and physical couplings of one-flavourD-dimensional QED, in terms of Γ functions and a singleF ₃₂ series, whose expansion nearD=4 is obtained, by wreath-product transformations, to the order required for five-loop calculations. Taking the limitD→4, we find that the \(\overline {MS} \) coupling \(\bar \alpha (\mu )\) satisfies the boundary condition $$\begin{gathered} \frac{{\bar \alpha (m)}}{\pi } = \frac{\alpha }{\pi } + \frac{{15}}{{16}}\frac{{\alpha ^3 }}{{\pi ^3 }} + \left\{ {\frac{{11}}{{96}}\zeta (3) - \frac{1}{3}\pi ^2 \log 2} \right. \hfill \\ \left. { + \frac{{23}}{{72}}\pi ^2 - \frac{{4867}}{{5184}}} \right\}\frac{{\alpha ^4 }}{{\pi ^4 }} + \mathcal{O}(\alpha ^5 ), \hfill \\ \end{gathered} $$ wherem is the physical lepton mass and α is the physical fine structure constant. Combining this new result for the finite part of three-loop on-shell charge renormalization with the recently revised four-loop term in the \(\overline {MS} \) β-function, we obtain $$\begin{gathered} \Lambda _{QED}^{\overline {MS} } \approx \frac{{me^{3\pi /2\alpha } }}{{(3\pi /\alpha )^{9/8} }}\left( {1 - \frac{{175}}{{64}}\frac{\alpha }{\pi } + \left\{ { - \frac{{63}}{{64}}\zeta (3)} \right.} \right. \hfill \\ \left. { + \frac{1}{2}\pi ^2 \log 2 - \frac{{23}}{{48}}\pi ^2 + \frac{{492473}}{{73728}}} \right\}\left. {\frac{{\alpha ^2 }}{{\pi ^2 }}} \right), \hfill \\ \end{gathered} $$ at the four-loop level of one-flavour QED.     

An analytical expression for the specific capacity of lithium ion cells

The concentration of lithium ions in the cathode of lithium ion cells has been obtained by solving the materials balance equation $$\frac{{\partial c}}{{\partial t}} = \varepsilon ^{1/2} D\frac{{\partial ^2 c}}{{\partial x^2 }} + \frac{{aj_n (1--t_ + )}}{\varepsilon }$$ by Laplace transform. On the assumption that the cell is fully discharged when there are zero lithium ions at the current collector of the cathode, the discharge timet _d is obtained as $$\tau = \frac{{r^2 }}{{\pi ^2 \varepsilon ^{1/2} }}\ln \left[ {\frac{{\pi ^2 }}{{r^2 }}\left( {\frac{{\varepsilon ^{1/2} }}{J} + \frac{{r^2 }}{6}} \right)} \right]$$ which, when substituted into the equationC=It _d /M, whereI is the discharge current andM is the mass of the separator and positive electrode, an analytical expression for the specific capacity of the lithium cell is given as $$C = \frac{{IL_c ^2 }}{{\pi {\rm M}D\varepsilon ^{1/2} }}\ln \left[ {\frac{{\pi ^2 }}{2}\left( {\frac{{FDc_0 \varepsilon ^{3/2} }}{{I(1 - t_ + )L_c }} + \frac{1}{6}} \right)} \right]$$      

Study of spin and decay-plane correlations of W bosons in the e + e$^-\rightarrow$ W + W- process at LEP

Data collected at LEP at centre-of-mass energies GeV are used to study correlations of the spin of W bosons using events. Spin correlations are favoured by data, and found to agree with the Standard Model predictions. In addition, correlations between the W-boson decay planes are studied in and events. Decay-plane correlations are measured to be consistent with the Standard Model predictions.Received: 26 October 2004, Revised: 15 January 2005, Published online: 3 March 2005     

Nonlinear Interaction of S-Polarized Incident Radiation and Surface Waves in Magnetoactive Plasma

The effect of an external magnetic field on the nonlinear interaction of S-polarized electromagnetic radiation incident on a S-polarized surface wave in a plasma layer was studied analytically. We have calculated the amplitudes of generated waves at combination frequencies. The generated waves are of P-polarization and can be either electromagnetic or surface waves, depending on the signal of the value=\documentclass{article}\pagestyle{empty}\begin{document}$ ^{\chi '^2 = \frac{{k'^2 }}{{\varepsilon '}} - \frac{{\omega '^2 }}{{c^2 }} + k'\frac{\partial }{{\partial x}}\frac{{\varepsilon '_2 }}{{\varepsilon '\varepsilon '_1 }}} $\end{document}.     

Reexploration of interacting holographic dark energy model: cases of interaction term excluding the Hubble parameter

In this paper, we make a deep analysis for the five typical interacting holographic dark energy models with the interaction terms \(Q=3\beta H_{0}\rho _\mathrm{{de}}\), \(Q=3\beta H_{0}\rho _\mathrm{{c}}\), \(Q=3\beta H_{0}(\rho _\mathrm{{de}}+\rho _\mathrm{c})\), \(Q=3\beta H_{0}\sqrt{\rho _\mathrm{{de}}\rho _\mathrm{c}}\), and \(Q=3\beta H_{0}\frac{\rho _\mathrm{{de}}\rho _{c}}{\rho _\mathrm{{de}}+\rho _\mathrm{c}}\), respectively. We obtain observational constraints on these models by using the type Ia supernova data (the Joint Light-Curve Analysis sample), the cosmic microwave background data (Planck 2015 distance priors), the baryon acoustic oscillations data, and the direct measurement of the Hubble constant. We find that the values of \(\chi _\mathrm{min}^2\) for all the five models are almost equal (around 699), indicating that the current observational data equally favor these IHDE models. In addition, a comparison with the cases of an interaction term involving the Hubble parameter H is also made.     

Empirical formulas for the fermion spectra and Yukawa matrices

We present empirical relations that connect the dimensionless ratios of low energy fermion masses for the charged lepton, up-type quark and down-type quark sectors and the CKM elements: and . Explaining these relations from first principles imposes strong constraints on the search for the theory of flavor. We present a simple set of normalized Yukawa matrices, with only two real parameters and one complex phase, which accounts with precision for these mass relations and for the CKM matrix elements and also suggests a simpler parametrization of the CKM matrix. The proposed Yukawa matrices accommodate the measured CP-violation, giving a particular relation between standard model CP-violating phases, . According to this relation the measured value of is close to the maximum value that can be reached, for . Finally, the particular mass relations between the quark and charged lepton sectors find their simplest explanation in the context of grand unified models through the use of the Georgi-Jarlskog factor.Received: 31 July 2004, Revised: 22 September 2004, Published online: 9 November 2004     

Collisional damping of transverse waves in a plasma

The effect of collisions on transverse waves in a homogeneous, field free plasma is investigated by means of Gross-Krook collision model. The dispersion relation is calculated by assuming the collision frequency to be small andKλ _D ?1. The damping rate ω _I is obtained as $$\omega _I = \frac{{\nu _{ei} }}{2}\frac{{\omega _p^2 }}{{\omega _0^2 }}\left[ {1 + \frac{{3K^2 \lambda _D^2 \omega _p^2 }}{{\omega _0^2 }} - \frac{{K^2 \lambda _D^2 \omega _p^4 }}{{\omega _0^4 }}} \right] + \frac{{\nu _{ee} }}{2}\frac{{\omega _p^2 }}{{\omega _0^2 }}\left( {\frac{{K^2 \lambda _D^2 \omega _p^2 }}{{\omega _0^2 }}} \right)$$ where ω ₀ ² =c ² K ²+ω ₂ ^p , andv _ei andv _ee are electron-ion and electron-electron collision frequency respectively.     

Measurement of the energy dependence of hadronic jet rates and the strong coupling $\alpha_s$ from the four-jet rate with the DELPHI detector at LEP

Hadronic events from the data collected with the DELPHI detector at LEP within the energy range from 89 Gev to 209 Gev are selected, their jet rates are determined and compared to predictions of four different event generators. One of them is the recently developed APACIC + + generator which performs a massive matrix element calculation matched to a parton shower followed by string fragmentation. The four-jet rate is used to measure in the next-to-leading-order approximation yielding The running of determined by using four-jet events has been tested. The logarithmic energy slope is measured to be Since the analysis is based on four-jet final states it represents an alternative approach to previous DELPHI measurements using event shape distributions.Received: 4 August 2004, Revised: 1 October 2004, Published online: 7 December 2004     

Solutions for a Cosmic String

For a conformally flat metric ds² = a²(η)(dη² – dx² – y² – dz²) Vilenkin obtained the equation $$\frac{\partial }{{\partial _{\eta } }}\left[ {\frac{{a^2 \left( {\eta } \right)\dot y}}{{\sqrt {1 + y'^2 - \dot y^2 } }}} \right] = \frac{\partial }{{\partial _x }}\left[ {\frac{{a^2 \left( {\eta } \right)\dot y'}}{{\sqrt {1 + y'^2 - \dot y^2 } }}} \right]$$ for a cosmic string and gave some particular solutionsboth for a = const and a const. The present workcompletely solves the equation for a = const and extendthe work of Vilenkin for a ≠ const.     

The color glass condensate: an overview

The color glass condensate is a theory of the dynamical properties of partons in the Regge limit of QCD: , and the center of mass energy squared . We provide a brief introduction to the theoretical ideas underlying the color glass condensate and discuss the application of these ideas to high energy scattering in QCD.Arrival of the final proofs: 5 April 2005R. Venugopalan: Present address: Institute for Theoretical Physics II, Univ. of Hamburg, Luruper Chaussee 49, 22761, Hamburg, Germany     

New gauge bosons from the littlest Higgs modeland the process $e^{ + }e^{-}\rightarrow t\bar{t}$

In the context of the littlest Higgs (LH) model, we study the process . We find that the new gauge bosons Z _H and B _H can produce significant correction effects on this process, which can be further enhanced by suitably polarized beams. In most of the parameter space preferred by the electroweak precision data, the absolute value of the relative correction parameter is larger than 5 %. As long as and the absolute value of the relative correction parameter is larger than . With reasonable values of the parameters of the LH model, the possible signals of the new gauge bosons B _H and Z _H can be detected via the process in the future LC experiments with the CM energy . B _H exchange and Z _H exchange can generate significantly corrections to the forward-backward asymmetry only in a small part of the parameter space.Received: 29 October 2004, Revised: 29 November 2004, Published online: 15 February 2005     

Polarized angular distributions in the decays of the 3D2 state of charmonium produced in unpolarized proton–antiproton annihilation

Using the helicity formalism, we calculate the combined angular distribution functions of the polarized gamma photons and electron in the triple cascade process $\bar{\mathrm{p}}\mathrm{p}\to{}^{3}\mathrm{D}_{\mathrm{2}}\to\chi_{\mathrm{\mathrm{{J}}}}+\gamma_{\mathrm{1}}\to(\psi +\gamma_{\mathrm{2}})+\gamma_{\mathrm{1}}\to(\mathrm{e}^{+}+\mathrm{e}^{-})+\gamma_{\mathrm{1}}+\gamma_{\mathrm{2}}\ (\mathrm{{J}}=0,1,2)$ , when $\bar{\mathrm{p}}$ and p are unpolarized. We also present the partially integrated angular distribution functions in different cases. Our results show that by measuring the two-particle angular distribution of γ ₁ and γ ₂ and that of γ ₂ and e^? with the polarization of either one of the two particles, one can determine the relative magnitudes as well as the relative phases of all the helicity amplitudes in the two radiative decay processes ³D₂→χ _J+γ ₁ and χ _J→ψ+γ ₂.     

Measurement of W-pair production in e<Superscript> + </Superscript>e<Superscript>-</Superscript> collisions at centre-of-mass energies from 183 to 209 GeV

The W ⁺ W^- production cross section is measured from a data sample corresponding to a total integrated luminosity of 683 pb^-1, collected by the ALEPH experiment at LEP at centre-of-mass energies from 183 to 209 GeV. Individual cross sections for the different topologies arising from W decays into leptons or hadrons, as well as the total W-pair cross section are given at eight centre-of-mass energies. The results are found to be in agreement with recently developed Standard Model calculations at the one percent level. The hadronic branching fraction of the W boson is measured to be = 67.13 0.37(stat.) 0.15(syst.)%, from which the CKM matrix element is determined to be 0.958 0.017(stat.) 0.008(syst.)Received: 1 October 2004, Published online: 15 November 2004     

Search for charged Higgs bosons at LEP in general two Higgs doublet models

A search for pair-produced charged Higgs bosons was performed in the data collected by the DELPHI detector at LEP II at centre-of-mass energies from 189 GeV to 209 GeV. Five different final states, , , , and were considered, accounting for the major expected decays in type I and type II Two Higgs Doublet Models. No significant excess of data compared to the expected Standard Model processes was observed. The existence of a charged Higgs boson with mass lower than 76.7 GeV/c² (type I) or 74.4 GeV/c² (type II) is excluded at the 95% confidence level, for a wide range of the model parameters. Model independent cross-section limits have also been calculated.Received: 30 September 2003, Revised: 12 February 2004, Published online: 8 April 2004     

Corrections to quark asymmetries at LEP

The most precise measurement of the weak mixing angle at LEP is from the forward-backward asymmetry at the Z-pole. In this note the QED and electroweak radiative corrections to obtain the pole asymmetry from the measured asymmetry for b- and c-quarks have been calculated using ZFITTER, which has been amended to allow a consistent treatment of partial two-loop corrections for the b-quark final asymmetries. A total correction of and has been found, where the remaining theoretical uncertainty is much too small to explain the apparent discrepancy between obtained from A _FB ^b and from the left-right asymmetry at SLD.Received: 1 December 2004, Published online: 9 March 2005     

Einfluß des Randes auf das effektive Verhalten heterogener Körper - Anwendung auf Rayleighwellen

Effective Elastic Properties of Finite Heterogeneous Media - Application to Rayleigh-waves Rayleigh waves in a heterogeneous material (multiphase mixtures, composite materials, polycrystals) are governed by integrodifferential equations derived by the aid of known methods for infinite heterogeneous media. According to this wave equation the velocity depends on the frequency, and the waves are damped. After some simplifications (isotropy, nonrandom elastic constants) the following is obtained: if the fluctuations of the mass density are restricted to the vicinity of the boundary, the frequency dependent part of the velocity behaves like \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{{l^3 \omega ^3}}{{{\mathop c\limits^\circ} _t^3}} $\end{document} and the damping is proportional to \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{{l^4 \omega ^5}}{{{\mathop c\limits^\circ} _t^5}} $\end{document}, whereas \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{{l^2 \omega ^2}}{{{\mathop c\limits^\circ} _t^2}} $\end{document} respectively \documentclass{article}\pagestyle{empty}\begin{document}$ \frac{{l^3 \omega ^4}}{{{\mathop c\limits^\circ} _t^4}} $\end{document} is found if the fluctuations are present in the whole half-space. From this it is seen, what assumptions are necessary to describe the waves by differential equations with frequenc y-dependent mass density.     

Study of Z pair production and anomalous couplingsin e + e- collisions at $\sqrt{s}$ between 190 GeV and 209 GeV

A study of Z-boson pair production in e ⁺ e^- annihilation at center-of-mass energies between 190 GeV and 209 GeV is reported. Final states containing only leptons, ( and ), quark and lepton pairs, ( , ) and only hadrons ( ) are considered. In all states with at least one Z boson decaying hadronically, lifetime, lepton and event-shape tags are used to separate pairs from final states. Limits on anomalous ZZ and ZZZ couplings are derived from the measured cross sections and from event kinematics using an optimal observable method. Limits on low scale gravity with large extra dimensions are derived from the cross sections and their dependence on polar angle.Received: 14 July 2003, Published online: 18 December 2003     

Flavour-independent h<Superscript>0</Superscript>A<Superscript>0</Superscript> search and two Higgs doublet model interpretation of neutral Higgs boson searches at LEP

Upper limits on the cross-section of the pair-production process , assuming 100 branching fraction to hadrons, are derived from a new search for the hadrons final state, independently of the hadronic flavour of the decay products. This study, combined with previously published searches for the neutral Higgs bosons h⁰ and A⁰, is used to constrain the Type II Two Higgs Doublet Model (2HDM(II)) with no CP violation in the Higgs sector and no additional non-Standard Model particles besides the five Higgs bosons. The analysis combines LEP1 and LEP2 data collected with the OPAL detector up to the highest available centre-of-mass energies. The searches are sensitive to the and decay modes of the Higgs bosons. A benchmark scan of the 2HDM(II) parameter space is performed. Large regions of the 2HDM(II) parameter space explored are excluded at the 95% CL in the ( and planes, using both direct neutral Higgs boson searches and indirect limits derived from Standard Model high precision measurements. The region GeV and GeV is excluded at 95 % CL, independently of and for selected values of which are representative of a complete -scan.Received: 28 July 2004, Revised: 4 January 2005, Published online: 3 March 2005     

Exclusive semileptonic rare decays $B \to K^{(*)} l^ + l^-$ in a SUSY SO(10) GUT

In the SUSY SO(10) GUT context, we study the exclusive processes . Using the Wilson coefficients of the relevant operators including the new operators which are induced by neutral Higgs boson (NHB) penguins, we evaluate some possible observables associated with these processes like the invariant mass spectrum (IMS), lepton pair forward-backward asymmetry (FBA), lepton polarization asymmetries etc. In this model the contributions from Wilson coefficients , among new contributions, are dominant. Our results show that the NHB effects are sensitive to the FBA, , and of decay, which are expected to be measured in B factories, the deviation of in can reach 0.1 from SM, which could be seen in B factories, and the average of the normal polarization can reach several percent for and it is 0.05 or so for , which could be measured in the future super B factories and provide useful information to probe new physics and discriminate different models.Received: 30 October 2004, Published online: 9 March 2005