Random and aperiodic quantum spin chains: A comparative study

According to the Harris-Luck criterion the relevance of a fluctuating interaction at the critical point is connected to the value of the fluctuation exponent omega. Here we consider different types of relevant fluctuations in the quantum Ising chain and investigate the universality class of the models. At the critical point the random and aperiodic systems behave similarly, due to the same type of extreme broad distribution of the energy scales at low energies. The critical exponents of some averaged quantities are found to be a universal function of omega, but some others do depend on other parameters of the distribution of the couplings. In the off-critical region there is an important difference between the two systems: there are no Griffiths singularities in aperiodic models.Comment: 4 pages RevTeX, 2 eps-figures include

A possible black hole binary in Mkn 501

A simple binary model for Mkn~501 is considered under the assumption that the TeV and X-ray periodicity of $\sim 23$ days, observed during the flaring state in 1997, may be basically interpreted as a doppler-shifted flux modulation due to the orbital motion of the relativistic jet. For the typical jet properties inferred from emission models, we find an intrinsic orbital period of $(6-14)$ yrs and a centre-of-mass distance of $(2-3.5) \times 10^{16}$ cm, the binary thus being a very close system. If the binary separation corresponds to that at which gravitational radiation becomes dominant, one may obtain a maximum allowed primary mass of $\sim 10^8 M_{\odot}$ and a corresponding maximum allowed secondary mass in the range of $\sim (1-9)\times 10^7 M_{\odot}$ assuming that gas accretion occurs on around the salpeter time scale. Interestingly such values agree with the black hole masses expected from merger scenarios.Comment: 4 pages, 2 figures; updated results of astro-ph/0005478; to appear in the Proc. of the Heidelberg International Symposium on High Energy Gamma-Ray Astronomy, Heidelberg, June 26-30, 2000, ed. by H.J. Voelk and F. Aharonian, AIP Conf. Pro

Critical exponents of random XX and XY chains: Exact results via random walks

We study random XY and (dimerized) XX spin-1/2 quantum spin chains at their quantum phase transition driven by the anisotropy and dimerization, respectively. Using exact expressions for magnetization, correlation functions and energy gap, obtained by the free fermion technique, the critical and off-critical (Griffiths-McCoy) singularities are related to persistence properties of random walks. In this way we determine exactly the decay exponents for surface and bulk transverse and longitudinal correlations, correlation length exponent and dynamical exponent.Comment: 4 pages RevTeX, 1 eps-figure include

Development of flexible rotor balancing criteria

Several studies in which analytical procedures were used to obtain balancing criteria for flexible rotors are described. General response data for a uniform rotor in damped flexible supports were first obtained for plain cylindrical bearings, tilting pad bearings, axial groove bearings, and partial arc bearings. These data formed the basis for the flexible rotor balance criteria presented. A procedure by which a practical rotor in bearings could be reduced to an equivalent uniform rotor was developed and tested. It was found that the equivalent rotor response always exceeded to practical rotor response by more than sixty percent for the cases tested. The equivalent rotor procedure was then tested against six practical rotor configurations for which data was available. It was found that the equivalent rotor method offered a procedure by which balance criteria could be selected for practical flexible rotors, using the charts given for the uniform rotor

The Random Transverse Ising Spin Chain and Random Walks

We study the critical and off-critical (Griffiths-McCoy) regions of the random transverse-field Ising spin chain by analytical and numerical methods and by phenomenological scaling considerations. Here we extend previous investigations to surface quantities and to the ferromagnetic phase. The surface magnetization of the model is shown to be related to the surviving probability of an adsorbing walk and several critical exponents are exactly calculated. Analyzing the structure of low energy excitations we present a phenomenological theory which explains both the scaling behavior at the critical point and the nature of Griffiths-McCoy singularities in the off-critical regions. In the numerical part of the work we used the free-fermion representation of the model and calculated the critical magnetization profiles, which are found to follow very accurately the conformal predictions for different boundary conditions. In the off-critical regions we demonstrated that the Griffiths-McCoy singularities are characterized by a single, varying exponent, the value of which is related through duality in the paramagnetic and ferromagnetic phases.Comment: 18 pages RevTeX (multicolumn), eps-figures include

Implications of a possible 23 day periodicity for binary black hole models in Mkn~501

We investigate the implications of a massive binary system in the centre of the gamma-ray blazar Mkn~501 and show that the periodical behaviour recently observed in the TeV and X-ray lightcurves may possibly be related to the orbital motion of the relativistic jet emerging from the less massive black hole. For the special relativistic jet properties inferred from emission models, we derive an intrinsic orbital period of $(6-14)$ yrs and a centre-of-mass distance of $(2.0-3.5) \times 10^{16}$ cm. If the binary is very close with a separation of the order of that for which gravitational radiation becomes dominant, we find a maximum primary mass of \sim 10^8 M_{\sun} and a corresponding secondary mass in the range of \sim (4-42)\times 10^6 M_{\sun} depending on the intrinsic jet properties. Such values are in line with the black hole masses expected from merger scenarios.Comment: 6 pages, 1 figure; Springer A&A LaTeX; final version (small typos corrected