Fusion barrier distributions in systems with finite excitation energy

Eigen-channel approach to heavy-ion fusion reactions is exact only when the excitation energy of the intrinsic motion is zero. In order to take into account effects of finite excitation energy, we introduce an energy dependence to weight factors in the eigen-channel approximation. Using two channel problem, we show that the weight factors are slowly changing functions of incident energy. This suggests that the concept of the fusion barrier distribution still holds to a good approximation even when the excitation energy of the intrinsic motion is finite. A transition to the adiabatic tunneling, where the coupling leads to a static potential renormalization, is also discussed.Comment: 9 pages, 4 figures, Submitted to Physical Review

Thermodynamic properties of the one-dimensional Kondo insulators studied by the density matrix renormalization group method

Thermodynamic properties of the one-dimensional Kondo lattice model at half-filling are studied by the density matrix renormalization group method applied to the quantum transfer matrix. Spin susceptibility, charge susceptibility, and specific heat are calculated down to T=0.1t for various exchange constants. The obtained results clearly show crossover behavior from the high temperature regime of nearly independent localized spins and conduction electrons to the low temperature regime where the two degrees of freedom couple strongly. The low temperature energy scales of the charge and spin susceptibilities are determined and shown to be equal to the quasiparticle gap and the spin gap, respectively, for weak exchange couplings.Comment: 4 pages, 3 Postscript figures, REVTeX, submitted to J. Phys. Soc. Jp

Spin resonance in the superconducting state of Li1−x_{1-x}Fex_{x}ODFe1−y_{1-y}Se observed by neutron spectroscopy

We have performed inelastic neutron scattering measurements on a powder sample of the superconductor lithium iron selenide hydroxide Li$_{1-x}$Fe$_{x}$ODFe$_{1-y}$Se ($x \simeq 0.16, y \simeq 0.02$, $T_{\rm c} = 41$\,K). The spectrum shows an enhanced intensity below $T_{\rm c}$ over an energy range $0.64\times2\Delta < E < 2\Delta$, where $\Delta$ is the superconducting gap, with maxima at the wave vectors $Q_1 \simeq 1.46$\,\AA$^{-1}$ and $Q_2 \simeq 1.97$\,\AA$^{-1}$. The behavior of this feature is consistent with the spin resonance mode found in other unconventional superconductors, and strongly resembles the spin resonance observed in the spectrum of the molecular-intercalated iron selenide, Li$_{0.6}$(ND$_{2}$)$_{0.2}$(ND$_{3}$)$_{0.8}$Fe$_{2}$Se$_{2}$. The signal can be described with a characteristic two-dimensional wave vector $(\pi, 0.67\pi)$ in the Brillouin zone of the iron square lattice, consistent with the nesting vector between electron Fermi sheets

Bumps and rings in a two-dimensional neural field: splitting and rotational instabilities

In this paper we consider instabilities of localised solutions in planar neural field firing rate models of Wilson-Cowan or Amari type. Importantly we show that angular perturbations can destabilise spatially localised solutions. For a scalar model with Heaviside firing rate function we calculate symmetric one-bump and ring solutions explicitly and use an Evans function approach to predict the point of instability and the shapes of the dominant growing modes. Our predictions are shown to be in excellent agreement with direct numerical simulations. Moreover, beyond the instability our simulations demonstrate the emergence of multi-bump and labyrinthine patterns. With the addition of spike-frequency adaptation, numerical simulations of the resulting vector model show that it is possible for structures without rotational symmetry, and in particular multi-bumps, to undergo an instability to a rotating wave. We use a general argument, valid for smooth firing rate functions, to establish the conditions necessary to generate such a rotational instability. Numerical continuation of the rotating wave is used to quantify the emergent angular velocity as a bifurcation parameter is varied. Wave stability is found via the numerical evaluation of an associated eigenvalue problem

Strong lensing constraints on the velocity dispersion and density profile of elliptical galaxies

We use the statistics of strong gravitational lensing from the CLASS survey to impose constraints on the velocity dispersion and density profile of elliptical galaxies. This approach differs from much recent work, where the luminosity function, velocity dispersion and density profile were typically {\it assumed} in order to constrain cosmological parameters. It is indeed remarkable that observational cosmology has reached the point where we can consider using cosmology to constrain astrophysics, rather than vice versa. We use two different observables to obtain our constraints (total optical depth and angular distributions of lensing events). In spite of the relatively poor statistics and the uncertain identification of lenses in the survey, we obtain interesting constraints on the velocity dispersion and density profiles of elliptical galaxies. For example, assuming the SIS density profile and marginalizing over other relevant parameters, we find 168 km/s < sigma_* < 200 km/s (68% CL), and 158 km/s < sigma_* < 220 km/s (95% CL). Furthermore, if we instead assume a generalized NFW density profile and marginalize over other parameters, the slope of the profile is constrained to be 1.50 < beta < 2.00 (95% CL). We also constrain the concentration parameter as a function of the density profile slope in these models. These results are essentially independent of the exact knowledge of cosmology. We briefly discuss the possible impact on these constraints of allowing the galaxy luminosity function to evolve with redshift, and also possible useful future directions for exploration.Comment: Uses the final JVAS/CLASS sample, more careful choice of ellipticals, added discussion of possible biases. Final results essentially unchanged. Matches the MNRAS versio

X-ray emission from the field of the hyperluminous IRAS galaxy IRASF15307+3252

We report on a 20-ks observation of the z = 0.93 hyperluminous galaxy IRAS F15307+3252 with the ROSAT HRI. No X-ray source is detected at the position of F15307+3252 at an upper limit of ∼4 × 10⁴³ erg s⁻¹. This is less than 2 × 10⁻⁴ of the bolometric luminosity of the object, and indicates either that the nucleus emits an unusually small fraction of its total power in X-rays, or that little of the nuclear X-ray flux is scattered into our line of sight by electrons. The lack of an X-ray detection around F15307+3252 also rules out it being at the centre of a cluster, such as is observed for IRAS P09104+4109. A weak, possibly extended, X-ray source is detected 13 arcsec south of the galaxy, spatially coincident with a clump of faint objects visible in a Keck K_s-band image of the field. This may be the core of a cluster near the line of sight to F15307+3252

Superconductivity induced by spark erosion in ZrZn2

We show that the superconductivity observed recently in the weak itinerant ferromagnet ZrZn2 [C. Pfleiderer et al., Nature (London) 412, 58 (2001)] is due to remnants of a superconducting layer induced by spark erosion. Results of resistivity, susceptibility, specific heat and surface analysis measurements on high-quality ZrZn2 crystals show that cutting by spark erosion leaves a superconducting surface layer. The resistive superconducting transition is destroyed by chemically etching a layer of 5 microns from the sample. No signature of superconductivity is observed in rho(T) of etched samples at the lowest current density measured, J=675 Am-2, and at T < 45 mK. EDX analysis shows that spark-eroded surfaces are strongly Zn depleted. The simplest explanation of our results is that the superconductivity results from an alloy with higher Zr content than ZrZn2.Comment: Final published versio

Reflectionless analytic difference operators II. Relations to soliton systems

This is the second part of a series of papers dealing with an extensive class of analytic difference operators admitting reflectionless eigenfunctions. In the first part, the pertinent difference operators and their reflectionless eigenfunctions are constructed from given ``spectral data'', in analogy with the IST for reflectionless Schr\"odinger and Jacobi operators. In the present paper, we introduce a suitable time dependence in the data, arriving at explicit solutions to a nonlocal evolution equation of Toda type, which may be viewed as an analog of the KdV and Toda lattice equations for the latter operators. As a corollary, we reobtain various known results concerning reflectionless Schr\"odinger and Jacobi operators. Exploiting a reparametrization in terms of relativistic Calogero--Moser systems, we also present a detailed study of $N$-soliton solutions to our nonlocal evolution equation

Complex networks created by aggregation

We study aggregation as a mechanism for the creation of complex networks. In this evolution process vertices merge together, which increases the number of highly connected hubs. We study a range of complex network architectures produced by the aggregation. Fat-tailed (in particular, scale-free) distributions of connections are obtained both for networks with a finite number of vertices and growing networks. We observe a strong variation of a network structure with growing density of connections and find the phase transition of the condensation of edges. Finally, we demonstrate the importance of structural correlations in these networks.Comment: 12 pages, 13 figure