Relativistic Coulomb Green's function in dd-dimensions

Using the operator method, the Green's functions of the Dirac and Klein-Gordon equations in the Coulomb potential $-Z\alpha/r$ are derived for the arbitrary space dimensionality $d$. Nonrelativistic and quasiclassical asymptotics of these Green's functions are considered in detail.Comment: 9 page

Study of the triangular lattice tV model near x=1/3

We study extended Hubbard model on a triangular lattice near doping $x=1/3$, which may be relevant for the recently discovered superconductor Na$_x$CoO$_2 \cdot y$H$_2$O. By generalizing this model to $N$ fermionic species, we formulate a meanfield description in the limit of large $N$. In meanfield, we find two possible phases: a renormalized Fermi liquid and a \rt3rt3 charge density wave state. The transition between the two phases is driven by increasing the nearest neighbor repulsion and is found to be first order for doping $x=1/3$, but occurs close to the point of the local instability of the uniform liquid. We also study fluctuations about the uniform meanfield state in a systematic 1/N expansion, focusing on the residual interaction of quasiparticles and possible superconducting instabilities due to this interaction. Upon moving towards the CDW instability, the increasing charge fluctuations favor a particular $f$-wave triplet state. (This state was recently discussed by Tanakaet al, cond-mat/0311266). We also report a direct Gutzwiller wavefunction study of the spin-1/2 model.Comment: 9 pages, 5 figure

On the Area of Hypercube Layouts

This paper precisely analyzes the wire density and required area in standard layout styles for the hypercube. The most natural, regular layout of a hypercube of N^2 nodes in the plane, in a N x N grid arrangement, uses floor(2N/3)+1 horizontal wiring tracks for each row of nodes. (The number of tracks per row can be reduced by 1 with a less regular design.) This paper also gives a simple formula for the wire density at any cut position and a full characterization of all places where the wire density is maximized (which does not occur at the bisection).Comment: 8 pages, 4 figures, LaTe

Quasiclassical Green function in an external field and small-angle scattering

The quasiclassical Green functions of the Dirac and Klein-Gordon equations in the external electric field are obtained with the first correction taken into account. The relevant potential is assumed to be localized, while its spherical symmetry is not required. Using these Green functions, the corresponding wave functions are found in the approximation similar to the Furry-Sommerfeld-Maue approximation. It is shown that the quasiclassical Green function does not coincide with the Green function obtained in the eikonal approximation and has a wider region of applicability. It is illustrated by the calculation of the small-angle scattering amplitude for a charged particle and the forward photon scattering amplitude. For charged particles, the first correction to the scattering amplitude in the non-spherically symmetric potential is found. This correction is proportional to the scattering angle. The real part of the amplitude of forward photon scattering in a screened Coulomb potential is obtained.Comment: 20 pages, latex, 1 figur

Electron-positron pair production in ion collisions at low velocity beyond Born approximation

We derive the spectrum and the total cross section of electromagnetic $e^{+}e^{-}$ pair production in the collisions of two nuclei at low relative velocity $\beta$. Both free-free and bound-free $e^{+}e^{-}$ pair production is considered. The parameters $\eta_{A,B}=Z_{A,B}\alpha$ are assumed to be small compared to unity but arbitrary compared to $\beta$ ($Z_{A,B}$ are the charge numbers of the nuclei and $\alpha$ is the fine structure constant). Due to a suppression of the Born term by high power of $\beta$, the first Coulomb correction to the amplitude appears to be important at $\eta_{A,B}\gtrsim \beta$. The effect of a finite nuclear mass is discussed. In contrast to the result obtained in the infinite nuclear mass limit, the terms $\propto M^{-2}$ are not suppressed by the high power of $\beta$ and may easily dominate at sufficiently small velocities.Comment: 9 pages, 1 figur

Predictable Patterns Of Disruptive Selection In Stickleback In Postglacial Lakes

Disruptive selection is often assumed to be relatively rare, because it is dynamically unstable and hence should be transient. However, frequency-dependent interactions such as intraspecific competition may stabilize fitness minima and make disruptive selection more common. Such selection helps explain the maintenance of genetic variation and may even contribute to sympatric speciation. There is thus great interest in determining when and where disruptive selection is most likely. Here, we show that there is a general trend toward weak disruptive selection on trophic morphology in three-spine stickleback (Gasterosteus aculeatus) in 14 lakes on Vancouver Island. Selection is inferred from the observation that, within a lake, fish with intermediate gill raker morphology exhibited slower growth than phenotypically extreme individuals. Such selection has previously been shown to arise from intraspecific competition for alternate resources. However, not all environments are equally conducive to disruptive selection, which was strongest in intermediate-sized lakes where both littoral and pelagic prey are roughly balanced. Also, consistent with theory, we find that sexual dimorphism in trophic traits tends to mitigate disruptive selection. These results suggest that it may be possible to anticipate the kinds of environments and populations most likely to experience disruptive selection.Integrative Biolog