Locally conformally K\"ahler manifolds with holomorphic Lee field

We prove that a compact lcK manifold with holomorphic Lee vector field is Vaisman provided that either the Lee field has constant norm or the metric is Gauduchon (i.e., the Lee field is divergence-free). We also give examples of compact lcK manifolds with holomorphic Lee vector field which are not Vaisman.Comment: 6 page

Compact homogeneous lcK manifolds are Vaisman

We prove that any compact homogeneous locally conformally K\"ahler manifold has parallel Lee form.Comment: 6 pages; final version, to appear in Math. An

Possible Triplet Electron Pairing and an Anisotropic Spin Susceptibility in Organic Superconductors (TMTSF)_2 X

We argue that (TMTSF)_2 PF_6 compound under pressure is likely a triplet superconductor with a vector order parameter d(k) \equiv (d_a(k) \neq 0, d_c(k) = ?, d_{b'}(k) = 0); |d_a(k)| > |d_c(k)|. It corresponds to an anisotropic spin susceptibility at T=0: \chi_{b'} = \chi_0, \chi_a \ll \chi_0, where \chi_0 is its value in a metallic phase. [The spin quantization axis, z, is parallel to a so-called b'-axis]. We show that the suggested order parameter explains why the upper critical field along the b'-axis exceeds all paramagnetic limiting fields, including that for a nonuniform superconducting state, whereas the upper critical field along the a-axis (a \perp b') is limited by the Pauli paramagnetic effects [I. J. Lee, M. J. Naughton, G. M. Danner and P. M. Chaikin, Phys. Rev. Lett. 78, 3555 (1997)]. The triplet order parameter is in agreement with the recent Knight shift measurements by I. J. Lee et al. as well as with the early results on a destruction of superconductivity by nonmagnetic impurities and on the absence of the Hebel-Slichter peak in the NMR relaxation rate.Comment: 4 pages, 1 eps figur

Exact partition function in U(2)×U(2)U(2)\times U(2) ABJM theory deformed by mass and Fayet-Iliopoulos terms

We exactly compute the partition function for $U(2)_k\times U(2)_{-k}$ ABJM theory on $\mathbb S^3$ deformed by mass $m$ and Fayet-Iliopoulos parameter $\zeta$. For $k=1,2$, the partition function has an infinite number of Lee-Yang zeros. For general $k$, in the decompactification limit the theory exhibits a quantum (first-order) phase transition at $m=2\zeta$.Comment: 11 pages, 1 figure. v2: references adde

On the nonlinear statistics of range image patches

In [A. B. Lee, K. S. Pedersen, and D. Mumford, Int. J. Comput. Vis., 54 (2003), pp. 83–103], the authors study the distributions of 3 × 3 patches from optical images and from range images. In [G. Carlsson, T. Ishkanov, V. de Silva, and A. Zomorodian, Int. J. Comput. Vis., 76 (2008), pp. 1–12], the authors apply computational topological tools to the data set of optical patches studied by Lee, Pedersen, and Mumford and find geometric structures for high density subsets. One high density subset is called the primary circle and essentially consists of patches with a line separating a light and a dark region. In this paper, we apply the techniques of Carlsson et al. to range patches. By enlarging to 5×5 and 7×7 patches, we find core subsets that have the topology of the primary circle, suggesting a stronger connection between optical patches and range patches than was found by Lee, Pedersen, and Mumford

Position of K atoms in doped single-walled carbon nanotube crystals

Recent experiments by Lee et al. [Nature (London) 363, 255 (1997)] show that doping carbon single-wall nanotube (SWNT) ropes with K, Rb, or Br2 leads to metallic conductivity, but the structure and properties are not known. We used molecular dynamics to predict structures and properties which should help motivate and interpret experiments on SWNT/K. We find the optimum stoichiometry to be KC16 if the K cannot penetrate the tubes and K1C10 ( K5exoK3endoC80, 3 within the tube) if they can. We predict the optimum structure and the associated powder-diffraction x-ray pattern expected for KnC80 from n = 0–10 (optimum is n = 5). The Young's modulus per tube along the tube axis varies from 640 to 525 GPa for n = 0 to 5

Scaling Relations in the Vortex State of Nodal Superconductors

In contrast to multigap superconductors (e.g. MgB$_{2}$), the low-temperature properties of nodal superconductors are dominated by nodal excitations. Here we extend for a variety of nodal superocnductors the earlier work by Simon and Lee and K\"ubert and Hirschfeld. The scaling relations seen in the thermodynamics and the thermal conductivity will provide an unequivocal test of nodal superconductivity.Comment: 9 pages, 3 figure