Exotic mitotic mechanisms

The emergence of eukaryotes around two billion years ago provided new challenges for the chromosome segregation machineries: the physical separation of multiple large and linear chromosomes from the microtubule-organizing centres by the nuclear envelope. In this review, we set out the diverse solutions that eukaryotic cells use to solve this problem, and show how stepping away from ‘mainstream’ mitosis can teach us much about the mechanisms and mechanics that can drive chromosome segregation. We discuss the evidence for a close functional and physical relationship between membranes, nuclear pores and kinetochores in generating the forces necessary for chromosome segregation during mitosis

On quantum and parallel transport in a Hilbert bundle over spacetime

We study the Hilbert bundle description of stochastic quantum mechanics in curved spacetime developed by Prugove\v{c}ki, which gives a powerful new framework for exploring the quantum mechanical propagation of states in curved spacetime. We concentrate on the quantum transport law in the bundle, specifically on the information which can be obtained from the flat space limit. We give a detailed proof that quantum transport coincides with parallel transport in the bundle in this limit, confirming statements of Prugove\v{c}ki. We furthermore show that the quantum-geometric propagator in curved spacetime proposed by Prugove\v{c}ki, yielding a Feynman path integral-like formula involving integrations over intermediate phase space variables, is Poincar\'e gauge covariant (i.e.$\!$ is gauge invariant except for transformations at the endpoints of the path) provided the integration measure is interpreted as a ``contact point measure'' in the soldered stochastic phase space bundle raised over curved spacetime.Comment: 25 pages, Plain TeX, harvmac/lanlma

Thermodynamics of the one-dimensional frustrated Heisenberg ferromagnet with arbitrary spin

The thermodynamic quantities (spin-spin correlation functions <{\bf S}_0{\bf S}_n>, correlation length {\xi}, spin susceptibility {\chi}, and specific heat C_V) of the frustrated one-dimensional J1-J2 Heisenberg ferromagnet with arbitrary spin quantum number S below the quantum critical point, i.e. for J2< |J1|/4, are calculated using a rotation-invariant Green-function formalism and full diagonalization as well as a finite-temperature Lanczos technique for finite chains of up to N=18 sites. The low-temperature behavior of the susceptibility {\chi} and the correlation length {\xi} is well described by \chi = (2/3)S^4 (|J1|-4J2) T^{-2} + A S^{5/2} (|J1|-4J2)^{1/2} T^{-3/2} and \xi = S^2 (|J1|-4J2) T^{-1} + B S^{1/2} (|J1|-4J2)^{1/2} T^{-1/2} with A \approx 1.1 ... 1.2 and B \approx 0.84 ... 0.89. The vanishing of the factors in front of the temperature at J2=|J1|/4 indicates a change of the critical behavior of {\chi} and {\xi} at T \to 0. The specific heat may exhibit an additional frustration-induced low-temperature maximum when approaching the quantum critical point. This maximum appears for S=1/2 and S=1, but was not found for S>1.Comment: 8 pages, 7 figure

Exact one- and two-particle excitation spectra of acute-angle helimagnets above their saturation magnetic field

The two-magnon problem for the frustrated XXZ spin-1/2 Heisenberg Hamiltonian and external magnetic fields exceeding the saturation field Bs is considered. We show that the problem can be exactly mapped onto an effective tight-binding impurity problem. It allows to obtain explicit exact expressions for the two-magnon Green's functions for arbitrary dimension and number of interactions. We apply this theory to a quasi-one dimensional helimagnet with ferromagnetic nearest neighbor J1 < 0 and antiferromagnetic next-nearest neighbor J2 > 0 interactions. An outstanding feature of the excitation spectrum is the existence of two-magnon bound states. This leads to deviations of the saturation field Bs from its classical value Bs(classical) which coincides with the one-magnon instability. For the refined frustration ratio |J2/J1|> 0.374661 the minimum of the two-magnon spectrum occurs at the boundary of the Brillouin zone. Based on the two-magnon approach, we propose general analytic expressions for the saturation field Bs, confirming known previous results for one-dimensional isotropic systems, but explore also the role of interchain and long-ranged intrachain interactions as well as of the exchange anisotropy.Comment: 21 pages, 6 Figures. submitted to Phys. Rev.

Electronic structure and magnetic properties of Li_2ZrCuO_4 - a spin 1/2 Heisenberg system in vicinity to a quantum critical point

Based on density functional calculations, we present a detailed theoretical study of the electronic structure and the magnetic properties of the quasi-one dimensional chain cuprate Li_2ZrCuO_4 (Li_2CuZrO_4). For the relevant ratio of the next-nearest neighbor exchange J_2 to the nearest neighbor exchange J_1 we find alpha = -J_2/J_1 = 0.22\pm0.02 which is very close to the critical point at 1/4. Owing this vicinity to a ferromagnetic-helical critical point, we study in detail the influence of structural peculiarities such as the reported Li disorder and the non-planar chain geometry on the magnetic interactions combining the results of LDA based tight-binding models with LDA+U derived exchange parameters. Our investigation is complemented by an exact diagonalization study of a multi-band Hubbard model for finite clusters predicting a strong temperature dependence of the optical conductivity for Li_2ZrCuO_4