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.

Thermodynamics of the two-dimensional frustrated J1-J2 Heisenberg ferromagnet in the collinear stripe regime: Susceptibility and correlation length

We calculate the temperature dependence of the correlation length xi and the uniform susceptibility chi_0 of the frustrated J1-J2 square-lattice Heisenberg ferromagnet in the collinear stripe phase using Green-function technique. The height chi_{max} and the position T(chi_{max}) of the maximum in the chi_0(T) curve exhibit a characteristic dependence on the frustration parameter J2/|J1|, which is well described by power laws, chi_{max}=a(J2-J2^c)^{-nu} and T(chi_{max})=b(J_2-J_2^c), where J2^c = 0.4 and nu is of the order of unity.The correlation length diverges at low temperatures as xi \propto e^{A/T}, where A increases with growing J2/|J1|. We also compare our results with recent measurements on layered vanadium phosphates and find reasonable agreement.Comment: 7 pages, 5 figures, version as published in Phys. Rev.

Sr2_2Cu(PO4_4)2_2: A real material realization of the 1D nearest neighbor Heisenberg chain

We present evidence that crystalline Sr_2Cu(PO_4)_2 is a nearly perfect one-dimensional (1D) spin-1/2 anti-ferromagnetic Heisenberg model (AHM) chain compound with nearest neighbor only exchange. We undertake a broad theoretical study of the magnetic properties of this compound using first principles (LDA, LDA+U calculations), exact diagonalization and Bethe-ansatz methodologies to decompose the individual magnetic contributions, quantify their effect, and fit to experimental data. We calculate that the conditions of one-dimensionality and short-ranged magnetic interactions are sufficiently fulfilled that Bethe's analytical solution should be applicable, opening up the possibility to explore effects beyond the infinite chain limit of the AHM Hamiltonian. We begin such an exploration by examining some extrinsic effects such as impurities and defects