The uniqueness of the invariant polarisation-tensor field for spin-1 particles in storage rings

We argue that the invariant tensor field introduced in [1] is unique under the condition that the invariant spin field is unique, and thereby complete that part of the discussion in that paper.Comment: 8 page

Contractile stresses in cohesive cell layers on finite-thickness substrates

Using a minimal model of cells or cohesive cell layers as continuum active elastic media, we examine the effect of substrate thickness and stiffness on traction forces exerted by strongly adhering cells. We obtain a simple expression for the length scale controlling the spatial variation of stresses in terms of cell and substrate parameters that describes the crossover between the thin and thick substrate limits. Our model is an important step towards a unified theoretical description of the dependence of traction forces on cell or colony size, acto-myosin contractility, substrate depth and stiffness, and strength of focal adhesions, and makes experimentally testable predictions.Comment: 5 pages, 3 figure

Quasiperiodic spin-orbit motion and spin tunes in storage rings

We present an in-depth analysis of the concept of spin precession frequency for integrable orbital motion in storage rings. Spin motion on the periodic closed orbit of a storage ring can be analyzed in terms of the Floquet theorem for equations of motion with periodic parameters and a spin precession frequency emerges in a Floquet exponent as an additional frequency of the system. To define a spin precession frequency on nonperiodic synchro-betatron orbits we exploit the important concept of quasiperiodicity. This allows a generalization of the Floquet theorem so that a spin precession frequency can be defined in this case too. This frequency appears in a Floquet-like exponent as an additional frequency in the system in analogy with the case of motion on the closed orbit. These circumstances lead naturally to the definition of the uniform precession rate and a definition of spin tune. A spin tune is a uniform precession rate obtained when certain conditions are fulfilled. Having defined spin tune we define spin-orbit resonance on synchro--betatron orbits and examine its consequences. We give conditions for the existence of uniform precession rates and spin tunes (e.g. where small divisors are controlled by applying a Diophantine condition) and illustrate the various aspects of our description with several examples. The formalism also suggests the use of spectral analysis to ``measure'' spin tune during computer simulations of spin motion on synchro-betatron orbits.Comment: 62 pages, 1 figure. A slight extension of the published versio

Exact clesed form of the return probability on the Bethe lattice

An exact closed form solution for the return probability of a random walk on the Bethe lattice is given. The long-time asymptotic form confirms a previously known expression. It is however shown that this exact result reduces to the proper expression when the Bethe lattice degenerates on a line, unlike the asymptotic result which is singular. This is shown to be an artefact of the asymptotic expansion. The density of states is also calculated.Comment: 7 pages, RevTex 3.0, 2 figures available upon request from [email protected], to be published in J.Phys.A Let

Slow dynamics at the smeared phase transition of randomly layered magnets

We investigate a model for randomly layered magnets, viz. a three-dimensional Ising model with planar defects. The magnetic phase transition in this system is smeared because static long-range order can develop on isolated rare spatial regions. Here, we report large-scale kinetic Monte Carlo simulations of the dynamical behavior close to the smeared phase transition which we characterize by the spin (time) autocorrelation function. In the paramagnetic phase, its behavior is dominated by Griffiths effects similar to those in magnets with point defects. In the tail region of the smeared transition the dynamics is even slower: the autocorrelation function decays like a stretched exponential at intermediate times before approaching the exponentially small asymptotic value following a power law at late times. Our Monte-Carlo results are in good agreement with recent theoretical predictions based on optimal fluctuation theory.Comment: 7 pages, 6 eps figures, final version as publishe

On the finite-size behavior of systems with asymptotically large critical shift

Exact results of the finite-size behavior of the susceptibility in three-dimensional mean spherical model films under Dirichlet-Dirichlet, Dirichlet-Neumann and Neumann-Neumann boundary conditions are presented. The corresponding scaling functions are explicitly derived and their asymptotics close to, above and below the bulk critical temperature $T_c$ are obtained. The results can be incorporated in the framework of the finite-size scaling theory where the exponent $\lambda$ characterizing the shift of the finite-size critical temperature with respect to $T_c$ is smaller than $1/\nu$, with $\nu$ being the critical exponent of the bulk correlation length.Comment: 24 pages, late