Inertial modes in stratified rotating neutron stars : An evolutionary description

With (non-barotropic) equations of state valid even when the neutron, proton and electron content of neutron star cores is not in beta equilibrium, we study inertial and composition gravity modes of relativistic rotating neutron stars. We solve the relativistic Euler equations in the time domain with a three dimensional numerical code based on spectral methods, in the slow rotation, relativistic Cowling and anelastic approximations. Principally, after a short description of the gravity modes due to smooth composition gradients, we focus our analysis on the question of how the inertial modes are affected by non-barotropicity of the nuclear matter. In our study, the deviation with respect to barotropicity results from the frozen composition of non-superfluid matter composed of neutrons, protons and electrons, when beta equilibrium is broken by millisecond oscillations. We show that already for moderatly fast rotating stars the increasing coupling between polar and axial modes makes those two cases less different than for very slowly rotating stars. In addition, as we directly solve the Euler equations, without coupling only a few number of spherical harmonics, we always found, for the models that we use, a discrete spectrum for the $l = m = 2$ inertial mode. Finally, we find that, for non-barotropic stars, the frequency of this mode, which is our main focus, decreases in a non-negligible way, whereas the time dependence of the energy transfer between polar and axial modes is substantially different due to the existence of low-frequencies gravity modes.Comment: 34 pages, 24 figures, published versio

Study of Chirality in the Two-Dimensional XY Spin Glass

We study the chirality in the Villain form of the XY spin glass in two--dimensions by Monte Carlo simulations. We calculate the chiral-glass correlation length exponent $\nu_{\scriptscriptstyle CG}$ and find that $\nu_{\scriptscriptstyle CG} = 1.8 \pm 0.3$ in reasonable agreement with earlier studies. This indicates that the chiral and phase variables are decoupled on long length scales and diverge as $T \to 0$ with {\em different} exponents, since the spin-glass correlation length exponent was found, in earlier studies, to be about 1.0.Comment: 4 pages. Latex file and 4 embedded postscript files are included in a self-unpacking compressed tar file. A postscript version is available at ftp://chopin.ucsc.edu/pub/xysg.p

Simplex solid states of SU(N) quantum antiferromagnets

I define a set of wavefunctions for SU(N) lattice antiferromagnets, analogous to the valence bond solid states of Affleck, Kennedy, Lieb, and Tasaki (AKLT), in which the singlets are extended over N-site simplices. As with the valence bond solids, the new simplex solid (SS) states are extinguished by certain local projection operators, allowing us to construct Hamiltonians with local interactions which render the SS states exact ground states. Using a coherent state representation, we show that the quantum correlations in each SS state are calculable as the finite temperature correlations of an associated classical model, with N-spin interactions, on the same lattice. In three and higher dimensions, the SS states can spontaneously break SU(N) and exhibit N-sublattice long-ranged order, as a function of a discrete parameter which fixes the local representation of SU(N). I analyze this transition using a classical mean field approach. For N>2 the ordered state is selected via an "order by disorder" mechanism. As in the AKLT case, the bulk representations fractionalize at an edge, and the ground state entropy is proportional to the volume of the boundary.Comment: 14 pages, 8 figures, minor typos correcte

Controlling high-harmonic generation and above-threshold ionization with an attosecond-pulse train

We perform a detailed analysis of how high-order harmonic generation (HHG) and above-threshold ionization (ATI) can be controlled by a time-delayed attosecond-pulse train superposed to a strong, near-infrared laser field. In particular we show that the high-harmonic and photoelectron intensities, the high-harmonic plateau structure and cutoff energies, and the ATI angular distributions can be manipulated by changing this delay. This is a direct consequence of the fact that the attosecond pulse train can be employed as a tool for constraining the instant an electronic wave packet is ejected in the continuum. A change in such initial conditions strongly affects its subsequent motion in the laser field, and thus HHG and ATI. In our studies, we employ the Strong-Field Approximation and explain the features observed in terms of interference effects between various electron quantum orbits. Our results are in agreement with recent experimental findings and theoretical studies employing purely numerical methods.Comment: 10 pages revtex and 6 figures (eps files

Finite-size effects on the Hamiltonian dynamics of the XY-model

The dynamical properties of the finite-size magnetization M in the critical region T<T_{KTB} of the planar rotor model on a L x L square lattice are analyzed by means of microcanonical simulations . The behavior of the q=0 structure factor at high frequencies is consistent with field-theoretical results, but new additional features occur at lower frequencies. The motion of M determines a region of spectral lines and the presence of a central peak, which we attribute to phase diffusion. Near T_{KTB} the diffusion constant scales with system size as D ~ L^{-1.6(3)}.Comment: To be published in Europhysics Letter

Non-equilibrium beta processes in superfluid neutron star cores

The influence of nucleons superfluidity on the beta relaxation time of degenerate neutron star cores, composed of neutrons, protons and electrons, is investigated. We numerically calculate the implied reduction factors for both direct and modified Urca reactions, with isotropic pairing of protons or anisotropic pairing of neutrons. We find that due to the non-zero value of the temperature and/or to the vanishing of anisotropic gaps in some directions of the phase-space, superfluidity does not always completely inhibit beta relaxation, allowing for some reactions if the superfluid gap amplitude is not too large in respect to both the typical thermal energy and the chemical potential mismatch. We even observe that if the ratio between the critical temperature and the actual temperature is very small, a suprathermal regime is reached for which superfluidity is almost irrelevant. On the contrary, if the gap is large enough, the composition of the nuclear matter can stay frozen for very long durations, unless the departure from beta equilibrium is at least as important as the gap amplitude. These results are crucial for precise estimation of the superfluidity effect on the cooling/slowing-down of pulsars and we provide online subroutines to be implemented in codes for simulating such evolutions.Comment: 11 pages, 6 Figs., published, minor changes, subroutines can be found on line at http://luth2.obspm.fr/~etu/villain/Micro/Resolution.htm

Conserved Growth on Vicinal Surfaces

A crystal surface which is miscut with respect to a high symmetry plane exhibits steps with a characteristic distance. It is argued that the continuum description of growth on such a surface, when desorption can be neglected, is given by the anisotropic version of the conserved KPZ equation (T. Sun, H. Guo, and M. Grant, Phys. Rev. A 40, 6763 (1989)) with non-conserved noise. A one--loop dynamical renormalization group calculation yields the values of the dynamical exponent and the roughness exponent which are shown to be the same as in the isotropic case. The results presented here should apply in particular to growth under conditions which are typical for molecular beam epitaxy.Comment: 10 pages, uses revte

Phase diagram of an anisotropic frustrated ferromagnetic spin-1/2 chain in a magnetic field: a density matrix renormalization group study

We study the phase diagram of a frustrated spin-1/2 ferromagnetic chain with anisotropic exchange interactions in an external magnetic field, using the density matrix renormalization group method. We show that an easy-axis anisotropy enhances the tendency towards multimagnon bound states, while an easy-plane anisotropy favors chirally ordered phases. In particular, a moderate easy-plane anisotropy gives rise to a quantum phase transition at intermediate magnetization. We argue that this transition is related to the finite-field phase transition experimentally observed in the spin-1/2 compound LiCuVO_4.Comment: The final published versio

A simulation study of energy transport in the Hamiltonian XY-model

The transport properties of the planar rotator model on a square lattice are analyzed by means of microcanonical and non--equilibrium simulations. Well below the Kosterlitz--Thouless--Berezinskii transition temperature, both approaches consistently indicate that the energy current autocorrelation displays a long--time tail decaying as t^{-1}. This yields a thermal conductivity coefficient which diverges logarithmically with the lattice size. Conversely, conductivity is found to be finite in the high--temperature disordered phase. Simulations close to the transition temperature are insted limited by slow convergence that is presumably due to the slow kinetics of vortex pairs.Comment: Submitted to Journal of Statistical Mechanics: theory and experimen