A solution to the problems of cusps and rotation curves in dark matter halos in the cosmological standard model

We discuss various aspects of the inner structure formation in virialized dark matter (DM) halos that form as primordial density inhomogeneities evolve in the cosmological standard model. The main focus is on the study of central cusps/cores and of the profiles of DM halo rotation curves, problems that reveal disagreements among the theory, numerical simulations, and observations. A method that was developed by the authors to describe equilibrium DM systems is presented, which allows investigating these complex nonlinear structures analytically and relating density distribution profiles within a halo both to the parameters of the initial small-scale inhomogeneity field and to the nonlinear relaxation characteristics of gravitationally compressed matter. It is shown that cosmological random motions of matter `heat up' the DM particles in collapsing halos, suppressing cusp-like density profiles within developing halos, facilitating the formation of DM cores in galaxies, and providing an explanation for the difference between observed and simulated galactic rotation curves. The analytic conclusions obtained within this approach can be confirmed by the N-body model simulation once improved spatial resolution is achieved for central halo regions.Comment: 44 pages, 16 figures, 1 tabl

Vortex wandering in a forest of splayed columnar defects

We investigate the scaling properties of single flux lines in a random pinning landscape consisting of splayed columnar defects. Such correlated defects can be injected into Type II superconductors by inducing nuclear fission or via direct heavy ion irradiation. The result is often very efficient pinning of the vortices which gives, e.g., a strongly enhanced critical current. The wandering exponent \zeta and the free energy exponent \omega of a single flux line in such a disordered environment are obtained analytically from scaling arguments combined with extreme-value statistics. In contrast to the case of point disorder, where these exponents are universal, we find a dependence of the exponents on details in the probability distribution of the low lying energies of the columnar defects. The analytical results show excellent agreement with numerical transfer matrix calculations in two and three dimensions.Comment: 11 pages, 9 figure

"1kF1k_F" Singularities and Finite Density ABJM Theory at Strong Coupling

We study non-analytic behavior in the static charge susceptibility in finite density states of the ABJM theory using its holographic dual. Emphasis is placed on a particular state characterized by vanishing entropy density at zero temperature, and Fermi surface-like singularities in various fermionic correlation functions. The susceptibility exhibits branch points in the complex momentum plane, with a real part quantitatively very similar to the location of the Fermi surface singularities.Comment: 29 pages, 5 figures; v2: Minor additions to overview and discussion, some references added, version to appear in JHE

Logarithmic corrections in the two-dimensional Ising model in a random surface field

In the two-dimensional Ising model weak random surface field is predicted to be a marginally irrelevant perturbation at the critical point. We study this question by extensive Monte Carlo simulations for various strength of disorder. The calculated effective (temperature or size dependent) critical exponents fit with the field-theoretical results and can be interpreted in terms of the predicted logarithmic corrections to the pure system's critical behaviour.Comment: 10 pages, 4 figures, extended version with one new sectio

Crossover Phenomena in the One-Dimensional SU(4) Spin-Orbit Model under Magnetic Fields

We study the one-dimensional SU(4) exchange model under magnetic fields, which is the simplest effective Hamiltonian in order to investigate the quantum fluctuations concerned with the orbital degrees of freedom in coupled spin-orbit systems. The Bethe ansatz approaches and numerical calculations using the density matrix renormalization group method are employed. The main concern of the paper is how the system changes from the SU(4) to the SU(2) symmetric limit as the magnetic field is increased. For this model the conformal field theory predicts an usual behavior: there is a jump of the critical exponents just before the SU(2) limit. For a finite-size system, however, the orbital-orbital correlation functions approach continuously to the SU(2) limit after interesting crossover phenomena. The crossover takes place in the magnetization range of 1/3 $\sim$ 1/2 for the system with 72 sites studied in this paper.Comment: 8 pages, 6 Postscript figures, REVTeX, submitted to Phys. Rev.

Persistence and survival in equilibrium step fluctuations

Results of analytic and numerical investigations of first-passage properties of equilibrium fluctuations of monatomic steps on a vicinal surface are reviewed. Both temporal and spatial persistence and survival probabilities, as well as the probability of persistent large deviations are considered. Results of experiments in which dynamical scanning tunneling microscopy is used to evaluate these first-passage properties for steps with different microscopic mechanisms of mass transport are also presented and interpreted in terms of theoretical predictions for appropriate models. Effects of discrete sampling, finite system size and finite observation time, which are important in understanding the results of experiments and simulations, are discussed.Comment: 30 pages, 12 figures, review paper for a special issue of JSTA

Slip avalanches in a fiber bundle model

We study slip avalanches in disordered materials under an increasing external load in the framework of a fiber bundle model. Over-stressed fibers of the model do not break, instead they relax in a stick-slip event which may trigger an entire slip avalanche. Slip avalanches are characterized by the number slipping fibers, by the slip length, and by the load increment, which triggers the avalanche. Our calculations revealed that all three quantities are characterized by power law distributions with universal exponents. We show by analytical calculations and computer simulations that varying the amount of disorder of slip thresholds and the number of allowed slips of fibers, the system exhibits a disorder induced phase transition from a phase where only small avalanches are formed to another one where a macroscopic slip appears.Comment: 6 pages, 6 figure

Hard hexagon partition function for complex fugacity

We study the analyticity of the partition function of the hard hexagon model in the complex fugacity plane by computing zeros and transfer matrix eigenvalues for large finite size systems. We find that the partition function per site computed by Baxter in the thermodynamic limit for positive real values of the fugacity is not sufficient to describe the analyticity in the full complex fugacity plane. We also obtain a new algebraic equation for the low density partition function per site.Comment: 49 pages, IoP styles files, lots of figures (png mostly) so using PDFLaTeX. Some minor changes added to version 2 in response to referee report