Numerical study of the localization length critical index in a network model of plateau-plateau transitions in the quantum Hall effect

We calculate numerically the localization length critical index within the Chalker-Coddington (CC) model for plateau-plateau transitions in the quantum Hall effect. Lyapunov exponents have been calculated with relative errors on the order $10^{-3}$. Such high precision was obtained by considering the distribution of Lyapunov exponents for large ensembles of relatively short chains and calculating the ensemble average values. We analyze thoroughly finite size effects and find the localization length critical index $\nu= 2.517\pm 0.018$.Comment: 4 pages, 4 figure

Destruction of Anderson localization by a weak nonlinearity

We study numerically a spreading of an initially localized wave packet in a one-dimensional discrete nonlinear Schr\"odinger lattice with disorder. We demonstrate that above a certain critical strength of nonlinearity the Anderson localization is destroyed and an unlimited subdiffusive spreading of the field along the lattice occurs. The second moment grows with time $\propto t^\alpha$, with the exponent $\alpha$ being in the range $0.3 - 0.4$. For small nonlinearities the distribution remains localized in a way similar to the linear case.Comment: 4 pages, 5 fig

Stripes in thin ferromagnetic films with out-of-plane anisotropy

We examine the T=0 phase diagram of a thin ferromagnetic film with a strong out-of-plane anisotropy in the vicinity of the reorientation phase transition (with Co on Pt as an example). The phase diagram in the anisotropy-applied field plane is universal in the limit where the film thickness is the shortest length scale. It contains uniform fully magnetized and canted phases, as well as periodically nonuniform states: a weakly modulated spin-density wave and strongly modulated stripes. We determine the boundaries of metastability of these phases and point out the existence of a critical point at which the difference between the SDW and stripes vanishes. Out-of-plane magnetization curves exhibit a variety of hysteresis loops caused by the coexistence of one or more phases. Additionally, we study the effect of a system edge on the orientation of stripes. We compare our results with recent experiments.Comment: added references and clarified derivations in response to referee comment

Perfect State Transfer: Beyond Nearest-Neighbor Couplings

In this paper we build on the ideas presented in previous works for perfectly transferring a quantum state between opposite ends of a spin chain using a fixed Hamiltonian. While all previous studies have concentrated on nearest-neighbor couplings, we demonstrate how to incorporate additional terms in the Hamiltonian by solving an Inverse Eigenvalue Problem. We also explore issues relating to the choice of the eigenvalue spectrum of the Hamiltonian, such as the tolerance to errors and the rate of information transfer.Comment: 8 pages, 2 figures. Reorganised, more detailed derivations provided and section on rate of information transfer adde

Short-time behavior of a classical ferromagnet with double-exchange interaction

We investigate the critical dynamics of a classical ferromagnet on the simple cubic lattice with double-exchange interaction. Estimates for the dynamic critical exponents $z$ and $\theta$ are obtained using short-time Monte Carlo simulations. We also estimate the static critical exponents $\nu$ and $\beta$ studying the behavior of the samples at an early time. Our results are in good agreement with available estimates and support the assertion that this model and the classical Heisenberg model belong to the same universality class

Global persistence exponent of the double-exchange model

We obtained the global persistence exponent $\theta_g$ for a continuous spin model on the simple cubic lattice with double-exchange interaction by using two different methods. First, we estimated the exponent $\theta_g$ by following the time evolution of probability $P(t)$ that the order parameter of the model does not change its sign up to time $t$ $[P(t)\thicksim t^{-\theta_g}]$. Afterwards, that exponent was estimated through the scaling collapse of the universal function $L^{\theta_g z} P(t)$ for different lattice sizes. Our results for both approaches are in very good agreement each other.Comment: 4 pages, 3 figures, and 3 tables. To appear in Physical Review

Nonuniqueness in spin-density-functional theory on lattices

In electronic many-particle systems, the mapping between densities and spin magnetizations, {n(r), m(r)}, and potentials and magnetic fields, {v(r), B(r)}, is known to be nonunique, which has fundamental and practical implications for spin-density-functional theory (SDFT). This paper studies the nonuniqueness (NU) in SDFT on arbitrary lattices. Two new, non-trivial cases are discovered, here called local saturation and global noncollinear NU, and their properties are discussed and illustrated. In the continuum limit, only some well-known special cases of NU survive.Comment: 4 pages, 1 figur

Massive Black Hole Binary Systems in Hierarchical Scenario of Structure Formation

The hierarchical scenario of structure formation describes how objects like galaxies and galaxy clusters are formed by mergers of small objects. In this scenario, mergers of galaxies can lead to the formation of massive black hole (MBH) binary systems. On the other hand, the merger of two MBH could produce a gravitational wave signal detectable, in principle, by the Laser Interferometer Space Antenna (LISA). In the present work, we use the Press-Schechter formalism, and its extension, to describe the merger rate of haloes which contain massive black holes. Here, we do not study the gravitational wave emission of these systems. However, we present an initial study to determine the number of systems formed via mergers that could permit, in a future extension of this work, the calculation of the signature in gravitational waves of these systems.Comment: to match the published version in International Journal of Modern Physics

Relativistic time dilatation and the spectrum of electrons emitted by 33 TeV lead ions penetrating thin foils

We study the energy distribution of ultrarelativistic electrons produced when a beam of 33 TeV Pb$^{81+}$(1s) ions penetrates a thin Al foil. We show that, because of a prominent role of the excitations of the ions inside the foil which becomes possible due to the relativistic time dilatation, the width of this distribution can be much narrower compared to the case when the ions interact with rarefied gaseous targets. We also show that a very similar shape of the energy distribution may arise when 33 TeV Pb$^{82+}$ ions penetrate a thin Au foil. These results shed some light on the origin of the very narrow electron energy distributions observed experimentally about a decade ago.Comment: Four pages, two figure