Barkhausen noise from zigzag domain walls

We investigate the Barkhausen noise in ferromagnetic thin films with zigzag domain walls. We use a cellular automaton model that describes the motion of a zigzag domain wall in an impure ferromagnetic quasi-two dimensional sample with in-plane uniaxial magnetization at zero temperature, driven by an external magnetic field. The main ingredients of this model are the dipolar spin-spin interactions and the anisotropy energy. A power law behavior with a cutoff is found for the probability distributions of size, duration and correlation length of the Barkhausen avalanches, and the critical exponents are in agreement with the available experiments. The link between the size and the duration of the avalanches is analyzed too, and a power law behavior is found for the average size of an avalanche as a function of its duration.Comment: 11 pages, 12 figure

Hysteresis and noise in ferromagnetic materials with parallel domain walls

We investigate dynamic hysteresis and Barkhausen noise in ferromagnetic materials with a huge number of parallel and rigid Bloch domain walls. Considering a disordered ferromagnetic system with strong in-plane uniaxial anisotropy and in-plane magnetization driven by an external magnetic field, we calculate the equations of motion for a set of coupled domain walls, considering the effects of the long-range dipolar interactions and disorder. We derive analytically an expression for the magnetic susceptivity, related to the effective demagnetizing factor, and show that it has a logarithmic dependence on the number of domains. Next, we simulate the equations of motion and study the effect of the external field frequency and the disorder on the hysteresis and noise properties. The dynamic hysteresis is very well explained by means of the loss separation theory.Comment: 13 pages, 11 figure

Resolving the Crab pulsar wind nebula at teraelectronvolt energies

The Crab nebula is one of the most-studied cosmic particle accelerators, shining brightly across the entire electromagnetic spectrum up to very-high-energy gamma rays1,2. It is known from observations in the radio to gamma-ray part of the spectrum that the nebula is powered by a pulsar, which converts most of its rotational energy losses into a highly relativistic outflow. This outflow powers a pulsar wind nebula, a region of up to ten light-years across, filled with relativistic electrons and positrons. These particles emit synchrotron photons in the ambient magnetic field and produce very-high-energy gamma rays by Compton up-scattering of ambient low-energy photons. Although the synchrotron morphology of the nebula is well established, it has not been known from which region the very-high-energy gamma rays are emitted3,4,5,6,7,8. Here we report that the Crab nebula has an angular extension at gamma-ray energies of 52 arcseconds (assuming a Gaussian source width), much larger than at X-ray energies. This result closes a gap in the multi-wavelength coverage of the nebula, revealing the emission region of the highest-energy gamma rays. These gamma rays enable us to probe a previously inaccessible electron and positron energy range. We find that simulations of the electromagnetic emission reproduce our measurement, pro

A trivial observation on time reversal in random matrix theory

It is commonly thought that a state-dependent quantity, after being averaged over a classical ensemble of random Hamiltonians, will always become independent of the state. We point out that this is in general incorrect: if the ensemble of Hamiltonians is time reversal invariant, and the quantity involves the state in higher than bilinear order, then we show that the quantity is only a constant over the orbits of the invariance group on the Hilbert space. Examples include fidelity and decoherence in appropriate models.Comment: 7 pages 3 figure

Microcanonical mean-field thermodynamics of self-gravitating and rotating systems

We derive the global phase diagram of a self-gravitating $N$-body system enclosed in a finite three-dimensional spherical volume $V$ as a function of total energy and angular momentum, employing a microcanonical mean-field approach. At low angular momenta (i.e. for slowly rotating systems) the known collapse from a gas cloud to a single dense cluster is recovered. At high angular momenta, instead, rotational symmetry can be spontaneously broken and rotationally asymmetric structures (double clusters) appear.Comment: 4 pages, 4 figures; to appear in Phys. Rev. Let

Hamiltonian dynamics and geometry of phase transitions in classical XY models

The Hamiltonian dynamics associated to classical, planar, Heisenberg XY models is investigated for two- and three-dimensional lattices. Besides the conventional signatures of phase transitions, here obtained through time averages of thermodynamical observables in place of ensemble averages, qualitatively new information is derived from the temperature dependence of Lyapunov exponents. A Riemannian geometrization of newtonian dynamics suggests to consider other observables of geometric meaning tightly related with the largest Lyapunov exponent. The numerical computation of these observables - unusual in the study of phase transitions - sheds a new light on the microscopic dynamical counterpart of thermodynamics also pointing to the existence of some major change in the geometry of the mechanical manifolds at the thermodynamical transition. Through the microcanonical definition of the entropy, a relationship between thermodynamics and the extrinsic geometry of the constant energy surfaces $\Sigma_E$ of phase space can be naturally established. In this framework, an approximate formula is worked out, determining a highly non-trivial relationship between temperature and topology of the $\Sigma_E$. Whence it can be understood that the appearance of a phase transition must be tightly related to a suitable major topology change of the $\Sigma_E$. This contributes to the understanding of the origin of phase transitions in the microcanonical ensemble.Comment: in press on Physical Review E, 43 pages, LaTeX (uses revtex), 22 PostScript figure

Recurrence of fidelity in near integrable systems

Within the framework of simple perturbation theory, recurrence time of quantum fidelity is related to the period of the classical motion. This indicates the possibility of recurrence in near integrable systems. We have studied such possibility in detail with the kicked rotor as an example. In accordance with the correspondence principle, recurrence is observed when the underlying classical dynamics is well approximated by the harmonic oscillator. Quantum revivals of fidelity is noted in the interior of resonances, while classical-quantum correspondence of fidelity is seen to be very short for states initially in the rotational KAM region.Comment: 13 pages, 6 figure

Charge fluctuations and electron-phonon interaction in the finite-UU Hubbard model

In this paper we employ a gaussian expansion within the finite-$U$ slave-bosons formalism to investigate the momentum structure of the electron-phonon vertex function in the Hubbard model as function of $U$ and $n$. The suppression of large momentum scattering and the onset a small-${\bf q}$ peak structure, parametrized by a cut-off $q_c$, are shown to be essentially ruled by the band narrowing factor $Z_{\rm MF}$ due to the electronic correlation. A phase diagram of $Z_{\rm MF}$ and $q_c$ in the whole $U$-$n$ space is presented. Our results are in more than qualitative agreement with a recent numerical analysis and permit to understand some anomalous features of the Quantum Monte Carlo data.Comment: 4 pages, eps figures include

Estimating purity in terms of correlation functions

We prove a rigorous inequality estimating the purity of a reduced density matrix of a composite quantum system in terms of cross-correlation of the same state and an arbitrary product state. Various immediate applications of our result are proposed, in particular concerning Gaussian wave-packet propagation under classically regular dynamics.Comment: 3 page

A Uniform Approximation for the Fidelity in Chaotic Systems

In quantum/wave systems with chaotic classical analogs, wavefunctions evolve in highly complex, yet deterministic ways. A slight perturbation of the system, though, will cause the evolution to diverge from its original behavior increasingly with time. This divergence can be measured by the fidelity, which is defined as the squared overlap of the two time evolved states. For chaotic systems, two main decay regimes of either Gaussian or exponential behavior have been identified depending on the strength of the perturbation. For perturbation strengths intermediate between the two regimes, the fidelity displays both forms of decay. By applying a complementary combination of random matrix and semiclassical theory, a uniform approximation can be derived that covers the full range of perturbation strengths. The time dependence is entirely fixed by the density of states and the so-called transition parameter, which can be related to the phase space volume of the system and the classical action diffusion constant, respectively. The accuracy of the approximations are illustrated with the standard map.Comment: 16 pages, 4 figures, accepted in J. Phys. A, special edition on Random Matrix Theor