Closed Strings in Misner Space: Stringy Fuzziness with a Twist

Misner space, also known as the Lorentzian orbifold $R^{1,1}/boost$, is the simplest tree-level solution of string theory with a cosmological singularity. We compute tree-level scattering amplitudes involving twisted states, using operator and current algebra techniques. We find that, due to zero-point quantum fluctuations of the excited modes, twisted strings with a large winding number $w$ are fuzzy on a scale $\sqrt{\log w}$, which can be much larger than the string scale. Wave functions are smeared by an operator $\exp(\Delta(\nu) \partial_+ \partial_-)$ reminiscent of the Moyal-product of non-commutative geometry, which, since $\Delta(\nu)$ is real, modulates the amplitude rather than the phase of the wave function, and is purely gravitational in its origin. We compute the scattering amplitude of two twisted states and one tachyon or graviton, and find a finite result. The scattering amplitude of two twisted and two untwisted states is found to diverge, due to the propagation of intermediate winding strings with vanishing boost momentum. The scattering amplitude of three twisted fields is computed by analytic continuation from three-point amplitudes of states with non-zero $p^+$ in the Nappi-Witten plane wave, and the non-locality of the three-point vertex is found to diverge for certain kinematical configurations. Our results for the three-point amplitudes allow in principle to compute, to leading order, the back-reaction on the metric due to a condensation of coherent winding strings.Comment: 29 pages, Latex2e, uses JHEP3.cls; v3: minor corrections, final version to appear in JCA

Approach to equilibrium of diffusion in a logarithmic potential

The late-time distribution function P(x,t) of a particle diffusing in a one-dimensional logarithmic potential is calculated for arbitrary initial conditions. We find a scaling solution with three surprising features: (i) the solution is given by two distinct scaling forms, corresponding to a diffusive (x ~ t^(1/2)) and a subdiffusive (x ~ t^{\gamma} with a given {\gamma} < 1/2) length scale, respectively, (ii) the overall scaling function is selected by the initial condition, and (iii) depending on the tail of the initial condition, the scaling exponent which characterizes the scaling function is found to exhibit a transition from a continuously varying to a fixed value.Comment: 4 pages, 3 figures; Published versio

Quantum evolution across singularities

Attempts to consider evolution across space-time singularities often lead to quantum systems with time-dependent Hamiltonians developing an isolated singularity as a function of time. Examples include matrix theory in certain singular time-dependent backgounds and free quantum fields on the two-dimensional compactified Milne universe. Due to the presence of the singularities in the time dependence, the conventional quantum-mechanical evolution is not well-defined for such systems. We propose a natural way, mathematically analogous to renormalization in conventional quantum field theory, to construct unitary quantum evolution across the singularity. We carry out this procedure explicitly for free fields on the compactified Milne universe and compare our results with the matching conditions considered in earlier work (which were based on the covering Minkowski space).Comment: revised with an emphasis on local counterterm subtraction rather than analyticity; version to be submitted for publicatio

1/f1/f noise and avalanche scaling in plastic deformation

We study the intermittency and noise of dislocation systems undergoing shear deformation. Simulations of a simple two-dimensional discrete dislocation dynamics model indicate that the deformation rate exhibits a power spectrum scaling of the type $1/f^{\alpha}$. The noise exponent is far away from a Lorentzian, with $\alpha \approx 1.5$. This result is directly related to the way the durations of avalanches of plastic deformation activity scale with their size.Comment: 6 pages, 5 figures, submitted to Phys. Rev.

Phase transitions in a disordered system in and out of equilibrium

The equilibrium and non--equilibrium disorder induced phase transitions are compared in the random-field Ising model (RFIM). We identify in the demagnetized state (DS) the correct non-equilibrium hysteretic counterpart of the T=0 ground state (GS), and present evidence of universality. Numerical simulations in d=3 indicate that exponents and scaling functions coincide, while the location of the critical point differs, as corroborated by exact results for the Bethe lattice. These results are of relevance for optimization, and for the generic question of universality in the presence of disorder.Comment: Accepted for publication in Phys. Rev. Let

Finite driving rates in interface models of Barkhausen noise

We consider a single-interface model for the description of Barkhausen noise in soft ferromagnetic materials. Previously, the model had been used only in the adiabatic regime of infinitely slow field ramping. We introduce finite driving rates and analyze the scaling of event sizes and durations for different regimes of the driving rate. Coexistence of intermittency, with non-trivial scaling laws, and finite-velocity interface motion is observed for high enough driving rates. Power spectra show a decay $\sim \omega^{-t}$, with $t<2$ for finite driving rates, revealing the influence of the internal structure of avalanches.Comment: 7 pages, 6 figures, RevTeX, final version to be published in Phys. Rev.

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

Helium condensation in aerogel: avalanches and disorder-induced phase transition

We present a detailed numerical study of the elementary condensation events (avalanches) associated to the adsorption of $^4$He in silica aerogels. We use a coarse-grained lattice-gas description and determine the nonequilibrium behavior of the adsorbed gas within a local mean-field analysis, neglecting thermal fluctuations and activated processes. We investigate the statistical properties of the avalanches, such as their number, size and shape along the adsorption isotherms as a function of gel porosity, temperature, and chemical potential. Our calculations predict the existence of a line of critical points in the temperature-porosity diagram where the avalanche size distribution displays a power-law behavior and the adsorption isotherms have a universal scaling form. The estimated critical exponents seem compatible with those of the field-driven Random Field Ising Model at zero temperature.Comment: 16 pages, 14 figure

Ground state optimization and hysteretic demagnetization: the random-field Ising model

We compare the ground state of the random-field Ising model with Gaussian distributed random fields, with its non-equilibrium hysteretic counterpart, the demagnetized state. This is a low energy state obtained by a sequence of slow magnetic field oscillations with decreasing amplitude. The main concern is how optimized the demagnetized state is with respect to the best-possible ground state. Exact results for the energy in d=1 show that in a paramagnet, with finite spin-spin correlations, there is a significant difference in the energies if the disorder is not so strong that the states are trivially almost alike. We use numerical simulations to better characterize the difference between the ground state and the demagnetized state. For d>=3 the random-field Ising model displays a disorder induced phase transition between a paramagnetic and a ferromagnetic state. The locations of the critical points R_c(DS), R_c(GS) differ for the demagnetized state and ground state. Consequently, it is in this regime that the optimization of the demagnetized stat is the worst whereas both deep in the paramagnetic regime and in the ferromagnetic one the states resemble each other to a great extent. We argue based on the numerics that in d=3 the scaling at the transition is the same in the demagnetized and ground states. This claim is corroborated by the exact solution of the model on the Bethe lattice, where the R_c's are also different.Comment: 13 figs. Submitted to Phys. Rev.

Power spectra of self-organized critical sandpiles

We analyze the power spectra of avalanches in two classes of self-organized critical sandpile models, the Bak-Tang-Wiesenfeld model and the Manna model. We show that these decay with a $1/f^\alpha$ power law, where the exponent value $\alpha$ is significantly smaller than 2 and equals the scaling exponent relating the avalanche size to its duration. We discuss the basic ingredients behind this result, such as the scaling of the average avalanche shape.Comment: 7 pages, 3 figures, submitted to JSTA