172 research outputs found
Closed Strings in Misner Space: Stringy Fuzziness with a Twist
Misner space, also known as the Lorentzian orbifold , 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 are fuzzy on a scale , which can be much larger than
the string scale. Wave functions are smeared by an operator reminiscent of the Moyal-product of non-commutative
geometry, which, since 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 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
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 . The noise exponent is far away from a
Lorentzian, with . 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 , with
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 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 power law, where the exponent value
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
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