234 research outputs found
Comment on ``Nonuniversal Exponents in Interface Growth''
Recently, Newman and Swift[T. J. Newman and M. R. Swift, Phys. Rev. Lett.
{\bf 79}, 2261 (1997)] made an interesting suggestion that the strong-coupling
exponents of the Kardar-Parisi-Zhang (KPZ) equation may not be universal, but
rather depend on the precise form of the noise distribution. We show here that
the decrease of surface roughness exponents they observed can be attributed to
a percolative effect
Non-perturbative renormalization of the KPZ growth dynamics
We introduce a non-perturbative renormalization approach which identifies
stable fixed points in any dimension for the Kardar-Parisi-Zhang dynamics of
rough surfaces. The usual limitations of real space methods to deal with
anisotropic (self-affine) scaling are overcome with an indirect functional
renormalization. The roughness exponent is computed for dimensions
to 8 and it results to be in very good agreement with the available
simulations. No evidence is found for an upper critical dimension. We discuss
how the present approach can be extended to other self-affine problems.Comment: 4 pages, 2 figures. To appear in Phys. Rev. Let
Universality and Crossover of Directed Polymers and Growing Surfaces
We study KPZ surfaces on Euclidean lattices and directed polymers on
hierarchical lattices subject to different distributions of disorder, showing
that universality holds, at odds with recent results on Euclidean lattices.
Moreover, we find the presence of a slow (power-law) crossover toward the
universal values of the exponents and verify that the exponent governing such
crossover is universal too. In the limit of a 1+epsilon dimensional system we
obtain both numerically and analytically that the crossover exponent is 1/2.Comment: LateX file + 5 .eps figures; to appear on Phys. Rev. Let
Upper critical dimension, dynamic exponent and scaling functions in the mode-coupling theory for the Kardar-Parisi-Zhang equation
We study the mode-coupling approximation for the KPZ equation in the strong
coupling regime. By constructing an ansatz consistent with the asymptotic forms
of the correlation and response functions we determine the upper critical
dimension d_c=4, and the expansion z=2-(d-4)/4+O((4-d)^2) around d_c. We find
the exact z=3/2 value in d=1, and estimate the values 1.62, 1.78 for z, in
d=2,3. The result d_c=4 and the expansion around d_c are very robust and can be
derived just from a mild assumption on the relative scale on which the response
and correlation functions vary as z approaches 2.Comment: RevTex, 4 page
Ground State Wave Function of the Schr\"odinger Equation in a Time-Periodic Potential
Using a generalized transfer matrix method we exactly solve the Schr\"odinger
equation in a time periodic potential, with discretized Euclidean space-time.
The ground state wave function propagates in space and time with an oscillating
soliton-like wave packet and the wave front is wedge shaped. In a statistical
mechanics framework our solution represents the partition sum of a directed
polymer subjected to a potential layer with alternating (attractive and
repulsive) pinning centers.Comment: 11 Pages in LaTeX. A set of 2 PostScript figures available upon
request at [email protected] . Physical Review Letter
An Exactly Solved Model of Three Dimensional Surface Growth in the Anisotropic KPZ Regime
We generalize the surface growth model of Gates and Westcott to arbitrary
inclination. The exact steady growth velocity is of saddle type with principal
curvatures of opposite sign. According to Wolf this implies logarithmic height
correlations, which we prove by mapping the steady state of the surface to
world lines of free fermions with chiral boundary conditions.Comment: 9 pages, REVTEX, epsf, 3 postscript figures, submitted to J. Stat.
Phys, a wrong character is corrected in eqs. (31) and (32
A numerical study of the development of bulk scale-free structures upon growth of self-affine aggregates
During the last decade, self-affine geometrical properties of many growing
aggregates, originated in a wide variety of processes, have been well
characterized. However, little progress has been achieved in the search of a
unified description of the underlying dynamics. Extensive numerical evidence
has been given showing that the bulk of aggregates formed upon ballistic
aggregation and random deposition with surface relaxation processes can be
broken down into a set of infinite scale invariant structures called "trees".
These two types of aggregates have been selected because it has been
established that they belong to different universality classes: those of
Kardar-Parisi-Zhang and Edward-Wilkinson, respectively. Exponents describing
the spatial and temporal scale invariance of the trees can be related to the
classical exponents describing the self-affine nature of the growing interface.
Furthermore, those exponents allows us to distinguish either the compact or
non-compact nature of the growing trees. Therefore, the measurement of the
statistic of the process of growing trees may become a useful experimental
technique for the evaluation of the self-affine properties of some aggregates.Comment: 19 pages, 5 figures, accepted for publication in Phys.Rev.
Topological relaxation of entangled flux lattices: Single vs collective line dynamics
A symbolic language allowing to solve statistical problems for the systems
with nonabelian braid-like topology in 2+1 dimensions is developed. The
approach is based on the similarity between growing braid and "heap of colored
pieces". As an application, the problem of a vortex glass transition in
high-T_c superconductors is re-examined on microscopic levelComment: 4 pages (revtex), 4 figure
Quantized Scaling of Growing Surfaces
The Kardar-Parisi-Zhang universality class of stochastic surface growth is
studied by exact field-theoretic methods. From previous numerical results, a
few qualitative assumptions are inferred. In particular, height correlations
should satisfy an operator product expansion and, unlike the correlations in a
turbulent fluid, exhibit no multiscaling. These properties impose a
quantization condition on the roughness exponent and the dynamic
exponent . Hence the exact values for two-dimensional
and for three-dimensional surfaces are derived.Comment: 4 pages, revtex, no figure
Low frequency response of a collectively pinned vortex manifold
A low frequency dynamic response of a vortex manifold in type-II
superconductor can be associated with thermally activated tunneling of large
portions of the manifold between pairs of metastable states (two-level
systems). We suggest that statistical properties of these states can be
verified by using the same approach for the analysis of thermal fluctuations
the behaviour of which is well known. We find the form of the response for the
general case of vortex manifold with non-dispersive elastic moduli and for the
case of thin superconducting film for which the compressibility modulus is
always non-local.Comment: 8 pages, no figures, ReVTeX, the final version. Text strongly
modified, all the results unchange
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