194 research outputs found
On the Two-Point Correlation Function in Dynamical Scaling and SCHR\"Odinger Invariance
The extension of dynamical scaling to local, space-time dependent rescaling
factors is investigated. For a dynamical exponent , the corresponding
invariance group is the Schr\"odinger group. Schr\"odinger invariance is shown
to determine completely the two-point correlation function. The result is
checked in two exactly solvable models.Comment: Geneva preprint UGVA/DPT 1992/09-783, plain Tex 6pp (to appear in
Int. J. Mod. Phys. C
Phase-ordering kinetics: ageing and local scale-invariance
Dynamical scaling in ageing systems, notably in phase-ordering kinetics, is
well-established. New evidence in favour of Galilei-invariance in
phase-ordering kinetics is reviewed.Comment: 7 pages, 1 figure,with AIP macros, based on invited talks given at
the 8th Granada Seminar on Computational and Statistical Physics (7-11
February 2005) and at the Symposium `Renormalization and Scaling' at Berlin
(5th of March 2005
Dynamical symmetries and causality in non-equilibrium phase transitions
Dynamical symmetries are of considerable importance in elucidating the
complex behaviour of strongly interacting systems with many degrees of freedom.
Paradigmatic examples are cooperative phenomena as they arise in phase
transitions, where conformal invariance has led to enormous progress in
equilibrium phase transitions, especially in two dimensions. Non-equilibrium
phase transitions can arise in much larger portions of the parameter space than
equilibrium phase transitions. The state of the art of recent attempts to
generalise conformal invariance to a new generic symmetry, taking into account
the different scaling behaviour of space and time, will be reviewed. Particular
attention will be given to the causality properties as they follow for
co-variant -point functions. These are important for the physical
identification of n-point functions as responses or correlators.Comment: Latex2e, 26 pages, 1 figure. Final form, a new example added & typos
correcte
Non-local meta-conformal invariance, diffusion-limited erosion and the XXZ chain
Diffusion-limited erosion is a distinct universality class of fluctuating
interfaces. Although its dynamical exponent , none of the known variants
of conformal invariance can act as its dynamical symmetry. In spatial
dimensions, its infinite-dimensional dynamic symmetry is constructed and shown
to be isomorphic to the direct sum of three loop-Virasoro algebras, with the
maximal finite-dimensional sub-algebra
.
The infinitesimal generators are spatially non-local and use the Riesz-Feller
fractional derivative. Co-variant two-time response functions are derived and
reproduce the exact solution of diffusion-limited erosion. The relationship
with the terrace-step-kind model of vicinal surfaces and the integrable XXZ
chain are discussed.Comment: Latex 2e, 28 pp, 4 figures (revised, with 2 new figures
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