Next weeks' seminar

[CM ICTP - Trieste]

									06/08

JOINT ICTP/SISSA CONDENSED MATTER SEMINARS
Academic Year 2006/07




Seminar Room - Main Building   (first floor)



Wednesday, 29 November -     4:00 p.m.



S. MAZUMDER   ( Bhabha Atomic Research Centre, Mumbai )


" Some open issues pertinent to the phenomenon of dynamical scaling of 
structure factor"


Abstract

The phenomenon of new phase formation is a representative example of 
first order transition. The phenomenon is fundamental and of immense 
interest as an example of a highly nonlinear process far from 
equilibrium. The second phase grows with time and in late stages all 
domain sizes are much larger than all microscopic lengths. In the large 
time limit, the new phase forming systems exhibit self-similar growth 
pattern with dilation symmetry, with time dependent scale, and scaling 
phenomenon. The phenomenon is indicative of the emergence of a 
morphological pattern of the domains at earlier times looking 
statistically similar to a pattern at later times apart from the global 
change of scale implied by the growth of time dependent characteristic 
length scale L(t) – a measure of the time dependent domain size of the 
new phase.
The scaling hypothesis assumes the existence of a single characteristic 
length scale L(t) such that the domain sizes and their spatial 
correlation are time invariant when the lengths are scaled by L(t). 
Quantitatively, for isotropic systems, the equal-time spatio-temporal 
composition modulation auto-correlation function g(r,t), reflects the 
way in which the mean density of the medium varies as a function of 
distance from a given point, should exhibit the scaling form with 
time-dependent dilation symmetry g(r,t)=f(r/L(t)). The scaling function 
f(r/L(t)) is universal in the sense that it is independent of initial 
conditions and also on interactions as long as they are short ranged. 
However, form of f(r/L(t)) depends non-trivially on n, the number of 
components in the vector order-parameter field exhibiting the scaling 
behavior, and d, the dimensionality of the system. It is important to 
note that the scaling hypothesis has not been proved conclusively 
except for some model systems.  Based on some of our recent 
observations [1-4], we propose to reexamine the extent of validity of 
scaling laws addressing issues like (i) uniqueness of characteristic 
length L(t); (ii) the extent of validity of the scaling laws for new 
phase formation in the case of non-Euclidean fractal systems; (iii) the 
extent of validity of the scaling laws for multicomponent systems.

References
[1] S. Mazumder, et al., Phys. Rev. B 60 (1999) 822.
[2] S. Mazumder, et al., Phys. Rev. Lett 93 (2004) 255704.
[3] S. Mazumder, et al., Phys. Rev. B 72 (2005) 224208.
[4] S. Mazumder, Physica B, in press.