Theoretical Physics Colloquium
Macroscopic fluctuation theory and its application
by Dr. Tridib Sadhu (CEA Saclay, France)
Tuesday, October 28, 2014
from
to
(Asia/Kolkata)
at AG69
at AG69
Description |
Non-equilibrium systems are ubiquitous in nature and exhibit a variety of new phenomena. Classical statistical mechanics does not cover such systems, and a general theoretical framework is lacking. A recently proposed macroscopic fluctuation theory offers a promising direction in building such a framework. It is based on the study of rare fluctuations of macroscopic variables in non-equilibrium diffusive systems. I shall present an overview of the theory based on two of my recent works: single-file diffusion and melting of an Ising quadrant. The first one is about motion of many particles in narrow channel where particles can not pass each other. As a consequence of the forbidden mutual passage the motion of individual particles is sub-diffusive. I shall apply the macroscopic fluctuation theory to analyze the probability distribution of the position of a tagged particle in a large class of single-file system. For the simplest case of point particles with hard-core repulsion this macroscopic approach leads to an explicit formula of the large deviation function of the tagged particle position. I shall compare the results with that obtained in an exact microscopic analysis. I shall also emphasize the unusual dependence of the statistics of the tracer position on the initial state. In the second example, I shall talk about a non-equilibrium problem of domain growth in two dimensional Ising ferromagnet endowed with zero temperature spin-flip dynamics. In one of the simplest scenario, starting with a quadrant of one phase in the sea of opposite phase I shall examine how the majority phase invades the minority phase. The area of the invaded region grows with time and the interface separating the phases exhibits non-trivial fluctuation. Utilizing a mapping to exclusion process I cast the problem in the framework of macroscopic fluctuation theory. This provides a systematic way of analyzing the statistics of the fluctuating interface and the area of the invaded region. I shall conclude with a brief discussion of other problems where macroscopic fluctuation theory has been successful and also talk about future directions. Ref: [1] Large deviations in single-file diffusion: P. L. Krapivsky, Kirone Mallick, Tridib Sadhu, Phys. Rev. Lett. 113, 078101 (2014). [2] Melting of an Ising quadrant: P. L. Krapivsky, Kirone Mallick, Tridib Sadhu, J. Phys. A: math theo (under review). |