Hydrodynamic Characterization of Ising Lattice Gases

Sen, Rajit (2025) Hydrodynamic Characterization of Ising Lattice Gases. Masters thesis, Indian Institute of Science Education and Research Kolkata.

Text (MS Dissertation of Rajit Sen (20MS068)) 20MS068_Thesis_file.pdf - Submitted Version Restricted to Repository staff only Download (1MB)

Abstract

Understanding how systems relax toward equilibrium is a central problem in statistical mechanics, especially when interactions between particles introduce correlations that affect transport. In this thesis, we investigate the density relaxation in lattice gas models with nearest-neighbor exclusion (NNE) and Ising-type interactions. We explore how these microscopic rules generate macroscopic transport behavior, quantified by hydrodynamic equations. By using both analytical and numerical methods, we explore time evolution of localized as well as sinusoidal initial density profiles. For the latter initial conditions, we quantify relaxation in terms of the time evolution of the amplitude of the large-wavelength density fluctuations, which decay exponentially at large (hydrodynamic) times. the bulk-diffusion coefficient and mobility, the fundamental quantities to describe the particle transport, have been calculated. Our results show how effects of interactions modify the effective transport properties and create nontrivial relaxation dynamics. This research documents the strength of hydrodynamic approximations in translating microscopic stochastic kinematics into macroscopic emergent laws. Its implications are interesting not just as a matter of understanding non-equilibrium statistical mechanisms at a simple level, but for transport models useful in crowded and interacting environments of practical interest as well. v

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