Title page for ETD etd-08292009-150038


Type of Document Dissertation
Author Mukherjee, Sayak
Author's Email Address smukhe04@vt.edu
URN etd-08292009-150038
Title Applications of Field Theory to Reaction Diffusion Models and Driven Diffusive Systems
Degree PhD
Department Physics
Advisory Committee
Advisor Name Title
Schmittmann, Beate Committee Chair
Kulkarni, Rahul V. Committee Member
Takeuchi, Tatsu Committee Member
Tauber, Uwe C. Committee Member
Keywords
  • Field Theory
  • Model A
  • Directed Percolation
  • Renormalization Group
  • Tasep
  • Power spectrum
Date of Defense 2009-08-25
Availability restricted
Abstract
In this thesis, we focus on the steady state properties of two systems which are genuinely out of equilibrium. The first project is an application of dynamic field theory to a specific non equilibrium critical phenomenon, while the second project involves both simulations and analytical calculations. The methods of field theory are used on both these projects. In the first part of this thesis, we investigate a generalization of the well-known field theory for directed percolation (DP). The DP theory is known to describe an evolving population, near extinction. We have coupled this evolving population to an environment with its own nontrivial spatio-temporal dynamics. Here, we consider the special case where the environment follows a simple relaxational (model A) dynamics. We find two marginal couplings with upper critical dimension of four, which couple the two theories in a nontrivial way. While the Wilson-Fisher fixed point remains completely unaffected, a mismatch of time scales destabilizes the usual DP fixed point. Some open questions and future work remain.

In the second project, we focus on a simple particle transport model far from equilibrium, namely, the totally asymmetric simple exclusion process (TASEP). While its stationary properties are well studied, many of its dynamic features remain unexplored. Here, we focus on the power spectrum of the total particle occupancy in the system. This quantity exhibits unexpected oscillations in the low density phase. Using standard Monte Carlo simulations and analytic calculations, we probe the dependence of these oscillations on boundary effects, the system size, and the overall particle density. Our simulations are fitted to the predictions of a linearized theory for the fluctuation of the particle density. Two of the fit parameters, namely the diffusion constant and the noise strength, deviate from their naive bare values [6]. In particular, the former increases significantly with the system size. Since this behavior can only be caused by nonlinear effects, we calculate the lowest order corrections in perturbation theory. Several open questions and future work are discussed.

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