Field theoretical studies of nonequilibrium systems with long-range interactions

Thesis

Characterising the effects of correlated fluctuations in nonequilibrium systems is an essential step in modelling many natural and synthetic processes. This thesis uses stochastic and field-theoretical approaches to investigate the rich macroscopic behaviour arising from nonequilibrium fluctuations in two systems: strong electrolytes driven by an external electric field and chemotactic particles with generalised gradient-sensing mechanisms. The common feature shared by these systems is the presence of nonlocal Coulombic interactions among their constituent particles. In electrolytes, these are electrostatic interactions governed by the Poisson equation; in chemotactic systems, on the other hand, diffusing chemical signals secreted by each particle mediate nonlocal interactions, which, in the limit of fast-diffusing signals, are governed by a similar Poisson relation.

In the first case, we study the stochastic dynamics of a driven electrolyte using the Dean-Kawasaki formalism and show that it exhibits scale invariance notwithstanding the Debye screening effects. Accordingly, the correlation functions of the driven electrolyte take power-law forms, in sharp contrast to the exponentially screened correlations in equilibrium electrolytes. These correlations give rise to fluctuation-induced forces between neutral boundaries that confine the electrolyte. In the Casimir geometry, we show that these nontrivial forces are generally long ranged and have transient parts that decay algebraically over time. We also find that the steady-state fluctuation force can be tuned in magnitude and direction by adjusting the external electric field.

In the second case, our focus is on self-chemotactic systems, namely collections of living or synthetic particles that release fast-diffusing chemical signals in their environment while responding to signal gradients by adjusting their motion. Based on scaling analysis and microscopic considerations, we devise a natural generalisation of the conventional Keller-Segel model by incorporating the effect of particle polarity into the stochastic density equations. We examine the associated large-scale properties of the system, first by studying its symmetry properties where we identify an emergent Galilean symmetry, and then through dynamical renormalisation group analysis of its critical state. We find exact scaling exponents, which show that density fluctuations are super-diffusive and the number fluctuations are non-Poissonian.

Authors: Mahdisoltani, S

• DOI: 10.5287/ora-kezq6k9p9
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: Scaling laws; Langevin dynamics; Electrolytes; Long-range interactions; Fluctuation-induced forces; Stochastic Field theory; Renormalisation group theory; Chemotaxis
• Subjects: Nonequilibrium statistical mechanics; Active matter