Dynamics of active condensation
by Aritra Bose
Date of Examination:2024-06-24
Date of issue:2025-06-12
Advisor:Prof. Dr. Ramin Golestanian
Referee:Prof. Dr. Matthias Krüger
Referee:Prof. Dr. Peter Sollich
Persistent Address:
http://dx.doi.org/10.53846/goediss-11326
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Abstract
English
Active matter represents a unique class of out-of-equilibrium systems, that are ubiquitous in our everyday life. Active particles convert energy into mechanical motion and this leads to collective self-organization into patterns or structures even in the absence of attractive interaction between the particles. Often, such self-organization leads to highly concentrated clusters also called as condensates. In this thesis, we focus on one particular class of active matter, known as scalar active matter, which consists of spherical self-propelled particles without any alignment interaction and yet show novel clustering. At the mesoscopic level, these systems can be described in terms of a continuum theory of the density field. It has been shown that the essential dynamics of condensation in scalar active matter can be captured with a minimal phenomenological model. In this approach, at the mean-field level, using a drift-diffusion type equation of the conserved density field, condensation can be induced by introducing a particular property called `diffusivity edge', which refers to a critical density threshold beyond which the diffusivity vanishes locally. In steady state, such a system undergoes spontaneous condensation at the ground state of an external confining potential. Although, the steady state properties of the condensation has been characterized extensively at the mean-field level, the dynamical features of the condensation still remains to be investigated. This thesis addresses these outlooks by characterizing the dynamics of the condensation at the mean-field model, and studying the consequences of noise in the generalized stochastic formulation of the diffusivity edge class. We start by investigating the mean-field model, and introduce steady-state currents via an external drive. In the regime of strong driving, the interplay between currents and the diffusivity edge leads to a re-entrant transition for sufficiently high densities. With decreasing effective temperature, the systems undergoes condensation, followed by a subsequent dilution of the condensate. Thermodynamic analysis of the condensate shows that these two transitions are similar in nature, despite their underlying dynamics being different. The dynamics in the mean-field model can be captured by the steady-state relaxation rates. We find that the dynamics changes from a diffusive to a mobility-driven one across the condensation transition. Using theoeretical arguments and simulations, we show that the system can be pushed towards a possible glassy-like dynamics by introducing an `edge' in the mobility. Next, the role of fluctuations on the dynamics is studied by introducing a conserved stochastic flux in the system. In this case, the stochastic diffusivity edge model maps to a microscopic inhomogeneous zero range process. We find that the onset of condensation is associated with the emergence of anomalous density fluctuations in the condensate. Far below condensation the flucuations become maximally anomalous and the dynamics slows down. Across the condensation transition, there exist three distinct regimes of fluctuations characterized by the anomalous scaling exponent of the variance of the condensate density distribution with its mean.
Keywords: Scalar active matter; Bose-Einstein-like Condensation; out-of-equilibrium statistical physics; self-organization; soft matter
