Dynamics of a noninteracting colloidal fluid in a quenched Gaussian random potential: A time-reversal-symmetry-preserving field-theoretic approach

Abstract

We develop a field-theoretic perturbation method preserving the fluctuation-dissipation relation (FDR) for the dynamics of the density fluctuations of a noninteracting colloidal gas plunged in a quenched Gaussian random field. It is based on an expansion about the Brownian noninteracting gas and can be considered and justified as a low-disorder or high-temperature expansion. The first-order bare theory yields the same memory integral as the mode-coupling theory (MCT) developed for (ideal) fluids in random environments, apart from the bare nature of the correlation functions involved. It predicts an ergodic dynamical behavior for the relaxation of the density fluctuations, in which the memory kernels and correlation functions develop long-time algebraic tails. A FDR-consistent renormalized theory is also constructed from the bare theory. It is shown to display a dynamic ergodic-nonergodic transition similar to the one predicted by the MCT at the level of the density fluctuations, but, at variance with the MCT, the transition does not fully carry over to the self-diffusion, which always reaches normal diffusive behavior at long time, in agreement with known rigorous results.

73 pages, 8 figures; version accepted for publication in Journal of Statistical Mechanics: Theory and Experiment

References in corpus (18)

• Theoretical perspective on the glass transition and amorphous materials
• Anomalous transport in the crowded world of biological cells
• Supercooled Liquids for Pedestrians
• Liquid-glass transition of a fluid confined in a disordered porous matrix: A mode-coupling theory
• Symmetries of generating functionals of Langevin processes with colored multiplicative noise
• Mode-coupling theory for the slow collective dynamics of fluids adsorbed in disordered porous media
• Speckle Optical Tweezers: Micromanipulation with Random Light Fields
• Cooperativity Beyond Caging: Generalized Mode Coupling Theory
• Tagged-particle dynamics in a fluid adsorbed in a disordered porous solid: interplay between the diffusion-localization and liquid-glass transitions
• Rounding of the localization transition in model porous media
• Persistent memory for a Brownian walker in a random array of obstacles
• On the Brownian gas: a field theory with a Poissonian ground state
• Experimental creation and characterization of random potential energy landscapes exploiting speckle patterns
• Persistent Sinai type diffusion in Gaussian random potentials with decaying spatial correlations
• Long-Wavelength Anomalies in the Asymptotic Behavior of Mode-Coupling Theory
• Dynamical transition for a particle in a squared Gaussian potential
• Dynamic heterogeneities and non-Gaussian behavior in two-dimensional randomly confined colloidal fluids
• Colloids Exposed to Random Potential Energy Landscapes: from Particle Number Density to Particle-Potential and Particle-Particle Interactions

Cited by in corpus (4)

• Classical dynamical density functional theory: from fundamentals to applications
• Perspective: New directions in dynamical density functional theory
• Diagrammatics for the Inverse Problem in Spin Systems and Simple Liquids
• Improved field theoretical approach to noninteracting Brownian particles in a quenched random potential