Statistical mechanics of a single active slider on a fluctuating interface

Abstract

We study the statistical mechanics of a single active slider on a fluctuating interface, by means of numerical simulations and theoretical arguments. The slider, which moves by definition towards the interface minima, is active as it also stimulates growth of the interface. Even though such a particle has no counterpart in thermodynamic systems, active sliders may provide a simple model for ATP-dependent membrane proteins that activate cytoskeletal growth. We find a wide range of dynamical regimes according to the ratio between the timescales associated with the slider motion and the interface relaxation. If the interface dynamics is slow, the slider behaves like a random walker in a random envinronment which, furthermore, is able to escape environmental troughs by making them grow. This results in different dynamic exponens to the interface and the particle: the former behaves as an Edward-Wilkinson surface with dynamic exponent 2 whereas the latter has dynamic exponent 3/2. When the interface is fast, we get sustained ballistic motion with the particle surfing a membrane wave created by itself. However, if the interface relaxes immediately (i.e., it is infinitely fast), particle motion becomes symmetric and goes back to diffusive. Due to such a rich phenomenology, we propose the active slider as a toy model of fundamental interest in the field of active membranes and, generally, whenever the system constituent can alter the environment by spending energy.

arXiv comment13 pages, 19 figures

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Cited by in corpus (11)

• Kinetic roughening in active interfaces
• Light and heavy particles on a fluctuating surface: Bunchwise balance, irreducible sequences and local density-height correlations
• Universal properties of active membranes
• Interface growth driven by a single active particle
• Inviscid limit of the active interface equations
• Effect of relative timescale on a system of particles sliding on a fluctuating energy landscape: Exact derivation of product measure condition
• Lattice models of random advection and diffusion and their statistics
• A renormalization group study of the dynamics of active membranes: universality classes and scaling laws
• Shape-specific fluctuations of an active colloidal interface
• A Novel Mechanism of Ordering in a Coupled Driven System: Vacancy Induced Phase Separation
• Spatial organisation of multiple species of active particles interacting with an interface