Symmetry breaking instabilities in illuminated systems

Abstract

Chemically nonreactive and reactive systems (closed and homogeneous) are shown to become unstable to inhomogeneous perturbations beyond given critical intensities of uniform illumination, so that macroscopic inhomogeneities (spatial patterns) arise. We classify symmetry‐breaking instabilities into two types: extrinsic length scaling, in which the characteristic length of the developing spatial pattern is determined by the dimensions of the system; and intrinsic length scaling, in which that characteristic length is determined by the dynamics of the system (reaction rates and transport relations). We analyze a variety of nonlinear systems by means of a linear stability analysis. In an illuminated, isothermal, isobaric, two‐species system, only extrinsic length scaling is possible; more degrees of freedom, either with increasing number of species or other state variables, are required for intrinsic scaling in the closed system. Next we consider a two‐component nonreactive illuminated gaseous system in which diffusion, thermal conduction, and thermal diffusion may occur. We show that if only one component in a thermal diffusion experiment tends towards the hotter region, then extrinsic symmetry‐breaking instability is possible. If, in addition, the two species are coupled by reaction (interconversion), then the spatial patterns at the onset of instability are of the intrinsic type. We then include pressure fluctuations in an analysis of a one‐component system under steady illumination at a wavelength that is absorbed by the molecules and then converted into heat. We show that such a system may generate and amplify sound waves; that is, the system becomes unstable to spatially periodic pressure (acoustic) variation. This process may be used for the measurement of vibration‐translation relaxation rates.