Mode-coupling theory of the glass transition for a liquid in a periodic potential
arXiv:2509.07697 · doi:10.1103/ks5t-xtvd
Abstract
We derive a microscopic theory for the structural dynamics in the vicinity of the glass transition for a liquid exposed to a one-dimensional periodic potential. The periodic potential breaks translational invariance, in particular, the density exhibits a periodic modulation. Using techniques familiar from solid-state theory, we define generalized intermediate scattering functions from fluctuating densities in wave-vector space. Exact equations of motion are derived within the Mori-Zwanzig projection-operator formalism reflecting the residual lattice symmetries. Due to the lack of rotational symmetry it is necessary to split the currents into components parallel and perpendicular to the modulation. We provide a closure of the equations in terms of a mode-coupling approximation for the force kernel. The theory reflects the usual analytic properties of correlation functions and encodes all phenomena known for mode-coupling theories. We prove that the theory reduces to the conventional mode-coupling theory in the case of vanishing amplitude of the modulation.
arXiv comment16 pages
References in corpus (45)
- Higher order glass-transition singularities in colloidal systems with attractive interactions
- Theory of nonlinear rheology and yielding of dense colloidal suspensions
- Nonergodicity transitions in colloidal suspensions with attractive interactions
- Inhomogeneous Mode-Coupling Theory and Growing Dynamic Length in Supercooled Liquids
- Ideal glass-glass transitions and logarithmic decay of correlations in a simple system
- Mode-Coupling Theory of the Glass Transition: A Primer
- Liquid-glass transition of a fluid confined in a disordered porous matrix: A mode-coupling theory
- Glassy dynamics of athermal self-propelled particles: Computer simulations and a nonequilibrium microscopic theory
- Active and Nonlinear Microrheology in Dense Colloidal Suspensions
- A First-Principles Constitutive Equation for Suspension Rheology
- Glass Transition in Confined Geometry
- Mode-coupling theory for the slow collective dynamics of fluids adsorbed in disordered porous media
- Cooperativity Beyond Caging: Generalized Mode Coupling Theory
- Single-particle and collective slow dynamics of colloids in porous confinement
- Mode-Coupling Theory for Active Brownian Particles
- Microscopic dynamics of supercooled liquids from first principles
- Dense colloidal suspensions under time-dependent shear
- Slow dynamics in random media: Crossover from glass to localization transition
- Glass Transition for Driven Granular Fluids
- Tagged-particle dynamics in a fluid adsorbed in a disordered porous solid: interplay between the diffusion-localization and liquid-glass transitions
- Multiple reentrant glass transitions in confined hard-sphere glasses
- Mode-coupling theory of the glass transition for confined fluids
- Test of mode coupling theory for a supercooled liquid of diatomic molecules.I. Translational degrees of freedom
- Test of mode coupling theory for a supercooled liquid of diatomic molecules. II. q-dependent orientational correlators
- Reorientational relaxation of a linear probe molecule in a simple glassy liquid
- Phase Transitions of Hard Disks in External Periodic Potentials: A Monte Carlo Study
- Completely monotone solutions of the mode-coupling theory for mixtures
- Colloidal suspensions in modulated light fields
- Structure and structure relaxation
- Observation of strongly heterogeneous dynamics at the depinning transition in a colloidal glass
- Mode-coupling theory for multiple decay channels
- Many-body correlations are non-negligible in both fragile and strong glassformers
- Active Glassy Dynamics is Unaffected by the Microscopic Details of Self-Propulsion
- Rheology of inelastic hard spheres at finite density and shear rate
- Generalized mode-coupling theory of the glass transition. I. Numerical results for Percus-Yevick hard spheres
- Critical force in active microrheology
- Laser induced reentrant freezing in two-dimensional attractive colloidal systems
- Long-time limit of correlation functions
- The mode-coupling glass transition in a fluid confined by a periodic potential
- Integration through transients for inelastic hard sphere fluids
- Dynamical Susceptibilities Near Ideal Glass Transitions
- Dynamical properties of densely packed confined hard-sphere fluids
- Scaling equations for mode-coupling theories with multiple decay channels
- Dynamic properties of quasi-confined colloidal hard-sphere liquids near the glass transition
- Glass transition in colloidal monolayers controlled by light-induced caging