Time Glass: A Fractional Calculus Approach

Abstract

Out of equilibrium states in glasses and crystals have been a major topic of research in condensed-matter physics for many years, and the idea of time crystals has triggered a flurry of new research. Here, we provide the first description for the recently conjectured Time Glasses using fractional calculus methods. An exactly solvable effective theory is introduced, with a continuous parameter describing the transition from liquid through normal glass, Time Glass, into the Gardner phase. The phenomenological description with a fractional Langevin equation is connected to a microscopic model of a particle in a sub-Ohmic bath in the framework of a generalized Caldeira-Leggett model.

Main text: 6 pages, 3 figures. SM: 10 pages, 4 figures

References in corpus (8)

• Theoretical perspective on the glass transition and amorphous materials
• Fractal free energy landscapes in structural glasses
• Absence of Quantum Time Crystals
• A Stochastic Mean-Field Approach For Nuclear Dynamics
• How active forces influence nonequilibrium glass transitions
• Determining the nonequilibrium criticality of a Gardner transition via a hybrid study of molecular simulations and machine learning
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Cited by in corpus (9)

• Algebraic Theory of Quantum Synchronization and Limit Cycles under Dissipation
• The fractional Landau-Lifshitz-Gilbert equation
• Non-Hermitian quantum gases: a platform for imaginary time crystals
• Quantizing Lévy flights
• Dynamic Gardner crossover in a simple structural glass
• Emergent time crystal from a fractional Langevin equation with white and colored noise
• Dissipative systems fractionally coupled to a bath
• Active Brownian particles in power-law viscoelastic media
• Correlations in Circular Quantum Cascades