Research

🔷 Topic on prethermalisation of coupled aperiodically kicked rotor systems: 

Time-dependent drivings may realise novel non-equilibrium phases of matter, however, they generally heat up to infinite temperature due to the absence of energy conservation. A long-lived prethermal state has been discovered in periodically driven systems. 

A natural question is whether prethermalisation can still exist without perfect periodicity. A positive answer is given here by a system of classical coupled rotors subject to a family of random kicks with n-multipolar temporal correlations. The heating, characterised by the averaged kinetic energy (fig.(a)), can be algebraically controlled by the kicking strength K, where the scaling exponent linearly depends on the multipolar order n (fig.(b)). In the limit of n going to infinity (the so-called quasi-periodic Thue-Morse sequence), the prethermal lifetime t* has an abnormal scaling in-between exponential and power law (fig.(c)). 

🔷 Topic on simple random maps: 

A random dynamical system consists of a setting in which different types of dynamics are generated randomly in time. 

Here, we consider a simplest possible case where an irregular or a regular dynamics is randomly selected at each time step. By varying the sampling probability p, the system exhibits a non-trivial transition from fully chaotic to completely regular dynamics. At the critical point p = 1/2, the anomalous behaviour is characterised by an infinite non-normalisable invariant density, weak ergodicity breaking and power-law correlation decay (see plot to the left).