Unusual ergodic and chaotic properties of trapped hard rods.

We investigate ergodicity, chaos, and thermalization for a one-dimensional classical gas of hard rods confined to an external quadratic or quartic trap, which breaks microscopic integrability. To quantify the strength of chaos in this system, we compute its maximal Lyapunov exponent numerically. The approach to thermal equilibrium is studied by considering the time evolution of particle position and velocity distributions and comparing the late-time profiles with the Gibbs state.

Digital herd immunity and COVID-19.

A population can be immune to epidemics even if not all of its individual members are immune to the disease, so long as sufficiently many are immune-this is the traditional notion of herd immunity. In the smartphone era a population can be immune to epidemics-a notion we call 'digital herd immunity', which is similarly an emergent characteristic of the population. This immunity arises because contact-tracing protocols based on smartphone capabilities can lead to highly efficient quarantining of infected population members and thus the extinguishing of nascent epidemics.

Superdiffusive transport of energy in one-dimensional metals.

Metals in one spatial dimension are described at the lowest energy scales by the Luttinger liquid theory. It is well understood that this free theory, and even interacting integrable models, can support ballistic transport of conserved quantities including energy. In contrast, realistic one-dimensional metals, even without disorder, contain integrability-breaking interactions that are expected to lead to thermalization and conventional diffusive linear response.

Incomplete Thermalization from Trap-Induced Integrability Breaking: Lessons from Classical Hard Rods.

We study a one-dimensional gas of hard rods trapped in a harmonic potential, which breaks integrability of the hard-rod interaction in a nonuniform way. We explore the consequences of such broken integrability for the dynamics of a large number of particles and find three distinct regimes: initial, chaotic, and stationary. The initial regime is captured by an evolution equation for the phase-space distribution function.

Solvable Hydrodynamics of Quantum Integrable Systems.

The conventional theory of hydrodynamics describes the evolution in time of chaotic many-particle systems from local to global equilibrium. In a quantum integrable system, local equilibrium is characterized by a local generalized Gibbs ensemble or equivalently a local distribution of pseudomomenta. We study time evolution from local equilibria in such models by solving a certain kinetic equation, the "Bethe-Boltzmann" equation satisfied by the local pseudomomentum density.