My research is in theoretical high-energy physics. I study quantum field theory with the goal of identifying universal principles that constrain non-perturbative dynamics. My current interests are topological field theory and its relation to gravity, and the emergence of statistical mechanics from unitary quantum evolution.
Random matrix theory and thermalization of many-body systems
The emergence of statistical mechanics from the unitary evolution of an isolated quantum system remains an active area with many open questions. For chaotic systems the organizing framework is the Eigenstate Thermalization Hypothesis (ETH), which asserts that matrix elements of local observables in the energy eigenbasis resemble those of a random matrix. My research concerns the scope of random matrix theory (RMT) in describing thermalization: at what energy scales RMT behavior sets in for local observables, how this onset is controlled by transport, and how deviations from RMT encode hydrodynamics and other slow dynamics.
Eigenstate thermalization in two-dimensional conformal field theories
In two-dimensional CFTs the Virasoro algebra gives rise to an infinite set of commuting conserved charges, the quantum KdV (qKdV) hierarchy, and thermalization must be understood in a generalized sense: the equilibrium state is a generalized Gibbs ensemble, and ETH holds only after the conserved charges are taken into account. I study how the qKdV charges constrain the structure of energy eigenstates and the matrix elements of local operators, how generalized ETH is realized in holographic CFTs, and how it fits with the RMT-based picture of chaos in systems without extended symmetry.
