Using Quantum Field Theory in Curved Spacetime to Study Quantum Quenches of Phononic Lattice Systems

Abstract

Quantum field theory in curved spacetime (QFTCS) is a semiclassical theory that approximates the behavior of quantum fields in the presence of gravitational fields but also has applications in studying condensed matter systems. This thesis uses QFTCS to study the continuous limits of quantum quenches in lattice systems. The theory of the Klein-Gordon field in curved spacetime is reviewed and applied to quenched systems. The computation of the Bogoliubov coefficients that relate pre- and post-quench quantized states in various systems of interest is discussed, and relevant 1D lattice Hamiltonians are explicitly shown to correspond to the Klein-Gordon field in (1+1)-dimensional curved spacetimes at the continuous limit. Numerical simulations of phonon systems are presented to demonstrate that results from QFTCS can predict some behavior of quenched lattice systems, although limitations remain due to the finite system size as well as the numerical methods used.