Quantum Quenches and Work Distributions in Ultralow-Density Systems

We present results on quantum quenches in lattice systems with a fixed number of particles in a much larger number of sites. Both local and global quenches in this limit generically have power-law work distributions (edge singularities). We show that this regime allows for large edge singularity exponents beyond that allowed by the constraints of the usual thermodynamic limit. This large-exponent singularity has observable consequences in the time evolution, leading to a distinct intermediate power-law regime in time. We demonstrate these results first using local quantum quenches in a low-density Kondo-like system, and additionally through global and local quenches in Bose-Hubbard, Aubry-Andre, and hard-core boson systems at low densities.