Many-body constraints and nonthermal behavior in one-dimensional open systems with Haldane exclusion statistics

We study the impact of the interlevel energy constraints imposed by Haldane exclusion statistics on energy relaxation processes in one-dimensional systems coupled to a bosonic bath. By formulating a second-quantized description of the relevant Fock space, we identify certain universal features of this relaxation dynamics, and show that it is generically slower than that of spinless fermions. Our study focuses on the Calogero-Sutherland model, which realizes Haldane Exclusion statistics exactly in one dimension; however, our results apply to any system that has the associated pattern of interlevel occupancy constraints in Fock space.