1307.7188 (Stephan Mandt et al.)

Relaxation towards negative temperatures in bosonic systems: generalized
Gibbs ensembles and beyond integrability    [PDF]

Stephan Mandt, Adrian E. Feiguin, Salvatore R. Manmana

Motivated by the recent experimental observation of negative absolute temperature states in systems of ultracold atomic gases on optical lattices [Braun et al., Science 339, 52-55 (2013)], we investigate theoretically the formation of these states. More specifically, we consider the relaxation after a sudden inversion of the external parabolic confining potential in the one-dimensional inhomogeneous Bose-Hubbard model. First, we focus on the integrable hard-core boson limit which allows us to treat large systems and arbitrarily long times, providing convincing numerical evidence for relaxation to a generalized Gibbs ensemble at negative temperatures T<0, being defined by us in this context. Second, going beyond one dimension, we demonstrate that the emergence of negative temperature states can be understood in a dual way in terms of positive temperatures, which relies on a dynamic symmetry of the Hubbard model. We complement the study by exact diagonalization simulations at finite values of the on-site interaction.

View original: http://arxiv.org/abs/1307.7188