1305.6937 (E. J. Torres-Herrera et al.)

Relationship between initial state and Hamiltonian as a main factor for
thermalization    [PDF]

E. J. Torres-Herrera, Lea F. Santos

We explore the role played by the initial state on the onset of thermalization in isolated quantum systems. If the initial state has a chaotic structure with respect to the Hamiltonian dictating its evolution, i.e. if it fills the energy shell ergodically, thermalization is certain to occur. This happens when the initial state is an eigenstate of a full random matrix and the eigenstates of the Hamiltonian are delocalized. In this case, the results for the observables are equivalent to those obtained with thermal states at infinite temperature. However, finite real systems with few-body short-range interactions are deprived of fully extended eigenstates, even when described by a non-integrable Hamiltonian. We examine how the observables in such real systems, be the model integrable or chaotic, approach thermal averages as the initial state gets closer to the middle of the spectrum, where it gets more delocalized. Our numerical studies are based on initial states with energies that cover the entire lower half of the spectrum of one-dimensional Heisenberg spin-1/2 systems.

View original: http://arxiv.org/abs/1305.6937