Date of Thesis
Honors Thesis (Bucknell Access Only)
Bachelor of Science
A variety of recent studies have shed light on the far from equilibrium behavior of quantum systems. Research suggests that this away from equilibrium approach may lead to the realization of unfamiliar dynamical quantum states. For instance, we see ballistic transport at finite temperature, an absence of thermalization, and development of long-range entanglement from initially uncorrelated states. It has been shown that in some cases a time-evolving quantum state is equivalent to the ground state of an "emergent" Hamiltonian where the time enters as a param- eter. This mapping gives us insight into the nature of correlations between particles. For high temperatures, we expect no long-range correlations to develop. However, the emergent model demonstrates that the time-evolved state can be realized as a low energy eigenstate, which naturally possesses long-range correlations. Here, we study the dynamical behavior of both noninteracting and interacting particles in a one-dimensional lattice under various conditions. As the system un- dergoes time evolution, we look at the distribution of particles as well as correlations between particles in the system. We then compare the actual time-evolving state of the system to the ground state of the emergent Hamiltonian to study how long this description is valid. We generally expect that the description is valid in a given region as long as the boundary effects do not propagate into the region. We first verify and reproduce results in the literature (see Vidmar et al. ). We proceed to study the effect of interaction strength in a particular interacting model that shows both ballistic and diffusive transport. We then apply this formalism to calculate infinite temperature dynamics of a noninteracting system. Interestingly, this system also develops long-range correlations over time in spite of starting out from an infinite temperature state.
Cadigan, Ryan Joseph, "Quench Dynamics of Fermions in One-Dimension" (2017). Honors Theses. 416.