Quantum Café is CCQ’s ongoing seminar series: open to all bona fide members of the greater NYC scientific community and held every second week, Quantum Café presents a series of informal, highly interactive talks, typically by external speakers, which present the most interesting recent developments and open questions in our field.
Title: Solving One Dimensional Quantum Problems
Abstract: One dimensional quantum systems have a remarkable physics, a priori quite different than the one from their higher dimensional counterparts. Excitations are collective and topological constraints and transitions are the norm rather than the exception. As a results most of the theoretical tools have to be rethought or rebuild. For a long time one had the choice between exact solutions, valid for specific models, field theory, giving only asymptotic behaviors, or numerical solutions, usually limited in time and space. More recently progress both on the numerical and analytical side have allowed to integrate all these aspects to provide essentially exact solutions of many rich one dimensional problems. I will illustrate how with some examples both in the field of quantum spin systems and cold atoms. I will also discuss where the frontier and future challenges are.