# Integrable One-Dimensional Three-Body Problems Based on Exceptional and Non-Crystallographic Root Systems and Relaxation in One-Dimensional Two-Mass Mixtures

**When:**Wednesday, November 13, 2013 at 3:00 pm

**Where:**DA 114

**Speaker**: Maxim Olshanii

**Organization**: University of Massachusetts, Boston

**Sponsor**: Condensed Matter Seminar

Normals to mirrors in a multidimensional kaleidoscope form a root system. Root systems are divided into crystallographic and non-crystallographic, and the former are further sub-divided into classic and exceptional. The importance of the classic root systems for quantum integrable many-body systems is widely recognized since the early 60-s [Girardeau (1960), Lieb-Liniger (1963), McGuire (1964), Gaudin (1983)]. At the same time, the exceptional crystallographic and non-crystallographic systems are generally assumed to be irrelevant to physics.

In this presentation, we show that for a set of mass ratios, a number of new integrable three-body hard-core problems associated with some underexplored root systems can be formulated. A special attention is payed to the (sqrt[5]+2):1:(sqrt[5]+2) as the simplest non-trivial generalization of the Newton’s cradle. When the integrable mass triplets are further embedded in a larger many-body system, integrability breaks, but traces of it remain, in a form a slower relaxation. We study these effects numerically. The targeted experimental realization of the effects we study is wave-guide ultracold bosons with masses controlled by optical lattices.

Host: Assistant Professor Adrian Feiguin