The importance of being integrable: out of the paper, into the lab

Abstract

The scattering matrix (S-matrix), relating the initial and final states of a physical system undergoing a scattering process, is a fundamental object in quantum mechanics and quantum field theory. The study of factorised S-matrices, in which many-body scattering factorizes into a product of two-body terms to yield an integrable model, has long been considered the domain of mathematical physics. Many beautiful results have been obtained over several decades for integrable models of this kind, with far reaching implications in both mathematics and theoretical physics. The viewpoint that these were only toy models changed dramatically with brilliant experimental advances in realizing low-dimensional quantum many-body systems in the lab. These recent experiments involve both the traditional setting of condensed matter physics and the trapping and cooling of atoms in optical lattices to engineer and study quasi-one-dimensional systems. In some cases the quantum physics of one-dimensional systems is arguably more interesting than their three-dimensional counterparts, because the effect of interactions is more pronounced when atoms are confined to one dimension. This article provides a brief overview of these ongoing developments, which highlight the fundamental importance of integrability.

13 pages, 8 figures. Based on Invited Talk, Conference in Honour of the 90th Birthday of Freeman Dyson, Singapore, Aug 26-29, 2013

References in corpus (3)

• Fermi gases in one dimension: From Bethe Ansatz to experiments
• From Few to Many: Observing the Formation of a Fermi Sea One Atom at a Time
• Pairing in few-fermion systems with attractive interactions

Cited by in corpus (7)

• Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics
• Yang-Baxter integrable models in experiments: from condensed matter to ultracold atoms
• One-Dimensional Traps, Two-Body Interactions, Few-Body Symmetries: I. One, Two, and Three Particles
• Quantum integrable multi-well tunneling models
• Critical phenomena in one dimension from a Bethe ansatz perspective
• Exact crystalline solution for a one-dimensional few-boson system with point interaction
• Universal TT- and TQ-relations via centrally extended q-Onsager algebra