Interacting bosons in one dimension and their relation to the KPZ universality class.

Statistical Physics and Complexity Group meeting

Interacting bosons in one dimension and their relation to the KPZ universality class.

Event details

The Lieb-Liniger model is one of the simplest examples of an exactly soluble many body quantum system. It consists of bosons in one dimension interacting via a delta function potential. It is of great interest in its own right, but in the last few years it has attracted attention because a number of problems in the Kadar–Parisi–Zhang (KPZ) universality class can be mapped on to it and this has lead to new insights into the KPZ.

The talk will start with a brief sketch of how the KPZ is related to the Lieb-Liniger model. The connection is made by mapping to the directed polymer in a random medium and then using replicas. However, most of the talk will be a step-by-step analysis of the Lieb-Liniger model. It provides a very simple example of the use of the Bethe ansatz and gives some insight into quantum integrability.

A good reference on the Lieb-Liniger is:

  • Sutherland, Bill. Beautiful models: 70 years of exactly solved quantum many-body problems. World Scientific Publishing Co Inc, 2004.

Two recent reviews on its use for solving stochastic and disordered problems are.

  • Quastel, Jeremy, and Herbert Spohn. "The one-dimensional KPZ equation and its universality class." Journal of Statistical Physics 160.4 (2015): 965-984.
  • Dotsenko, Viktor S. "Universal randomness." Physics-Uspekhi54.3 (2011): 259.