We discuss a connection [1] between the low-temperature dynamical phenomenon in a discrete Nonlinear Schrodinger Equation (DNLS), a.k.a., Gross–Pitaevskii equation and nonlinear fluctuating hydrodynamics (NFH). We show that the resulting nonlinear stochastic field theory can be recast as a set of coupled KPZ-like equations. The behavior of these equations most often fall under Kardar-Parisi-Zhang (KPZ) universality class [2].
We will then discuss few multi-component integrable and non-integrable models that, in principle, appear in the context of coupled cold gases and nonlinear optics. I will discuss connections with PDE’s (such as KdV), dynamics, quenches and shock-waves in these models [3].
[1] M. Kulkarni, D. A. Huse, H. Spohn, Phys. Rev. A 92, 043612 (2015)
[2] M. Kulkarni and A. Lamacraft, Phys. Rev. A 88, 021603 (2013)
[3] S. Swarup, V. Vasan, M. Kulkarni (in preparation, 2018)
Host: Nir Navon