27-31 March 2022
Europe/Berlin timezone

Integrable matrix models in discrete space-time: A paradigm of Kardar-Parisi-Zhang physics

30 Mar 2022, 14:00
60 min Talk


Prof. Tomaz Prosen (University of Ljubljana)


I will discuss a class of very simple integrable dynamics on a discrete space-time lattice, which is generated by a 2-site matrix-valued rational map.
The phase spaces of the matrix variable can be selected from diverse families of symmetric spaces, e.g. complex Grassmannians, and are equipped with a natural symplectic structure.
This precise form of the map follows from a simple consistency condition for a parallel transport (aka Lax zero curvature condition) on a space-time lattice using
a minimalistic Lax operator, which is linear in the spectral and matrix variables. I will discuss the Yang-Baxter property and conservation laws of these maps.

Physically, the model represents an integrable discretization and SU(N) generalization of Landau-Lifshitz magnet. Using numerical computations, we have demonstrated that the
transport of Noether charges follows Kardar-Parisi-Zhang universality with superdiffusive dynamical exponent 3/2. Most interesting open questions will be discussed.

Primary author

Prof. Tomaz Prosen (University of Ljubljana)

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