Aleksandra Ziołkowska: Yang-Baxter Integrable Lindblad Equations
Aleksandra Ziołkowska (University of Oxford)
Open quantum systems are ubiquitous in the contexts of atomic and molecular physics, circuit QED and optomechanics. Couplings to an environment can also have very interesting effects on the dynamics of many-particle quantum systems. In order to arrive at a tractable description of such problems, it is customary to work within the Markovian approximation with the dynamics averaged over the environment, whereby the system is described by a Lindblad master equation. While much progress has been made in analysing Lindblad equations for many-particle systems by employing, for example, perturbative and matrix product states methods, it is clearly highly desirable to have exact solutions in specific, and hopefully representative, cases. This talk aims to show that for a number of interacting open quantum systems, it is possible to obtain exact analytic solutions through a connection with integrable models. I will describe how a correspondence between a Lindblad equation and an integrable Hamiltonian can be established and what information about the open systems it provides. In particular, I will discuss the equivalence in structure of generalised Hubbard models and vectorised Lindblad equations, which are already visible in the R-matrix of the integrable model. I will also mention how this construction can be extended by focusing purely on the integrability of the invariant subspaces of the Lindblad equations. The talk is based on the work presented in SciPost Phys. 8, 044 (2020) (doi: 10.21468/SciPostPhys.8.3.044).
More information on the seminar webpage.