Iterative construction of conserved quantities ‌in dissipative nearly integrable systems

I. Ulčakar,1,2 Z. Lenarčič1

1Jožef Stefan Institute, SI-1000 Ljubljana, Slovenia

2University of Ljubljana, Faculty for physics and mathematics, SI-1000 Ljubljana, Slovenia

Integrable systems offer rare examples of solvable many-body problems in the quantum world. Due to the fine-tuned structure, their realization in nature and experiment is never completely accurate, therefore effects of integrability are observed only transiently. One way to surpass that is to couple nearly integrable systems to baths and driving: these will stabilize integrable effects up to arbitrary time, as encoded in the time dependent, and eventually, the stationary state of form of a generalized Gibbs ensemble. However, the description of such driven dissipative nearly integrable models is challenging and no exact analytical methods have been proposed so far. Here we develop an iterative scheme in which integrability breaking perturbations (baths) determine the most necessary conserved quantities to be added into a truncated generalized Gibbs ensemble description. Our scheme significantly reduces the complexity of the problem, paving the way for thermodynamic results.

1. I. Ulčakar and Z. Lenarčič, arXiv:2310.03809 (2023)