# Double Ramification Cycles and Quantum Integrable Systems

@article{Buryak2015DoubleRC,
title={Double Ramification Cycles and Quantum Integrable Systems},
author={Alexandr Buryak and Paolo Rossi},
journal={Letters in Mathematical Physics},
year={2015},
volume={106},
pages={289-317}
}
• Published 12 March 2015
• Mathematics
• Letters in Mathematical Physics
In this paper, we define a quantization of the Double Ramification Hierarchies of Buryak (Commun Math Phys 336:1085–1107, 2015) and Buryak and Rossi (Commun Math Phys, 2014), using intersection numbers of the double ramification cycle, the full Chern class of the Hodge bundle and psi-classes with a given cohomological field theory. We provide effective recursion formulae which determine the full quantum hierarchy starting from just one Hamiltonian, the one associated with the first descendant…

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