Linear response and exact hydrodynamic projections in Lindblad equations with decoupled Bogoliubov hierarchies, by Patrik Penc, Fabian H. L. Essler
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SciPost Physics Home Authoring Refereeing Submit a manuscript About Linear response and exact hydrodynamic projections in Lindblad equations with decoupled Bogoliubov hierarchies Patrik Penc, Fabian H. L. Essler SciPost Phys. 20, 058 (2026) · published 25 February 2026 doi: 10.21468/SciPostPhys.20.2.058 pdf BiBTeX RIS Submissions/Reports Abstract We consider a class of spinless-fermion Lindblad equations that exhibit decoupled BBGKY hierarchies. In the cases where particle number is conserved, their late time behaviour is characterized by diffusive dynamics, leading to an infinite temperature steady state. Some of these models are Yang-Baxter integrable, others are not. The simple structure of the BBGKY hierarchy makes it possible to map the dynamics of Heisenberg-picture operators on few-body imaginary-time Schrödinger equations with non-Hermitian Hamiltonians. We use this formulation to obtain exact hydrodynamic projections of operators quadratic in fermions, and to determine linear response functions in Lindbladian non-equilibrium dynamics. × TY - JOURPB - SciPost FoundationDO - 10.21468/SciPostPhys.20.2.058TI - Linear response and exact hydrodynamic projections in Lindblad equations with decoupled Bogoliubov hierarchiesPY - 2026/02/25UR - https://scipost.org/SciPostPhys.20.2.058JF - SciPost PhysicsJA - SciPost Phys.VL - 20IS - 2SP - 058A1 - Penc, PatrikAU - Essler, Fabian H. L.AB - We consider a class of spinless-fermion Lindblad equations that exhibit decoupled BBGKY hierarchies. In the cases where particle number is conserved, their late time behaviour is characterized by diffusive dynamics, leading to an infinite temperature steady state. Some of these models are Yang-Baxter integrable, others are not. The simple structure of the BBGKY hierarchy makes it possible to map the dynamics of Heisenberg-picture operators on few-body imaginary-time Schrödinger equations with non-Hermitian Hamiltonians. We use this formulation to obtain exact hydrodynamic projections of operators quadratic in fermions, and to determine linear response functions in Lindbladian non-equilibrium dynamics.ER - × @Article{10.21468/SciPostPhys.20.2.058, title={{Linear response and exact hydrodynamic projections in Lindblad equations with decoupled Bogoliubov hierarchies}}, author={Patrik Penc and Fabian H. L. Essler}, journal={SciPost Phys.}, volume={20}, pages={058}, year={2026}, publisher={SciPost}, doi={10.21468/SciPostPhys.20.2.058}, url={https://scipost.org/10.21468/SciPostPhys.20.2.058},} Ontology / Topics See full Ontology or Topics database. Hydrodynamics Integrability/integrable models Open quantum systems Authors / Affiliation: mappings to Contributors and Organizations See all Organizations. 1 Patrik Penc, 1 Fabian H. L. Essler 1 Rudolf Peierls Centre for Theoretical Physics Funder for the research work leading to this publication Engineering and Physical Sciences Research Council [EPSRC]