%0 Journal Article %T Stochastic dissipative quantum spin chains (I) : Quantum fluctuating discrete hydrodynamics %+ Institut de Physique Théorique - UMR CNRS 3681 (IPHT) %+ Université Paris sciences et lettres (PSL) %+ Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure] (LPTENS) %+ Laboratoire de Physique Théorique de l'ENS [École Normale Supérieure] (LPTENS) %A Bauer, Michel %A Bernard, Denis %A Jin, Tony %Z Revised version. Main text: 19 pages, Appendices+References: 10 pages %< avec comité de lecture %@ 2542-4653 %J SciPost Physics %I SciPost Foundation %8 2017 %D 2017 %Z 1706.03984 %R 10.21468/SciPostPhys.3.5.033 %Z Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech] %Z Physics [physics]/Mathematical Physics [math-ph] %Z Physics [physics]/Quantum Physics [quant-ph]Journal articles %X Motivated by the search for a quantum analogue of the macroscopic fluctuation theory, we study quantum spin chains dissipatively coupled to quantum noise. The dynamical processes are encoded in quantum stochastic differential equations. They induce dissipative friction on the spin chain currents. We show that, as the friction becomes stronger, the noise induced dissipative effects localize the spin chain states on a slow mode manifold, and we determine the effective stochastic quantum dynamics of these slow modes. We illustrate this approach by studying the quantum stochastic Heisenberg spin chain. %G English %2 https://cea.hal.science/cea-01626328/document %2 https://cea.hal.science/cea-01626328/file/1706.03984.pdf %L cea-01626328 %U https://cea.hal.science/cea-01626328 %~ CEA %~ ENS-PARIS %~ UPMC %~ CNRS %~ LPTENS %~ DSM-IPHT %~ CEA-UPSAY %~ TDS-MACS %~ PSL %~ UNIV-PARIS-SACLAY %~ CEA-UPSAY-SACLAY %~ UPMC_POLE_2 %~ CEA-DRF %~ SORBONNE-UNIVERSITE %~ SU-INF-2018 %~ SU-SCIENCES %~ UP-SCIENCES %~ TEST-HALCNRS %~ ENS-PSL %~ SU-TI %~ ANR %~ GS-MATHEMATIQUES %~ GS-PHYSIQUE %~ ALLIANCE-SU