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Non-compact quantum spin chains as integrable stochastic particle processes
Frassek, Rouven ; Giardinà, Cristian ; Kurchan, Jorge
arXiv, 1904.01048 / Harvested from arXiv
In this paper we discuss a family of models of particle and energy diffusion on a one-dimensional lattice, related to those studied previously in [Sasamoto-Wadati], [Barraquand-Corwin] and [Povolotsky] in the context of KPZ universality class. We show that they may be mapped onto an integrable $\mathfrak{sl}(2)$ Heisenberg spin chain whose Hamiltonian density in the bulk has been already studied in the AdS/CFT and the integrable system literature. Using the quantum inverse scattering method, we study various new aspects, in particular we identify boundary terms, modeling reservoirs in non-equilibrium statistical mechanics models, for which the spin chain (and thus also the stochastic process) continues to be integrable. We also show how the construction of a "dual model" of probability theory is possible and useful. The fluctuating hydrodynamics of our stochastic model corresponds to the semiclassical evolution of a string that derives from correlation functions of local gauge invariant operators of $\mathcal{N}=4$ super Yang-Mills theory (SYM), in imaginary-time. As any stochastic system, it has a supersymmetric completion that encodes for the thermal equilibrium theorems: we show that in this case it is equivalent to the $\mathfrak{sl}(2|1)$ superstring that has been derived directly from $\mathcal{N}=4$ SYM.
Publié le : 2019-04-01
Classification:  Mathematical Physics,  Condensed Matter - Statistical Mechanics,  High Energy Physics - Theory,  Mathematics - Probability
@article{1904.01048,
     author = {Frassek, Rouven and Giardin\`a, Cristian and Kurchan, Jorge},
     title = {Non-compact quantum spin chains as integrable stochastic particle
  processes},
     journal = {arXiv},
     volume = {2019},
     number = {0},
     year = {2019},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1904.01048}
}
Frassek, Rouven; Giardinà, Cristian; Kurchan, Jorge. Non-compact quantum spin chains as integrable stochastic particle
  processes. arXiv, Tome 2019 (2019) no. 0, . http://gdmltest.u-ga.fr/item/1904.01048/