Duality, intertwining, and non-equilibrium steady states

量子物理学・ナノサイエンス第106回特別セミナー

概要

For a class of stochastic models of mass/energy transport, we prove several intertwining relations, which in turn follow from Markov duality. As a consequence of these relations, we deduce a special property of the dynamics: certain mixture measures are closed for the dynamics, and their evolution can be followed over time. As a main application, we consider the non-equilibrium steady state that arises when these models are put in contact with multiple external reservoirs and prove that, remarkably, it is a mixture on any graph. For a distinguished example in the class (namely, the interacting particle system associated with the integrable XXX non-compact spin chain) the mixture measure can be explicitly characterized in terms of the ordered Dirichlet distribution.

• 量子物理学・ナノサイエンス第106回特別セミナー

• 東京科学大学理学院・物理学系 ナノサイエンスを拓く量子物理学拠点　共催