Duality and Hidden Symmetries in Interacting Particle Systems
Duality and Hidden Symmetries in Interacting Particle Systems
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DOI：
10.1007/s10955-009-9716-2
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发表时间：
2008-10
影响因子：
1.6
通讯作者：
C. Giardinà;J. Kurchan;F. Redig;K. Vafayi
中科院分区：
文献类型：
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作者：
C. Giardinà;J. Kurchan;F. Redig;K. Vafayi
在马尔可夫过程的背景下，无论是在离散和连续设置，我们显示了一般的对偶函数和对称性的生成器之间的关系。如果生成元可以写成量子自旋系统的哈密顿量的形式，那么“隐藏”对称性就很容易导出。我们在对称排斥型过程中说明了我们的方法，其中对称性是SU（2）型，以及Kipnis-Marchioro-Presutti（KMP）模型，我们揭示了它的SU（1，1）对称性。KMP模型又是一个能量过程的瞬时热化极限，它与一个大的相互作用扩散模型家族相关联，我们称之为布朗能量过程（BEP），它们都具有SU（1，1）对称性。我们详细处理的情况下，该系统是在与水库和双重过程成为吸收。
In the context of Markov processes, both in discrete and continuous setting, we show a general relation between duality functions and symmetries of the generator. If the generator can be written in the form of a Hamiltonian of a quantum spin system, then the “hidden” symmetries are easily derived. We illustrate our approach in processes of symmetric exclusion type, in which the symmetry is ofSU(2) type, as well as for the Kipnis-Marchioro-Presutti (KMP) model for which we unveil itsSU(1,1) symmetry. The KMP model is in turn an instantaneous thermalization limit of the energy process associated to a large family of models of interacting diffusions, which we call Brownian energy process (BEP) and which all possess theSU(1,1) symmetry. We treat in details the case where the system is in contact with reservoirs and the dual process becomes absorbing.