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首页> 外文期刊>Journal of Physics, A. Mathematical and General: A Europhysics Journal >THE DUALITY RELATION BETWEEN GLAUBER DYNAMICS AND THE DIFFUSION-ANNIHILATION MODEL AS A SIMILARITY TRANSFORMATION
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THE DUALITY RELATION BETWEEN GLAUBER DYNAMICS AND THE DIFFUSION-ANNIHILATION MODEL AS A SIMILARITY TRANSFORMATION

机译：相似度变换的Glauber动力学与扩散-消除模型之间的对偶关系

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In this paper we address the relationship between zero temperature Glauber dynamics and the diffusion-annihilation problem in the free fermion case. We show that the well known duality transformation between the Mo problems can be formulated as a similarity transformation if one uses appropriate (toroidal) boundary conditions. This allows us to establish and clarify the precise nature of the relationship between the two models. In this way we obtain a one-to-one correspondence between observables and initial states in the two problems. A random initial state in Glauber dynamics is related to a short-range correlated state in the annihilation problem. In particular, the long-time behaviour of the density in this state is seen to depend on the initial conditions. Hence, we show that the presence of correlations in the initial state determine the dependence of the long-time behaviour of the density on the initial conditions, even if such correlations are short ranged. We also apply a field-theoretical method to the calculation of multi-time correlation functions in this initial state. [References: 21]
机译：在本文中，我们解决了自由费米子情况下零温度Glauber动力学与扩散-灭问题之间的关系。我们表明，如果人们使用适当的（环形）边界条件，那么Mo问题之间众所周知的对偶变换可以表示为相似性变换。这使我们能够建立和阐明两个模型之间关系的精确性质。通过这种方式，我们获得了两个问题中可观察值和初始状态之间的一一对应关系。 Glauber动力学中的随机初始状态与the灭问题中的短程相关状态有关。特别是，在此状态下密度的长期行为被视为取决于初始条件。因此，我们表明，初始状态下相关性的存在决定了密度的长期行为对初始条件的依赖性，即使这种相关性是短距离的。我们还将场论方法应用于此初始状态下的多次相关函数的计算。 [参考：21]

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