Reaction-diffusion processes can be adopted to model a large number of dynamics on complex networks, such as transport processes or epidemic outbreaks. In most cases, however, they have been studied from a fermionic perspective, in which each vertex can be occupied by at most one particle. While still useful, this approach suffers from some drawbacks, the most important probably being the difficulty to implement reactions involving more than two particles simultaneously. Here we introduce a general framework for the study of bosonic reaction-diffusion processes on complex networks, in which there is no restriction on the number of interacting particles that a vertex can host. We describe these processes theoretically by means of continuous time heterogeneous mean-field theory and divide them into two main classes: steady state and monotonously decaying processes. We analyze specific examples of both behaviors within the class of one-species process, comparing the results (whenever possible) with the corresponding fermionic counterparts. We find that the time evolution and critical properties of the particle density are independent of the fermionic or bosonic nature of the process, while differences exist in the functional form of the density of occupied vertices in a given degree class k. We implement a continuous time Monte Carlo algorithm, well suited for general bosonic simulations, which allow us to confirm the analytical predictions formulated within mean-field theory. Our results, both at the theoretical and numerical level, can be easily generalized to tackle more complex, multi-species, reaction-diffusion processes, and open a promising path for a general study and classification of this kind of dynamical systems on complex networks.
Monte Carlo simulations of bosonic reaction-diffusion systems and comparison to Langevin equation description
利用最近提出的玻色子反应扩散系统的蒙特卡罗模拟方法[S.- C. Park，Phys. Rev. E { \bf 72}，036111（2005）]中，研究了一维玻色子模型，并将其与从相干态路径积分形式主义导出的相应朗之万方程进行了比较。对于单物种湮灭模型，给出了关联函数的精确渐近形式，并在数值上证明了离散变量主方程与连续变量Langevin方程的完全等价性.我们还研究了与扩散对接触过程（PCPD）有关的玻色子循环耦合模型。从路径积分形式主义，朗之万方程，预计将描述的临界行为的PCPD推导和比较的离散模型的蒙特卡罗模拟。
