Balls-in-boxes condensation on networks.
Balls-in-boxes condensation on networks.
复制标题
网络上的盒中球凝结。
作者：
L. Bogacz;Z. Burda;W. Janke;B. Wacław
我们讨论了两种不同的制度的冷凝物形成在网络上的零程过程：在一个q-正规网络，其中冷凝物是作为一个自发的对称性破缺的结果，并在一个不规则的网络，其中的配分函数的对称性被明确打破。在后一种情况下，我们考虑由度Q>q的单个Q节点引入的q-正则网络的最小不规则性。凝聚的静力学和动力学取决于参数α =ln Q/q，其控制规则节点上的粒子分布的指数衰减和Q节点上的凝聚物熔化的典型时间尺度，其随系统尺寸N呈指数增加。这种行为与q-正则网络不同，其中α =0，并且凝聚是由配分函数的自发对称破缺引起的，这在网络的q节点上的粒子占据数的排列下是不变的。在这种情况下，已知用于冷凝物熔化的典型时间尺度典型地作为系统尺寸的幂而增加。
We discuss two different regimes of condensate formation in zero-range processes on networks: on a q-regular network, where the condensate is formed as a result of a spontaneous symmetry breaking, and on an irregular network, where the symmetry of the partition function is explicitly broken. In the latter case we consider a minimal irregularity of the q-regular network introduced by a single Q node with degree Q>q. The statics and dynamics of the condensation depend on the parameter alpha=ln Q/q, which controls the exponential falloff of the distribution of particles on regular nodes and the typical time scale for melting of the condensate on the Q node, which increases exponentially with the system size N. This behavior is different than that on a q-regular network, where alpha=0 and where the condensation results from the spontaneous symmetry breaking of the partition function, which is invariant under a permutation of particle occupation numbers on the q nodes of the network. In this case the typical time scale for condensate melting is known to increase typically as a power of the system size.