The nonextensivity for a general quantum dissipative system driven by an external force is investigated. The dynamics of the system is characterized by a nonextensivity parameter q which indicates the degree of departure from extensivity for the system. The wave function of the system in the coherent state is derived with the aid of the linear invariant operator which obeys the Liouville–von Neumann equation. It is confirmed that, although the corresponding quantum energy dissipates with time like the classical energy, its time behavior is somewhat different from that of the usual dissipative systems depending on the scale of nonextensivity. The rate of such a dissipation becomes slightly larger as q increases. The effects of nonextensivity on other quantum characteristics of the system, such as fluctuations and uncertainty relations for canonical variables, are also analyzed rigorously. It is shown that the authors' results in the nonextensive regime recover to those of the well known standard ones in the limit $q\to 1$.

中文翻译：

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非延展性对相干态中一般驱动耗散振荡器的影响

研究了由外力驱动的一般量子耗散系统的非延展性。系统的动态特性由非扩展性参数q表征，该参数表示系统与扩展性的偏离程度。系统在相干状态下的波函数是在线性不变算子的帮助下推导出来的，该算子服从 Liouville-von Neumann 方程。已经证实，虽然相应的量子能量像经典能量一样随时间消散，但其时间行为与通常的耗散系统的时间行为有所不同，这取决于非扩展性的尺度。这种耗散的速率随着q变得稍大增加。非延展性对系统其他量子特性的影响，如规范变量的波动和不确定关系，也得到了严格的分析。结果表明，作者在非扩展机制中的结果在极限范围内恢复到众所周知的标准结果$q\to 1$.