Tay B A, Ordonez G
Center for Studies in Statistical Mechanics and Complex Systems, The University of Texas at Austin, 1 University Station C1609, Austin, Texas 78712, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2006 Jan;73(1 Pt 2):016120. doi: 10.1103/PhysRevE.73.016120. Epub 2006 Jan 18.
We derive an exact Markovian kinetic equation for an oscillator linearly coupled to a heat bath, describing quantum Brownian motion. Our work is based on the subdynamics formulation developed by Prigogine and collaborators. The space of distribution functions is decomposed into independent subspaces that remain invariant under Liouville dynamics. For integrable systems in Poincaré's sense the invariant subspaces follow the dynamics of uncoupled, renormalized particles. In contrast, for nonintegrable systems, the invariant subspaces follow a dynamics with broken time symmetry, involving generalized functions. This result indicates that irreversibility and stochasticity are exact properties of dynamics in generalized function spaces. We comment on the relation between our Markovian kinetic equation and the Hu-Paz-Zhang equation.
我们推导了一个与热库线性耦合的振子的精确马尔可夫动力学方程，该方程描述了量子布朗运动。我们的工作基于普里戈金及其合作者提出的子动力学公式。分布函数空间被分解为在刘维尔动力学下保持不变的独立子空间。对于庞加莱意义下的可积系统，不变子空间遵循未耦合的、重整化粒子的动力学。相反，对于不可积系统，不变子空间遵循具有时间对称性破缺的动力学，涉及广义函数。这一结果表明，不可逆性和随机性是广义函数空间中动力学的精确性质。我们评论了我们的马尔可夫动力学方程与胡 - 帕兹 - 张方程之间的关系。
