Yuen-Zhou Joel, Rodríguez-Rosario César, Aspuru-Guzik Alán
Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, MA 02138, USA.
Phys Chem Chem Phys. 2009 Jun 14;11(22):4509-22. doi: 10.1039/b903064f. Epub 2009 May 11.
In this article, we prove the one-to-one correspondence between vector potentials and particle and current densities in the context of master equations with arbitrary memory kernels, therefore extending time-dependent current-density functional theory (TD-CDFT) to the domain of generalized many-body open quantum systems (OQS). We also analyse the issue of A-representability for the Kohn-Sham (KS) scheme proposed by D'Agosta and Di Ventra for Markovian OQS [Phys. Rev. Lett. 2007, 98, 226403] and discuss its domain of validity. We suggest ways to expand their scheme, but also propose a novel KS scheme where the auxiliary system is both closed and non-interacting. This scheme is tested numerically with a model system, and several considerations for the future development of functionals are indicated. Our results formalize the possibility of practising TD-CDFT in OQS, hence expanding the applicability of the theory to non-Hamiltonian evolutions.
在本文中，我们证明了在具有任意记忆核的主方程背景下矢量势与粒子及电流密度之间的一一对应关系，从而将含时电流密度泛函理论（TD-CDFT）扩展到广义多体开放量子系统（OQS）领域。我们还分析了达戈斯塔和迪文特拉针对马尔可夫开放量子系统提出的科恩-沈（KS）方案[《物理评论快报》2007年，98卷，226403]的A可表示性问题，并讨论其有效性范围。我们提出了扩展他们方案的方法，同时还提出了一种新颖的KS方案，其中辅助系统既是封闭的又是非相互作用的。该方案通过一个模型系统进行了数值测试，并指出了泛函未来发展的若干考虑因素。我们的结果使在开放量子系统中实践TD-CDFT的可能性形式化，从而将该理论的适用性扩展到非哈密顿演化。
