论文标题
Hohenberg-Kohn定理的不确定性关系
Uncertainty relations for the Hohenberg-Kohn theorem
论文作者
论文摘要
电荷密度如何限制自然界中的多体波形？ Hohenberg-Kohn定理用于非偏见，相互作用的多体Schrödinger系统是众所周知的，并使用\ emph {reductio-ad-ad-absurdum}证明了；但是，尚未理解实现本质定理的物理机制或原则。在这里，我们在相互作用的多体问题中获得了有效的规范操作员 - （i）局部电场介导颗粒之间的相互作用，并有助于势能； （ii）粒子矩形，这有助于动能。这些操作员的换向导致电荷密度分布。因此，相互作用的多粒子系统的量子波动受电荷密度的约束，从而提供了一种机制，通过该机制通过与电荷密度耦合，通过该机制来调整量子机械多体向波函数。作为初始测试，我们获得了相互作用多个粒子系统的总能量的功能形式，并且在均匀的密度极限中，找到与量子蒙特卡洛模拟的有希望的一致性。
How does charge density constrain many-body wavefunctions in nature? The Hohenberg-Kohn theorem for non-relativistic, interacting many-body Schrödinger systems is well-known and was proved using \emph{reductio-ad-absurdum}; however, the physical mechanism or principle which enables this theorem in nature has not been understood. Here, we obtain effective canonical operators in the interacting many-body problem -- (i) the local electric field, which mediates interaction between particles, and contributes to the potential energy; and (ii) the particle momenta, which contribute to the kinetic energy. The commutation of these operators results in the charge density distribution. Thus, quantum fluctuations of interacting many-particle systems are constrained by charge density, providing a mechanism by which an external potential, by coupling to the charge density, tunes the quantum-mechanical many-body wavefunction. As an initial test, we obtain the functional form for total energy of interacting many-particle systems, and in the uniform density limit, find promising agreement with Quantum Monte Carlo simulations.
