论文标题
非分离量子哈密顿人的指数统一集成符
Exponential unitary integrators for nonseparable quantum Hamiltonians
论文作者
论文摘要
量子哈密顿量含有不可分割的不可分割的操作员，例如$ \ hat {\ bf x}^m \ hat {\ bf p}^n $，对于使用拆分操纵器技术的数值研究而言是有问题的x}）$。在古典物理学的情况下，下巴[Phys。 Rev. E $ \ bf 80 $，037701（2009）]开发了一个程序，以大约表示可分离的术语。我们将Chin的想法扩展到量子系统。我们通过数值发展KERR型振荡器的Wigner分布来证明我们的发现，其Hamiltonian包含不可分割的术语$ \ hat {\ bf x}^2 \ hat {\ bf p}^\ bf p}^2 + \ hat + \ hat hat {\ bf p}^\ bf p}^2 \ hat hat^\ hat {\ bf bf bf x} Chin的方法对多项式形式的任何哈密顿量的总体适用性得到了证明。
Quantum Hamiltonians containing nonseparable products of non-commuting operators, such as $\hat{\bf x}^m \hat{\bf p}^n$, are problematic for numerical studies using split-operator techniques since such products cannot be represented as a sum of separable terms, such as $T(\hat{\bf p}) + V(\hat{\bf x})$. In the case of classical physics, Chin [Phys. Rev. E $\bf 80$, 037701 (2009)] developed a procedure to approximately represent nonseparable terms in terms of separable ones. We extend Chin's idea to quantum systems. We demonstrate our findings by numerically evolving the Wigner distribution of a Kerr-type oscillator whose Hamiltonian contains the nonseparable term $\hat{\bf x}^2 \hat{\bf p}^2 + \hat{\bf p}^2 \hat{\bf x}^2$. The general applicability of Chin's approach to any Hamiltonian of polynomial form is proven.
