论文标题
为多维系统生成融合的特征力界限：一个新的力矩表示，代数，量化形式主义
Generating Converging Eigenenergy Bounds for Multidimensional Systems: A New Moment Representation, Algebraic, Quantization Formalism
论文作者
论文摘要
对于承认力矩方程表示（MER）的低维系统，到目前为止，适用于所有离散状态的有效特征力边界理论的发展仍然难以捉摸。尽管Handy等人（1988Phys。Rev.Lett。60253）证明了基于{\ it Moment问题}的有效性，基于特征值矩（EMM），用于为多维，正，正，波斯型，波斯尼克的基础状态产生任意紧密的界限，其or ortensions ordensions ordensions ordensition ordension ordension ordension to to to toction for to notary激发状态似乎是可行的。我们发现了一种基于瞬间的新量化形式主义，可以实现这一目标。与EMM不同，不需要凸优化方法。整个配方都是代数。由于我们的初步研究，我们能够匹配或超过Kravchenko等人（1996Phys。Phys。ARev。A 54 287）的出色但复杂的分析，就二次Zeeman效应而言，对于广泛的磁场强度。与他们的分析不同，所提出的方法很简单，不涉及截断，并且在每个力矩子空间内，量子运算符的投影都是精确的。我们的新方法，即正交多项式投影量化的方法（OPPQ-BM），利用了Handy and Vrinceanu开发的先前方法的隐式边界能力（2013 J. ofPhys。A：Math。46135202）。出现的是一种全新的分析类型（即受约束的二次形式最小化），它验证了矩方程表示对物理系统的重要性。尽管EMM的基本原则保证它比OPPQ-BM更有效，但实施代数计算的能力与追求非线性凸优化方法（可以通过线性编程替代方案放松）相反，建议使用OPPQ-BM。我们对应用程序的新方法进行了概述。
For low dimension systems admitting a moment equation representation (MER), the development of an effective eigenenergy bounding theory applicable to all discrete states had remained elusive, until now. Whereas Handy et al (1988 Phys. Rev. Lett. 60 253) demonstrated the effectiveness of the {\it Moment Problem} based, Eigenvalue Moment Method (EMM), for generating arbitrarily tight bounds to the multidimensional, positive, bosonic ground state, its extension to arbitrary excited states seemed intractable. We have discovered a new, moment representation based, quantization formalism that achieves this. Unlike EMM, no convex optimization methods are required. The entire formulation is algebraic. As a result of our preliminary investigation, we are able to match, or surpass, the excellent, but intricate, analysis of Kravchenko et al (1996 Phys. Rev. A 54 287) with respect to the quadratic Zeeman effect, for a broad range of magnetic field strengths. Unlike their analysis, the proposed method is simple, involves no truncations, and the projection of the quantum operator is exact, within each moment subspace. Our new approach, the Orthogonal Polynomial Projection Quantization-Bounding Method (OPPQ-BM), exploits the implicit bounding capabilities of a previous method developed by Handy and Vrinceanu (2013 J. of Phys. A: Math. Theor. 46 135202). What emerges is a completely new type of analysis (i.e. constrained quadratic form minimization) that validates the importance of moment equation representations for quantizing physical systems. Whereas the underlying principles of EMM guarantee it to be more efficient than OPPQ-BM, the ability to implement algebraic computations, as opposed to pursuing nonlinear convex optimization methods (which can be relaxed through linear programming alternatives) recommends OPPQ-BM. We give an overview of the new method with applications.
