Affiliation:
1. Department of Physics and Astronomy, Texas A&M University , College Station, Texas 77843, USA
Abstract
The direct integration of the harmonic oscillator path integral obscures the fundamental structure of its discrete, imaginary time propagator (density matrix). This work, by first proving an operator identity for contracting two free propagators into one in the presence of interaction, derives the discrete propagator by simple algebra without doing any integration. This discrete propagator is universal, having the same two hyperbolic coefficient functions for all short-time propagators. Individual short-time propagator only modifies the coefficient function’s argument, its portal parameter, whose convergent order is the same as the thermodynamic energy. Moreover, the thermodynamic energy can be given in a closed form for any short-time propagator. Since the portal parameter can be systematically optimized by matching the expansion of the product of the two coefficients, any short-time propagator can be optimized sequentially, order by order, by matching the product coefficient’s expansion alone, without computing the energy. Previous empirical findings on the convergence of fourth and sixth-order propagators can now be understood analytically. An eight-order convergent short-time propagator is also derived.
Subject
Physical and Theoretical Chemistry,General Physics and Astronomy
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献