Physics – Quantum Physics
Scientific paper
2012-03-20
Physics
Quantum Physics
11 page, 1 figure, 4 footnotes, 35 references
Scientific paper
Fully analytic formulas, which do not involve any numerical integration, are derived for the discretized influence functionals of a very extensive assortment of spectral distributions. For Feynman integrals derived using the Trotter splitting and Strang splitting, we present general formulas for the discretized influence functionals in terms of proper integrals of the bath response function. When an analytic expression exists for the bath response function, these integrals can almost always be evaluated analytically. In cases where these proper integrals cannot be integrated analytically, numerically computing them is much faster and less error-prone than calculating the discretized influence functionals in the traditional way, which involves numerically calculating integrals whose bounds are both infinite. As an example, we present the analytic discretized influence functional for a bath response function of the form \alpha(t)=\sum_{j}^{K}p_{j}e^{\Omega_{j}t}, which is a natural form for many spectral distribution functions (including the very popular Lorentz-Drude/Debye function), and for other spectral distribution functions it is a form that is easily obtainable by a least-squares fit . Evaluating our analytic formulas for this example case is much faster and easier to implement than numerically calculating the discretized influence funcitonal in the traditional way. In the appendix we provide analytic expressions for p_{j} and \Omega_{j} for a variety of spectral distribution forms, and as a second example we provide the analytic bath response function and analytic influence functionals for spectral distributions of the form J(\omega)\propto\omega^{s}e^{-(\omega/\omega_{c})^{q}}. The value of the analytic expression for this bath response function extends beyond its use for calculating Feynman integrals.
Dattani Nikesh S.
Pollock Felix A.
Wilkins David M.
No associations
LandOfFree
Analytic influence functionals for numerical Feynman integrals in most open quantum systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Analytic influence functionals for numerical Feynman integrals in most open quantum systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Analytic influence functionals for numerical Feynman integrals in most open quantum systems will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-496669