Fast Converging Path Integrals for Time-Dependent Potentials I: Recursive Calculation of Short-Time Expansion of the Propagator

Autor:	Balaz, Antun, Vidanovic, Ivana, Bogojevic, Aleksandar, Belic, Aleksandar, Pelster, Axel
Rok vydání:	2009
Předmět:	Condensed Matter - Statistical Mechanics Condensed Matter - Other Condensed Matter Condensed Matter - Quantum Gases High Energy Physics - Theory Physics - Computational Physics Quantum Physics
Zdroj:	J.Stat.Mech.2011:03004,2011
Druh dokumentu:	Working Paper
DOI:	10.1088/1742-5468/2011/03/P03004
Popis:	In this and subsequent paper arXiv:1011.5185 we develop a recursive approach for calculating the short-time expansion of the propagator for a general quantum system in a time-dependent potential to orders that have not yet been accessible before. To this end the propagator is expressed in terms of a discretized effective potential, for which we derive and analytically solve a set of efficient recursion relations. Such a discretized effective potential can be used to substantially speed up numerical Monte Carlo simulations for path integrals, or to set up various analytic approximation techniques to study properties of quantum systems in time-dependent potentials. The analytically derived results are numerically verified by treating several simple models. Comment: 29 pages, 5 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0912.2743 Zobrazit plný text záznamu View this record from Arxiv