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

Balaz, Antun and Vidanovic, Ivana and Bogojevic, Aleksandar and Belic, Aleksandar and Pelster, Axel (2011) Fast Converging Path Integrals for Time-Dependent Potentials I: Recursive Calculation of Short-Time Expansion of the Propagator. Journal of Statistical Mechanics: Theory and Experiment (3). P3004. ISSN 1742-5468 (FP7- 261323)

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Abstract

In this and subsequent paper [1] 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.

Keywords

Low-dimensional systems; Time-dependent potential; Evolution operator; Effective action

Item Type:	Article
FP7 Grant Agreement Number:	261323
FrameWork Programmes:	SP4-Capacities
Scientific Areas:	Research Infrastructures
Contact Email Address:	antun@ipb.ac.rs
Last Modified:	07 Aug 2012 07:19
Access rights:	Open access
URI:	http://eprints.kobson.nb.rs/id/eprint/24

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