Fast Converging Path Integrals for Time-Dependent Potentials II: Generalization to Many-body Systems and Real-Time Formalism

Balaz, Antun and Vidanovic, Ivana and Bogojevic, Aleksandar and Belic, Aleksandar and Pelster, Axel (2011) Fast Converging Path Integrals for Time-Dependent Potentials II: Generalization to Many-body Systems and Real-Time Formalism. Journal of Statistical Mechanics: Theory and Experiment (3). 03005. ISSN 1742-5468 (FP7- 261323)

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Abstract

Based on a previously developed recursive approach for calculating the short-time expansion of the propagator for systems with time-independent potentials and its time-dependent generalization for simple single-particle systems, in this paper we present a full extension of this formalism to a general quantum system with many degrees of freedom in a time-dependent potential. Furthermore, we also present a recursive approach for the velocity-independent part of the effective potential, which is necessary for calculating diagonal amplitudes and partition functions, as well as an extension from the imaginary-time formalism to the real-time one, which enables to study the dynamical properties of quantum systems. The recursive approach developed here allows an analytic derivation of the short-time expansion to orders that have not been accessible before, using the implemented SPEEDUP symbolic calculation code. The analytically derived results are extensively numerically verified by treating several models in both imaginary and real time.

Keywords

Low-dimensional systems; Time-dependent potential; Many-body effective action; Real time

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:	06 Aug 2012 10:52
Access rights:	Open access
URI:	http://eprints.kobson.nb.rs/id/eprint/26

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