Fast Converging Path Integrals for Time-Dependent Potentials I: Recursive Calculation of Short-Time Expansion of the Propagator
arXiv:0912.2743 · doi:10.1088/1742-5468/2011/03/P03004
Abstract
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.
29 pages, 5 figures
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Cited by in corpus (6)
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- Dynamics of one-dimensional tight-binding models with arbitrary time-dependent external homogeneous fields
- Fast Converging Path Integrals for Time-Dependent Potentials II: Generalization to Many-body Systems and Real-Time Formalism
- Time-of-flight expansion of trapped dipolar Fermi gases: From the collisionless to the hydrodynamic regime