Recursive Schr\" odinger Equation Approach to Faster Converging Path Integrals

Abstract

By recursively solving the underlying Schr\" odinger equation, we set up an efficient systematic approach for deriving analytic expressions for discretized effective actions. With this we obtain discrete short-time propagators for both one and many particles in arbitrary dimension to orders which have not been accessible before. They can be used to substantially speed up numerical Monte Carlo calculations of path integrals, as well as for setting up a new analytical approximation scheme for energy spectra, density of states, and other statistical properties of quantum systems.

8 pages, 2 figures, uses revtex4

References in corpus (7)

• Anderson localization of a non-interacting Bose-Einstein condensate
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Critical temperature of interacting Bose gases in two and three dimensions
• Thermodynamical Properties of a Rotating Ideal Bose Gas
• Equation of state of an interacting Bose gas at finite temperature: a Path Integral Monte Carlo study
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• Properties of Quantum Systems via Diagonalization of Transition Amplitudes II: Systematic Improvements of Short-time Propagation
• Onset temperature of Bose-Einstein condensation in incommensurate solid 4He
• Effects of spatially inhomogeneous atomic interactions on Bose-Einstein condensates in optical lattices
• Properties of Quantum Systems via Diagonalization of Transition Amplitudes I: Discretization Effects
• Fast Converging Path Integrals for Time-Dependent Potentials I: Recursive Calculation of Short-Time Expansion of the Propagator
• Faraday and resonant waves in binary collisionally-inhomogeneous Bose-Einstein condensates
• Fast Converging Path Integrals for Time-Dependent Potentials II: Generalization to Many-body Systems and Real-Time Formalism
• SPEEDUP Code for Calculation of Transition Amplitudes via the Effective Action Approach
• On the information entropy of matter-waves in quasi-disorder potentials
• Applications of the worldline Monte Carlo formalism in quantum mechanics
• A quantum field theoretical approach to the P vs. NP problem via the sign of the fermionic Quantum Monte Carlo