Analysis of the growth in complexity of a symmetry-invariant perturbation method for large N-body systems

The work required to solve for the fully interacting N boson wavefunction, which is widely believed to scale exponentially with N, has been previously shown to scale as N0 when the problem is rearranged using analytic building blocks. The exponential complexity reappears in an exponential scaling wi...

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Bibliographic Details
Published in:Journal of physics. B, Atomic, molecular, and optical physics Atomic, molecular, and optical physics, 2012-05, Vol.45 (9), p.95002-1-8
Main Authors: Watson, Deborah K, Dunn, Martin
Format: Article
Language:English
Subjects:
Atomic and molecular physics
body
Boson systems
Bosons
Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations)
Complexity
Electronic structure of atoms, molecules and their ions: theory
Exact sciences and technology
Mathematical analysis
Perturbation methods
Perturbation theory
Physics
Quantum statistical mechanics
Statistical physics, thermodynamics, and nonlinear dynamical systems
symmetry-invariant
Wavefunctions
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Summary:The work required to solve for the fully interacting N boson wavefunction, which is widely believed to scale exponentially with N, has been previously shown to scale as N0 when the problem is rearranged using analytic building blocks. The exponential complexity reappears in an exponential scaling with the order of our perturbation series allowing exact analytical calculations for very large N systems through low order. In this paper, we analyse the growth in complexity with order when a normal mode basis is used.
ISSN:0953-4075
1361-6455
DOI:10.1088/0953-4075/45/9/095002