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Rearranging the exponential wall for large N-body systems
Deborah K Watson1, Martin Dunn
1Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, Oklahoma 73019, USA.
Physical Review Letters
|September 28, 2010
Summary
Solving the N boson wave function problem is computationally intensive. This new method rearranges the complexity, enabling exact analytical calculations for large systems by scaling with system size, not exponential complexity.
Area of Science:
- Quantum mechanics
- Many-body physics
Background:
- The N boson wave function problem is crucial in quantum mechanics.
- Solving it typically involves exponential computational scaling with the number of particles (N).
Purpose of the Study:
- To reformulate the N boson wave function problem to reduce computational complexity.
- To enable exact analytical solutions for large N systems.
Main Methods:
- Rearranging the computational approach for the N boson wave function.
- Utilizing a perturbation series that scales polynomially with N (N^0).
Main Results:
- The problem's complexity is shifted from exponential scaling with N to exponential scaling with the order of the perturbation series.
- This allows for exact analytical calculations in low orders of the perturbation series for large N.
Conclusions:
- The reformulated approach offers a computationally tractable method for analyzing large N boson systems.
- This work provides a pathway for exact analytical solutions in quantum many-body problems.
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