Order 1/N corrections to the time-dependent Hartree approximation for a system of N+1 oscillators
- Department of Physics, University of New Hampshire, Durham, New Hampshire 03824 (United States)
- Theoretical Division, MS B285, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States)
We solve numerically to order 1/N the time evolution of a quantum dynamical system of N oscillators of mass m coupled quadratically to a massless dynamic variable. We use Schwinger{close_quote}s closed time path formalism to derive the equations. We compare two methods which differ by terms of order 1/N{sup 2}. The first method is a direct perturbation theory in 1/N using the path integral. The second solves exactly the theory defined by the effective action to order 1/N. We compare the results of both methods as a function of N. At N=1, where we expect the expansion to be quite innacurate, we compare our results to an exact numerical solution of the Schr{umlt o}dinger equation. In this case we find that when the two methods disagree they also diverge from the exact answer. We also find at N=1 that the 1/N corrected evolutions track the exact answer for the expectation values much longer than the mean field (N={infinity}) result. {copyright} {ital 1997} {ital The American Physical Society}
- OSTI ID:
- 543882
- Journal Information:
- Physical Review, D, Vol. 56, Issue 9; Other Information: PBD: Nov 1997
- Country of Publication:
- United States
- Language:
- English
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