Exact and approximate dynamics of the quantum mechanical O(N) model

Details Exact and approximate dynamics of the quantum mechanical O(N) model Exact and approximate dynamics of the quantum mechanical O(N) model

2000-03-10

arxiv.org/abs/hep-ph/0003105v1

Phys.Rev. D62 (2000) 125015

Physics

High Energy Physics

High Energy Physics - Phenomenology

16 pages, 12 figrures, revtex

Scientific paper

10.1103/PhysRevD.62.125015

We study a quantum dynamical system of N, O(N) symmetric, nonlinear oscillators as a toy model to investigate the systematics of a 1/N expansion. The closed time path (CTP) formalism melded with an expansion in 1/N is used to derive time evolution equations valid to order 1/N (next-to-leading order). The effective potential is also obtained to this order and its properties areelucidated. In order to compare theoretical predictions against numerical solutions of the time-dependent Schrodinger equation, we consider two initial conditions consistent with O(N) symmetry, one of them a quantum roll, the other a wave packet initially to one side of the potential minimum, whose center has all coordinates equal. For the case of the quantum roll we map out the domain of validity of the large-N expansion. We discuss unitarity violation in the 1/N expansion; a well-known problem faced by moment truncation techniques. The 1/N results, both static and dynamic, are also compared to those given by the Hartree variational ansatz at given values of N. We conclude that late-time behavior, where nonlinear effects are significant, is not well-described by either approximation.

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