Exact and approximate dynamics of the quantum mechanical O(N) model
We study the dynamics of the quantum mechanical O(N) model as a specific example to investigate the systematics of a 1/N expansion. The closed time path 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 are elucidated. In order to compare theoretical predictions against numerical solutions of the time-dependent Schro''dinger 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 also discuss the existence of unitarity violation in this expansion, a well-known problem faced by moment truncation techniques. The 1/N results, both static and dynamic, are contrasted with those given by a Hartree variational ansatz at given values of N. A comparison against numerical results leads us to conclude that late-time dynamical behavior, where nonlinear effects are significant, is not well described by either approximation.
- Sponsoring Organization:
- (US)
- OSTI ID:
- 40205241
- Journal Information:
- Physical Review D, Vol. 62, Issue 12; Other Information: DOI: 10.1103/PhysRevD.62.125015; Othernumber: PRVDAQ000062000012125015000001; 053018PRD; PBD: 15 Dec 2000; ISSN 0556-2821
- Publisher:
- The American Physical Society
- Country of Publication:
- United States
- Language:
- English
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