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

Abstract

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.

Authors:
; ; ; ;
Publication Date:
Sponsoring Org.:
(US)
OSTI Identifier:
40205241
Resource Type:
Journal Article
Journal Name:
Physical Review D
Additional Journal Information:
Journal Volume: 62; Journal Issue: 12; Other Information: DOI: 10.1103/PhysRevD.62.125015; Othernumber: PRVDAQ000062000012125015000001; 053018PRD; PBD: 15 Dec 2000; Journal ID: ISSN 0556-2821
Publisher:
The American Physical Society
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; NUMERICAL SOLUTION; SYMMETRY; UNITARITY; WAVE PACKETS

Citation Formats

Mihaila, Bogdan, Athan, Tara, Cooper, Fred, Dawson, John, and Habib, Salman. Exact and approximate dynamics of the quantum mechanical O(N) model. United States: N. p., 2000. Web. doi:10.1103/PhysRevD.62.125015.
Mihaila, Bogdan, Athan, Tara, Cooper, Fred, Dawson, John, & Habib, Salman. Exact and approximate dynamics of the quantum mechanical O(N) model. United States. https://doi.org/10.1103/PhysRevD.62.125015
Mihaila, Bogdan, Athan, Tara, Cooper, Fred, Dawson, John, and Habib, Salman. 2000. "Exact and approximate dynamics of the quantum mechanical O(N) model". United States. https://doi.org/10.1103/PhysRevD.62.125015.
@article{osti_40205241,
title = {Exact and approximate dynamics of the quantum mechanical O(N) model},
author = {Mihaila, Bogdan and Athan, Tara and Cooper, Fred and Dawson, John and Habib, Salman},
abstractNote = {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.},
doi = {10.1103/PhysRevD.62.125015},
url = {https://www.osti.gov/biblio/40205241}, journal = {Physical Review D},
issn = {0556-2821},
number = 12,
volume = 62,
place = {United States},
year = {Fri Dec 15 00:00:00 EST 2000},
month = {Fri Dec 15 00:00:00 EST 2000}
}