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Title: Functional renormalization group for quantized anharmonic oscillator

Abstract

Highlights: > RG analysis with field dependent wavefunction renormalization. > The Taylor expansion does not work for the wavefunction renormalization. > The gap energy is RG scheme-dependent. > The O (N) symmetric anharmonic oscillator exhibits only a single phase. > The evolution equation for the 2PI effective action for the oscillator is solved. - Abstract: Functional renormalization group methods formulated in the real-time formalism are applied to the O(N) symmetric quantum anharmonic oscillator, considered as a 0 + 1 dimensional quantum field-theoric model, in the next-to-leading order of the gradient expansion of the one- and two-particle irreducible effective action. The infrared scaling laws and the sensitivity-matrix analysis show the existence of only a single, symmetric phase. The Taylor expansion for the local potential converges fast while it is found not to work for the field-dependent wavefunction renormalization, in particular for the double-well bare potential. Results for the gap energy for the bare anharmonic oscillator potential hint on improving scheme-independence in the next-to-leading order of the gradient expansion, although the truncated perturbation expansion in the bare quartic coupling provides strongly scheme-dependent results for the infrared limits of the running couplings.

Authors:
 [1];  [1]
  1. Department of Theoretical Physics, University of Debrecen, P.O. Box 5, H-4010 Debrecen (Hungary)
Publication Date:
OSTI Identifier:
21583326
Resource Type:
Journal Article
Journal Name:
Annals of Physics (New York)
Additional Journal Information:
Journal Volume: 326; Journal Issue: 8; Other Information: DOI: 10.1016/j.aop.2011.04.011; PII: S0003-4916(11)00070-4; Copyright (c) 2011 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Journal ID: ISSN 0003-4916
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACTION INTEGRAL; ANHARMONIC OSCILLATORS; COUPLING; DISTURBANCES; EXPANSION; MATRICES; ONE-DIMENSIONAL CALCULATIONS; OSCILLATORS; PERTURBATION THEORY; POTENTIALS; QUANTUM MECHANICS; RENORMALIZATION; SCALING LAWS; SENSITIVITY; SYMMETRY; WAVE FUNCTIONS; ELECTRONIC EQUIPMENT; EQUIPMENT; FUNCTIONS; INTEGRALS; MECHANICS

Citation Formats

Nagy, S, and Sailer, K. Functional renormalization group for quantized anharmonic oscillator. United States: N. p., 2011. Web. doi:10.1016/j.aop.2011.04.011.
Nagy, S, & Sailer, K. Functional renormalization group for quantized anharmonic oscillator. United States. doi:10.1016/j.aop.2011.04.011.
Nagy, S, and Sailer, K. Mon . "Functional renormalization group for quantized anharmonic oscillator". United States. doi:10.1016/j.aop.2011.04.011.
@article{osti_21583326,
title = {Functional renormalization group for quantized anharmonic oscillator},
author = {Nagy, S and Sailer, K},
abstractNote = {Highlights: > RG analysis with field dependent wavefunction renormalization. > The Taylor expansion does not work for the wavefunction renormalization. > The gap energy is RG scheme-dependent. > The O (N) symmetric anharmonic oscillator exhibits only a single phase. > The evolution equation for the 2PI effective action for the oscillator is solved. - Abstract: Functional renormalization group methods formulated in the real-time formalism are applied to the O(N) symmetric quantum anharmonic oscillator, considered as a 0 + 1 dimensional quantum field-theoric model, in the next-to-leading order of the gradient expansion of the one- and two-particle irreducible effective action. The infrared scaling laws and the sensitivity-matrix analysis show the existence of only a single, symmetric phase. The Taylor expansion for the local potential converges fast while it is found not to work for the field-dependent wavefunction renormalization, in particular for the double-well bare potential. Results for the gap energy for the bare anharmonic oscillator potential hint on improving scheme-independence in the next-to-leading order of the gradient expansion, although the truncated perturbation expansion in the bare quartic coupling provides strongly scheme-dependent results for the infrared limits of the running couplings.},
doi = {10.1016/j.aop.2011.04.011},
journal = {Annals of Physics (New York)},
issn = {0003-4916},
number = 8,
volume = 326,
place = {United States},
year = {2011},
month = {8}
}