Functional renormalization group for quantized anharmonic oscillator

Journal Article · Mon Aug 15 00:00:00 EDT 2011 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2011.04.011· OSTI ID:21583326

Nagy, S ^[1]; Sailer, K ^[1]

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1. Department of Theoretical Physics, University of Debrecen, P.O. Box 5, H-4010 Debrecen (Hungary)

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.

• OSTI ID: 21583326
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 8 Vol. 326; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ACTION INTEGRAL
ANHARMONIC OSCILLATORS
COUPLING
DISTURBANCES
ELECTRONIC EQUIPMENT
EQUIPMENT
EXPANSION
FUNCTIONS
INTEGRALS
MATRICES
MECHANICS
ONE-DIMENSIONAL CALCULATIONS
OSCILLATORS
PERTURBATION THEORY
POTENTIALS
QUANTUM MECHANICS
RENORMALIZATION
SCALING LAWS
SENSITIVITY
SYMMETRY
WAVE FUNCTIONS