Excitation threshold for the discrete coupled Schroedinger lattice system

Journal Article · Tue Feb 15 00:00:00 EST 2011 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3548078· OSTI ID:21501276

Ming, Cheng ^[1]

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1. College of Mathematics, Jilin University, Changchun 130012 (China)

This paper is concerned with the excitation threshold for the ground state in the coupled discrete nonlinear Schroedinger lattice system. Excitation threshold is characterized by the variational methods. We establish the existence of the excitation threshold connected with the dimensionality d of the lattice. We prove that if d{>=} 2, then the excitation threshold exists and the ground state exists if and only if the total power is greater than the excitation threshold. The compactness of the minimizing sequence follows by the concentration compactness principle. We also prove the upper estimates on the excitation threshold and the frequency of the ground state.

• OSTI ID: 21501276
• Journal Information: Journal of Mathematical Physics, Vol. 52, Issue 2; Other Information: DOI: 10.1063/1.3548078; (c) 2011 American Institute of Physics; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
EXCITATION
GROUND STATES
LATTICE FIELD THEORY
NONLINEAR PROBLEMS
SCHROEDINGER EQUATION
VARIATIONAL METHODS
CALCULATION METHODS
CONSTRUCTIVE FIELD THEORY
DIFFERENTIAL EQUATIONS
ENERGY LEVELS
ENERGY-LEVEL TRANSITIONS
EQUATIONS
FIELD THEORIES
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM FIELD THEORY
WAVE EQUATIONS