On Schr{umlt o}dinger equations with concentrated nonlinearities

Journal Article · Mon May 01 04:00:00 EDT 1995 · Annals of Physics (New York)

DOI:https://doi.org/10.1006/aphy.1995.1040· OSTI ID:282098

Jona-Lasinio, G ^[1]; Presilla, C ^[1]; Sjoestrand, J ^[2]

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1. Dipartimento di Fisica, Universita di Roma ``La Sapienza,`` Piazzale A. Moro 2, Rome, (Italy) 00185
2. Departement de Mathematiques, Bat. 425, Universite de Paris-Sud, Orsay, (France) 91405

Schr{umlt o}dinger equations with nonlinearities concentrated in some regions of space are good models of various physical situations and have interesting mathematical properties. We show that in the semiclassical limit it is possible to separate the relevant degrees of freedom by noting that in the regions where the nonlinearities are effective all states are suppressed but the metastable ones (resonances). In this way the description of the nonlinear regions is reduced to ordinary differential equations weakly coupled to standard Schr{umlt o}dinger equations valid in the linear regions. The idea is illustrated through the study of a prototype equation recently proposed for resonant tunneling of electrons through a double barrier heterostructure and for which nonlinear oscillations have been numerically predicted. Copyright {copyright} 1995 Academic Press, Inc.

• Sponsoring Organization: USDOE
• OSTI ID: 282098
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 1 Vol. 240; ISSN APNYA6; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ADIABATIC APPROXIMATION
ANHARMONIC OSCILLATORS
HETEROSTRUCTURES
NONLINEAR PROBLEMS
NUMERICAL SOLUTION
RESONANCE
SCHROEDINGER EQUATION
SINGLE-PARTICLE MODES
TUNNEL EFFECT