Nonlinear doublewell Schrödinger equations in the semiclassical limit

Journal of Statistical Physics

Volumn 119, Issue 5-6, 2005, Pages 1347-1382

  Sacchetti, Andrea ^a  

^a UNIVERSITY OF MODENA AND REGGIO EMILIA   (Italy)

Author keywords

Gross Pitaevskii equation; Nonlinear Schr dinger operator; Norm estimate of solutions

Indexed keywords

EID: 23744466181     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10955-005-3766-x     Document Type: Article

References (16)

1. W. H. Aschbacher, J. Froehlich, G. M. Graf, K. Schnee, and M. Troyer, Symmetry breaking regime in the nonlinear Hartree equation, J. Math. Phys. 43:3879-3891 (2002).
2. F. A. Berezin and M. A. Shubin, The Schrödinger equation, (Kluwer Academic publishers, 1991).
3. R. Carles, Nonlinear Schrödinger equations with repulsive harmonic potential and applications, SIAM J. Math. Anal. 35:823-843 (2003).
4. 1, Manuscripta Math. 61:477-494 (1988).
5. T. Cazenave, Semilinear Schrödinger Equations: Courant Lecture Notes in Mathematics (New York, 2003).
6. J. Ginibre, An Introduction to Nonlinear Schrödinger Equations in Nonlinear waves, R. Agemi, Y. Giga, T. Ozawa, eds. (1997).
7. V. Grecchi and A. Martinez Non-linear Stark effect and molecular localization, Comm. Math. Phys. 166:533-548 (1995).
8. V. Grecchi, A. Martinez and A. Sacchetti, Destruction of the beating effect for a nonlinear Schrödinger equation, Comm. Math. Phys. 227:191-209 (2002).
9. B. Helffer and J. Sjöstrand, Multiple wells in the semi-classical limit I. Comm. P.D.E. 9:337-408 (1984).
10. B. Helffer, Semi-Classical Analysis for the Schrödinger Operator and Applications: Lecture Notes in Mathematics 1336 (Springer-Verlag: Berlin Heidelberg, 1988).
11. G. Jona-Lasinio, C. Presilla, and C. Toninelli, Interaction induced localization in a gas of pyramidal molecules, Phys. Rev. Lett. 88:123001 (2002).
12. E. H. Lieb, R. Seiringer, J. Yngvason, A rigorous derivation of the Gross-Pitaevskii energy functional for a two-dimensional Bose gas, Comm. Math. Phys. 224:17-31 (2001).
13. S. Raghavan, A. Smerzi, S. Fantoni, and S. R. Shenoy Coherent oscillations between two weakly coupled Bose-Einstein condensates: Josephson effects, π oscillations, and macroscopic quantum self-trapping, Phys. Rev. A 59:620-633 (1999).
14. A. Sacchetti, Nonlinear time-dependent one-dimensional Schrödinger equation with double well potential, SIAM J. Math. Anal. 35:1160-1176 (2003).
15. C. Sulem and P. L. Sulem, The Nonlinear Schrödinger Equation: Self-focusing and Wave Collapse. (Springer-Verlag, New York 1999).
16. A. Vardi and J. R. Anglin, Bose-Einstein condensates beyond mean field theory: Quantum back reaction as decoherence, Phys. Rev. Lett. 86:568-571 (2001).