Solution to the double-well nonlinear Schrödinger equation with Stark-type external field

作者: Andrea Sacchetti

DOI: 10.1088/1751-8113/48/3/035303

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摘要: Here we consider one- and two-dimensional nonlinear Schrodinger equations with double well potential a Stark-type perturbation term. In the semiclassical limit give an explicit solution to these for times of order unperturbed beating period, up exponentially small remainder particular, it turns out that has periodic behavior period is explicitly computed.

参考文章(29)
Thierry Cazenave, Semilinear Schrodinger Equations ,(2003)
I. Faragó, Splitting methods and their application to the abstract cauchy problems international conference on numerical analysis and its applications. pp. 35- 45 ,(2004) , 10.1007/978-3-540-31852-1_4
C. Presilla, G. Jona-Lasinio, C. Toninelli, Classical versus Quantum Structures: The Case of Pyramidal Molecules Multiscale Methods in Quantum Mechanics. pp. 119- 127 ,(2004) , 10.1007/978-0-8176-8202-6_10
T. Cazenave, A. Haraux, OSCILLATORY PHENOMENA ASSOCIATED TO SEMILINEAR WAVE EQUATIONS IN ONE SPATIAL DIMENSION Transactions of the American Mathematical Society. ,vol. 300, pp. 207- 233 ,(1987) , 10.1090/S0002-9947-1987-0871673-2
B. V. Hall, S. Whitlock, R. Anderson, P. Hannaford, A. I. Sidorov, Condensate splitting in an asymmetric double well for atom chip based sensors. Physical Review Letters. ,vol. 98, pp. 030402- ,(2007) , 10.1103/PHYSREVLETT.98.030402
Immanuel Bloch, Ultracold quantum gases in optical lattices Nature Physics. ,vol. 1, pp. 23- 30 ,(2005) , 10.1038/NPHYS138
Vincenzo Grecchi, André Martinez, Andrea Sacchetti, Destruction of the Beating Effect for a Non-Linear Schrödinger Equation Communications in Mathematical Physics. ,vol. 227, pp. 191- 209 ,(2002) , 10.1007/S002200200643
I. Danshita, J. E. Williams, C. A. R. Sá de Melo, C. W. Clark, Quantum phases of bosons in double-well optical lattices Physical Review A. ,vol. 76, pp. 043606- ,(2007) , 10.1103/PHYSREVA.76.043606