Stability and control of a 1D quantum system with confining time dependent delta potentials

作者: Andrea Mantile

DOI: 10.1088/1751-8113/44/14/145305

关键词:

摘要: The evolution problem for a quantum particle confined in 1D box and interacting with one fixed point through time dependent interaction is considered. Under suitable assumptions of regularity the profile Hamiltonian, we prove existence strict solutions to corresponding Schrodinger equation. result used discuss stability steady-state local controllability wavefunction when strenght as control parameter.

参考文章(17)
J. Kisyński, Sur les opérateurs de Green des problèmes de Cauchy abstraits Studia Mathematica. ,vol. 23, pp. 285- 328 ,(1964) , 10.4064/SM-23-3-285-328
Adalbert Kerber, Hector O. Fattorini, The Cauchy problem ,(1984)
Antonio Ambrosetti, G. Prodi, A primer of nonlinear analysis ,(1993)
Barry Simon, Michael Reed, Methods of Modern Mathematical Physics ,(1972)
G.F. Dell'Antonio, R. Figari, A. Teta, A Limit Evolution Problem for Time-Dependent Point Interactions Journal of Functional Analysis. ,vol. 142, pp. 249- 275 ,(1996) , 10.1006/JFAN.1996.0149
Riccardo Adami, Alessandro Teta, A Class of Nonlinear Schrödinger Equations with Concentrated Nonlinearity Journal of Functional Analysis. ,vol. 180, pp. 148- 175 ,(2001) , 10.1006/JFAN.2000.3697
Vahagn Nersesyan, Growth of Sobolev Norms and Controllability of the Schrödinger Equation Communications in Mathematical Physics. ,vol. 290, pp. 371- 387 ,(2009) , 10.1007/S00220-009-0842-0
Karine Beauchard, Local controllability of a 1-D Schrödinger equation Journal de Mathématiques Pures et Appliquées. ,vol. 84, pp. 851- 956 ,(2005) , 10.1016/J.MATPUR.2005.02.005
Toufik Hmidi, Andrea Mantile, Francis Nier, Time-dependent Delta-interactions for 1D Schrödinger Hamiltonians Mathematical Physics Analysis and Geometry. ,vol. 13, pp. 83- 103 ,(2010) , 10.1007/S11040-009-9070-2
S. Albeverio, Z. Brzezniak, L. Dabrowski, Fundamental Solution of the Heat and Schrödinger Equations with Point Interaction Journal of Functional Analysis. ,vol. 130, pp. 220- 254 ,(1995) , 10.1006/JFAN.1995.1068