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| HAL: hal-00448868, version 1 |
| arXiv: 1001.3665 |
| Detailed view |  Export this paper |
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| Available versions: | v1 (2010-01-20) | v2 (2010-02-12) | v3 (2010-02-22) | v4 (2010-05-31) |
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| Adiabatic evolution of 1D shape resonances: an artificial interface conditions approach. |
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Ali Faraj 1Andrea Mantile 1 |
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| (2010-01-20) |
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| Artificial interface conditions parametrized by a complex number $\theta_{0}$ are introduced for 1D-Schr{ö}dinger operators. When this complex parameter equals the parameter $\theta\in i\R$ of the complex deformation which unveils the shape resonances, the Hamiltonian becomes dissipative. This makes possible an adiabatic theory for the time evolution of resonant states for arbitrarily large time scales. The effect of the artificial interface conditions on the important stationary quantities involved in quantum transport models is also checked to be as small as wanted, in the polynomial scale $(h^N)_{N\in \N}$ as $h\to 0$, according to $\theta_{0}$. |
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| 1: | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| Subject | : | Mathematics/Analysis of PDEs Mathematics/Spectral Theory Physics/Quantum Physics |
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| Shape resonances – Spectral analysis – Asymptotic analysis – Adiabatic theory |
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| Attached file list to this document: | ||||||||||
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| hal-00448868, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00448868 | |
| oai:hal.archives-ouvertes.fr:hal-00448868 | |
| From: Ali Faraj | |
| Submitted on: Wednesday, 20 January 2010 12:20:09 | |
| Updated on: Thursday, 21 January 2010 14:49:07 | |
