Space-Adiabatic Perturbation Theory
| dc.creator | Panati, Gianluca | |
| dc.creator | Spohn, Herbert | |
| dc.creator | Teufel, Stefan | |
| dc.date | 2002-01-25 | |
| dc.date | 2003-12-24 | |
| dc.date.accessioned | 2026-07-07T04:28:57Z | |
| dc.date.available | 2026-07-07T04:28:57Z | |
| dc.description | We study approximate solutions to the Schrödinger equation $i\epsi\partialψ_t(x)/\partial t = H(x,-i\epsi\nabla_x) ψ_t(x)$ with the Hamiltonian given as the Weyl quantization of the symbol $H(q,p)$ taking values in the space of bounded operators on the Hilbert space $\Hi_{\rm f}$ of fast ``internal'' degrees of freedom. By assumption $H(q,p)$ has an isolated energy band. Using a method of Nenciu and Sordoni \cite{NS} we prove that interband transitions are suppressed to any order in $\epsi$. As a consequence, associated to that energy band there exists a subspace of $L^2(\mathbb{R}^d,\Hi _{\rm f})$ almost invariant under the unitary time evolution. We develop a systematic perturbation scheme for the computation of effective Hamiltonians which govern approximately the intraband time evolution. As examples for the general perturbation scheme we discuss the Dirac and Born-Oppenheimer type Hamiltonians and we reconsider also the time-adiabatic theory. | |
| dc.description | 49 pages | |
| dc.identifier | https://arxiv.org/abs/math-ph/0201055 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0201055 | |
| dc.identifier | Adv. Theor. Math. Phys. 7 (2003) 145-204 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/56983 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 81Q05, 81Q15 | |
| dc.title | Space-Adiabatic Perturbation Theory | |
| dc.type | text |