An Adiabatic Theorem for Singularly Perturbed Hamiltonians
| dc.creator | Joye, Alain | |
| dc.date | 1994-11-02 | |
| dc.date.accessioned | 2026-07-07T09:13:30Z | |
| dc.date.available | 2026-07-07T09:13:30Z | |
| dc.description | The adiabatic approximation in quantum mechanics is considered in the case where the self-adjoint hamiltonian $H_0(t)$, satisfying the usual spectral gap assumption in this context, is perturbed by a term of the form $εH_1(t)$. Here $ε\to 0$ is the adiabaticity parameter and $H_1(t)$ is a self-adjoint operator defined on a smaller domain than the domain of $H_0(t)$. Thus the total hamiltonian $H_0(t)+εH_1(t)$ does not necessarily satisfy the gap assumption, $\forall ε>0$. It is shown that an adiabatic theorem can be proven in this situation under reasonnable hypotheses. The problem considered can also be viewed as the study of a time-dependent system coupled to a time-dependent perturbation, in the limit of large coupling constant. | |
| dc.description | 17 pages, LaTex | |
| dc.identifier | https://arxiv.org/abs/funct-an/9411001 | |
| dc.identifier | http://arxiv.org/abs/funct-an/9411001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152348 | |
| dc.subject | Functional Analysis | |
| dc.title | An Adiabatic Theorem for Singularly Perturbed Hamiltonians | |
| dc.type | text |