Nonlinear subelliptic Schrodinger equations with external magnetic field
| dc.contributor.author | Tintarev, Kyril | |
| dc.date.accessioned | 2021-05-14T17:03:04Z | |
| dc.date.available | 2021-05-14T17:03:04Z | |
| dc.date.issued | 2004-10-18 | |
| dc.description.abstract | To account for an external magnetic field in a Hamiltonian of a quantum system on a manifold (modelled here by a subelliptic Dirichlet form), one replaces the momentum operator 1/i d in the subelliptic symbol by 1/i d - α, where α ∈ TM* is called a magnetic potential for the magnetic field β =dα. We prove existence of ground state solutions (Sobolev minimizers) for non-linear Schrödinger equation associated with such Hamiltonian on a generally, non-compact Riemannian manifold, generalizing the existence result of Esteban-Lions [5] for the nonlinear Schrödinger equation with a constant magnetic field on ℝN and the existence result of [6] for a similar problem on manifolds without a magnetic field. The counterpart of a constant magnetic field is the magnetic field, invariant with respect to a subgroup of isometries. As an example to the general statement we calculate the invariant magnetic fields in the Hamiltonians associated with the Kohn Laplacian and for the Laplace-Beltrami operator on the Heisenberg group. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 9 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.citation | Tintarev, K. (2004). Nonlinear subelliptic Schrodinger equations with external magnetic field. Electronic Journal of Differential Equations, 2004(123), pp. 1-9. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/13544 | |
| dc.language.iso | en | |
| dc.publisher | Texas State University-San Marcos, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 2004, San Marcos, Texas: Texas State University-San Marcos and University of North Texas. | |
| dc.subject | Homogeneous spaces | |
| dc.subject | Magnetic field | |
| dc.subject | Schrödinger operator | |
| dc.subject | Subelliptic operators | |
| dc.subject | Semilinear equations | |
| dc.subject | Weak convergence | |
| dc.subject | Concentration compactness | |
| dc.title | Nonlinear subelliptic Schrodinger equations with external magnetic field | |
| dc.type | Article |