Quantum Dot Potentials: Symanzik Scaling, Resurgent Expansions and Quantum Dynamics
| dc.creator | Surzhykov, A. | |
| dc.creator | Lubasch, M. | |
| dc.creator | Zinn-Justin, J. | |
| dc.creator | Jentschura, U. D. | |
| dc.date | 2006-09-01 | |
| dc.date | 2006-11-27 | |
| dc.date.accessioned | 2026-07-07T07:23:24Z | |
| dc.date.available | 2026-07-07T07:23:24Z | |
| dc.description | This article is concerned with a special class of the ``double-well-like'' potentials that occur naturally in the analysis of finite quantum systems. Special attention is paid, in particular, to the so-called Fokker-Planck potential, which has a particular property: the perturbation series for the ground-state energy vanishes to all orders in the coupling parameter, but the actual ground-state energy is positive and dominated by instanton configurations of the form exp(-a/g), where a is the instanton action. The instanton effects are most naturally taken into account within the modified Bohr-Sommerfeld quantization conditions whose expansion leads to the generalized perturbative expansions (so-called resurgent expansions) for the energy values of the Fokker-Planck potential. Until now, these resurgent expansions have been mainly applied for small values of coupling parameter g, while much less attention has been paid to the strong-coupling regime. In this contribution, we compare the energy values, obtained by directly resumming generalized Bohr-Sommerfeld quantization conditions, to the strong-coupling expansion, for which we determine the first few expansion coefficients in powers of g^(-2/3). Detailed calculations are performed for a wide range of coupling parameters g and indicate a considerable overlap between the regions of validity of the weak-coupling resurgent series and of the strong-coupling expansion. Apart from the analysis of the energy spectrum of the Fokker-Planck Hamiltonian, we also briefly discuss the computation of its eigenfunctions. These eigenfunctions may be utilized for the numerical integration of the (single-particle) time-dependent Schroedinger equation and, hence, for studying the dynamical evolution of the wavepackets in the double-well-like potentials. | |
| dc.description | 13 pages; RevTeX | |
| dc.identifier | https://arxiv.org/abs/cond-mat/0609027 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0609027 | |
| dc.identifier | Phys.Rev.B 74 (2006) 205317 | |
| dc.identifier | doi:10.1103/PhysRevB.74.205317 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115968 | |
| dc.subject | Other Condensed Matter | |
| dc.title | Quantum Dot Potentials: Symanzik Scaling, Resurgent Expansions and Quantum Dynamics | |
| dc.type | text |