Projects / Programmes
Nonlinear dynamics and applied mathematics
| Code |
Science |
Field |
Subfield |
| 1.02.02 |
Natural sciences and mathematics |
Physics |
Theoretical physics |
| Code |
Science |
Field |
| P190 |
Natural sciences and mathematics |
Mathematical and general theoretical physics, classical mechanics, quantum mechanics, relativity, gravitation, statistical physics, thermodynamics |
| P240 |
Natural sciences and mathematics |
Gases, fluid dynamics, plasmas |
nonlinear dynamics, chaos theory, Hamiltonian systems, quantum chaos, integrability, morphology of eigenstates, statistics of energy spectra and of matrix elements, semiclassical methods, tunneling effects
Researchers (3)
| no. |
Code |
Name and surname |
Research area |
Role |
Period |
No. of publicationsNo. of publications |
| 1. |
19199 |
George Krylov |
Physics |
Researcher |
1999 - 2001 |
3 |
| 2. |
18141 |
PhD Junxian Liu |
Physics |
Researcher |
1996 - 2001 |
5 |
| 3. |
11337 |
PhD Marko Robnik |
Physics |
Head |
1998 - 2001 |
363 |
Organisations (1)
Abstract
Broad and detailed understanding of some major problems in quantum chaos, especially the stationary problem: morphology of eigenstates (eigenfunctions in configuration space and their Wigner functions in the phase space), their structural (global and local) properties, statistical properties, statistics of energy spectra and of the matrix elements of other observables, and the analysis of universality classes (GOE/GUE for classical ergodicity, and Poisson for classical integrability), and in the first place study of generic systems in the transition region between integrability and ergodicity. Here we deal with the study of the principle of uniform semiclassical condensation of the Wigner functions in the semiclassical limit, its application, and deviation from it (dynamical quantum localization, when the effective Planck constant is not large enough). We study also the semiclassical methods (WKB methods in one and higher dimensions, and develop the powerful numerical methods). The model systems are billiards, quantum dots, hydrogen atom in strong magnetic field, helium atom, and others. The results are important e.g. for the nanotechnology of mesoscopic systems as the foundation for the electronic technology of new generation. We also study the still open problems of chaotic behaviour in generic classical Hamiltonian systems relevant for quantum chaos. We shall take up problems in fluid mechanics, plasma theory and computer algebra when we get the financial support and the man power.
