Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2000-12-15
Physics
Condensed Matter
Strongly Correlated Electrons
4 pages
Scientific paper
During the adiabatic time evolution levels crossing violates the adiabaticity and makes transitions between levels possible. Conventionally only two energy levels cross simultaneously. The transition probabilities for this case were found by Landau and Zener. However, the multilevel crossing happens systematically rather than occasionally if the Hamiltonian possesses a special symmetry. The simplest physical realization of the multilevel crossing are the Zeeman multiplet in a varying magnetic field and an electron in one-dimensional chain driven by the time-dependent electric field. We present asymptotics of the transition amplitudes for these kinds of the multilevel crossing. They are based on an exact solution for a model n-state, time-dependent Schr\"{o}dinger equation.
Pokrovsky Valery L.
Sinitsyn Nikolai A.
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