2000/12/15 by V. L. Pokrovsky, Nikolai A. Sinitsyn, Pokrovsky, V. L. +2
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Quantum chaos and dynamical systems #Spectroscopy and Quantum Chemical Studies #Strongly Correlated Electrons (cond-mat.str-el) #cond-mat.str-el
paper · pdf · doi:10.48550/arxiv.cond-mat/0012303
4 pages
arxiv created 2000/12/15 · openalex publication_date 2000/12/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Schrödinger equation.