2011/12/19 by J. Chee, James Chee, Chee, James +3
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Quantum, superfluid, helium dynamics #Spectroscopy and Quantum Chemical Studies #cond-mat.mes-hall #math-ph #math.MP #quant-ph
paper · pdf · doi:10.48550/arxiv.1112.4283
arxiv created 2011/12/19 · openalex publication_date 2011/12/19 · arxiv updated 2011/12/20 · openalex created_date 2016/09/16 · openalex updated_date 2026/07/28
Consider the quantum evolution of a charged particle subjected to a uniform magnetic field and an electric field E(t) that exists for a finite period of time. The electric field can induce intra-Landau level transitions (magnetic translations) that do not change the energy of the particle. It may also induce energy changing inter-Landau level transitions. Our purpose in this paper is two-fold: We first demonstrate that the inter-Landau level transition probability is completely determined by the Fourier component of the electric field corresponding to the cyclotron frequency. Then we point out that the Fejer asymptotic form of Laguerre polynomials implies that no matter how small the Fourier component is inter-Landau level transition probability from a fixed Landau level to other energy levels can be arbitrarily close to 1 if the original Landau energy level is high enough, i.e., influenced by a given electric field, Landau levels of higher energy are less stable asymptotically and their transition probabilities are explicitly predicted by the Fejer formula.