Density-Matrix Theory of Quantum Dynamics under a Strong External Field Switched on Nonadiabatically

Quantum time-evolution equations for the density matrix are formulated in the unrestricted Hartree-Fock approximation, with an emphasis on the nonperturbative effect due to a sudden or gradual onset of a strong external field. Numerical simulations are performed for ideal Fermi gas around a squarewell potential which is switched on dynamically. When the switching is fast enough, an oscillatory motion of the particle is induced by a nonadiabatic transition at the Landau-Zener crossing point, which is most clearly seen in a small-size system. When the switching is sufficiently slow, the simulation corroborates the adiabatic theorem. It is shown that the Anderson's infrared catastrophe in a metal is strongly enhanced by the nonperturbative effect. The Keldysh formula of atomic multiphoton ionization can also be derived from the nonperturbative term in the density-matrix equation, indicating a wide applicability of the present theory. (C) 2014 Wiley Periodicals, Inc.