The time-dependent Schrödinger equation, the most fundamental equation
governing the dynamics of many-particle systems, can be expressed in the
form of quantum density-matrix equations, which provide insight into a link between microscopic quantum mechanics
and mesoscopic/macroscopic transport. By means of this formalism, we have
been analyzing diverse phenomena such as quantum oscillation of an electron
induced by nonadiabatic perturbation, nonlinear response of electron gas
to an impurity, plasma oscillation, atomic multiphoton ionization, etc[1].
Wigner density operator formalism is suitable to construct quantum kinetic
theories of plasmas. The ac electric conductivity (optical conductivity)
, which is controlled by quantum inelastic scattering between electrons
and ions, can be described by the generalized Drude model [2]; it is a
nontrivial issue whether its zero-frequency limit coincides with the usual
dc conductivity [2].
X-ray free-electron lasers have enabled one to excite inner-shell electrons
in solids within femtosecond time scales and to change their electronic
structures and optical constants drastically [3]. Time-dependent Hartree-Fock
calculations have predicted a shift of the absorption edge in metallic
copper, which can be interpreted as a third-order nonlinear effect [4].
Collisional relaxation dynamics of high-energy electrons produced by X-ray
irradiation is relevant to the stopping power or damage problems in radiation
physics [5].
Lattice vibration in solids is a actually a complex superposition of collective
motions at long wavelengths and individual atomic motions at short wavelengths.
With the aid of the Debye model, we have been developing a multiphonon
scattering theory of dynamic structure factors describing the density fluctuation
spectra in solids over the entire wavelength and frequency regime.
Fig. 1: Quantum oscillation of an electron induced by a suddenly applied potential well.
Fig. 2: Thermalization dynamics of primary and secondary electrons in metallic
copper.