## Section: New Results

### Application of Vlasov codes in nanophysics

Participants : Nicolas Crouseilles, Paul-Antoine Hervieux, Giovanni Manfredi, Omar Morandi.

For a few works, our team has been involved in several research projects involving the application of Vlasov-like equations to the physics of nano-sized objects, such as thin metal films, nanoparticles, quantum wells and quantum dots. It is a topic with tremendous potential for a broad spectrum of applications, ranging from materials science to biology and medicine. Our approach – based on a phase-space description of the dynamics – is not widely used in the nanophysics community, which constitutes one of the originalities of our project.

#### Quantum hydrodynamics with spin

In previous years, a quantum hydrodynamical (QHD) model was used to investigate
the self-consistent electron dynamics in a thin metal film
[73] .
This QHD model can be viewed as a velocity-moment expansion of the quantum Vlasov (or Wigner) equation.
More recently, we have extended the QHD model to include the effect of *spin* .
In this model, the electron population is described by a two-component spinor that evolves according to
a modified Pauli equation. The numerical code is currently being validated
by comparison with some available exact solutions. It will also be necessary to develop a
realistic physical model for the spin-spin interactions. The first relevant results are expected for 2010.

#### Breather mode in a confined quantum electron gas

This work was performed in collaboration with F. Haas and P. Shukla, from the Theoretical Physics Department of the Ruhr Universität, Bochum (Allemagne).

By using a version of the quantum hydrodynamic model, we have demonstrated
the existence of a novel breather mode in
the self-consistent dynamics of a confined electron gas.
This mode corresponds to oscillations of *size* of the electron density,
as measured by the variance .
A variational method was used to determine the salient features of the
electron breather mode. Numerical simulations of the
time-dependent Wigner-Poisson equations were shown to be
in excellent agreement with our analytical results. For
asymmetric confinement, a signature of the breather mode is
observed in the dipole response, which can be detected by standard
optical means.

These results have potential applications to the electron dynamics of nanosized semiconductor devices, such as quantum dots and quantum wells.

#### Ultrafast magnetization dynamics in diluted magnetic semiconductors

We have developed a dynamical model that successfully explains the observed time evolution of the magnetization in diluted magnetic semiconductor quantum wells after weak laser excitation. Based on a many-particle expansion of the exact p-d exchange interaction, our approach goes beyond the usual mean-field approximation. It includes both the sub-picosecond demagnetization dynamics and the slower relaxation processes which restore the initial ferromagnetic order on a nanosecond timescale. In agreement with experimental results, our numerical simulations show that, depending on the value of the initial lattice temperature, a subsequent enhancement of the total magnetization may be observed on a timescale of few hundreds of picoseconds.

More recently, our model was augmented in order to include the role played by the quantum confinement and the band structure. It was shown that the sample thickness and the background hole density strongly influence the phenomenon of demagnetization. Quantitative results were given for III-V ferromagnetic GaMnAs quantum wells of thickness 4 and 6 nm.