The changes of the spin depolarization length in zinc-blende semiconductors when an external component of correlated noise is added to a static driving electric field are analyzed for different values of field strength, noise amplitude and correlatio
n time. Electron dynamics is simulated by a Monte Carlo procedure which keeps into account all the possible scattering phenomena of the hot electrons in the medium and includes the evolution of spin polarization. Spin depolarization is studied by examinating the decay of the initial spin polarization of the conduction electrons through the Dyakonov-Perel process, the only relevant relaxation mechanism in III-V crystals. Our results show that, for electric field amplitude lower than the Gunn field, the dephasing length shortens with the increasing of the noise intensity. Moreover, a nonmonotonic behavior of spin depolarization length with the noise correlation time is found, characterized by a maximum variation for values of noise correlation time comparable with the dephasing time. Instead, in high field conditions, we find that, critically depending on the noise correlation time, external fluctuations can positively affect the relaxation length. The influence of the inclusion of the electron-electron scattering mechanism is also shown and discussed.
The evolutionary dynamics of a system of cancerous cells in a model of chronic myeloid leukemia (CML) is investigated by a statistical approach. Cancer progression is explored by applying a Monte Carlo method to simulate the stochastic behavior of ce
ll reproduction and death in a population of blood cells which can experience genetic mutations. In CML front line therapy is represented by the tyrosine kinase inhibitor imatinib which strongly affects the reproduction of leukemic cells only. In this work, we analyze the effects of a targeted therapy on the evolutionary dynamics of normal, first-mutant and cancerous cell populations. Several scenarios of the evolutionary dynamics of imatinib-treated leukemic cells are described as a consequence of the efficacy of the different modeled therapies. We show how the patient response to the therapy changes when an high value of the mutation rate from healthy to cancerous cells is present. Our results are in agreement with clinical observations. Unfortunately, development of resistance to imatinib is observed in a proportion of patients, whose blood cells are characterized by an increasing number of genetic alterations. We find that the occurrence of resistance to the therapy can be related to a progressive increase of deleterious mutations.
