Доповідач
Опис
Correlations effect on driven dynamics of complex quantum systems
S. V. Radionov
Institute for Nuclear Research, National Academy of Sciences of Ukraine, Kyiv, Ukraine
I study the perturbative response of a complex quantum system on time variations of a classical external variable $Q$. Such a study is important to clarify the nature of dissipative and fluctuative properties of large-amplitude collective motion in highly-excited heavy nuclei.
The driven quantum dynamics is considered in adiabatic basis of the system's Hamilton operator $\hat{H}[Q(t)]$. Within a random matrix approach, I derived non-Markovian master equation for the occupancies, $|a_{nn} |^{2} (t)$, of the adiabatic states:
$$\frac{d|a_{nn} |^{2} (t)}{dt} =-\dot{Q}(t)\int _{0}^{t}\dot{Q}(t')dt'\sum _{m\ne n}K(t-t')\left[|a_{nn} |^{2} (t')-|a_{mm} |^{2} (t')\right].$$ Here, the memory kernel, $K(t-t')$, is proportional to the distribution of the coupling matrix elements $\left(\partial \hat{H}(Q)/\partial Q\right)_{nm}$, which are treated as independent normally distributed random numbers with zero mean value and autocorrelation function: $$\left\langle \left(\frac{\partial \hat{H}}{\partial Q} \right)_{nm} (Q)\left(\frac{\partial \hat{H}}{\partial Q} \right)_{n'm'} (Q')\right\rangle \propto \frac{1}{1+([E_{n} -E_{m} ]/\Gamma )^{2} } \times \exp \left(-\frac{|Q-Q'|}{\xi } \right).$$ The spreading width $\Gamma$ measures the overlap between the complex eigen-states of the system's Hamilton operator and the correlation width $\xi$ is introduced to include into consideration possible correlations between the coupling matrix elements, caused by their dependence on the macroscopic variable $Q(t)$. By requiring the constancy of an expectation value of the $\hat{H}[Q(t)]$, I obtained an equation of motion for the classical macroscopic variable $Q(t)$. This equation was then applied to schematic description of the fission width and time of descent from the fission barrier of highly-excited heavy nuclei. I measured the impact of the parameters of the coupling matrix elements' distribution on the nuclear fission's observables.
