Dissipative dynamics within stochastic mean-field approach

Authors : İbrahim ULGEN, Bulent YILMAZ

Pages : 104-108

Doi:10.17678/beuscitech.633558

View : 18 | Download : 7

Publication Date : 2019-12-27

Article Type : Conference Paper

Abstract :The time-dependent Hartree-Fock insert ignore into journalissuearticles values(TDHF); and density functional theory insert ignore into journalissuearticles values(DFT); are among the most useful approaches within mean-field theories for studying static and dynamic properties of complex many-body systems in different branches of physics. Despite the fact that they provide a good approximation for the average properties of one-body degrees of freedoms, they are known to fail to include quantal fluctuations of collective observables and they do not provide sufficient dissipation of collective motion. In order to incorporate these missing effects the stochastic mean-field insert ignore into journalissuearticles values(SMF); approach was proposed insert ignore into journalissuearticles values(Ayik 2008);. In the SMF approach a set of stochastic initial one-body densities are evolved. Each stochastic one-body density matrix consists of a set of stochastic Gaussian random numbers that satisfy the first and second moments of collective one-body observables. Recent works indicate that the SMF approach provides a good description of the dynamics of the nuclear systems insert ignore into journalissuearticles values(Yilmaz et al. 2018; Ayik et al. 2019);. In this work, the one-dimensional Fermi-Hubbard model is simulated with the SMF approach by using different distributions such as Gaussian, uniform, bimodal and two-point distributions. The dissipative dynamics are discussed and the predictive power of the SMF approach with different probability distributions are compared with each other and the exact dynamics. As a result it is shown that by considering different distributions, the predictive power of the SMF approach can be improved.
Keywords : Mean Field, Stochastic Mean Field, Fluctuation, Dissipation, The Fermi Hubbard Model