Dissipative dynamics within stochastic mean-field approach

Year 2019, , 104 - 108, 27.12.2019

İbrahim Ulgen , Bulent Yılmaz

https://doi.org/10.17678/beuscitech.633558

Abstract

The
time-dependent Hartree-Fock (TDHF) and density functional theory (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 (SMF) approach was proposed (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 (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

Supporting Institution

TUBITAK

Project Number

2211-A

Thanks

This work was supported in part by the Scientific and Technological Research Council of Turkey (TUBITAK).

References

• Ayik, S., 2008. A stochastic mean-field approach for nuclear dynamics. Phys. Lett. B 658, 174.
• Ayik, S., Yilmaz, B., Yilmaz O., and Umar, A. S., 2019. Quantal diffusion approach for multinucleon transfers in Xe + Pb collisions, Phys. Rev. C 100, 014609 .
• Bogoliubov, N. N., 1946. Kinetic Equations, J. Phys. (URSS) 10, 256.
• Born, H. and Green, H.S., 1946. A general kinetic theory of liquids I. The molecular distribution functions. Proc. R. Soc. A 188, 10.
• Essler, F. H. L. Frahm, H., Göhmann, F., Klümper, A. and Korepin, E., 2005. The One-Dimensional Hubbard Model. Cambridge University Press.
• Jafari, S. A., 2008. Introduction to Hubbard model and exact diagonalization. IJPR 8, 113.
• Kingsley, O. N. and Robinson, O., 2013. Exact Diagonalization of the Hubbard Model: Ten-electrons on Ten-sites. Res. J. Appl. Sci. Eng. Technol., 6(21), 4098.
• Lin, H. Q., 1990. Exact diagonalization of quantum-spin models. Phys. Rev. B 42, 6561.
• Lin, H. Q. and Gubernatis J. E., 1993. Exact diagonalization methods for quantum systems. Computers in Physics, 7, 400.
• Kirwood, J.G., 1946. The statistical mechanical theory of transport processes I. General theory. J. Chem. Phys. 14, 180.
• Lacroix, D., Hermanns, S., Hinz, C. M. and Bonitz, M., 2014. Ultrafast dynamics of finite Hubbard clusters: A stochastic mean-field approach. Phys. Rev. B 90, 125112.
• Lacroix, D. and Ayik, S., 2014. Stochastic quantum dynamics beyond mean field, Eur. Phys. J. A 50: (94).
• Polkovnikov, A., 2003. Quantum corrections to the dynamics of interacting bosons: Beyond the truncated Wigner approximation. Phys. Rev. A 68, 053604.
• Siro, T. and Harju, A., 2012. Exact diagonalization of the Hubbard model on graphics processing units. Comp. Phys. Comm. 183, 1884.
• Ulgen I., Yilmaz, B., Lacroix, D., 2019. Impact of the initial fluctuations on the dissipative dynamics of interacting Fermi systems: a model case study, arXiv:1908.05520v1.
• Yilmaz, B., Ayik, S., Yilmaz O., and Umar, A. S., 2018. Multinucleon transfer in 58Ni+60Ni and 60Ni+60Ni in a stochastic mean-field approach, Phys. Rev. C 98, 034604.