Fluctuation Approach to Many-Body Quantum Dynamics

The dynamics of quantum many-body systems following external excitation is of great interest in many areas such as dense plasmas or correlated solids. At present, only the formalism of nonequilibrium Green functions (NEGF) can rigorously describe such processes in more than one dimension. However, NEGF simulations are computationally expensive, among other things, due to their cubic scaling with simulation time T. Only recently, linear scaling with T could be achieved within the G1-G2 scheme [1]. Here a new fluctuation based approach to the NEGF formalism is presented. While in theory the resulting equations are fully equivalent to the G1-G2 scheme, in practice the new approach has interesting complementary features such as the capability to simulate many-body effects using stochastic methods [2], which further reduce the computational complexity and increase numerical stability for stronger coupling. Additionally, this approach provides direct access to spectral two-particle quantities such as the density response function or polarizability. 

[1] N. Schlünzen et al., Phys. Rev. Lett. 124, 076601 (2020)

[2] D. Lacroix et al., Phys. Rev. B  90, 125112 (2014)