Nonequilibrium open quantum systems with multiple bosonic and fermionic environments: A hierarchical equations of motion approach

Abstract

We present a hierarchical quantum master equation (HQME) approach, which allows a numerically exact simulation of nonequilibrium transport in general open quantum systems involving multiple bosonic and fermionic environments. The performance of the method is demonstrated for a model of a nanosystem, which involves interacting electronic and vibrational degrees of freedom and is coupled to fermionic and bosonic baths. The results show the intricate interplay of electronic and vibrational degrees of freedom in this nonequilibrium transport scenario for both voltage and thermally driven transport processes. Furthermore, the use of importance criteria to improve the efficiency of the method is discussed.

Spin Dynamics in Magnetic Nano-Junctions

“…Therefore, the dynamics of the magnetic junction is reduced to the central part only. To describe the dynamics of the magnetic junction, we use a hierarchical equations of motion approach [105,106]. For the case of non-interacting fermions, studied in present paper, the hierarchy of equations of motion for the auxiliary density matrices terminates at second tier exactly [107][108][109][110][111][112].…”

“…Namely, a quantum-classical equations of motion (QC-EOM) approach for open quantum systems. QC-EOM combines equations of motion for the classical spins with the hierarchical equations of motion approach for the conduction electrons [105,106]. Its advantage is that in the case of non-interacting fermions, the hierarchy is terminated exactly at the second tier [107][108][109][110][111][112].…”

Efficient Steady-State Solver for the Hierarchical Equations of Motion Approach: Formulation and Application to Charge Transport through Nanosystems

“…While we have focused on nonequilibrium charge transport in the present work, other interesting processes such as heat transport through single-molecule junctions − can also be investigated with the iterative steady-state solver. Furthermore, the extension of the method to systems that additionally include bosonic environments is possible . Because of the small amount of memory available on current GPGPU generations, such investigations have been restricted to small model systems. − Being efficient in terms of memory usage, the implementation of the proposed iterative method on GPGPU devices is thus very promising.…”

Hierarchical equations of motion approach to hybrid fermionic and bosonic environments: Matrix product state formulation in twin space

“…This closure has been reported to ease the stability and positivity issues of the HEOM approach at low temperatures. 84 By taking advantage of the self-similarity of the exponential functions with respect to a time-derivative, one can introduce a group of auxiliary density operators (ADOs) {ρ n,m (t)} and formulate a hierarchical set of equations of motion, 38,43,[85][86][87][88] dρ n,m (t)…”