On the Steady State Correlation Functions of Open Interacting Systems

Abstract

Abstract. We address the existence of steady state Green-Keldysh correlation functions of interacting fermions in mesoscopic systems for both the partitioning and partition-free scenarios. Under some spectral assumptions on the non-interacting model and for sufficiently small interaction strength, we show that the system evolves to a NESS which does not depend on the profile of the time-dependent coupling strength/bias. For the partitioned setting we also show that the steady state is independent of the initial state of the inner sample. Closed formulae for the NESS two-point correlation functions (Green-Keldysh functions), in the form of a convergent expansion, are derived. In the partitioning approach, we show that the 0 th order term in the interaction strength of the charge current leads to the Landauer-Büttiker formula, while the 1 st order correction contains the mean-field (Hartree-Fock) results.

Nonequilibrium density matrix in quantum open systems: Generalization for simultaneous heat and charge steady-state transport

“…[8][9][10][11][12][13][14][15]. It is also been argued that a system will always reach a steadystate if it is a (or if it is connected to another) system in the thermodynamic limit regardless the presence (or absence) of adiabatic switching of the interactions 15,38,39 . We are now facing different possible choices to perform the separation of the full Hamiltonian into H 0 and W .…”

“…In the asymptotic limit, the NE density matrix will have matrix elements spreading over all the three different subspaces. Since the NE density matrix is independent of the initial conditions in the steady state [8][9][10][11][12][13][14][15] , one can take a convenient choice for the initial conditions that makes the derivations more easily tractable 45 . Finally, the left and right electrodes are prepared in a Gibbs grand-canonical ensemble with density matrices ρ α (α = L, R)…”

“…In such approaches, the Gibbsian statistical mechanics method is extended to include steady-state NE conditions in the density matrix leading to the so-called NE statistical operator method (NESOM). More rigorous analysis of the existence and stability of the NE steady state have been performed using C * algebraic methods [8][9][10][11][12][13][14][15][16] . The existence of conducting steady states has also been critically discussed in Refs.…”

Nonequilibrium Thermodynamics and Steady State Density Matrix for Quantum Open Systems

“…The questions related to the possibility of reaching an NE steady-state have been addressed in [23][24][25][26][27][28][29][30][31]. It has also been argued that a system will always reach a steady-state if it is a (or if it is connected to another) system in the thermodynamic limit, regardless of the presence (or absence) of adiabatic switching of the interactions [32,33].…”

Nonequilibrium distribution functions for quantum transport: Universality and approximation for the steady state regime

“…[6][7][8][9][10]. Rigorous mathematical methods based on the C * algebra have been used to study the existence and stability of such NE steady state, i.e., its independence of the way the division into subsystems and reservoirs is performed and its stability against local perturbations, in the absence [11][12][13][14] and in the presence of interaction 15,16 .…”