General response formula and application to topological insulator in quantum open system

Area of Science:

• Quantum Physics
• Condensed Matter Physics
• Statistical Mechanics

Background:

• Quantum linear response theory relies on first-order perturbation theory, limiting its application to systems in thermal equilibrium.
• This theory is inadequate for systems in steady states far from thermal equilibrium where higher-order perturbations are significant.

Purpose of the Study:

• To develop a nonlinear response theory for quantum open systems operating far from thermal equilibrium.
• To apply this theory to derive Hall conductance for open systems at finite temperatures.
• To investigate the robustness of topological phase transitions in quantum open systems.

Main Methods:

• Formulation of a general nonlinear response theory for quantum open systems.
• Application of the theory to derive Hall conductance using a two-band model.
• Calculation of Hall conductance for a two-dimensional ferromagnetic electron gas and a lattice model.

Main Results:

• The derived nonlinear response theory successfully calculates Hall conductance in open systems.
• Topological phase transition points are shown to be robust against environmental influences.
• The study provides a framework for manipulating nonlinear responses in quantum open systems.

Conclusions:

• The developed nonlinear response theory is applicable to quantum open systems beyond thermal equilibrium.
• Environmental effects do not destabilize topological phase transitions in the studied models.
• This research offers potential for advancements in quantum information processing and statistical physics through coherent manipulation of nonlinear responses.