Quantum Response Theory and Momentum-Space Gravity

Area of Science:

• Quantum physics
• Condensed matter theory
• Gravitational physics

Background:

• Dissipative multiband systems exhibit complex quantum phenomena.
• Understanding quantum geometry is crucial for describing system responses.
• Existing models may not fully capture gravitational aspects in these systems.

Purpose of the Study:

• To present a quantum response approach to momentum-space gravity.
• To investigate the role of quantum geometry and equations of motion.
• To classify nonlinear responses using a novel geometric tensor.

Main Methods:

• Utilizing a quantum response approach.
• Applying an interband Weyl transformation to dress quantum geometry.
• Analyzing contorsion and symplectic terms.
• Introducing a three-state quantum geometric tensor.

Main Results:

• Dressed quantum geometry and equations of motion in dissipative multiband systems.
• Clarified roles of contorsion and symplectic terms.
• Introduced a three-state quantum geometric tensor for nonlinear response classification.
• Identified a dual quantum geometric drag force in momentum space.

Conclusions:

• The quantum response approach provides new insights into momentum-space gravity.
• The three-state quantum geometric tensor is essential for geometric classification.
• The emergent drag force acts as an entropic source term in Einstein field equations.