Quantum

Kinematic Quantum Geometry

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Briefings

A new theoretical framework called Kinematic Quantum Geometry describes fast degrees of freedom that adiabatically follow slow ones, extending Born-Oppenheimer geometry by introducing mixed Berry curvatures. The framework modifies the effective theory governing slow degrees of freedom and has been tested in two setups: spinful particles in magnetic textures and Dirac electrons in graphene coupled to an LC circuit. In the first setup, it produces a velocity-dependent effective mass tensor and a Lorentz-like force nonlinear in velocity. In the second setup, it renormalizes circuit capacitance and generates a Hall current nonlinear in the electric field. For small velocities, it reproduces recent results for electronic dynamics in external electromagnetic fields and in pseudospin textures, though the framework can remain valid at large velocities beyond the perturbative regime.

Key points

• Kinematic quantum geometry introduces mixed Berry curvatures to extend Born-Oppenheimer geometry by describing fast degrees of freedom that adiabatically follow slow ones.
• The framework modifies the effective theory governing slow degrees of freedom and has been tested in spinful particles in magnetic textures and Dirac electrons in graphene coupled to an LC circuit.

Context

This article presents a new theoretical framework for quantum mechanics that extends Born-Oppenheimer geometry by introducing mixed Berry curvatures. It modifies the effective theory governing slow degrees of freedom and has been tested in spinful particles in magnetic textures and Dirac electrons in graphene coupled to an LC circuit.

Limitations

The framework can remain valid at large velocities beyond the perturbative regime, provided the kinematic states are sufficiently slowly varying. The evidence is limited to two specific setups: spinful particles in magnetic textures and Dirac electrons in graphene coupled to an LC circuit. The article does not provide additional background on the broader implications of the framework or its experimental verification status.

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