Quantum geometry and adiabaticity in molecules and in condensed matter

Area of Science:

• Quantum mechanics
• Condensed matter physics
• Molecular physics

Background:

• The adiabatic theorem is a fundamental concept in quantum mechanics.
• It states that a quantum system remains in its instantaneous eigenstate if its Hamiltonian evolves infinitely slowly.
• However, the adiabatic evolution of observables is not solely determined by the expectation value over instantaneous eigenstates.

Purpose of the Study:

• To investigate the adiabatic evolution of generic observables beyond simple expectation values.
• To demonstrate the significance of an additional quantum-geometrical term in adiabatic observables.
• To provide a transparent and compact derivation for specific molecular and condensed matter properties.

Main Methods:

• The study applies principles of quantum geometry to derive expressions for adiabatic observables.
• It explicitly analyzes cases including polarizability and infrared tensors in molecules and condensed matter.
• Rotational g factor and magnetizability in molecules are also examined.

Main Results:

• An additional adiabatic term of quantum-geometrical origin is identified as crucial for several static and adiabatic observables.
• This quantum geometrical approach offers a transparent derivation and compact expressions for these observables.
• The derived expressions are shown to be an alternative to traditional sum-over-states Kubo formulas.

Conclusions:

• Adiabatic evolution of observables involves a quantum-geometrical contribution beyond instantaneous expectation values.
• Quantum geometry provides a powerful and elegant framework for understanding and calculating adiabatic properties.
• This work offers a new perspective and alternative methods for calculating important physical observables.