Dynamics of the Molecular Geometric Phase

Area of Science:

• Quantum mechanics
• Molecular dynamics
• Chemical physics

Background:

• The molecular geometric phase, a key concept in quantum mechanics, describes the phase acquired by a quantum system undergoing a cyclic change.
• Its behavior in exact dynamical frameworks, particularly beyond the adiabatic approximation, is not fully understood.

Purpose of the Study:

• To investigate the fate of the molecular geometric phase within an exact dynamical framework.
• To introduce a new definition of the geometric phase applicable to arbitrary paths in nuclear configuration space.
• To analyze the conditions under which the geometric phase retains its topological character versus dynamic influences.

Main Methods:

• Utilizing the exact factorization of the molecular wave function.
• Employing a quantum hydrodynamical description for the system's dynamics.
• Introducing an instantaneous, gauge-invariant phase based on hydrodynamical variables.

Main Results:

• An instantaneous, gauge-invariant phase is defined, reducing to the adiabatic geometric phase for closed adiabatic paths.
• The phase evolution follows a Maxwell-Faraday induction law, with electron dynamics acting as electromotive forces.
• Nonconservative forces are identified as capable of altering the phase, challenging purely topological interpretations.

Conclusions:

• The molecular geometric phase is not strictly topological and can be influenced by dynamic forces.
• In approximately adiabatic situations, the geometric phase remains a valid descriptor for certain dynamic observables.
• This work provides a more comprehensive understanding of geometric phase dynamics in molecular systems.