Fluctuation, time-correlation function and geometric Phase

Abstract

We establish a fluctuation-correlation theorem by relating the quantum fluctuations in the generator of the parameter change to the time integral of the quantum correlation function between the projection operator and force operator of the ``fast'' system. By taking a cue from linear response theory we relate the quantum fluctuation in the generator to the generalised susceptibility. Relation between the open-path geometric phase, diagonal elements of the quantum metric tensor and the force-force correlation function is provided and the classical limit of the fluctuation-correlation theorem is also discussed.

Latex, 12 pages, no figures, submitted to J. Phys. A: Math & Gen

References in corpus (4)

• Adiabatic geometric phases and response functions
• Extending the quantal adiabatic theorem: Geometry of noncyclic motion
• Adiabatic Berry Phase and Hannay Angle for Open Paths
• Relativistic Adiabatic Approximation and Geometric Phase

Cited by in corpus (6)

• Geometric phases for mixed states in interferometry
• Berry and Pancharatnam Topological Phases of Atomic and Optical Systems
• Adiabatic Berry Phase and Hannay Angle for Open Paths
• Geometric Phases for Mixed States during Cyclic Evolutions
• Switching of Geometric Phase in Degenerate Systems
• Pancharatnam phase deficit can detect macroscopic entanglement