Supersymmetric Berry Index

TL;DR

This paper introduces the supersymmetric Berry index, analyzing supersymmetric adiabatic evolution in quantum mechanics and calculating the index for specific models like holomorphic and meromorphic quantum mechanics.

Contribution

It defines the supersymmetric Berry index and explores its properties and calculations in supersymmetric quantum mechanical models.

Findings

Supersymmetric Berry index is analogous to the Witten index.

Conditions for supersymmetric adiabatic evolution are identified.

Berry indexes are explicitly calculated for specific models.

Abstract

We revise the sequences of SUSY for a cyclic adiabatic evolution governed by the supersymmetric quantum mechanical Hamiltonian. The condition (supersymmetric adiabatic evolution) under which the supersymmetric reductions of Berry (nondegenerated case) or Wilczek-Zee (degenerated case) phases of superpartners are taking place is pointed out. The analogue of Witten index (supersymmetric Berry index) is determined. As the examples of suggested concept of supersymmetric adiabatic evolution the Holomorphic quantum mechanics on complex plane and Meromorphic quantum mechanics on Riemann surface are considered. The supersymmetric Berry indexes for the models are calculated.