Adiabatic approximation in the second quantized formulation

TL;DR

This paper proposes a reliable criterion for the adiabatic approximation based on approximate diagonalization of the effective Hamiltonian in second quantization, clarifying previous controversies.

Contribution

It introduces a new criterion for the adiabatic approximation using second quantized effective Hamiltonian diagonalization, with applications to specific models.

Findings

The criterion is reliable and unambiguous.

Application to Marzlin and Sanders model confirms validity.

Exact diagonalization demonstrated for a geometric phase model.

Abstract

Recently there have been some controversies about the criterion of the adiabatic approximation. It is shown that an approximate diagonalization of the effective Hamiltonian in the second quantized formulation gives rise to a reliable and unambiguous criterion of the adiabatic approximation. This is illustrated for the model of Marzlin and Sanders and a model related to the geometric phase which can be exactly diagonalized in the present sense.