Recent advances in the theory of Bogoliubov Hamiltonians

TL;DR

This paper reviews recent theoretical advances in bosonic quadratic Hamiltonians, highlighting their role in many-boson systems and discussing the challenges in their time-dependent diagonalization.

Contribution

It provides an overview of recent progress in understanding bosonic quadratic Hamiltonians and their diagonalization, connecting these results to the time-dependent problem.

Findings

Enhanced understanding of the structure of Bogoliubov Hamiltonians

Progress in solving the time-dependent diagonalization problem

Connections to many-boson system approximations

Abstract

Bosonic quadratic Hamiltonians, often called Bogoliubov Hamiltonians, play an important role in the theory of many-boson systems where they arise in a natural way as an approximation to the full many-body problem. In this note we would like to give an overview of recent advances in the study of bosonic quadratic Hamiltonians. In particular, we relate the reported results to what can be called the time-dependent diagonalization problem.