Squeezing and adiabaticity breaking in time-dependent quantum harmonic oscillators

Fuente: arXiv
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Main Authors: Orlandini, Mattia, Donelli, Beatrice, Buffoni, Lorenzo, Gherardini, Stefano
Format: Preprint
Published: 2026
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author Orlandini, Mattia
Donelli, Beatrice
Buffoni, Lorenzo
Gherardini, Stefano
author_facet Orlandini, Mattia
Donelli, Beatrice
Buffoni, Lorenzo
Gherardini, Stefano
contents The quantum harmonic oscillator with time-dependent frequency is a paradigmatic model of driven quantum dynamics and one of the few nontrivial systems that admits an exact analytical solution. In this review paper, we present a unified treatment of the time-dependent oscillator based on the Lewis-Riesenfeld invariant method, Bogoliubov transformations and the Ermakov-Pinney equation. We show how these approaches naturally connect to squeezing for the description of excitations production, and to the breakdown of adiabaticity under generic frequency protocols. Exact results for sudden quenches and smooth ramps are discussed in detail. By explicitly bridging invariant methods and squeezing formalism, this review is meant to provide a comprehensive framework for understanding nonequilibrium dynamics in quadratic potentials, with applications ranging from thermodynamics and condensed matter to quantum control theory.
format Preprint
id arxiv_https___arxiv_org_abs_2605_12124
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Squeezing and adiabaticity breaking in time-dependent quantum harmonic oscillators
Orlandini, Mattia
Donelli, Beatrice
Buffoni, Lorenzo
Gherardini, Stefano
Quantum Physics
Statistical Mechanics
The quantum harmonic oscillator with time-dependent frequency is a paradigmatic model of driven quantum dynamics and one of the few nontrivial systems that admits an exact analytical solution. In this review paper, we present a unified treatment of the time-dependent oscillator based on the Lewis-Riesenfeld invariant method, Bogoliubov transformations and the Ermakov-Pinney equation. We show how these approaches naturally connect to squeezing for the description of excitations production, and to the breakdown of adiabaticity under generic frequency protocols. Exact results for sudden quenches and smooth ramps are discussed in detail. By explicitly bridging invariant methods and squeezing formalism, this review is meant to provide a comprehensive framework for understanding nonequilibrium dynamics in quadratic potentials, with applications ranging from thermodynamics and condensed matter to quantum control theory.
title Squeezing and adiabaticity breaking in time-dependent quantum harmonic oscillators
topic Quantum Physics
Statistical Mechanics
url https://arxiv.org/abs/2605.12124