Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1705.02838 · Communications in Mathematical Physics

The Adiabatic Theorem and Linear Response Theory for Extended Quantum Systems

Sven Bachmann, Wojciech De Roeck, Martin Fraas

Published Mar 18, 2018• 59 citations
arXivHTMLPDF
DOI
10.1007/s00220-018-3117-9

Related papers

Linear response and the fluctuation–dissipation theorem in quantum systems: equilibrium and small deviations

C. Di Castro, Roberto Raimondi

Cambridge University Press eBooks•Aug 27, 2015•0 citations

Non-adiabatic linear response in open quantum systems

Xiaotian Nie, Wei Zheng

Adiabatic theorem and non-adiabatic corrections have been widely applied in modern quantum technology. Recently, non-adiabatic linear response theory has been developed to probe the many-body correlations in closed systems. In this work, we generalize the non-adiabatic linear response theory to open quantum many-body systems. We show that, similar to the closed case, the first-order deviation from the instantaneous steady state is memoryless—it depends only on the final parameters and not on the initial state or ramping path. When ramping the Hamiltonian, the linear response of observables is governed by the derivative of the retarded Green’s function, as in closed systems. In contrast, ramping the dissipation gives rise to a different response, characterized by a high-order correlation function defined in the steady state. Our results offer a compact and physically transparent formulation of non-adiabatic response in open systems, and demonstrate that ramping dynamics can serve as a versatile tool for probing many-body correlations beyond equilibrium.

arXiv:2501.08826•SciPost Physics•Dec 19, 2025•0 citations

Adiabatic theorem for finite dimensional quantum mechanical systems

Mikhail Orionovich Katanaev

arXiv:0909.0370•Russian Physics Journal•Aug 1, 2011•5 citations

Justifying Kubo’s formula for gapped systems at zero temperature: A brief review and some new results

Joscha Henheik, Stefan Teufel

We first review the problem of a rigorous justification of Kubo’s formula for transport coefficients in gapped extended Hamiltonian quantum systems at zero temperature. In particular, the theoretical understanding of the quantum Hall effect rests on the validity of Kubo’s formula for such systems, a connection that we review briefly as well. We then highlight an approach to linear response theory based on non-equilibrium almost-stationary states (NEASS) and on a corresponding adiabatic theorem for such systems that was recently proposed and worked out by one of us in [51] for interacting fermionic systems on finite lattices. In the second part of our paper, we show how to lift the results of [51] to infinite systems by taking a thermodynamic limit.

arXiv:2002.08669•Reviews in Mathematical Physics•Feb 21, 2020•18 citations

Adiabatic Theorems for Quantum Resonances

Walid K. Abou Salem, Jürg Martin Fröhlich

arXiv:math-ph/0607054•Communications in Mathematical Physics•Mar 16, 2007•35 citations

On the adiabatic theorem in quantum theory

Kurt O. Friedrichs

•Jan 1, 1956•8 citations
Adiabatic theorem and non-adiabatic corrections have been widely applied in modern quantum technology. Recently, non-adiabatic linear response theory has been developed to probe the many-body correlations in closed systems. In this work, we generalize the non-adiabatic linear response theory to open quantum many-body systems. We show that, similar to the closed case, the first-order deviation from the instantaneous steady state is memoryless—it depends only on the final parameters and not on the initial state or ramping path. When ramping the Hamiltonian, the linear response of observables is governed by the derivative of the retarded Green’s function, as in closed systems. In contrast, ramping the dissipation gives rise to a different response, characterized by a high-order correlation function defined in the steady state. Our results offer a compact and physically transparent formulation of non-adiabatic response in open systems, and demonstrate that ramping dynamics can serve as a versatile tool for probing many-body correlations beyond equilibrium.
We first review the problem of a rigorous justification of Kubo’s formula for transport coefficients in gapped extended Hamiltonian quantum systems at zero temperature. In particular, the theoretical understanding of the quantum Hall effect rests on the validity of Kubo’s formula for such systems, a connection that we review briefly as well. We then highlight an approach to linear response theory based on non-equilibrium almost-stationary states (NEASS) and on a corresponding adiabatic theorem for such systems that was recently proposed and worked out by one of us in [51] for interacting fermionic systems on finite lattices. In the second part of our paper, we show how to lift the results of [51] to infinite systems by taking a thermodynamic limit.