Non-perturbative approach to non-Markovianity and entropy production in the Caldeira-Leggett model

Abstract: We study the emergence of non-Markovian dynamics in the Caldeira-Leggett model, describing a quantum harmonic oscillator bilinearly coupled to a bath consisting of a finite or infinite number of quantum harmonic oscillators. We consider a definition and measure of non-Markovianity which is based on the notion of information flow between the open system and the environment. Non-Markovianity is quantified using the Bures metric (fidelity) as distance measure for quantum states. The assumption of Gaussian initial conditions allows us to study quantum memory effects for arbitrary couplings, temperatures and frequency cutoffs with help of an exact analytical approach. We find that the non-Markovianity is maximal at intermediate coupling strengths and decreases as the coupling increases. Moreover, the comparison of our results concerning the non-Markovianity dependence on the frequency cutoff and the initial bath temperature and an analogue study on the Spin-Boson model reveals interesting similarities.
Furthermore, we investigate if the Caldeira-Leggett master equation is able to produce non-Markovian dynamics and point out in which parameter regime it is a valid approximation to the exact approach.

In addition we use a recently proposed expression for the entropy production in non-equilibrium processes to investigate the relation between mutual information and intra environment correlations for a finite number of bath modes in the time evolution of Gaussian states.
We find that the dominant contribution to the entropy production is due to the displacement of the reduced bath state from equilibrium. This statement holds for all studied parameter regimes and structures of the spectral density

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch
• Notes: Universität Freiburg, Masterarbeit, 2020

Classification and Topics

• Keyword: Entropy

Contributors, Places and Time

• Event: Veröffentlichung
• (where): Freiburg
• (who): Universität
• (when): 2020
• Creator: Einsiedler, Simon
• Contributor: Breuer, Heinz-Peter

Further information

• DOI: 10.6094/UNIFR/165942
• URN: urn:nbn:de:bsz:25-freidok-1659425
• Rights: Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 25.03.2025, 1:49 PM CET