Standard theoretical descriptions of the dynamics of open quantum systems rely on the assumption that the correlations with the environment can be neglected at some reference (initial) time. While being reasonable in specific instances, such as when the coupling between the system and the environment is weak or when the interaction starts at a distinguished time, the use of initially uncorrelated states is questionable if one wants to deal with general models, taking into account the mutual influence that the open-system and environmental evolutions perform on each other. Here we introduce a perturbative method that can be applied to any microscopic modeling of the system-environment interaction, including fully general initial correlations. Extending the standard technique based on projection operators that single out the relevant part of the global dynamics, we define a family of projections adapted to a convenient decomposition of the initial state, which involves a convex mixture of product operators with proper environmental states. This leads us to characterize the open-system dynamics via an uncoupled system of differential equations, which are homogeneous and whose number is limited by the dimensionality of the open system, for any kind of initial correlations. Our method is further illustrated by means of two case studies, for which it reproduces the expected dynamical behavior in the long-time regime more consistently than the standard projection technique.

Adapted projection operator technique for the treatment of initial correlations / A. Trevisan, A. Smirne, N. Megier, B. Vacchini. - In: PHYSICAL REVIEW A. - ISSN 2469-9926. - 104:5(2021 Nov 18), pp. 052215.052215-1-052215.052215-18. [10.1103/PhysRevA.104.052215]

Adapted projection operator technique for the treatment of initial correlations

A. Smirne
Secondo
;
B. Vacchini
Ultimo
2021

Abstract

Standard theoretical descriptions of the dynamics of open quantum systems rely on the assumption that the correlations with the environment can be neglected at some reference (initial) time. While being reasonable in specific instances, such as when the coupling between the system and the environment is weak or when the interaction starts at a distinguished time, the use of initially uncorrelated states is questionable if one wants to deal with general models, taking into account the mutual influence that the open-system and environmental evolutions perform on each other. Here we introduce a perturbative method that can be applied to any microscopic modeling of the system-environment interaction, including fully general initial correlations. Extending the standard technique based on projection operators that single out the relevant part of the global dynamics, we define a family of projections adapted to a convenient decomposition of the initial state, which involves a convex mixture of product operators with proper environmental states. This leads us to characterize the open-system dynamics via an uncoupled system of differential equations, which are homogeneous and whose number is limited by the dimensionality of the open system, for any kind of initial correlations. Our method is further illustrated by means of two case studies, for which it reproduces the expected dynamical behavior in the long-time regime more consistently than the standard projection technique.
Settore FIS/03 - Fisica della Materia
Settore FIS/02 - Fisica Teorica, Modelli e Metodi Matematici
PSR2015-1718BVACC_01 - PIANO DI SOSTEGNO ALLA RICERCA 2015-2017 - TRANSITION GRANT LINEA 1A PROGETTO "UNIMI PARTENARIATI H2020" - VACCHINI, BASSANO MARIA - PSR2015-17 - Piano di sviluppo di ricerca 2015-17 - 2018
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/890020
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