Collision models: Markovian and Non-Markovian impurity models
Abstract
Collision models provide a flexible framework for studying open quantum systems and introducing non-Markovianity. We present a novel class of collision models, which we term Markovian impurity models, motivated by physical scenarios in which information backflow is periodically blocked. Using the Breuer-Laine-Piilo (BLP) measure of non-Markovianity, we show that if a p-impurity model is non-Markovian, then the corresponding (p+1)-impurity model is also non-Markovian, implying the existence of a critical p at which the process transitions from Markovian to non-Markovian. Numerical simulations are used to investigate how this critical parameter depends on the system-ancilla and ancilla-ancilla interaction strengths. We find that, altough exceptions exist, increasing either interaction strength generally lowers the critical p, while sufficiently weak ancilla-ancilla interactions lead to a regime in which the dynamics remain Markovian even in the absence of impurities. Finally, we briefly introduce the complementary non-Markovian impurity model.
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BibTeX
@misc{werner2026collision,
title = {{Collision models: Markovian and Non-Markovian impurity models}},
author = {Jacob Werner},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.01814},
eprint = {2610.01814},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.01814},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Collision models: Markovian and Non-Markovian impurity models
AU - Jacob Werner
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.01814
UR - https://arxiv.org/abs/2610.01814
AB - Collision models provide a flexible framework for studying open quantum systems and introducing non-Markovianity. We present a novel class of collision models, which we term Markovian impurity models, motivated by physical scenarios in which information backflow is periodically blocked. Using the Breuer-Laine-Piilo (BLP) measure of non-Markovianity, we show that if a p-impurity model is non-Markovian, then the corresponding (p+1)-impurity model is also non-Markovian, implying the existence of a critical p at which the process transitions from Markovian to non-Markovian. Numerical simulations are used to investigate how this critical parameter depends on the system-ancilla and ancilla-ancilla interaction strengths. We find that, altough exceptions exist, increasing either interaction strength generally lowers the critical p, while sufficiently weak ancilla-ancilla interactions lead to a regime in which the dynamics remain Markovian even in the absence of impurities. Finally, we briefly introduce the complementary non-Markovian impurity model.
ER -