Spontaneous synchronization in spin systems

Rodrigo Bort, Lucía (Supervisors Zambrini, Roberta; Giorgi, Gian Luca)
Master Thesis (2021)

This Master Thesis is focused on the study of the fundamental properties that a system must
possess to be able to show synchronization in the quantum regime. In the article “Synchronizing
the Smallest Possible System” [1] it was claimed that quantum two-level systems are not a good
candidate, as they lack a limit cycle and cannot be seen as self-sustained oscillators, therefore the
smallest system to be a three-level system.
Our intention is to raise objections to this idea using two main arguments. First, we start questioning the definition of the limit cycle proposed in this article, as well as the premise that only
systems with a limit cycle can be synchronized. And secondly, we point out that the quantum
features observed in the article “Synchronization and Entanglement Generation” [2], in which the
same authors submit the spontaneous synchronization between two coupled spins s = 1 systems,
can be replicated with a pair of spin s =1/2 systems, emphasizing the similarity between both systems.
After this, in order to verify that the measure Srel(φ), proposed in the article “Synchronization and
Entanglement Generation”, is actually entailing the synchronization between the pair of spins, we
analyse the evolution of the spin observables using an alternative measure of synchronization, the
time correlation coefficient. This review suggests that the measure Srel(φ) is not related to the
synchronization between the interacting spins. We also question the relationship between Srel(φ)
and the entanglement in the steady state, characterized by the negativity of the bipartite system.

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