English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We derive explicitly the thermal state of the two coupled harmonic oscillatorsystem when the spring and coupling constants are arbitrarily time-dependent.In particular, we focus on the case of sudden change of frequencies. In thiscase we compute purity function, R\'{e}nyi and von Neumann entropies, andmutual information analytically and examine their temperature-dependence. Wealso discuss on the thermal entanglement phase transition by making use of thenegativity-like quantity. Our calculation shows that the critical temperature$T_c$ increases with increasing the difference between the initial and finalfrequencies. In this way we can protect the entanglement against the externaltemperature by introducing large difference of initial and final frequencies.

Thermal Entanglement Phase Transition in Coupled Harmonic Oscillators with Arbitrary Time-Dependent Frequencies