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 consider a random matrix model of interaction between a small $n$-levelsystem, $S$, and its environment, a $N$-level heat reservoir, $R$. Theinteraction between $S$ and $R$ is modeled by a tensor product of a fixed $%n\times n$ matrix and a $N\times N$ hermitian Gaussian random matrix. We showthat under certain "macroscopicity" conditions on $R$, the reduced densitymatrix of the system $\rho _{S}=\mathrm{Tr}_{R}\rho _{S\cup R}^{(eq)} $, isgiven by $\rho _{S}^{(c)}\sim \exp {\{-\beta H_{S}\}}$, where $H_{S}$ is theHamiltonian of the isolated system. This holds for all strengths of theinteraction and thus gives some justification for using $% \rho _{S}^{(c)}$ todescribe some nano-systems, like biopolymers, in equilibrium with theirenvironment \cite{Se:12}. Our results extend those obtained previously in\cite{Le-Pa:03,Le-Co:07} for a special two-level system.

On the Equilibrium State of a Small System with Random Matrix Coupling to Its Environment