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/

Global: Zendy Plus annual

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

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider a toy model for the study of monitored dynamics in a many-bodyquantum systems. We study the stochastic Schrodinger equation resulting fromthe continuous monitoring with a rate $\Gamma$ of a random hermitian operatorchosen at every time from the gaussian unitary ensemble (GUE). Due toinvariance by unitary transformations, the dynamics of the eigenvalues$\{\lambda_\alpha\}_{\alpha=1}^n$ of the density matrix can be decoupled fromthat of the eigenvectors. Thus, stochastic equations are derived that exactlydescribe the dynamics of $\lambda$'s. We consider two regimes: in the presenceof an extra dephasing term, which can be generated by imperfect quantummeasurements, the density matrix has a stationary distribution, and we showthat in the limit of large sizes the distribution of $\lambda$'s is describedby an inverse Marchenko Pastur distribution. In the case of perfectmeasurements instead, purification eventually occurs and we focus onfinite-time dynamics. In this case, remarkably, we find an exact solution forthe joint probability distribution of $\lambda$'s at each time $t$ and for eachsize $n$. Two relevant regimes emerge: at small times $t\Gamma= O(1)$, thespectrum is in a Coulomb gas regime, with a well-defined continuous spectraldistribution in the limit of $n\to\infty$. In that case, all moments of thedensity matrix become self-averaging and it is possible to characterize theentanglement spectrum exactly. In the limit of large times $t \Gamma = O(n)$one enters instead a regime in which the eigenvalues are exponentiallyseparated $\log(\lambda_\alpha/\lambda_\beta) = O(\Gamma t/n)$, butfluctuations $\sim O(\sqrt{\Gamma t/n})$ play an essential role. We are stillable to characterize the asymptotic behaviors of entanglement entropy in thisregime.

A Dyson Brownian motion model for weak measurements in chaotic quantum systems