Time-dependent entropy of simple quantum model systems (12 pages)

Piotr Garbaczewski

Krzysztof Andrzejewski

Daniel L. Nedel

In this work new interaction terms between two SYK models are proposed, which allow to define an interaction picture such that it is possible to calculate the vacuum time dependent entanglement entropy at the conformal and large N limit. It is shown that the vacuum evolves as a time dependent SU(2) squeezed state and the time dependent entanglement entropy has the same form of the Page curve of Black Hole formation and evaporation.

Jonas Glatthard

The entanglement entropy of a black hole and that of its Hawking radiation are expected to follow the so-called Page curve: After an increase in line with Hawking’s calculation, it is expected to decrease back to zero once the black hole has fully evaporated, as demanded by unitarity. Recently, a simple system-plus-bath model has been proposed which shows a similar behavior. Here, we make a general argument as to why such a Page-curve-like entanglement dynamics should be expected to hold generally for system-plus-bath models at small coupling and low temperatures, when the system is initialized in a pure state far from equilibrium. The interaction with the bath will then generate entanglement entropy, but it eventually has to decrease to the value prescribed by the corresponding mean-force Gibbs state. Under those conditions, it is close to the system ground state. We illustrate this on two paradigmatic open-quantum-system models, the exactly solvable harmonic quantum Brownian motion and the spin-boson model, which we study numerically. In the first example we find that the intermediate entropy of an initially localized impurity is higher for more localized initial states. In the second example, for an impurity initialized in the excited state, the Page time—when the entropy reaches its maximum—occurs when the excitation has half decayed. Published by the American Physical Society 2024

K. Lendi

Pablo Bayona-Pena, Elena Gramellini, Lorenzo Piroli

We study the von Neumann operator-space entanglement entropy (OSEE) of initial product operators evolved under random gaussian dynamics, as modeled by a Brownian SYK$_2$ model. By exploiting a mapping to a domain-wall melting problem, we derive an exact expression for the time-dependent bipartite OSEE in the thermodynamic limit, and obtain an analytic characterization of the corresponding gaussian Page curve emerging at late times. Our results build on recent work on the entanglement dynamics in the all-to-all quantum simple exclusion process, leveraging tools from RMT, including the Coulomb-gas approach and a mapping to the free Jacobi process. Finally, based on our results, we discuss the possibility of relating the OSEE with non-gaussianity measures in the Heisenberg picture.