Exact quantum jump approach to open systems in bosonic and spin baths (8 pages)

Heinz‐Peter Breuer

A general method is developed which enables the exact treatment of the non-Markovian quantum dynamics of open systems through a Monte Carlo simulation technique. The method is based on a stochastic formulation of the von Neumann equation of the composite system and employs a pair of product states following a Markovian random jump process. The performance of the method is illustrated by means of stochastic simulations of the dynamics of open systems interacting with a Bosonic reservoir at zero temperature and with a spin bath in the strong coupling regime.

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

Gerhard C. Hegerfeldt

The quantum jump approach (QJA), a discretized version of continuous observations of systems coupled to a bath, such as photons, is outlined and it is shown how it avoids the quantum Zeno effect by temporal coarse-graining. Applications to quantum counting processes and spin-boson models for detecting a particle are given.

Konstantin A. Makarov, Eduard Tsekanovskiı̆