# Exact Quantum Dynamics in Structured Environments

## TL;DR

This paper demonstrates that the time-evolving matrix product operator method can accurately simulate the complex dynamics of two quantum systems in structured environments, revealing how environmental tuning influences system behavior.

## Contribution

It introduces the application of the time-evolving matrix product operator approach to structured environments with spatial correlations, enabling precise simulation of complex quantum dynamics.

## Key findings

- Tuning system separation to environmental wavelength alters dynamics significantly.
- Full bath dynamics can be inferred from system dynamics.
- The method handles long-lived bath correlations effectively.

## Abstract

The dynamics of a wide range of technologically important quantum systems are dominated by their interaction with just a few environmental modes. Such highly structured environments give rise to long-lived bath correlations that induce complex dynamics which are very difficult to simulate. These difficulties are further aggravated when spatial correlations between different parts of the system are important. By modeling the dynamics of a pair of two-level quantum systems in a common, structured, environment we show that a recently developed numerical approach, the time-evolving matrix product operator, is capable of accurate simulation under exactly these conditions. We find that tuning the separation to match the wavelength of the dominant environmental modes can drastically modify the system dynamics. To further explore this behavior, we show that the full dynamics of the bath can be calculated directly from those of the system, thus allowing us to develop intuition for the complex system dynamics observed.