# Mapping repulsive to attractive interaction in driven-dissipative quantum systems

## TL;DR

This paper establishes a theoretical mapping between repulsive and attractive interactions in driven-dissipative quantum systems, revealing a fundamental connection that broadens understanding of their nonequilibrium dynamics.

## Contribution

It introduces a one-to-one mapping for a class of open quantum systems, linking repulsive and attractive interactions and demonstrating its applicability to various lattice geometries.

## Key findings

- Mapping valid for Markovian open quantum systems with time-reversal symmetry
- Demonstrates equivalence of dynamics in frustrated and non-frustrated spin lattices
- Broad applicability to different quantum many-body systems

## Abstract

Repulsive and attractive interactions usually lead to very different physics. Striking exceptions exist in the dynamics of driven-dissipative quantum systems. For the example of a photonic Bose-Hubbard dimer, we establish a one-to-one mapping relating the cases of onsite repulsion and attraction. We prove that the mapping is valid for an entire class of Markovian open quantum systems with time-reversal invariant Hamiltonian and physically meaningful inverse-sign Hamiltonian. To underline the broad applicability of the mapping, we illustrate the one-to-one correspondence between the nonequilibrium dynamics in a geometrically frustrated spin lattice and that in a non-frustrated partner lattice.