Understanding the quantum dynamics of driven–dissipative many-body systems is becoming central for quantum simulation and next-generation quantum technologies. Even in the classical (large-occupation) limit, their dynamics can already be rich, with multistability, nonequilibrium phase transitions, and topological phenomena beyond equilibrium settings. A key challenge is to access the genuinely quantum regime, since many platforms mix finite-dimensional matter (spins/atoms) with bosonic modes (photons/phonons) in an effectively infinite-dimensional space, making exact calculations hard. This joint PhD project, supervised by Miguel Bello and Javier del Pino at IFIMAC, will develop a practical toolbox based on variational methods and the time-dependent variational principle, with strong links to experimental platforms. It is particularly suitable for students with strong computational interests, with open-source deliverables that enrich the student’s portfolio, and it also offers analytical depth through the geometry of variational manifolds. We strongly encourage applications from women and other underrepresented genders in physics.
