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arXiv · 2507.14076

Variational Multi-Gaussian Phase-Space Dynamics via Automatic Differentiation

Jacopo Tosca·Francesco Carnazza·Luca Giacomelli·Cristiano Ciuti
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Abstract

We introduce a variational method for simulating the dynamics of interacting open quantum bosonic systems deep in the quantum regime. The method is based on a multi-dimensional Wigner phase-space representation and employs a Variational Multi-Gaussian (VMG) ansatz, whose accuracy is systematically controlled by the number of Gaussian components. The variational equations of motion are derived from the Dirac-Frenkel principle and evaluated efficiently by combining the analytical structure of Gaussian functions with automatic differentiation. As a key first physical application, we study a driven-dissipative two-dimensional Bose-Hubbard lattice with two-boson coherent driving and two-body losses. Using our dynamical approach, we compute the finite-size scaling of the Liouvillian spectral gap, extracted from the relaxation dynamics, which vanishes in the thermodynamic limit. Our results reveal critical slowing down with dynamical exponents of the 2D quantum Ising universality class, demonstrating the power of our method to capture complex quantum dynamics in large open systems.

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Jacopo Tosca, Francesco Carnazza, Luca Giacomelli, Cristiano Ciuti. 2025-07-18. Variational Multi-Gaussian Phase-Space Dynamics via Automatic Differentiation. https://arxiv.org/abs/2507.14076

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