Variational Multi-Gaussian Phase-Space Bosonic Dynamics via Automatic Differentiation
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 multidimensional Wigner phase-space representation and employs a variational multi-Gaussian , 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 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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BibTeX
@article{tosca2026variational,
title = {{Variational Multi-Gaussian Phase-Space Bosonic Dynamics via Automatic Differentiation}},
author = {Jacopo Tosca and Francesco Carnazza and Luca Giacomelli and Cristiano Ciuti},
journal = {Physical Review X},
year = {2026},
month = sep,
doi = {10.1103/q3m5-q44b},
eprint = {2507.14076},
archivePrefix = {arXiv},
url = {https://hal.science/hal-05842833v1},
note = {CC BY},
}
RIS
TY - JOUR
TI - Variational Multi-Gaussian Phase-Space Bosonic Dynamics via Automatic Differentiation
AU - Jacopo Tosca
AU - Francesco Carnazza
AU - Luca Giacomelli
AU - Cristiano Ciuti
PY - 2026
DA - 2026/09/24
JO - Physical Review X
DO - 10.1103/q3m5-q44b
UR - https://hal.science/hal-05842833v1
AB - 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 multidimensional Wigner phase-space representation and employs a variational multi-Gaussian , 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 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.
SN - 2160-3308
ER -