Capturing thermalization with Gaussian states in a virtual environment*

While many-body systems in equilibrium are well understood by statistical mechanics, a general understanding of thermalization dynamics is still out of reach. One crucial obstacle is the formulation of suitable variational descriptions. The variational class of Gaussian states excellently describes early time dynamics by accounting for both mean field dynamics and spontaneous quasiparticle excitations. At late times, however, these linearized fluctuations inadequately capture the growth of entanglement.

We extend the Gaussian theory by coupling the system to an artificial environment, generalizing the evolution of observables to stochastic trajectories. At the expense of generating an ensemble of states, the environment provides a decoherence which suppresses entanglement within each trajectory, allowing to capture the evolution with Gaussian states beyond early times. The approach is applied to the dynamics of a quenched spinor condensate [Phys. Rev. A 105, 013305 (2022)] and the thermalization of cold atoms in an optical lattice. In the latter case, the trajectory approach proves an elegant solution to the UV catastrophe present in semiclassical field theories.