Abstract
In the study of closed many-body quantum systems one is often interested in the evolution of a subset of degrees of freedom. On many occasions it is possible to approach the problem by performing an appropriate decomposition into a bath and a system. In the simplest case the evolution of the reduced state of the system is governed by a quantum master equation with a time-independent, i.e. Markovian, generator. Such evolution is typically emerging under the assumption of a weak coupling between the system and an infinitely large bath. Here, we are interested in understanding to which extent a neural network function approximator can predict open quantum dynamics - described by time-local generators - from an underlying unitary dynamics. We investigate this question using a class of spin models, which is inspired by recent experimental setups. We find that indeed time-local generators can be learned. In certain situations they are even time-independent and allow to extrapolate the dynamics to unseen times. This might be useful for situations in which experiments or numerical simulations do not allow to capture long-time dynamics and for exploring thermalization occurring in closed quantum systems.
Highlights
The investigation of isolated quantum systems out of equilibrium is a central problem in physics [1,2]
We have presented two simple examples of neural network architectures that can learn the dynamical features of reduced quantum states
One can extrapolate the dynamics of reduced degrees of freedom to times that were unexplored during the training procedure
Summary
The investigation of isolated quantum systems out of equilibrium is a central problem in physics [1,2]. Partial information that concerns a spatially localized subsystem S is sufficient to study dynamical effects related to relaxation or thermalization This information is encoded in the so-called reduced quantum state ρS, [c.f. Figs. Our approach, which uses machine learning tools and provides a directly interpretable object such as the physical generator of the dynamics, highlights a possible route for the application of neural networks in the study of the long-time dynamics of local observables in closed quantum systems. It may find applications in the context of quantifying the degree of non-Markovianity in reduced quantum dynamics [8]
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