Higher-order solutions to non-Markovian quantum dynamics via hierarchical functional derivative

Solving realistic quantum systems coupled to an environment is a challenging task. Here we develop a hierarchical functional derivative (HFD) approach for efficiently solving the non-Markovian quantum trajectories of an open quantum system embedded in a bosonic bath. An explicit expression for arbitrary order HFD equation is derived systematically. Moreover, it is found that for an analytically solvable model, this hierarchical equation naturally terminates at a given order and thus becomes exactly solvable. This HFD approach provides a systematic method to study the non-Markovian quantum dynamics of an open system coupled to a bosonic environment.Comment: 5 pages, 2 figure

Dynamical invariants in non-Markovian quantum state diffusion equation

We find dynamical invariants for open quantum systems described by the non-Markovian quantum state diffusion (QSD) equation. In stark contrast to closed systems where the dynamical invariant can be identical to the system density operator, these dynamical invariants no longer share the equation of motion for the density operator. Moreover, the invariants obtained with from bi-orthonormal basis can be used to render an exact solution to the QSD equation and the corresponding non-Markovian dynamics without using master equations or numerical simulations. Significantly we show that we can apply these dynamic invariants to reverse-engineering a Hamiltonian that is capable of driving the system to the target state, providing a novel way to design control strategy for open quantum systems.Comment: 6 pages, 2 figure

Exposing the Functionalities of Neurons for Gated Recurrent Unit Based Sequence-to-Sequence Model

The goal of this paper is to report certain scientific discoveries about a Seq2Seq model. It is known that analyzing the behavior of RNN-based models at the neuron level is considered a more challenging task than analyzing a DNN or CNN models due to their recursive mechanism in nature. This paper aims to provide neuron-level analysis to explain why a vanilla GRU-based Seq2Seq model without attention can achieve token-positioning. We found four different types of neurons: storing, counting, triggering, and outputting and further uncover the mechanism for these neurons to work together in order to produce the right token in the right position.Comment: 9 pages (excluding reference), 10 figure

Statistical mechanical modeling of catalytic polymerization within surface-functionalized mesoporous materials

A discrete lattice model is developed to describe diffusion-mediated polymerization occurring within mesopores, where reaction is enhanced at catalytic sites distributed within the interior of the pores. Diffusive transport of monomers and polymers is one-dimensional, diffusion coefficients for the latter decreasing with polymer length. Kinetic Monte Carlo simulation is utilized to analyze model behavior focusing on a clogging regime, where the amount of polymer within the pores grows. We characterize the evolution of the overall and mean length of polymers, the mean number of polymers, as well as the polymer spatial and length distributions