Non-Hermitian dynamics of slowly-varying Hamiltonians

We develop a theoretical description of non-Hermitian time evolution that accounts for the break- down of the adiabatic theorem. We obtain closed-form expressions for the time-dependent state amplitudes, involving the complex eigen-energies as well as inter-band Berry connections calculated using basis sets from appropriately-chosen Schur decompositions. Using a two-level system as an example, we show that our theory accurately captures the phenomenon of "sudden transitions", where the system state abruptly jumps from one eigenstate to another.Comment: 12 pages, 4 figure

Weyl points and topological nodal superfluids in a face-centered cubic optical lattice

We point out that a face-centered cubic (FCC) optical lattice, which can be realised by a simple scheme using three lasers, provides one a highly controllable platform for creating Weyl points and topological nodal superfluids in ultracold atoms. In non-interacting systems, Weyl points automatically arise in the Floquet band structure when shaking such FCC lattices, and sophisticated design of the tunnelling is not required. More interestingly, in the presence of attractive interaction between two hyperfine spin states, which experience the same shaken FCC lattice, a three-dimensional topological nodal superfluid emerges, and Weyl points show up as the gapless points in the quasiparticle spectrum. One could either create a double Weyl point of charge 2, or split it to two Weyl points of charge 1, which can be moved in the momentum space by tuning the interactions. Correspondingly, the Fermi arcs at the surface may be linked with each other or separated as individual ones.Comment: 5 pages, 2 figures in the main text; 2 pages, 2 figures in the supplemental materia

A class of skin discrete breathers emerging from a high-order exceptional point

We study the perturbation by a Kerr nonlinearity to a linear exceptional point (EP) of $L$th order formed by a unidirectionally hopping model and find a class of breathers, dubbed {\it skin discrete breathers} (skin breathers for short), that are aggregated to one boundary the hopping drives to. The nonlinear spectrum of these skin breathers demonstrates a hierarchical power-law scaling near the EP, i.e., the response of nonlinear energy to the perturbation $E_m\propto \Gamma^{\alpha_{m}}$, where $\alpha_m=3^{m-1}$ is the power with $m=1,\cdots,L$ labeling the nonlinear energy bands. This is in sharp contrast to the $L$th root of a generally linear perturbation. These skin breathers decay in a double-exponential way, not in the exponential way as the edge states or skin modes in linear systems. Moreover, these skin breathers can survive over the full nonlinearity strength, continuously connected to the self-trapped states at the large limit, and they are also stable according to the stability analysis, which are reflected by a defined nonlinear fidelity of an adiabatic evolution.Since the nonreciprocal models are experimentally realized in optical systems where the Kerr's nonlinearity naturally exits, our results may stimulate more studies of interplay between nonlinearity and non-Hermiticity, especially the linear EPs.Comment: 8 pages, 4 figure

A Multi-task Learning Approach for Improving Product Title Compression with User Search Log Data

It is a challenging and practical research problem to obtain effective compression of lengthy product titles for E-commerce. This is particularly important as more and more users browse mobile E-commerce apps and more merchants make the original product titles redundant and lengthy for Search Engine Optimization. Traditional text summarization approaches often require a large amount of preprocessing costs and do not capture the important issue of conversion rate in E-commerce. This paper proposes a novel multi-task learning approach for improving product title compression with user search log data. In particular, a pointer network-based sequence-to-sequence approach is utilized for title compression with an attentive mechanism as an extractive method and an attentive encoder-decoder approach is utilized for generating user search queries. The encoding parameters (i.e., semantic embedding of original titles) are shared among the two tasks and the attention distributions are jointly optimized. An extensive set of experiments with both human annotated data and online deployment demonstrate the advantage of the proposed research for both compression qualities and online business values.Comment: 8 Pages, accepted at AAAI 201

General mapping of one-dimensional non-Hermitian mosaic models to non-mosaic counterparts: Mobility edges and Lyapunov exponents

We establish a general mapping from one-dimensional non-Hermitian mosaic models to their non-mosaic counterparts. This mapping can give rise to mobility edges and even Lyapunov exponents in the mosaic models if critical points of localization or Lyapunov exponents of localized states in the corresponding non-mosaic models have already been analytically solved. To demonstrate the validity of this mapping, we apply it to two non-Hermitian localization models: an Aubry-Andr\'e-like model with nonreciprocal hopping and complex quasiperiodic potentials, and the Ganeshan-Pixley-Das Sarma model with nonreciprocal hopping. We successfully obtain the mobility edges and Lyapunov exponents in their mosaic models. This general mapping may catalyze further studies on mobility edges, Lyapunov exponents, and other significant quantities pertaining to localization in non-Hermitian mosaic models.Comment: 9 pages, 2 figure