Conjectures on hidden Onsager algebra symmetries in interacting quantum lattice models

We conjecture the existence of hidden Onsager algebra symmetries in two interacting quantum integrable lattice models, i.e. spin-1/2 XXZ model and spin-1 Zamolodchikov-Fateev model at arbitrary root of unity values of the anisotropy. The conjectures relate the Onsager generators to the conserved charges obtained from semi-cyclic transfer matrices. The conjectures are motivated by two examples which are spin-1/2 XX model and spin-1 U(1)-invariant clock model. A novel construction of the semi-cyclic transfer matrices of spin-1 Zamolodchikov-Fateev model at arbitrary root of unity values of the anisotropy is carried out via the transfer matrix fusion procedure.

On the Q operator and the spectrum of the XXZ model at root of unity

The spin-\frac{1}{2}12 Heisenberg XXZ chain is a paradigmatic quantum integrable model. Although it can be solved exactly via Bethe ansatz techniques, there are still open issues regarding the spectrum at root of unity values of the anisotropy. We construct Baxter’s Q operator at arbitrary anisotropy from a two-parameter transfer matrix associated to a complex-spin auxiliary space. A decomposition of this transfer matrix provides a simple proof of the transfer matrix fusion and Wronskian relations. At root of unity a truncation allows us to construct the Q operator explicitly in terms of finite-dimensional matrices. From its decomposition we derive truncated fusion and Wronskian relations as well as an interpolation-type formula that has been conjectured previously. We elucidate the Fabricius–McCoy (FM) strings and exponential degeneracies in the spectrum of the six-vertex transfer matrix at root of unity. Using a semicyclic auxiliary representation we give a conjecture for creation and annihilation operators of FM strings for all roots of unity. We connect our findings with the `string-charge duality’ in the thermodynamic limit, leading to a conjecture for the imaginary part of the FM string centres with potential applications to out-of-equilibrium physics.

Target Localization Based on Bistatic T/R Pair Selection in GNSS-Based Multistatic Radar System

To cope with the increasingly complex electromagnetic environment, multistatic radar systems, especially the passive multistatic radar, are becoming a trend of future radar development due to their advantages in anti-electronic jam, anti-destruction properties, and no electromagnetic pollution. However, one problem with this multi-source network is that it brings a huge amount of information and leads to considerable computational load. Aiming at the problem, this paper introduces the idea of selecting external illuminators in the multistatic passive radar system. Its essence is to optimize the configuration of multistatic T/R pairs. Based on this, this paper respectively proposes two multi-source optimization algorithms from the perspective of resolution unit and resolution capability, the Covariance Matrix Fusion Method and Convex Hull Optimization Method, and then uses a Global Navigation Satellite System (GNSS) as an external illuminator to verify the algorithms. The experimental results show that the two optimization methods significantly improve the accuracy of multistatic positioning, and obtain a more reasonable use of system resources. To evaluate the algorithm performance under large number of transmitting/receiving stations, further simulation was conducted, in which a combination of the two algorithms were applied and the combined algorithm has shown its effectiveness in minimize the computational load and retain the target localization precision at the same time.

TD-LSTM: Temporal Dependence-Based LSTM Networks for Marine Temperature Prediction

Changes in ocean temperature over time have important implications for marine ecosystems and global climate change. Marine temperature changes with time and has the features of closeness, period, and trend. This paper analyzes the temporal dependence of marine temperature variation at multiple depths and proposes a new ocean-temperature time-series prediction method based on the temporal dependence parameter matrix fusion of historical observation data. The Temporal Dependence-Based Long Short-Term Memory (LSTM) Networks for Marine Temperature Prediction (TD-LSTM) proves better than other methods while predicting sea-surface temperature (SST) by using Argo data. The performances were good at various depths and different regions.