Quantum states of a binary mixture of spinor Bose-Einstein condensates

We study the structure of quantum states for a binary mixture of spin-1 atomic Bose-Einstein condensates. In contrast to collision between identical bosons, the s-wave scattering channel between inter-species does not conform to a fixed symmetry. The spin-dependent Hamiltonian thus contains non-commuting terms, making the exact eigenstates more challenging to obtain because they now depend more generally on both the intra- and inter-species interactions. We discuss two limiting cases, where the spin-dependent Hamiltonian reduces respectively to sums of commuting operators. All eigenstates can then be directly constructed, and they are independent of the detailed interaction parameters.Comment: 5 pages, no figure

Nonlinear Model Predictive Controller Design for Identified Nonlinear Parameter Varying Model

In this paper, a novel nonlinear model predictive controller (MPC) is proposed based on an identified nonlinear parameter varying (NPV) model. First, an NPV model scheme is present for process identification, which is featured by its nonlinear hybrid Hammerstein model structure and varying model parameters. The hybrid Hammerstein model combines a normalized static artificial neural network with a linear transfer function to identify general nonlinear systems at each fixed working point. Meanwhile, a model interpolating philosophy is utilized to obtain the global model across the whole operation domain. The NPV model considers both the nonlinearity of transition dynamics due to the variation of the working-point and the nonlinear mapping from the input to the output at fixed working points. Moreover, under the new NPV framework, the control action is computed via a multistep linearization method aimed for nonlinear optimization problems. In the proposed scheme, only low cost tests are needed for system identification and the controller can achieve better output performance than MPC methods based on linear parameter varying (LPV) models. Numerical examples validate the effectiveness of the proposed approach

Atomic number fluctuations in a mixture of two spinor condensates

We study particle number fluctuations in the quantum ground states of a mixture of two spin-1 atomic condensates when the interspecies spin-exchange coupling interaction $c_{12}\beta$ is adjusted. The two spin-1 condensates forming the mixture are respectively ferromagnetic and polar in the absence of an external magnetic (B-) field. We categorize all possible ground states using the angular momentum algebra and compute their characteristic atom number fluctuations, focusing especially on the the AA phase (when $c_{12}\beta >0$), where the ground state becomes fragmented and atomic number fluctuations exhibit drastically different features from a single stand alone spin-1 polar condensate. Our results are further supported by numerical simulations of the full quantum many-body system.Comment: 5 pages, 2 figures, in press PR

Nature of Intelligence

The human brain is the substrate for human intelligence. By simulating the human brain, artificial intelligence builds computational models that have learning capabilities and perform intelligent tasks approaching the human level. Deep neural networks consist of multiple computation layers to learn representations of data and improve the state-of-the-art in many recognition domains. However, the essence of intelligence commonly represented by both humans and AI is unknown. Here, we show that the nature of intelligence is a series of mathematically functional processes that minimize system entropy by establishing functional relationships between datasets over space and time. Humans and AI have achieved intelligence by implementing these entropy-reducing processes in a reinforced manner that consumes energy. With this hypothesis, we establish mathematical models of language, unconsciousness and consciousness, predicting the evidence to be found by neuroscience and achieved by AI engineering. Furthermore, a conclusion is made that the total entropy of the universe is conservative, and intelligence counters the spontaneous processes to decrease entropy by physically or informationally connecting datasets that originally exist in the universe but are separated across space and time. This essay should be a starting point for a deeper understanding of the universe and us as human beings and for achieving sophisticated AI models that are tantamount to human intelligence or even superior. Furthermore, this essay argues that more advanced intelligence than humans should exist if only it reduces entropy in a more efficient energy-consuming way