IntroductionWe assessed the correlation between iron deposition and the change of gliocyte metabolism in healthy subjects’ basal ganglia region, by using 3D-enhanced susceptibility weighted angiography (ESWAN) and proton magnetic resonance spectroscopy (1H-MRS).Material and methodsSeventy-seven healthy volunteers (39 female and 38 male subjects; age range: 24–82 years old) were enrolled in the experiment including ESWAN and proton MRS sequences, consent for which was provided by themselves or their guardians. For each subject, the mean phase value gained by ESWAN was used to evaluate the iron deposition; choline/creatine (Cho/Cr) and mI/Cr ratios gained by 1H-MRS were used to evaluate gliocyte metabolism in the basal ganglia region of both sides. The paired t test was used to test the difference between the two sides of the basal ganglia region. Linear regression was performed to evaluate the relation between mean phase value and age. Pearson's correlation coefficient was calculated to analyze the relationship between the result of ESWAN and 1H-MRS.ResultsThere was no difference between the two sides of the basal ganglia region in the mean phase value and Cho/Cr. But in mI/Cr the mean phase value of each nucleus in bilateral basal ganglia decreased with increasing age. There are 16 r-values between the mean phase value and Cho/Cr and mI/Cr in bilateral basal ganglia region. And each of all p-values is less than 0.001 (p < 0.001).ConclusionsIron deposition in the bilateral basal ganglia is associated with the change of gliocyte metabolism with increasing age. Iron deposition in each nucleus of the basal ganglia region changes with age.

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The topological properties of non-Hermitian Hamiltonian is a hot topic, and the theoretical studies along this research line are usually based on the two-level non-Hermitian Hamiltonian (or, equivalently, a spin-1/2 non-Hermitian Hamiltonian). We are motivated to study the geometrical phases of a three-level Lieb lattice model (or, equivalently, a spin-1 non-Hermitian Hamiltonian) with the flat band in the context of a polariton condensate. The topological invariants are calculated by both winding numbers in the Brillouin zone and the geometrical phase of Majorana stars on the Bloch sphere. Besides, we provide an intuitive way to study the topological phase transformation with the higher spin, and the flat band offers a platform to define the topological phase transition on the Bloch sphere. According to the trajectories of the Majorana stars, we calculate the geometrical phases of the Majorana stars. We study the Lieb lattice with a complex hopping and find their phases have a jump when the parameters change from the trivial phase to the topological phase. The correlation phase of Majorana stars will rise along with the increase of the imaginary parts of the hopping energy. Besides, we also study the Lieb lattice with different intracell hopping and calculate the geometrical phases of the model using non-Bloch factor under the Majorana's stellar representation. In this case, the correlation phases will always be zero because of the normalized coefficient is always a purely real number and the phase transition is vividly shown with the geometrical phases of the Majorana stars calculated by the mean values of the total phases of both right and the joint left eigenstates.

Non-adiabatic holonomic quantum computation in decoherence-free subspaces protects quantum information from control imprecisions and decoherence. For the non-collective decoherence that each qubit has its own bath, we show the implementations of two non-commutable holonomic single-qubit gates and one holonomic nontrivial two-qubit gate that compose a universal set of non-adiabatic holonomic quantum gates in decoherence-free-subspaces of the decoupling group, with an encoding rate of . The proposed scheme is robust against control imprecisions and the non-collective decoherence, and its non-adiabatic property ensures less operation time. We demonstrate that our proposed scheme can be realized by utilizing only two-qubit interactions rather than many-qubit interactions. Our results reduce the complexity of practical implementation of holonomic quantum computation in experiments. We also discuss the physical implementation of our scheme in coupled microcavities.

By presenting the quantum evolution with the trajectories of points on the Bloch sphere, the Majorana representation provides an intuitive way to study a high dimensional quantum evolution. In this work, we study the dynamical evolution of the nonlinear two-mode boson system both in the mean-field model by one point on the Bloch sphere and the second-quantized model by the Majorana points, respectively. It is shown that the evolution of the state in the mean-field model and the self-trapping effect can be perfectly characterized by the motion of the point, while the quantum evolution in the second-quantized model can be expressed by an elegant formula of the Majorana points. We find that the motions of states in the two models are the same in linear case. In the nonlinear case, the contribution of the boson interactions to the formula of Majorana points in the second quantized model can be decomposed into two parts:one is the single point part which equals to the nonlinear part of the equation in mean-field model under lager boson number limit; the other one is related to the correlations between the Majorana points which cannot be found in the equation of the point in mean-field model. This means that, the quantum fluctuation which is neglected in the mean-field model can be represented by these correlations. To illustrate our results and shed more light on these two different models, we discussed the quantum state evolution and corresponding self-trapping phenomenon with different boson numbers and boson interacting strength by using the fidelity between the states of the two models and the correlation between the Majoranapoints and the single points in the mean-field model. The result show that the dynamics evolution of the two models are quite different with small boson numbers, since the correlation between the Majorana stars cannot be neglected. However, the second-quantized evolution and the mean-field evolution still vary in both the fidelity population difference between the two boson modes and the fidelity of the states in the two models. The difference between the continuous changes of the second quantized evolution with the boson interacting strength and the critical behavior of the mean-field evolution which related to the self-trapping effect is also discussed. These results can help us to investigate how to include the quantum fluctuation into the mean-field model and find a method beyond the mean field approach.