Degeneracy of Landau Level and Quantum Group SL_q(2)

We show that there is a kind of quantum group symmetry $sl_{q}(2)$ in the usual Landau problem and it is this quantum group symmetry that governs the degeneracy of Landau levels. We find that under the periodic boundary condition, the degree of degeneracy of Landau levels is finite, and it just equals the dimension of the irreducible cyclic representation of the quantum group $sl_{q}(2)$.Comment: 10 pages, Preprint ( reprint ) of Nankai Institute of Mathematics. For hard copy, write to Prof. Mo-lin GE, Director of Nankai Institute of Mathematics. Do not send emails to this computer accoun

Early Functional and Cognitive Declines Measured by Auditory-Evoked Cortical Potentials in Mice With Alzheimer’s Disease

Alzheimer’s disease (AD) is characterized by a progressive loss of memory and cognitive decline. However, the assessment of AD-associated functional and cognitive changes is still a big challenge. Auditory-evoked cortical potential (AECP) is an event-related potential reflecting not only neural activation in the auditory cortex (AC) but also cognitive activity in the brain. In this study, we used the subdermal needle electrodes with the same electrode setting as the auditory brainstem response (ABR) recording and recorded AECP in normal aging CBA/CaJ mice and APP/PS1 AD mice. AECP in mice usually appeared as three positive peaks, i.e., P1, P2, and P3, and three corresponding negative peaks, i.e., N1, N2, and N3. In normal aging CBA mice, the early sensory peaks P1, N1, and P2 were reduced as age increased, whereas the later cognitive peaks N2, P3, and N3 were increased or had no changes with aging. Moreover, the latency of the P1 peak was increased as age increased, although the latencies of later peaks had a significant reduction with aging. In AD mice, peak P1 was significantly reduced in comparison with wild-type (WT) littermates at young ages, proceeding AD phenotype presentation. In particular, the later cognitive peak P3 was diminished after 3 months old, different from the normal aging effect. However, the latencies of AECP peaks in AD mice generally had no significant delay or changes with aging. Finally, consistent with AECP changes, the accumulation of amyloid precursor protein (APP) at the AC was visible in AD mice as early as 2 months old. These data suggest that AECP could serve as an early, non-invasive, and objective biomarker for detecting AD and AD-related dementia (ADRD)

The Critical Behavior of Quantum Stirling Heat Engine

We investigate the performance of a Stirling cycle with a working substance (WS) modeled as the quantum Rabi model (QRM), exploring the impact of criticality on its efficiency. Our findings indicate that the criticality of the QRM has a positive effect on improving the efficiency of the Stirling cycle. Furthermore, we observe that the Carnot efficiency is asymptotically achievable as the WS parameter approaches the critical point, even when both the temperatures of the cold and hot reservoirs are finite. Additionally, we derive the critical behavior for the efficiency of the Stirling cycle, demonstrating how the efficiency asymptotically approaches the Carnot efficiency as the WS parameter approaches the critical point. Our work deepens the understanding of the impact of criticality on the performance of a Stirling heat engine.Comment: 7 pages, 3 figure

trans-Diacetonitrile­tetra­kis(1H-pyrazole-κN 2)nickel(II) dinitrate

In the title complex, [Ni(CH3CN)2(C3H4N2)4](NO3)2, the cation lies on an inversion center and adopts an octa­hedral coordination geometry about the Ni atom. The two acetonitrile ligands are in a trans conformation. N—H⋯O hydrogen bonds between cations and anions link the complex mol­ecules into one-dimensional chains running parallel to [100]

Variational quantum circuit learning of entanglement purification in multi-degree-of-freedom

Quantum entanglement purification (EP) is a crucial technique for promising the effective function of entanglement channel in noisy large-scale quantum network. The previous EP protocols lack of a general circuit framework and become complicated to design in high-dimensional cases. In this paper, we propose a variational quantum circuit framework and demonstrate its feasibility of learning optimal protocols of EP in multi-degree-of-freedom (DoF). By innovatively introducing the additional circuit lines for representing the ancillary DoFs, e.g. space and time, the parameterized quantum circuit can effectively simulate the scalable EP process. As examples, well-known protocols in linear optics including PSBZ, HHSZ+ and etc., are learnt successfully with high fidelities and the alternative equivalent operations are discovered in low-depth quantum circuit. Our work pays the way for exploring the EP protocols with multi-DoF by quantum machine learning.Comment: 8 pages, 5 figures, comments are welcome