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关键词： Physics and astronomy/quantum physics/ quantum information and quantum computation/mathematical physics  

ISBN: (数字)9781108534468 ISBN: (纸本)9781108534468

摘要： Designed for a two-semester advanced undergraduate or graduate level course, this distinctive and modern textbook provides students with the physical intuition and mathematical skills to tackle even complex problems in quantum mechanics with ease and fluency. Beginning with a detailed introduction to quantum states and Dirac notation, the book then develops the overarching theoretical framework of quantum mechanics, before explaining physical quantum mechanical properties such as angular momentum and spin. Symmetries and groups in quantum mechanics, important components of current research, are covered at length. The second part of the text focuses on applications, and includes a detailed chapter on quantum entanglement, one of the most exciting modern applications of quantum mechanics, and of key importance in quantum information and computation. Numerous exercises are interspersed throughout the text, expanding upon key concepts and further developing students' understanding. A fully worked solutions manual and lecture slides are available for instructors.

关键词： Fractional p-Laplacian equation   Asymptotically periodic   Ground states   Variational methods  

摘要： In this paper, we study a class of fractional p-Laplacian equation with asymptotically periodic conditions. Under some suitable conditions we obtain two new existence results of ground state solutions by using variational methods. (C) 2021 Elsevier Ltd. All rights reserved.

关键词： Schrodinger-Poisson system   Variational methods   p-Laplacian  

摘要： In this paper we establish by variational methods the existence of nontrivial solutions for a Schrodinger-Poisson system. This system is new one coupled by Schrodinger equation of p-Laplacian with a Poisson equation. Some techniques are applied to obtain the boundedness of the Palais-Smale sequence. (C) 2021 Elsevier Ltd. All rights reserved.

关键词： p-Laplace systems   First order terms   Non-variational systems   Axial symmetry   Radial symmetry   Qualitative properties  

摘要： In this paper we obtain symmetry and monotonicity results for positive solutions to some p-Laplacian cooperative systems in bounded domains involving first-order terms and under zero Dirichlet boundary condition.

关键词： Heisenberg group   Sub-Laplacian   Twisted Laplacian   Non-self-adjoint operators  

摘要： We compute the spectrum of the non-self-adjoint twisted Laplacian. This answers a question raised by Thangvelu (Math Ann 335:879-899, 2006).

关键词： Signless Laplacian eigenvalues   Distance signless Laplacian eigenvalues   Diameter  

摘要： Let Q(G), D(G) and D-Q(G) = Diag(Tr) + D(G) be, respectively, the signless Laplacian matrix, the distance matrix and the distance signless Laplacian matrix of graph G, where Diag( Tr) denotes the diagonal matrix of the vertex transmissions in G. The eigenvalues of Q(G) and DQ(G) will be denoted by q(1) >= q(2) >= center dot center dot center dot >= q(n-1) >= q(n) and partial derivative(Q)(1) >= partial derivative(Q)(2) >= center dot center dot center dot >= partial derivative(Q)(n-1) >= partial derivative(n)Q, respectively. AgraphG which does not share its distance signless Laplacian spectrum with any other non-isomorphic graphs is said to be determined by its distance signless Laplacian spectrum. Characterizing graphs with respect to spectra of graph matrices is challenging. In literature, there are many graphs that are proved to be determined by the spectra of some graph matrices (adjacency matrix, Laplacian matrix, signless Laplacian matrix, distance matrix etc.). But there are much fewer graphs that are proved to be determined by the distance signless Laplacian spectrum. Namely, the path graph, the cycle graph, the complement of the path and the complement of the cycle are proved to be determined by the distance signless Laplacian spectra. In this paper, we establish Nordhaus-Gaddum-type results for the least signless Laplacian eigenvalue of graph G. Moreover, we prove that the join graph G. Kq is determined by the distance singless Laplacian spectrum when G is a p - 2 regular graph of order p. Finally, we show that the short kite graph and the complete split graph are determined by the distance signless Laplacian spectra. Our approach for characterizing these graphs with respect to distance signless Laplacian spectra is different from those given in literature.

关键词： 格林函数  

ISBN: (纸本)9787502489403

摘要： 本书介绍了基于密度泛函理论 (DFT) 的第一性原理计算在材料科学中的应用, 结合非平衡格林函数 (NEGF) 方法, 特别适用于磁性自旋极化输运中的理论模拟应用场景。全书共分为7章, 主要内容包括绪论、密度泛函理论和第一性原理计算方法、电极材料稳定性研究、磁电阻结在不同异质界面下的能态特征及其自旋极化输运性质、电极材料的能带结构特征对磁输运的性能影响等。

摘要： The accumulation rate of authigenic barite (BaSO4) in marine sediments is a promising proxy for reconstructing marine export production, but many aspects of barite precipitation and dissolution in the water column remain unknown. Here, we collected, imaged, and quantitatively analyzed 5481 barite microcrystals in bottle casts from the Eastern Pacific water column to gain a better understanding of in situ barite dynamics. Barite crystal abundance increases rapidly between the surface and 500 m in depth and then declines to predominantly low abundances below similar to 1000 m. The falloff in barite abundance between the oxygen minimum zone (OMZ) and the ocean interior suggests 60% +/- 20% loss of barite by dissolution, nearly all of which is complete by water depths of 1000 m. However, there are occasional samples, as deep as 1250 m, with unusually high barite abundance that may represent marine snow deposition events. We found that microcrystals associated with organic matter substrates were smaller and less solid than free crystals, which suggests ongoing barite precipitation toward larger, more regularly shaped microcrystals within organic matter aggregates. Trends in barite microcrystal size with depth suggest that organic matter aggregates also play a role in shielding barite microcrystals from dissolution. In addition, our extensive data set raises new questions regarding marine barite nucleation and spatial heterogeneity. By helping bridge the gap between hypothesized barite dynamics and in situ observations of barite microcrystals, this study advances our understanding of water column Ba processes and the utility of sediment barite as an export production proxy.

关键词： Stereo EEG   Epileptogenicity index   Biomarkers   Classifiers   Intracranial EEG  

摘要： Objective: To compare the performance of different ictal quantitative biomarkers of the seizure onset zone (SOZ) across many seizures in a cohort of consecutive patients with a variety of seizure onset patterns. Methods: The Epileptogenicity Index (EI, a measure of fast activity) and Slow Polarizing Shift index (SPS, a measure of infraslow activity) were calculated for 212 seizures (22 patients). After stratification by onset pattern, median index values inside and outside the SOZ were compared in aggregate and for each of the onset patterns. Receiver Operating Characteristic (ROC) curves were constructed to compare the performance of each index. Results: Median values of EI (0.056 vs 0.0087), SPS (0.27 vs 0.19), and CI (0.21 vs 0.12) were significantly higher for contacts inside the SOZ, all p < 0.0001. Analysis of AUC showed variable performance of these indices across seizure types, although AUC for EI and SPS was generally greatest for seizures with fast activity at onset. Conclusions: All indices were significantly higher for contacts inside the SOZ;however, the performance of these indices varied depending on the pattern of seizure onset. Significance: These findings suggest that future studies of quantitative biomarkers of the SOZ should account for seizure onset pattern.

关键词： Variable exponent spaces   Free boundary problems   Mean curvature  

摘要： In the present article we study a minimization problem in R-N involving the perimeter of the positivity set of the solution u and the integral of vertical bar del u vertical bar(p(x)). Here p(x) is a Lipschitz continuous function such that 1 < p(min <=) p(x) <= p(max) < infinity. We prove that such a minimizing function exists and that it is a classical solution to a free boundary problem. In particular, the reduced free boundary is a C-2 surface and the dimension of the singular set is at most N - 8. Under further regularity assumptions on the exponent p(x) we get more regularity of the free boundary. In particular, if p is an element of C-infinity we have that partial derivative(red) {u > 0} is a C-infinity surface.