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摘要： The discovery of the counter-intuitive laws of quantum mechanics at the beginning of the 20th century revolutionized physics. Quantum-mechanical properties, such as superposition and entanglement, can be harnessed to create quantum technology that opens a computing power far beyond the computing power that we know today. A quantum computer would enable efficient simulations of chemical reactions and material properties, which is expected to greatly impact healthcare and the energy transition. Practical quantum computation requires millions of qubits, either with neighbour-to-neighbour connectivity, or connected via quantum links. Spin qubits in electrically-defined silicon quan- tum dots are promising qubit candidates due to their small footprint and relatively long co- herence time. The last decade meant a leap for the understanding and control of spin qubit systems with devices up to three quantum dots. Y et building systems capable of performing useful quantum calculations has proven difficult due to low sample yield, as well as challenges in controlling and scaling these systems. In this thesis, we explore quantum-dot-based spin qubits and their suitability for scaling to larger systems. This quest was threefold and can be summarized as: More, Distant, Industrial. More: Increasing the number of quantum dots and thus qubits to numbers greater than three was proven challenging, among others due to the the cross-capacitance that was posed upon quantum dots by the metallic gate electrodes of their neighbours. Here, we develop a material platform-independent method to individually control the chemical potential of each quantum dot and the number of electrons in it without affecting the quantum dots in their vicinity. We demonstrate the method by tuning up a linear array of eight GaAs quantum dots, containing exactly one electron each. Distant: Thereafter, we shift our focus to creating quantum links between distant quantum dots by shuttling electron spins across a ch

关键词： Elliptic equation   Dirichlet Laplacian   Critical point   Principal eigenfunction   The upper half of a topological torus  

摘要： We consider the principal eigenvalue problem for the Laplace-Beltrami operator on the upper half of a topological torus under the Dirichlet boundary condition. We present a construction of the upper half of a topological torus that admits the principal eigenfunction having exact numbers of critical points. Furthermore, we manage to identify the locations of all the critical points of the principal eigenfunction explicitly.(c) 2021 Elsevier Inc. All rights reserved.

关键词： Heisenberg group   Q-Laplacian operator   Exponential growth   Variational methods   Nodal solutions  

摘要： This paper deals with the existence of nodal solutions (sign-changing) to the following elliptic equation involving Q-Laplacian:& nbsp;{-delta(Q)u = lambda f(xi, u) in omega,u = 0 on & part;omega,& nbsp;where delta(Q)(center dot) := div(H)(n) (| & nabla;(n)(H)(middot)|(nQ-2)(H)& nabla;& nbsp;(n)(H) (center dot)) is the Q-Laplacian operator, omega is an open, smooth bounded domain in the Heisenberg group H-n, Q = 2n + 2 is the homogeneous dimension of H-n, lambda is a positive parameter, and nonlinear term f(xi, u) Q behaves like exp(beta|s|(Q/Q-1)) as s -> infinity. Under suitable conditions on f, together with the constraint variational method and the quantitative deformation lemma, we obtain the existence, energy estimates and the convergence property of the least energy sign-changing solutions for the above problem in subcritical and critical exponential growth cases. (C)& nbsp;2021 Elsevier Inc. All rights reserved.

摘要： Out-of-equilibrium dynamics generalizes the study of ground states of quantum Hamiltonians at zero temperature, to that of dynamical quasi-steady states of quantum systems far from equilibrium. In this dissertation I discuss dynamical quantum phase transitions and out-of-equilibrium phases of matter in models of collective spins with multi-body interactions. These models, based on collective degrees of freedom, allow an exact description of the thermodynamic limit via the mean-field description. In this limit, the nonequilibrium dynamics of properties of quantum states is mapped to the nonlinear dynamics of classical variables, and thus it can be analyzed using tools from the theory of classical dynamical systems. The description of the novel dynamical quantum phase transitions and out-of-equilibrium phases of matter enabled by multi-body interactions, is complemented with an experimental protocol consisting on measurement-based quantum feedback control techniques for their implementation. The work in this dissertation constitutes a first step into the investigation of out-of-equilibrium dynamics of quantum systems with multi-body interactions and their implementations using quantum control techniques.

关键词： Arterial spin labeling   Glioma   Magnetic resonance imaging  

摘要： Objective To evaluate the value of synthetic MRI combined with three dimensional‑arterial spin labeling (3D‑ASL) imaging in the grading of diffuse glioma and its correlation with tumor cell proliferative activity (Ki‑67). Methods This study was prospective. The clinical and imaging manifestations of 66 patients with diffuse glioma who underwent synthetic MRI combined with 3D‑ASL imaging from August 2020 to June 2021 in General Hospital of Ningxia Medical University were analyzed. Among 66 patients, there were 36 males and 30 females, aged 4-76 years, and divided into low grade glioma (LGG) group (n=25) (WHO Ⅱ) and high grade glioma (HGG) group (n=41) (WHO Ⅲ and vⅣ). T₁, T₂, proton density (PD) and cerebral blood flow (CBF) of tumor parenchyma were measured by GE ADW4.7 postprocessing software. The Ki‑67 label index (Ki‑67 LI) in postoperative pathological sections was detected by immunohistochemistry. Independent sample t test or Mann‑Whitney U test was used to compare the differences of quantitative parameters between HGG group and LGG group. Receiver operating characteristic (ROC) curve was used to analyze the diagnostic efficacy of T₁, PD, CBF and the combination. Spearman test was used to analyze the correlation between the parameters and Ki‑67 label index (LI). Results T₁[(1 573±173)ms], PD[(86.2±2.4)pu] and CBF[(129±48)ml·100 g^-1·min^-1] in HGG group were significantly higher than those in LGG group [(1 376±134)ms, (83.0±2.5)pu and (77±49)ml·100g^-1·min^-1 respectively], and difference had statistical significance (t=-4.86, -5.08, -4.24, P<0.01). ROC confirmed that the area under curve (AUC) of T₁, PD and CBF in differentiating HGG from LGG were 0.847, 0.843 and 0.777, respectively. In multi‑parameter analysis, the combination of three parameters had the best diagnostic efficiency (AUC=0.973) and the sensitivity and specificity were 87.8% and 100%, respectively. In

关键词： Electronic structure  

摘要： Accurate and efficient methods to simulate nonadiabatic and quantum nuclear effects in high-dimensional and dissipative systems are crucial for the prediction of chemical dynamics in the condensed phase. To facilitate effective development, code sharing, and uptake of newly developed dynamics methods, it is important that software implementations can be easily accessed and built upon. Using the Julia programming language, we have developed the *** package, which provides a framework for established and emerging methods for performing semiclassical and mixed quantum-classical dynamics in the condensed phase. The code provides several interfaces to existing atomistic simulation frameworks, electronic structure codes, and machine learning representations. In addition to the existing methods, the package provides infrastructure for developing and deploying new dynamics methods, which we hope will benefit reproducibility and code sharing in the field of condensed phase quantum dynamics. Herein, we present our code design choices and the specific Julia programming features from which they benefit. We further demonstrate the capabilities of the package on two examples of chemical dynamics in the condensed phase: the population dynamics of the spin-boson model as described by a wide variety of semiclassical and mixed quantum-classical nonadiabatic methods and the reactive scattering of H-2 on Ag(111) using the molecular dynamics with electronic friction method. Together, they exemplify the broad scope of the package to study effective model Hamiltonians and realistic atomistic systems.& nbsp;Published under an exclusive license by AIP Publishing.

关键词： 群论  

ISBN: (纸本)9787040576412

摘要： 本书连贯且系统地论述了群论在量子力学中的应用。外尔先生首先详细介绍了群的经典理论, 接下去叙述了量子物理学的那些基本结果, 随后缜密地探究了与此相关的数学理论和物理理论之间的种种关系。本书涵盖的主题有: 酉几何, 量子理论 (薛定谔波动方程、跃迁概率、方向量子化、碰撞现象、塞曼效应与斯塔克效应); 群及其表示 (子群和共轭类、线性变换、旋转群与洛伦兹群、闭连续群、不变量和协变量、李理论); 群论在量子力学中的应用 (简单态和谱项分析、自旋电子、多重态结构、能量和动量、泡利不相容原理、多体问题、麦克斯韦-狄拉克场方程等); 对称置换群; 对称变换的代数 (群空间和张量空间中的各种不变子空间、子群、杨氏对称算子、自旋与价、原子光谱的群论分类、分支定律等)。外尔先生自始至终都强调对称置换群的表示与完备线性群的表示之间的“互易性”。他对“互易性”克莱布希-戈丹级数, 以及若尔当-霍尔德定理及其类似内容的简化处理, 有助于澄清这些主题和其他一些复杂的主题。

关键词： 神经胶质瘤   磁共振成像   动脉自旋标记  

摘要： 目的探讨合成MRI联合三维动脉自旋标记(3D-ASL)成像对弥漫性胶质瘤分级诊断的应用价值及与肿瘤细胞增殖活性(Ki-67)的相关性。方法本研究为前瞻性研究。分析2020年8月至2021年6月在宁夏医科大学总医院接受颅脑合成MRI和3D-ASL成像的66例弥漫性胶质瘤患者的临床及影像表现。66例患者中男36例、女30例,年龄4~76岁,分为低级别胶质瘤(LGG)组25例(WHOⅡ级)和高级别胶质瘤(HGG)组41例(WHOⅢ、Ⅳ级)。利用GE ADW4.7后处理软件测量肿瘤实质部分T_(1)、T_(2)、质子密度(PD)、脑血流量(CBF)。术后病理切片通过免疫组化检测Ki-67标记指数(Ki-67 LI)。采用独立样本t检验或Mann-Whitney U检验比较HGG组与LGG组各定量参数的差异,采用受试者操作特征(ROC)曲线分析T_(1)、PD、CBF和三者联合的诊断效能,利用Spearman检验分析各参数与Ki-67 LI的相关性。结果HGG组T_(1)[(1573±173)ms]、PD[(86.2±2.4)pu]、CBF[(129±48)ml·100 g^(-1)·min^(-1)]均高于LGG组[分别为(1376±134)ms、(83.0±2.5)pu、(77±49)ml·100 g^(-1)·min^(-1)],差异具有统计学意义(t分别为-4.86、-5.08、-4.24,P<0.01)。ROC显示T_(1)、PD、CBF鉴别HGG与LGG的曲线下面积(AUC)分别为0.847、0.843、0.777。多参数分析中,三者联合的诊断效能最高(AUC=0.973),灵敏度和特异度分别为87.8%和100%。在LGG和HGG组中,T_(1)、T_(2)、PD、CBF与Ki-67 LI无相关性;整体胶质瘤患者中,T_(1)、PD、CBF与Ki-67 LI呈正相关性(r分别为0.394、0.411、0.406,P<0.01);T_(2)与Ki-67 LI无相关性(r=-0.100,P=0.423)。结论合成MRI和3D-ASL可无创评估弥漫性胶质瘤的病理分级并预测Ki-67 LI,其中T_(1)和PD是较好的影像学新指标。

关键词： Coupled mixed derivative nonlinear Schrodinger equation   Generalized Darboux transformation   Soliton   Inelastic colli-osions   Bound states  

摘要： In this paper,the dynamics of the higher-order soliton solutions for the coupled mixed derivative nonlinear Schrodinger equation¨are investigated via generalized Darboux *** a pair of linearly independent solutions of the Lax pair,the oneto three-soliton solutions are obtained via algebraic ***,two and three solitons are respectively displayed via numerical ***,the dynamics of solitons are illustrated with corresponding evolution plots,such as elastic collisions,inelastic collisions,and bound *** is found that there are some novel phenomena of interactions among solitons,which may provide a theoretical basis for studying optical solitons in experiments.