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关键词： Eigenvalues   (p, q)-Laplacian   Sobolev space   Nehari manifold   Variational methods  

摘要： In this paper we consider in a bounded domain Omega subset of R-Nu with smooth boundary an eigenvalue problem for the negative (p, q)-Laplacian with a Steklov-like boundary condition, where p, q is an element of(1, infinity), p not equal q, including the open case p is an element of(1, infinity), q is an element of(1, 2), p not equal q. A full description of the set of eigenvalues of this problem is provided. Our results complement those previously obtained by Abreu-Madeira [1], Barbu-Morosanu [2], Farcaseanu-Mihailescu-Stancu Dumitru [9], Mihailescu [16], Mihailescu-Morosanu [17]. (C) 2021 Elsevier Inc. All rights reserved.

摘要： The syntheses of Si-H-substituted oligosilanes, that contain up to four Si H functionalities, are described. The Si-H groups allow the selective generation of cationic Si centres by hydride transfer. The cations are then stabilised by the formation of 2e3c Si-H-Si bridges. If multiple Si-H unit are present, it is shown how the Si-H units interact with the 2e3c Si-H-Si bridges. The presence of four Si-H units is used to synthesise, and NMR spectroscopically characterise the first example of an oligosilanylsilyl dication stabilised by 2e3c Si-H-Si bridges. Moreover, the competition between stabilising effects of 2e3c Si-H-Si bridges and destabilising effects due to ring strain are investigated. It is shown that ring strain can lead to the formation of inter- instead of intramolecular Si-H-Si bridges whose formation is entropically disadvantageous. The structural properties of 2e3c Si-H-Si bridges in acyclic and (poly)cyclic oligosilanylsilyl cations are elucidated by quantum chemistry.

关键词： Transition metal oxides   iridate   ruthenate   spin-orbit interaction   magnetic frustration   quantum liquid   metal-insulator transition   superconductivity   spin-orbit coupled state   Transition metal oxides   iridate   ruthenate   spin-orbit interaction   magnetic frustration   quantum liquid   metal-insulator transition   superconductivity   spin-orbit coupled state  

ISBN: (数字)9780191861277 ISBN: (纸本)9780199602025

摘要： Prior to 2010, most research on the physics and chemistry of transition metal oxides was dominated by compounds of the 3d-transition elements such as Cr, Mn, Fe, Co, Ni, and Cu. These materials exhibited novel, important phenomena that include giant magnetoresistance in manganites, as well as high-temperature superconductivity in doped La2CuO4 and related cuprates. The discovery in 1994 of an exotic superconducting state in Sr2RuO4 shifted some interest toward ruthenates. Moreover, the realization in 2008 that a novel variant of the classic Mott metal-insulator transition was at play in Sr2IrO4 provided the impetus for a burgeoning group of studies of the influence of strong spin-orbit interactions in “heavy” (4d- and 5d-) transition-element oxides. This book reviews recent experimental and theoretical evidence that the physical and structural properties of 4d- and 5d-oxides are decisively influenced by strong spin-orbit interactions that compete or collaborate with comparable Coulomb, magnetic exchange, and crystalline electric field interactions. The combined effect leads to unusual ground states and magnetic frustration that are unique to this class of materials. Novel couplings between the orbital/lattice and spin degrees of freedom, which lead to unusual types of magnetic order and other exotic phenomena, challenge current theoretical models. Of particular interest are recent investigations of iridates and ruthenates focusing on strong spin-orbit interactions that couple the lattice and spin degrees of freedom.

关键词： Cylinder phenylene chain   degree-Kirchhoff index   normalized Laplacian   spanning tree  

摘要： Let PHn denote a linear phenylene chain with n hexagons and n - 1 quadrangles. Then the cylinder phenylene chain CPn is the graph obtained from the PHn by identifying the opposite lateral edges in ordered way. In this paper, using the normalized Laplacian decomposition theorem, the normalized Laplacian spectrum of CPn consisting of the eigenvalues of two symmetric quasi-tridiagonal matrices and of order 3n is determined. Together with the relationship between the roots and coefficients of the characteristic polynomials of the above two matrices, an explicit closed-form formulas of the degree-Kirchhoff index, the Kemeny's constant and the number of spanning trees of CPn are obtained in terms of the index n.

关键词： Excitons   Quantum dots   Tunneling   Auger recombination   Kinetics  

摘要： In this study, we report the negative trion and biexciton Auger dynamics in very high-quality InP/ZnSe/ZnS quantum dots (QDs) having varying amounts of indium-based traps in the ZnSe shell. Negative trion times are determined by time-correlated photon-counting measurements on QDs that have been photoreduced with lithium triethylborohydride. We find that the Auger times vary from 280 to 425 ps and scale linearly with the total particle volume. Excess indium in the ZnSe shell gives rise to hole traps that are transiently populated following photoexcitation. Comparing stoichiometric and nonstoichiometric particles, we find that the negative trion lifetimes are independent of the presence of indium in the ZnSe shell. Biexciton dynamics are determined from transient absorption (TA) bleach recovery measurements. Absorption of two photons results in the formation of two types of biexcitons: those having both holes in the InP core (XX state) and those having one hole trapped in the ZnSe shell (XT state). XX state Auger times are measured in stoichiometric QDs, and for these particles, the Auger times are similar to 80 ps. Nonstoichiometric QDs show an additional long TA decay component, assigned to Auger recombination of the XT state. A previous study (J. Phys. Chem. C 2021, 125, 4110-4118) found that hole trapping at indium-based shell traps results in a slow photoluminescence (PL) rise component. We find that the fraction of the XT state formed by the absorption of two photon correlates with the product of the fraction of slow PL rise and the rise time constant following one-photon excitation.

关键词： Charge transfer  

摘要： We computed fully quantum nuclear dynamics, which accompanies electron transfer mediated decay (ETMD) in weakly bound polyatomic clusters. We considered two HeLi2 clusters - with Li-2 being either in the singlet electronic ground state or in the triplet first excited state - in which ETMD takes place after ionization of He. The electron transfer from Li-2 to He+ leads to the emission of another electron from Li-2 into the continuum. Due to the weak binding of He to Li-2 in the initial states of both clusters, the involved nuclear wavepackets are very extended. This makes both the calculation of their evolution and the interpretation of the results difficult. We showed that despite the highly delocalized nature of the wavepackets the nuclear dynamics in the decaying state is imprinted on the ETMD electron spectra. The analysis of the latter helps understanding the effect which electronic structure and binding strength in the cluster produce on the quantum motion of the nuclei in the decaying state. The results produce a detailed picture of this important charge transfer process in polyatomic systems.

关键词： Exciton polariton   Optical lattices & traps   Vortices in superfluids  

摘要： If a quantum fluid is driven with enough angular momentum, at equilibrium the ground state of the system is given by a lattice of quantized vortices whose density is prescribed by the quantization of circulation. We report on the first experimental study of the Feynman-Onsager relation in a nonequilibrium polariton fluid, free to expand and rotate. Upon initially imprinting a lattice of vortices in the quantum fluid, we track the vortex core positions on picosecond timescales. We observe an accelerated stretching of the lattice and an outward bending of the linear trajectories of the vortices, due to the repulsive polariton interactions. Access to the full density and phase fields allows us to detect a small deviation from the Feynman-Onsager rule in terms of a transverse velocity component, due to the density gradient of the fluid envelope acting on the vortex lattice.

关键词： Superfluid vortex rings in He II   Particle-laden flows   Hall-Vinen-Bekarevich-Khalatnikov (HVBK) hydrodynamics  

摘要： The decay of quantum vortex rings in counterflow regimes, visualized in Helium II with the help of solid hydrogen particles trapped to their cores, has been a puzzling issue within the usual description of superfluid vortex dynamics, grounded on the hypothesis that a vortex filament is, effectively, an extended massless object subject to a canceling superposition of Magnus and mutual friction forces. We discuss, from a general energy-budget point of view, a phenomenological solution of this problem, which relies on viscous and quantum dissipation mechanisms, the later associated to the backreaction of vortex singular structures on the surrounding two-component fluid mixture. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Pseudocapacitance   Quantum capacitance   Density functional theory calculation   Electronic structure   Transport kinetics  

摘要： The boundary between quantum capacitance and pseudocapacitance is blurred due to their similarity in electronic populations. Here we propose the rules to classify the contributions of quantum capacitance and pseudocapacitance and their effects on the intrinsic ion transport kinetics based on the applied voltages and electronic structures. Systems including graphite, LiFePO4, LiTiS2, LiCoO2, and Ti3C2Tx MXene are employed to illustrate their different intrinsic kinetics according to the classifications based on the density functional theory calculations and the reported experimental measurements. These results can facilitate the step to screen the electrode materials with different kinetics through calculations.