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关键词： Besov   Regularity   Elliptic   p(x)-Laplacian   Logarithmic   Weak solutions  

摘要： In this paper we establish the local regularity estimates in Besov spaces of weak solutions for the elliptic p(x)-Laplacian equation with the logarithmic growth in divergence form div(vertical bar del u vertical bar(p(x)-2) In(e +vertical bar del u vertical bar)del u) = div F under some proper assumptions on the functions p(x) and F. Moreover, it is worth noting that our results improve the known results for these types of equations. (C) 2021 Elsevier Inc. All rights reserved.

关键词： Graphene-like quantum dots   Magnetic and thermodynamic properties   Phase diagrams   Hysteresis behaviors   Monte Carlo simulation  

摘要： Based on the Monte Carlo simulation, we have investigated the magnetic and thermodynamic behaviors of the graphene-like quantum dots described by a ferrimagnetic mixed-spin (3/2, 5/2) Ising model. The curves of the magnetization, magnetic susceptibility, internal energy and the specific heat as a function of temperature have been given under various physical parameters. The interesting turnover phenomenon has been found owing to the competition between the crystal field and temperature. It is found that the value of the blocking temperature increases with decreasing the crystal field or increasing the exchange coupling and external magnetic field. We have also investigated the hysteresis loops and found the impossibility of the triple-loop hysteresis behavior for certain parameters. The area of the hysteresis loops can be improved by increasing the exchange coupling and decreasing the absolute values of the crystal field and temperature.

关键词： Quantum dots   Ligands   Oscillation   Power   Kinetics  

摘要： Gold nanoclusters (AuNCs) are a recently developed class of photoluminescent nanomaterial with potential for detection and imaging applications in both chemistry and biology. The AuNC small size (Au104NC) in combination with their long-lived, near-infrared (NIR) emission suggests that they could be applied as a biological label directly and also as a potential acceptor for energy transfer-based biosensing. Previous studies have shown that functionalized AuNCs can act as energy-transfer acceptors;however, the underlying mechanism appears to be complex and does not necessarily follow a classical Forster process with a (1/R)(6) distance dependence. Here, we report a femtosecond and nanosecond time-resolved spectroscopy study to examine the energy dissipation and transfer processes of photoluminescent AuNC acceptors displaying different functionalized end groups and coupled with 625 nm emitting semiconductor quantum dot (QD) donors. Examination of AuNCs alone on the femtosecond timescale show coherent vibrational oscillations within the first 15 ps after excitation in the visible and NIR region. Fourier transform of the kinetic data reveal similar to 0.18 and 0.40 THz low-frequency vibrations in aqueous AuNC solutions, with the latter attributed to coherent vibrations following hot electronic relaxation. A biphasic decay of the AuNC excited state on the microsecond timescales confirm their exceptionally long-lived lifetimes and that the photophysics is largely unaffected by the functional end group on the ligand. Finally, ultrafast studies of AuNCs coupled to the 625 QD donors reveal excited-state quenching and wavelength shifts of the QD's ground-state bleach and the appearance of the excited state of the AuNC resulting from energy transfer occurring on the similar to 200 ps timescale.

关键词： Nonequilibrium statistical mechanics   Quantum simulation   Quantum transport   Lattice models in condensed matter  

摘要： In a recent milestone experiment, Google’s processor Sycamore heralded the era of “quantum supremacy” by sampling from the output of (pseudo-)random circuits. We show that such random circuits provide tailor-made building blocks for simulating quantum many-body systems on noisy intermediate-scale quantum (NISQ) devices. Specifically, we propose an algorithm consisting of a random circuit followed by a trotterized Hamiltonian time evolution to study hydrodynamics and to extract transport coefficients in the linear response regime. We numerically demonstrate the algorithm by simulating the buildup of spatiotemporal correlation functions in one- and two-dimensional quantum spin systems, where we particularly scrutinize the inevitable impact of errors present in any realistic implementation. Importantly, we find that the hydrodynamic scaling of the correlations is highly robust with respect to the size of the Trotter step, which opens the door to reach nontrivial time scales with a small number of gates. While errors within the random circuit are shown to be irrelevant, we furthermore unveil that meaningful results can be obtained for noisy time evolutions with error rates achievable on near-term hardware. Our work emphasizes the practical relevance of random circuits on NISQ devices beyond the abstract sampling task.

关键词： Time-dependent interaction   Two-mode converter   Finite entangled states  

摘要： This paper considers a qubit interacting time-dependently with parametric converter two-mode cavity fields. The dynamics of quantum effects, population inversion and quantum coherence, have been investigated when the cavity fields start from entangled coherent states. The qubit starts from a superposition state. We have examined the effects of the difference between the two-mode photon numbers, the qubit time-dependent location, and the initial qubit state on the dynamics of the generated quantum coherence. It is found that the dynamics of the population inversion, the entropies, and the negativity qubit-cavity entanglement can be controlled by the difference between the two-mode photon numbers, the qubit location parameter as well as the initial qubit state.

关键词： Optimal control   fractional Laplacian   variational methods   saddle points   stability   Kuratowski-Painleve limit  

摘要： We consider some optimal control problem governed by a class of differential equations with the spectral Dirichlet fractional Laplacian. Some sufficient condition for the existence of optimal processes are proved. The proof of the main result relies on the variational structure of the problem. To show that differential equations with the Dirichlet fractional Laplacian have a weak solution we employ the Ky Fan Theorem.

关键词： Wave function   Energy   Quantum mechanics   Mathematical methods   Computational chemistry  

摘要： The Madelung-de Broglie-Bohm formulation of the Schrodinger equation casts the time-evolution of a wave function as dynamics of an ensemble of quantum, or Bohmian, trajectories, interacting via the nonlocal quantum potential. This trajectory perspective gives insight into the quantumness (or classicality) of a given system due to clear partitioning of the energy into classical and quantum components. Here, we propose a system-independent measure of the quantumness of dynamics, based on the energy time-change, referred to as "quantum power". This measure is local in the coordinate space. Based on applications to model chemical systems, we argue that during the transition from the quantum to classical regime, defined as compression of quantization, the quantum features in dynamics do not "disappear" but are pushed forward in time. This feature may be used to gauge the validity of the semiclassical and other approximate dynamics approaches in applications to anharmonic systems.

关键词： Central serous chorioretinopathy   half-dose photodynamic therapy   vessel density   diameters of choroidal big vessels  

摘要： Purpose To determine vessel changes in retinochoroid with optical coherence tomographic angiography (OCT angiography) and spectral-domain OCT (SD-OCT) of patients with central serous chorioretinopathy (CSC) after half-dose photodynamic therapy (hd-PDT). Methods A prospective observational study of 62 eyes of 58 patients undergoing hd-PDT was followed for 3 months. Fundus fluorescein angiography (FFA) and indocyanine green angiography (ICGA) were performed at baseline;best-corrected visual acuity (BCVA), fundus photography, OCT angiography and SD-OCT were performed at baseline, 1-month, and 3-month follow-up visits. Results The mean vessel density of inner retina (VDIR) layer was 50.72 +/- 3.17 at baseline, then decreased to 48.97 +/- 4.34 at 1-month follow-up (p < .001), and partially recovered to 49.00 +/- 4.28 at 3-month follow-up (p < .001);the mean area of foveal avascular zone (FAZ) was 0.303 +/- 0.107 mm(2) at baseline, and then increased to 0.339 +/- 0.121 mm(2) and 0.342 +/- 0.125 mm(2) at 1-month and 3-month follow-up after hd-PDT (p < .001, p < .001). The mean diameters of choroidal big vessels (DCV) were 309.66 +/- 72.24 microns at baseline, then decreased to 300.13 +/- 69.38 microns at 1-month and 293.39 +/- 69.92 microns at 3-month after treatment (p < .001, p < .001). Conclusions Currently common applied hd-PDT for patients with CSC has significantly impact on both retinal and choroidal vessels. The retinal capillary flow decreased, therefore optimizing PDT parameters for treating CSC may still be necessary in the future.

关键词： Spin dynamics  

摘要： The modular path integral (MPI) formulation for one-dimensional extended systems, such as spin arrays or molecular aggregates, allows evaluation of spin- or exciton-vibration dynamics with effort that scales linearly with the number of units. This work presents a small matrix decomposition of the modular path integral (SMatMPI), which eliminates tensor storage and enables iterative long-time propagation.