Transport through quantum dots in mesoscopic circuits

We study the transport through a quantum dot, in the Kondo Coulomb blockade valley, embedded in a mesoscopic device with finite wires. The quantization of states in the circuit that hosts the quantum dot gives rise to finite size effects. These effects make the conductance sensitive to the ratio of the Kondo screening length to the wires length and provide a way of measuring the Kondo cloud. We present results obtained with the numerical renormalization group for a wide range of physically accessible parameters.     

透平叶栅气膜冷却效果的数值研究

本文基于二维粘性数值模拟分析了某透平叶片气膜冷却的效果。在系统分析了冷却气流的喷射速度、喷射角度和温度的影响之后，得到了一些对叶片设计非常有用的结果和结论，同时探讨了本研究发展的数值方法和程序用于工程设计的可能性。     

Lensing effects in Q-switched unstable laser cavities with side-pumped Nd:YAG and ruby crystal rods

We present a comprehensive numerical model that accounts for non-uniform pumping and a related thermal and electronic lensing effects in Q-switched unstable laser cavities. We study the influence of these effects on the output beam profile in Nd:YAG and ruby laser systems with side-pumped crystal rods. We also constructed both lasers to experimentally validate the numerical results and found very good agreement. The results show that both types of lensing effects are particularly detrimental in ruby, while they are insignificant in Nd:YAG.     

Nonlinear wave interaction in photonic band gap materials

We present detailed analytical and numerical studies of nonlinear wave interaction processes in one-dimensional (1D) photonic band gap (PBG) materials with a Kerr nonlinearity. We demonstrate that some of these processes provide efficient mechanisms for dynamically controlling so-called gap-solitons. We derive analytical expressions that accurately determine the phase shifts experienced by nonlinear waves for a large class of non-resonant interaction processes. We also present comprehensive numerical studies of inelastic interactions, and show that rather distinct regimes of interaction exist. The predicted effects should be experimentally observable, and can be utilized for probing the existence and parameters of gap solitons. Our results are directly applicable to other nonlinear periodic structures such as Bose–Einstein condensates in optical lattices.     

Second mode transition in microstructured optical fibers: determination of the critical geometrical parameter and study of the matrix refractive index and effects of cladding size

We carried out a numerical study of the second mode transition in finite-sized, microstructured optical fibers (MOFs) for several values of the matrix refractive index. We determined a unique critical geometrical parameter for the second mode cutoff that is valid for all the matrix refractive indices studied. Finite size effects and extrapolated results for infinite structures are described. Using scaling laws, we provide a generalized phase diagram for solid-core MOFs that is valid for all refractive indices, including those of the promising chalcogenide MOFs.     

Refractive index dispersion properties of collagen for microscopic second-harmonic generation

We theoretically simulate second-harmonic generation (SHG) in collagen under linearly polarized focused laser beam. With this model, the effects of numerical aperture (NA) and refractive index dispersion on SHG emission have been investigated. Dispersion properties of collagen are significant under incident wavelength in the visible range. Our results show that the efficient SHG is obtained by controlling the NA, and the higher NA is a necessity when the dispersion effect is considered. Our theoretical simulation results provide useful clues for experimental study of microscopic SHG emission in collagen excited by focused beam.     

Transport through quantum dots: a combined DMRG and embedded-cluster approximation study

The numerical analysis of strongly interacting nanostructures requires powerful techniques. Recently developed methods, such as the time-dependent density matrix renormalization group (tDMRG) approach or the embedded-cluster approximation (ECA), rely on the numerical solution of clusters of finite size. For the interpretation of numerical results, it is therefore crucial to understand finite-size effects in detail. In this work, we present a careful finite-size analysis for the examples of one quantum dot, as well as three serially connected quantum dots. Depending on “odd-even” effects, physically quite different results may emerge from clusters that do not differ much in their size. We provide a solution to a recent controversy over results obtained with ECA for three quantum dots. In particular, using the optimum clusters discussed in this paper, the parameter range in which ECA can reliably be applied is increased, as we show for the case of three quantum dots. As a practical procedure, we propose that a comparison of results for static quantities against those of quasi-exact methods, such as the ground-state density matrix renormalization group (DMRG) method or exact diagonalization, serves to identify the optimum cluster type. In the examples studied here, we find that to observe signatures of the Kondo effect in finite systems, the best clusters involving dots and leads must have a total z-component of the spin equal to zero.     

Nonlinear dynamics and manipulation of dripping in capillary flow focusing

In this study, we carried out experimental and numerical investigations on the dripping dynamics in axisymmetric capillary flow focusing. For the direct numerical simulations, we solved the Navier-Stokes equations coupled with a diffuse interface method.For the experiments, we observed both periodic and non-periodic dripping modes at different focused and focusing liquid flow rates. The non-periodic dripping that results in polydispersed droplets downstream the orifice can be attributed to the nonlinear dynamics of the flow; thus, we constructed numerical plots of the streamlines and temporal evolutions of the focused liquid cone in different modes. We identified a phase diagram of the dripping regimes in the plane of mainly dimensionless parameters, which led us to further investigate the effects of liquid physical properties, such as viscosity and interface tension, on the mode transition.For suppression of the nonlinear dynamics, we proposed a geometrical optimization that imports a guiding rod positioning along the axis of the capillary tube. Here, we conducted a numerical analysis on the manipulation of the dripping process, as well as scaling analysis on the appearance of the nonlinear dripping. We expect this study to provide an insight into the underlying physical mechanisms of dripping in flow focusing, which are advantageous in the generation of monodispersed microdroplets for various applications.     

Approach to the Extended States Conjecture

We develop a rather explicit approach concerning the extended states conjecture for the discrete random Schrödinger operator, or more generally for the so-called Anderson-type Hamiltonian. Our work is based on deep mathematical results by Jak?i?–Last (Duke Math. J. 133(1):185–204, 2006). Concretely, we suggest two new directions of research: We provide a formula which may lead the way to a rigorous proof of the conjecture, and an implementation of the proposed approach which yields numerical evidence in favor of the conjecture being true for the discrete random Schrödinger operator in dimension two. Not being based on scaling theory, this method eliminates problems due to boundary conditions, common to previous numerical methods in the field. At the same time, as with any numerical experiment, one cannot exclude finite-size effects with complete certainty. We numerically track the “bulk distribution” (here: the distribution of where we most likely find an electron) of a wave packet initially located at the origin, after iterative application of the discrete random Schrödinger operator.     

Enhancing light slow-down in semiconductor optical amplifiers by optical filtering

We show that the degree of light-speed control in a semiconductor optical amplifier can be significantly extended by the introduction of optical filtering. We achieve a phase shift of approximately 150 degrees at 19 GHz modulation frequency, corresponding to a several-fold increase of the absolute phase shift as well as the achievable bandwidth. We show good quantitative agreement with numerical simulations, including the effects of population oscillations and four-wave mixing, and provide a simple physical explanation based on an analytical perturbation approach.     

Turing Patterns in a Reaction-Diffusion System

We have further investigated Turing patterns in a reaction-diffusion system by theoretical analysis and numerical simulations. Simple Turing patterns and complex superlattice structures are observed. We find that the shape and type of Turing patterns depend on dynamical parameters and external periodic forcing, and is independent of effective diffusivity rate σ in the Lengyel-Epstein model. Our numerical results provide additional insight into understanding the mechanism of development of Turing patterns and predicting new pattern formations.     

Kondo screening cloud around a quantum dot: large-scale numerical results

Measurements of the persistent current in a ring containing a quantum dot would afford a unique opportunity to finally detect the elusive Kondo screening cloud. We present the first large-scale numerical results on this controversial subject using exact diagonalization and density matrix renormalization group (RG). These extremely challenging numerical calculations confirm RG arguments for weak to strong coupling crossover with varying ring length and give results on the universal scaling functions. We also study, analytically and numerically, the important and surprising effects of particle-hole symmetry breaking.     

Asymptotic distribution of global errors in the numerical computations of dynamical systems

We propose an analysis of the effects introduced by finite-accuracy and round-off arithmetic on numerical computations of discrete dynamical systems. Our method, which uses the statistical tool of the decay of fidelity, computes the error by directly comparing the numerical orbit with the exact one (or, more precisely, with another numerical orbit computed with a much higher accuracy). Furthermore, as a model of the effects of round-off arithmetic on the map, we also consider a random perturbation of the exact orbit with an additive noise, for which exact results can be obtained for some prototype maps. We investigate the decay laws of fidelity and their relationship with the error probability distribution for regular and chaotic maps, for both additive and numerical noise. In particular, for regular maps we find an exponential decay for additive noise, and a power-law decay for numerical noise. For chaotic maps, numerical noise is equivalent to additive noise, and our method is suitable for identifying a threshold for the reliability of numerical results, i.e., the number of iterations below which global errors can be ignored. This threshold grows linearly with the number of bits used to represent real numbers.     

Semiclassical mechanism for the quantum decay in open chaotic systems

We address the decay in open chaotic quantum systems and calculate semiclassical corrections to the classical exponential decay. We confirm random matrix predictions and, going beyond, calculate Ehrenfest time effects. To support our results we perform extensive numerical simulations. Within our approach we show that certain (previously unnoticed) pairs of interfering, correlated classical trajectories are of vital importance. They also provide the dynamical mechanism for related phenomena such as photoionization and photodissociation, for which we compute cross-section correlations. Moreover, these orbits allow us to establish a semiclassical version of the continuity equation.     

Landau parameters and pairing-on the shores of the nuclear Fermi sea

We present a systematic scheme for calculating the ground-state energy, single-particle energies and the effective mass, Fermi-liquid parameters, and pairing matrix elements for nuclear and neutron matter with realistic state-dependent interactions. The method retains much of the clarity of more conventional treatments while permitting reliable numerical calculations. Deficiencies in the central Jastrow correlation operator ansatz are largely overcome by low-order perturbation theory in the correlated basis generated by the Jastrow operator. Calculations of these quantities are presented for the Reid and Bethe-Johnson interactions. An analysis of the results emphasizes the importance of state-dependent correlations arising directly from the interaction or indirectly through many-body effects. The numerical results provide insight into the actual structure of the self-energy operator in nuclear and neutron matter and into the usefulness of sum rules for the quasiparticle interaction and the Landau parameters.     

Multi-scale properties of large eddy simulations: correlations between resolved-scale velocity-field increments and subgrid-scale quantities

We provide analytical and numerical results concerning multi-scale correlations between the resolved velocity field and the subgrid-scale (SGS) stress-tensor in large eddy simulations (LES). Following previous studies for Navier–Stokes equations, we derive the exact hierarchy of LES equations governing the spatio-temporal evolution of velocity structure functions of any order. The aim is to assess the influence of the subgrid model on the inertial range intermittency. We provide a series of predictions, within the multifractal theory, for the scaling of correlation involving the SGS stress and we compare them against numerical results from high-resolution Smagorinsky LES and from a-priori filtered data generated from direct numerical simulations (DNS). We find that LES data generally agree very well with filtered DNS results and with the multifractal prediction for all leading terms in the balance equations. Discrepancies are measured for some of the sub-leading terms involving cross-correlation between resolved velocity increments and the SGS tensor or the SGS energy transfer, suggesting that there must be room to improve the SGS modelisation to further extend the inertial range properties for any fixed LES resolution.