Computational difficulty of finding matrix product ground states

We determine the computational difficulty of finding ground states of one-dimensional (1D) Hamiltonians, which are known to be matrix product states (MPS). To this end, we construct a class of 1D frustration-free Hamiltonians with unique MPS ground states and a polynomial gap above, for which finding the ground state is at least as hard as factoring. Without the uniqueness of the ground state, the problem becomes NP complete, and thus for these Hamiltonians it cannot even be certified that the ground state has been found. This poses new bounds on convergence proofs for variational methods that use MPS.     

Scale-renormalized matrix-product states for correlated quantum systems

A generalization of matrix product states (MPS) for interacting quantum systems in two and three dimensions is introduced. These scale-renormalized matrix-product states (SR-MPS) are based on a coarse graining of the lattice in which the blocks at each level are associated with matrix products that are further transformed (scale renormalized) with other matrices before they are assembled to form blocks at the next level. Using the two-dimensional transverse-field Ising model as a test, it is shown that the SR-MPS converge much more rapidly with the matrix size than a standard MPS. It is also shown that the use of lattice symmetries speeds up the convergence very significantly.     

Influence of elastic strain on the density of phonon states and characteristics of discrete breathers in the gap of the phonon spectrum of a crystal with a NaCl structure

Appreciable elastic strain may considerably change the physical properties of crystals. This effect underlies the elastic stress technology, which has been intensively developed in recent years. The influence of elastic strain on the density of phonon states and on the properties of discrete breathers in the gap of the phonon spectrum of a crystal with a NaCl structure and a considerable difference between the anion and cation masses is studied using the molecular dynamics method. A number of crystal straining modes are considered. It is shown that the shear components of the strain tensor may significantly change the density of phonon states but slightly influence the frequencies of discrete breathers. Compression (tensile) strains raise (lower) the frequency of discrete breathers with a respective polarization.     

Accuracy and stability in incompressible SPH (ISPH) based on the projection method and a new approach

The stability and accuracy of three methods which enforce either a divergence-free velocity field, density invariance, or their combination are tested here through the standard Taylor–Green and spin-down vortex problems. While various approaches to incompressible SPH (ISPH) have been proposed in the past decade, the present paper is restricted to the projection method for the pressure and velocity coupling. It is shown that the divergence-free ISPH method cannot maintain stability in certain situations although it is accurate before instability sets in. The density-invariant ISPH method is stable but inaccurate with random-noise like disturbances. The combined ISPH, combining advantages in divergence-free ISPH and density-invariant ISPH, can maintain accuracy and stability although at a higher computational cost. Redistribution of particles on a fixed uniform mesh is also shown to be effective but the attraction of a mesh-free method is lost. A new divergence-free ISPH approach is proposed here which maintains accuracy and stability while remaining mesh free without increasing computational cost by slightly shifting particles away from streamlines, although the necessary interpolation of hydrodynamic characteristics means the formulation ceases to be strictly conservative. This avoids the highly anisotropic particle spacing which eventually triggers instability. Importantly pressure fields are free from spurious oscillations, up to the highest Reynolds numbers tested.     

Wave-packet discretization of a continuum: Path toward practically solving few-body scattering problems

A new method for discretizing a three-body continuum with the aid of the L ₂ basis of stationary wave packets is considered within the problem of three-body scattering. Substantial advantages of employing this basis in solving problems of few-body scattering are demonstrated. Specific applications of this approach are exemplified by exploring the problem of scattering of a composite particle on a heavy nucleus with allowance for the excitation of this particle to continuum states. This is done within two alternative approaches: a direct wave-packet discretization of a three-body continuum and a method that is based on the Feshbach projection formalism. It is shown explicitly that the resulting scattering amplitudes are convergent as the number of wave-packet states that are taken into account is increased. The results obtained here are compared with the results of other authors whose treatment was based on alternative methods for discretizing a continuum.     

Piezoresistive effect in single-walled carbon nanotubes

This paper reports on the results of the theoretical investigation of the piezoresistive effect in single-walled carbon nanotubes of two structural modifications: arm-chair type and zig-zag type. The variation in the band gap of semiconducting nanotubes under the influence of the compressive and tensile deformations has been analyzed. The main quantitative characteristic of the piezoresistive effect—the longitudinal component of the elastic conductivity tensor—has been calculated, and its dependence on the diameter of semiconducting nanotubes has been shown. The variants of practical implementation of the effect under study have been proposed.     

Surface morphological response of crystalline solids to mechanical stresses and electric fields

Surface morphological evolution under the action of external fields is a fascinating topic that has attracted considerable attention within the surface science community over the past two decades. In addition to the interest in a fundamental understanding of field-induced nonlinear response and stability of surface morphology, the problem has been technologically significant in various engineering applications such as microelectronics and nanofabrication. In this report, we review theoretical progress in modeling the surface morphological response of stressed elastic solids under conditions that promote surface diffusion and of electrically conducting solids under surface electromigration conditions. A self-consistent model of surface transport and morphological evolution is presented that has provided the basis for the theoretical and computational work that is reviewed. According to this model, the surface morphological response of electrically conducting elastic solids to the simultaneous action of mechanical stresses and electric fields is analyzed. Emphasis is placed on metallic surfaces, including surfaces of voids in metallic thin films.Surfaces of stressed elastic solids are known to undergo morphological instabilities, such as the Asaro–Tiller or Grinfeld (ATG) instability that leads to emanation of crack-like features from the surface and their fast propagation into the bulk of the solid material. This instability is analyzed theoretically, simulated numerically, and compared with experimental measurements. The surface morphological evolution of electrically conducting, single-crystalline, stressed elastic solids under surface electromigration conditions is also examined. We demonstrate that, through surface electromigration, a properly applied and sufficiently strong electric field can stabilize the surface morphology of the stressed solid against both crack-like ATG instabilities and newly discovered secondary rippling instabilities; the effects of important parameters, such as surface crystallographic orientation, on the surface morphological response to the simultaneous action of an electric field and mechanical stress also are reviewed. In addition, electromigration-driven surface morphological response is analyzed systematically, focusing on the current-driven surface morphological evolution of voids in metallic thin films; this analysis has been motivated largely by the crucial role of void dynamics in determining the reliability of metallic interconnects in integrated circuits and has led to the interpretation of a large body of experimental observations and measurements. The electromigration-driven translational motion of morphologically stable voids, effects of current-driven void dynamics on the evolution of the electrical resistance of metallic thin films, and current-driven void–void interactions also are reviewed. Furthermore, theoretical studies are reviewed that demonstrated very interesting current-driven nonlinear void dynamics in stressed metallic thin films, including the inhibition of electromigration-induced instabilities due to the action of biaxial tensile stress, and stress effects on the electromigration-driven translational motion of morphologically stable voids.Complex, oscillatory surface states under surface electromigration conditions have been observed in numerical studies. In this report, emphasis is placed on void surfaces in metallic thin films, for which stable time-periodic states have been demonstrated. It is shown that increasing parameters such as the electric-field strength or the void size past certain critical values leads to morphological transitions from steady to time-periodic states; the latter states are characterized by wave propagation on the surface of a void that migrates along the metallic film at constant speed. The transition onset corresponds to a Hopf bifurcation that may be either supercritical or subcritical, depending on the symmetry of the surface diffusional anisotropy as determined by the crystallographic orientation of the film plane. It is also shown that, in the case where the Hopf bifurcation is subcritical, the simultaneous action of mechanical stress leads the current-driven void morphological response to the stabilization of chaotic attractors; in such cases, as the applied stress level increases, the void dynamics is set on a route to chaos through a sequence of period-doubling bifurcations. The observation of current-driven chaotic dynamics in homoepitaxial islands also is discussed.     

Electronic and magnetic properties of single-layer and double-layer VX_2(X=Cl,Br) under biaxial stress

First-principles calculations and Monte Carlo simulations reveal that single-layer and double-layer VX_2(X = Cl, Br)can be tuned from antiferromagnetic(AFM) semiconductors to ferromagnetic(FM) state when biaxial tensile stress is applied. Their ground states are all T phase. The biaxial tensile stress at the phase transition point of the double-layer VX_2 is larger than that of the single-layer VX_2. The direct band gaps can be also manipulated by biaxial tensile stress as they increases with increasing tensile stress to a critical point and then decreases. The Néel temperature(TN) of double-layer VX_2 are higher than that of single-layer. As the stress increases, the TNof all materials tend to increase. The magnetic moment increases with the increase of biaxial tensile stress, and which become insensitive to stress after the phase transition points.Our research provides a method to control the electronic and magnetic properties of VX_2 by stress, and the single-layer and double-layer VX_2 may have potential applications in nano spintronic devices.     

Design of X-ray super-mirrors using simulated annealing algorithm

An adaptive local search-based simulated annealing (ALSA) algorithm is proposed for the design of the wide band-pass multilayer optical elements operating in the hard and soft X-ray wavelength ranges. At present the SA algorithm has been kept as simple as possible and its performance is being studied before a series of modifications are made to tailor the SA algorithm to optimize super-mirror for particular applications. The algorithm has also been developed with two specific areas in mind: a W/C broad angle super-mirror for hard X-ray applications and a Mo/Si wide band super-mirror operating at normal incidence in the EUV spectral region. The design results show that the ALSA algorithm method has the flexibility to design a wide range of multilayer structures and in comparison to other techniques has good results although computationally more intensive.     

Instability of water jet: Aerodynamically induced acoustic and capillary waves

High-speed water jet cutting has important industrial applications. To further improve the cutting performance it is critical to understand the theory behind the onset of instability of the jet. In this paper, instability of a water jet flowing out from a nozzle into ambient air is studied. Capillary forces and compressibility of the liquid caused by gas bubbles are taken into account, since these factors have shown to be important in previous experimental studies. A new dispersion equation, generalizing the analogous Rayleigh equation, is derived. It is shown how instability develops because of aerodynamic forces that appear at the streamlining of an initial irregularity of the equilibrium shape of the cross-section of the jet and how instability increases with increased concentration of gas bubbles. It is also shown how resonance phenomena are responsible for strong instability. On the basis of the theoretical explanations given, conditions for stable operation are indicated.     

限域量子态调控研究

电子、激子和声子等量子态在固体中的行为早已被人们所熟知. 然而,当体系的尺寸只有纳米量级的时候,已有的固体理论常常不能适用,需要新的低维物理理论的建立. 我们系统研究了低维体系限域量子态（包括电子、激子和声子）的行为对环境、应力、压力及光的响应和性质的调控. 较早认识到低维体系之显著的表面-体积比对量子态性质调控之有效性,系统地揭示了低维体系的一系列由表面和应力决定的新颖性质,证明了低维体系的表面和应力效应同量子限域效应同等重要. 本文概况了如下五个方面的结果：（1）一种使用应力效应调控电子能带结构的方法和（2）一种使用表面效应调控电子能带结构的方法（这两个方法都可将低维体系能带从间接能隙调控至直接能隙能带结构）;（3）一种低维体系表面掺杂方法,该方法将在低维体系掺杂中取代传统方法;（4）量子点表面诱导的光致异构现象;（5）基于表面自催化半导体低维结构的形成机理. 希望我们的研究工作有助于促进低维体系在光电子、纳电子、环境、能源、生物和医学等领域的应用.     

基于大涡模拟的移动粒子半隐式算法

移动粒子半隐式方法(MPS)是一种粒子方法,多用于模拟带有自由表面的不可压缩流动。工程实际中的自由表面流动往往是复杂的湍流流动,本文借鉴网格类方法的亚格子应力模型发展了基于Smagorinsky模型的亚粒子应力模型,并将其耦合到MPS方法中,实现了基于大涡模拟的MPS方法并用于研究自由表面湍流问题。为了提高计算的准确性和稳定性,SPS模型中出现的一阶导数项采用最小二乘法拟合得到,SPS项采用显式算法进行计算。使用这一算法模拟了溃坝问题,结果表明,采用亚粒子应力模型的模拟结果与实验的吻合程度明显提高。     

The elimination of zero-order diffraction of 10.6 μm infrared digital holography

A new method of eliminating the zero-order diffraction in infrared digital holography has been raised in this paper. Usually in the reconstruction of digital holography, the spatial frequency of the infrared thermal imager, such as microbolometer, cannot be compared to the common visible CCD or CMOS devices. The infrared imager suffers the problems of large pixel size and low spatial resolution, which cause the zero-order diffraction a severe influence of the reconstruction process of digital holograms. The zero-order diffraction has very large energy and occupies the central region in the spectrum domain. In this paper, we design a new filtering strategy to overcome this problem. This filtering strategy contains two kinds of filtering process which are the Gaussian low-frequency filter and the high-pass phase averaging filter. With the correct set of the calculating parameters, these filtering strategies can work effectively on the holograms and fully eliminate the zero-order diffraction, as well as the two crossover bars shown in the spectrum domain. Detailed explanation and discussion about the new method have been proposed in this paper, and the experiment results are also demonstrated to prove the performance of this method.     

On the nonlinear instability of the solutions of hydrodynamic-type systems

New exact solutions (including periodic) of three-dimensional nonstationary Navier-Stokes equations containing arbitrary functions are described. The problems of the nonlinear stability/instability of the solutions have been analyzed. It has been found that a feature of a wide class of the solutions of hydrodynamic-type systems is their instability. It has been shown that instability can occur not only at sufficiently large Reynolds numbers, but also at arbitrary small Reynolds numbers (and can be independent of the fluid velocity profile). A general physical interpretation of the solution under consideration is given. It is important to note that the instability of the solutions has been proven using a new exact method (without any assumptions and approximations), which can be useful for analyzing other nonlinear physical models and phenomena.     

Disturbance-free digital holographic microscopy via a micro-phase-step approach

This work proposes a cost-effective, simple, micro-phase-step (MPS) method for suppressing the zero-order diffraction and conjugate-image interferences that are caused during digital holographic microscopic image reconstruction. The proposed MPS method replaces the conventional phase modulation approach; it uses a rotatable cover glass that enables smooth modification of the incidence angle and the optical path of the reference beam. This setup allows the phase step to be accurately estimated by shifting the reference wave phase more freely close to π/2, at which the background noise can be suppressed more effectively. In the proposed MPS method, the optimal conditions for suppressing conjugate-image interference are identified using a relatively moderate intensity distribution and suppression of noise in the numerically reconstructed object wave-field. In addition, the proposed method mitigates the effect of disturbances that are caused by environmental factors, such as minor vibrations and small changes in temperature and humidity. Importantly, only two holograms are required to satisfy the objective of image reconstruction. The results in this work reveal that even with intentional interference caused by minor vibrations, conjugate-image interference can still be suppressed by determining the phase deviation between the two original holograms.     

Effect of temperature on inhomogeneous elastic deformation and negative stiffness of NiAl and FeAl alloy nanofilms

The uniaxial tension of NiAl and FeAl intermetallic alloy nanofilms at different temperatures has been investigated by the molecular dynamics method. It was previously shown that nanofilms at 0 K are elastically deformed by almost 40% and that, under strain-controlled tension, there is a region in the stress—strain curves, where an increase in the strain is accompanied by a decrease in the tensile stress, i.e., the stiffness of nanofilms is negative. Deformation of the films in the thermal instability region is associated with the appearance of domains with different elastic strains. The influence of the temperature on these effects is investigated. Particularly, it is shown that as the temperature increases, both the elastic strain and the negative stiffness of nanofilms decrease. The inhomogeneous elastic strain and negative stiffness for FeAl films are observed in a broader temperature range (to 1000 K) than for NiAl films (to 300 K), which constitutes 0.16 and 0.65 of the melting point of these materials, respectively.     

Atomistic level studies on the tensile behavior of GaN nanotubes under uniaxial tension

Molecular dynamics method with the Stillinger-Weber (SW) potential has been employed to study the responses of GaN nanotubes (GaNNTs) to a uniaxial tensile load along the axial direction. It has been revealed that GaNNTs exhibits a completely different tensile behavior at different temperatures, i.e. ductility at higher deformation temperatures and brittleness at lower temperatures, leading to a brittle to ductile transition (BDT). Both the BDT temperature and the critical stress increases with increasing thickness of GaNNTs, and the critical stress at higher temperature are lower than those at lower temperature. These results on the tensile behaviors of GaNNTs in an atomic level will provide a good reference to its promising applications.     

Oscillating viscosity in a lyotropic lamellar phase under shear flow

We report some time-dependent behavior of lyotropic lamellar phase under shear flow. At fixed stress, near a layering instability, the system presents an oscillating shear rate. We build up a new stress versus shear rate diagram that includes temporal behavior. This diagram is made of two distinct branches of stationary states which correspond, respectively, to disordered and ordered multilamellar vesicle phases. When increasing the shear stress, prior to the transition to the ordered structural state, sustained oscillations of the viscosity are recorded. They correspond to periodic structural change of the entire sample between a disordered and a ordered state of multilamellar vesicles.     

Pattern selection in biaxially stressed solids

We analyze the morphological instability of the surface of a solid which is subject to a biaxial stress. The stability calculation reveals a new favored pattern: a diamond morphology. This occurs if the stress is tensile in one direction and compressive in the orthogonal one and the ratio exceeds a certain value. A nonlinear analysis shows that the bifurcation is subcritical and hints to a nontrivial competition between tilted stripes and diamonds. This study opens a new line of inquiries in the field of stress-induced pattern selection.