A quantum search algorithm of two entangled registers to realize quantum discrete Fouriertransform of signal processing

The discrete Fourier transform （DFT） is the base of modern signal processing. 1-dimensional fast Fourier transform （1D FFT） and 2D FFT have time complexity O（N log N） and O（N^2 log N） respectively. Since 1965, there has been no more essential breakthrough for the design of fast DFT algorithm. DFT has two properties. One property is that DFT is energy conservation transform. The other property is that many DFT coefficients are close to zero. The basic idea of this paper is that the generalized Grover＇s iteration can perform the computation of DFT which acts on the entangled states to search the big DFT coefficients until these big coefficients contain nearly all energy. One-dimensional quantum DFT （1D QDFT） and two-dimensional quantum DFT （2D QDFT） are presented in this paper. The quantum algorithm for convolution estimation is also presented in this paper. Compared with FFT, 1D and 2D QDFT have time complexity O（v/N） and O（N） respectively. QDFT and quantum convolution demonstrate that quantum computation to process classical signal is possible.     

Density functionals and model Hamiltonians: Pillars of many-particle physics

Density-functional theory (DFT) and model Hamiltonians are conceptually distinct approaches to the many-particle problem, which can be developed and applied independently. In practice, however, there are multiple connections between the two. This review focuses on these connections. After some background and introductory material on DFT and on model Hamiltonians, we describe four distinct, but complementary, connections between the two approaches: (i) the use of DFT as input for model Hamiltonians, in order to calculate model parameters such as the Hubbard U and the Heisenberg J. (ii) The use of model Hamiltonians as input for DFT, as in the LDA + U functional. (iii) The use of model Hamiltonians as theoretical laboratories to study aspects of DFT. (iv) The use of special formulations of DFT as computational tools for studying spatially inhomogeneous model Hamiltonians. We mostly focus on this fourth combination, model DFT, and illustrate it for the Hubbard model and the Heisenberg model. Other models that have been treated with DFT, such as the PPP model, the Gaudin–Yang δ$\delta$-gas model, the XXZ chain, variations of the Anderson and Kondo models and Hooke’s atom are also briefly considered. Representative applications of model DFT to electrons in crystal lattices, atoms in optical lattices, entanglement measures, dynamics and transport are described.     

Exchange interactions and Tc in rhenium-doped silicon: DFT, DFT + U and Monte Carlo calculations

Interactions between rhenium impurities in silicon are investigated by means of the density functional theory (DFT) and the DFT + U scheme. All couplings between impurities are ferromagnetic except the Re-Re dimers which in the DFT method are nonmagnetic, due to the formation of the chemical bond supported by substantial relaxation of the geometry. The critical temperature is calculated by means of classical Monte Carlo (MC) simulations with the Heisenberg Hamiltonian. The uniform ferromagnetic phase is obtained with the DFT exchange interactions at room temperature for the impurities concentration of 7%. With the DFT + U exchange interactions, the ferromagnetic clusters form above room temperature in MC samples containing only 3% Re.     

Corrections to the density-functional theory electronic spectrum: copper phthalocyanine

A method for improving the electronic spectrum of standard Density-Functional Theory (DFT) calculations (i.e., LDA or GGA approximations) is presented, and its application is discussed for the case of the copper phthalocyanine (CuPc) molecule. The method is based on a treatment of exchange and correlation in a many-body Hamiltonian, and it leads to easy-to-evaluate corrections to the DFT eigenvalues. Self-interaction is largely corrected, so that the modified energy levels do not suffer from spurious crossings, as often encountered for CuPc in DFT, and they remedy the standard underestimation of the gap. As a specific example we study the sequence and position of the CuPc molecular orbitals, which are wrongly calculated by standard DFT, and show that they are correctly reproduced after our corrections are included. The suggested method is fast and simple and, while not as accurate as hybrid or semiempirical functionals for molecular levels, it can be easily applied to any local-orbital DFT approach, improving on several important limitations of standard DFT methods.     

Density functional theory approach to the freezing transition in two-dimensional colloid system

The freezing transition of two-dimensional colloid system is studied by the density functional theory (DFT). The liquid direct-pair correlation function (DPCF) is simulated by molecular dynamics simulations. With the DPCF, the freezing transition is determined using DFT with the Fourier components of the density ρ _K as the order parameters. The DFT results are consistent with the simulation results if ρ _Ks of the lowest three shells of reciprocal lattice vector (RLV) are used in the DFT calculation. The first order freezing transition takes place at DPCF ρ₀ C(k_a) = 0.788 on the first RLV shell. The laser induced freezing of colloid system is also studied using the DFT.     

氮气在MCM-41中毛细凝聚的模拟和理论研究

采用巨正则系综 Monte Carlo 方法(GCMC)以及基于扩展基本度量理论和 MBWR 状态方程的密度泛函理论,研究了 77.4 K 时氮气在不同孔径的 MCM-41 分子筛中吸附的密度分布和吸附等温线.提出的平均场权重密度泛函理论,克服了平均场近似预测主体相热力学性质时的偏差,获得的密度分布和吸附等温线与 GCMC 分子模拟结果有着很好的一致性.     

Surface properties of clean and Au or Pd covered hematite (α-Fe(2)O(3)) (0001)

The structure and electronic properties of different terminations of the α-Fe(2)O(3)(0001) surface were studied with spin-polarized density functional theory (DFT) and the DFT + U method accounting for the effect of strong on-site Coulomb correlations. The results for lattice relaxation, electronic and magnetic properties are presented and discussed. Though the DFT and DFT + U methods provide qualitatively very similar surface geometries they differ very much in the prediction of the electronic and magnetic properties, and the surface energetics of the clean α-Fe(2)O(3)(0001). The most stable single iron terminated (0001) surface and the oxygen-rich termination were chosen to study Au and Pd atom adsorption. The results show that both Au and Pd bind strongly to hematite surfaces and induce large changes in their geometry. The DFT + U bonding is weaker by 0.3-0.6 eV than DFT on the iron terminated surface and about 2 eV stronger on the oxygen terminated one. The binding is stronger for Pd than Au and for both adsorbates is distinctly stronger at the oxygen than at the iron terminated surface. On the iron terminated surface the adsorption binding energy per adatom increases both with Au and Pd coverage, whereas for the oxygen terminated one the opposite trend is observed.     

Can the Highly Symmetric SU(4) Spin—Orbital Model Be Realized in α-ZrCl3?

JETP Letters - We study physical properties of layered α-ZrCl3 as a potential candidate for the physical realization of the SU(4) spin—orbital model. Both DFT and DFT + U + SOC...     

Simple approximate physical orbitals for GW quasiparticle calculations

Generating unoccupied orbitals within density functional theory (DFT) for use in GW calculations of quasiparticle energies becomes prohibitive for large systems. We show that, without any loss of accuracy, the unoccupied orbitals may be replaced by a set of simple approximate physical orbitals made from appropriately prepared plane waves and localized basis DFT orbitals that represent the continuum and resonant states of the system, respectively. This approach allows for accurate quasiparticle calculations using only a very small number of unoccupied DFT orbitals, resulting in an order of magnitude gain in speed.     

Studying the occupied and unoccupied electronic structure of LaCoO<Subscript>3</Subscript> by using DFT+embedded DMFT method with the calculated value of <Emphasis Type="Italic">U</Emphasis>

In this work, we present a systematic study of the occupied and unoccupied electronic states of LaCoO₃ compound using DFT, DFT+U and DFT+embedded DMFT methods. The value of U used here is evaluated by using constrained DFT method and found to be ~6.9 eV. It is found that DFT result has limitations with energy positions of PDOS peaks due to its inability of creating a hard gap although the DOS distribution appears to be fine with experimental attributes. The calculated value of U is not an appropriate value for carrying out DFT+U calculations as it has created an insulating gap of ~1.8 eV with limitations in redistribution of DOS which is inconsistent with experimental spectral behavior for the occupied states mainly. However, this value of U is found to be an appropriate one for DFT+embedded DMFT method which creates a gap of ~1.1 eV. The calculated PDOS of Co 3d, La 5d, La 4f and O 2p states are giving a remarkably good explanation for the occupied and unoccupied states of the experimental spectra in the energy range ~–9.0 eV to ~12.0 eV.     

NLO characteristics of D-π-A coumarin-thiophene bridged azo dyes by Z-scan and DFT methods

ABSTRACT

The structural, electronic, intramolecular charge transfer (ICT) and nonlinear optical (NLO) properties of the donor-π-acceptor (D-π-A) azo linked dyes bearing coumarin thiophene bridge with different acceptors were inspected by Z-scan and DFT methods. The dye 3a exhibits bathochromic absorption maxima (649 and 650?nm) in the near IR region in DMF and DMSO. The dye 3a holds low HOMO–LUMO gap elucidated by CV and DFT indicating strong ICT character. The thermal stability is high for 3a and it shows enhanced NLO property by Z-scan and DFT methods as predicted in both global and range-separated hybrid functionals. The molecular geometry was optimised using B3LYP/6-311?+?g(d,p). The ICT characteristics are correlated with NLO properties obtained by Z-scan and DFT techniques.     

胞嘧啶分子拉曼光谱研究

本文通过实验测量了胞嘧啶的常规拉曼光谱,有四个弱拉曼峰在以前胞嘧啶的常规拉曼光谱中未检测到。采用密度泛函(Density Function Theory)B3LYP/6-31+G(d,p)计算了胞嘧啶分子的拉曼光谱。结合理论计算结果对实验拉曼光谱振动模式进行了指认,并对其中几个拉曼峰非常弱的原因进行了分析。     

Strain Effect on the Absorption Threshold Energy of Silicon Circular Nanowires

In this work,the influence of strain on threshold energy of absorption in Silicon circular nanowires is investigated.For this purpose,we first have used the density functional theory(DFT) to calculate the electron and hole effective masses.Then,we have obtained absorption threshold energy with two different procedures,DFT and effective mass approximation(EMA).We have also obtained the band structures of Si nanowires both DFT and EMA.The results show that:i) the expansive strain increases the hole effective mass while compressive strain increases the electron effective mass,ii) the electron and hole effective masses reduce with decreasing the wire size,iii) the absorption threshold energy decreases by increasing strain for compressive and tensile strain and its behavior as a function of strain is approximately parabolic,iv) the absorption threshold energy(for all sizes) obtained using EMA is greater than the DFT results.     

MR knee imaging: axial 3DFT GRASS pulse sequence versus spin-echo imaging for detecting meniscal tears.

The knees of 17 patients (34 menisci) referred for magnetic resonance (MR) imaging to evaluate knee pain were examined using thin axial three-dimensional Fourier transform (3DFT) gradient-refocused acquisition in a steady state (GRASS) images through the menisci, to determine if this method is sensitive and specific for detecting meniscal tears. Results were compared with spin-echo images with long TR and double-echo TE in both coronal and sagittal planes. Arthroscopy results, available in each case, were used as the "gold standard." Twelve meniscal tears were identified at arthroscopy. Axial 3DFT GRASS technique detected 10 of the 12 meniscal tears compared to 9 or 12 using spin-echo technique. With axial 3DFT GRASS technique one false-positive meniscal tear was reported, compared with two false-positive tears on spin-echo images. Axial 3DFT GRASS images were very useful in detecting peripheral tears, showing displaced meniscal fragments, and evaluating complex tears. In this small study, thin axial 3DFT GRASS images were comparable to spin-echo images for detecting meniscal tears, and were helpful in complicated cases in which they provided complementary information to that obtained from spin-echo images.     

Electron spin resonance spectra of nitrogen heterocyclic radical ions

Abstract

We introduce a representative benchmark database of 20 cycloreversion reaction energies obtained by means of the high-level W1 thermochemical protocol. We use these benchmark values to assess the performance of a variety of contemporary DFT, double-hybrid DFT (DHDFT), standard ab initio, and compound thermochemistry methods. We show that this set of reaction energies provides an extremely challenging test for nearly all of the considered DFT and DHDFT methods. For example, about 80% of the considered functionals result in root-mean-square deviations (RMSDs) above 10 kJ mol^?1. The best DFT and DHDFT procedures are ωB97X and DSD-PBEP86-D3, with RMSDs of 4.7 and 7.9 kJ mol^?1, respectively. Coupled with the fact that the barrier heights for these reactions also pose a significant challenge for many DFT methods, this work shows that only a handful of functionals can quantitatively describe all aspects of the potential energy surface of this important class of reactions. In addition, this work shows that London dispersion effects are particularly large for this class of reactions. For example, empirical D3 dispersion corrections reduce the RMSDs for the DFT and DHDFT procedures by amounts ranging from 3.5 (PBE and B2K-PLYP) to 22.0 (BLYP) kJ mol^?1.