Gaussian beam decomposition of high frequency wave fields using expectation–maximization

A new numerical method for approximating highly oscillatory wave fields as a superposition of Gaussian beams is presented. The method estimates the number of beams and their parameters automatically. This is achieved by an expectation–maximization algorithm that fits real, positive Gaussians to the energy of the highly oscillatory wave fields and its Fourier transform. Beam parameters are further refined by an optimization procedure that minimizes the difference between the Gaussian beam superposition and the highly oscillatory wave field in the energy norm.     

Separation of different wave components in the Bethe–Salpeter wave function

The scalar products of polarization tensor and unit vectors are presented explicitly in spherical coordinate system expanded in terms of spherical harmonic functions. By applying the obtained formulae, different wave components in the Salpeter wave function can be shown explicitly, and the results are consistent with the results obtained by L–S coupling analysis. The cancelation formula is given, by which the terms with pure L = J + 1 wave components in the Salpeter wave function for the bound state with h_P=(-1)^J\eta_{\rm P}=(-1)^J can be obtained by separating the L = J − 1 wave components from mixing terms. This separation provides the basis for studying higher-order contributions from the coupling of L = J − 1 and J + 1 wave states, and for solving the Salpeter equation exactly without approximation.     

A meshless method of line radial base function study of Gaussian wave packet broadening in few semiconducting mediums: electron–electron interaction effects

In this paper, we have studied the effect of electron–electron interaction on wave packet broadening in different semiconducting mediums in the presence of conduction band non-parabolicity. We have solved the resulting one dimensional fourth order Schrödinger equation by means of a meshless radial base function approach and 2nd order Runge Kutta method. We have compared different semiconducting mediums GaAs, GaN, AlN, InSb and GaSb and showed that in the absence of the electron–electron interaction, the Gaussian wave packet decays with time elapse while in the presence of the electron–electron interaction, the Gaussian wave packet localizes when time increases. Finally, Gaussian wave packet also localizes faster when we increase the electron–electron interaction strength.     

Coulomb wave function corrections for n-particle Bose–Einstein correlations

The effect of multi-particle Coulomb final state interactions on higher-order intensity correlations is determined in general, based on a scattering wave function which is a solution of the n-body Coulomb Schr?dinger equation in (a large part of) the asymptotic region of n-body configuration space. In particular, we study Coulomb effects on the n-particle Bose–Einstein correlation functions of similarly charged particles and remove a systematic error as big as 100% from higher-order multi-particle Bose–Einstein correlation functions. Received: 24 November 1999 / Published online: 17 March 2000     

Reduction of the Bethe–Salpeter wave function: Fermion–scalar case and scalar–scalar case

In this paper, the general forms of the nonrelativistic Bethe–Salpeter wave functions for fermion–scalar bound state and scalar–scalar bound state are presented. Using the obtained normalization conditions and the corresponding Schrödinger equations for these bound states, the nonrelativistic Bethe–Salpeter wave functions can be calculated and can be used to compute the amplitude for the process involving these bound states.     

The inhomogeneous Schrödinger equation for the off-shell wave function

A method has been developed for calculating the off-shell wave function by solving the inhomogeneous Schrödinger equation with allowance for the nuclear and Coulomb interactions. The off-shell wave function makes it possible to construct the off-shell scattering amplitude in order to solve the problems for three or more particles. An important application of the method is the Trojan Horse calculations of nuclear reactions that are important in nuclear astrophysics. Specific calculations are performed for neutron and proton scattering on the ⁷Be nucleus. The Woods-Saxon potential is used and the spin-orbital interaction is taken into account.     

Resonances of a hydrogen atom in strong parallel electric and magnetic fields using B-spline basis sets

The B-spline basis set plus complex scaling method is applied to the numerical calculation of the exact resonance parameters Er and Г/2 of a hydrogen atom in parallel electric and magnetic fields. The method can calculate the ground and higher excited resonances accurately and efficiently. The resonance parameters with accuracies of 10^-9 - 10^-12 for hydrogen atom in parallel fields with different field strengths and symmetries are presented and compared with previous ones. Extension to the calculation of Rydberg atom in crossed electric and magnetic fields and of atomic double excited states in external electric fields is discussed.     

Bose–Einstein condensate wave function and nonlinear Schrödinger equation

The nonlinear Schrödinger equation for the ground-state wave function of an inhomogeneous boson system is derived in the self-consistent Hartree–Fock approximation without the use of the formalism of anomalous averages. The results obtained correspond to the Gross–Pitaevskii equation for the Bose–Einstein condensate wave function when using the delta-shaped boson interaction potential.     

High-order mode Laguerre–Gaussian beam transformation using a 127-actuator deformable mirror: numerical simulations

Transforming high-order mode Laguerre–Gaussian beams in the far-field using a 127-actuator deformable mirror controlled by a stochastic parallel gradient descent algorithm is presented. As a phase shift of half wave exists between every neighboring lobes of high-order mode Laguerre–Gaussian beams, there are multiple lobes in the far-field. The suitable beam radius related to the aperture size of the deformable mirror is discussed. Three system performance metrics are evaluated, and encircled energy is preferred. Simulation results show that it is possible to compensate for the phase shifts and other phase aberrations of a high-order mode Laguerre–Gaussian beam and achieve a single bright lobe with this approach. Transforming the far-field intensity distribution of high-order mode Laguerre–Gaussian beams into Gaussian and super Gaussian distributions are also investigated.     

Bessel–Gaussian Shifted Paraxial Beams: I

Optics and Spectroscopy - We have considered a new family of localized solutions of a parabolic (paraxial wave) equation that generalizes the well-known Bessel–Gaussian beams and includes...     

Optimized auxiliary basis sets for density fitted post-Hartree–Fock calculations of lanthanide containing molecules

Optimised auxiliary basis sets for lanthanide atoms (Ce to Lu) for four basis sets of the Karlsruhe error-balanced segmented contracted def2 - series (SVP, TZVP, TZVPP and QZVPP) are reported. These auxiliary basis sets enable the use of the resolution-of-the-identity (RI) approximation in post Hartree–Fock methods – as for example, second-order perturbation theory (MP2) and coupled cluster (CC) theory. The auxiliary basis sets are tested on an enlarged set of about a hundred molecules where the test criterion is the size of the RI error in MP2 calculations. Our tests also show that the same auxiliary basis sets can be used together with different effective core potentials. With these auxiliary basis set calculations of MP2 and CC quality can now be performed efficiently on medium-sized molecules containing lanthanides.     

The Green function for the Duffin–Kemmer–Petiau equation

We present a calculation of the Green function for the Duffin–Kemmer–Petiau equation in the case of scalar and vectorial particles interacting with a square barrier potential, and relate it to that of the Klein–Gordon equation. A formal Hamiltonian of the Duffin–Kemmer–Petiau theory is first developed using the Feshbach–Villars analogy and the Sakata and Taketani decomposition. The coefficients of reflection and transmission are deduced.     

Super-resolution microscope using a two-color phase plate for generating quasi-Laguerre–Gaussian beam

To achieve high lateral resolution overcoming the diffraction limit, a two-color phase plate (TPP) for generating a quasi-Laguerre–Gaussian beam was applied to super-resolution microscopy (SRM) based on fluorescence depletion. Putting the TPP into a robust optical path in a commercial laser-scanning microscope, we obtained a point spread function with a full width at half maximum three times smaller than diffraction limit. The measured contrast transfer function shows that line and space patterns finer than the diffraction limit were clearly resolved and the image contrast was improved. Since the TPP can easily improve lateral resolution in SRM without any precise adjustment, our setup provides a practical super-resolution microscope.     

de Broglie–Bohm interpretation for wave function of a toroidal black hole

The mass function of a toroidal black hole as a dynamical variable is given by using Kuchar’s approach. Then the toroidal black hole is investigated by using the de Broglie–Bohm approach, and its quantum potential and quantum trajectories are obtained. In our process the vector potential of the electromagnetic field in the toroidal black hole is treated as a canonical variable.     

ISTBC: A spectrally efficient distributed transmission scheme using incremental redundancy with space–time block coding

Cooperative communication is a promising paradigm that could address many of the challenges encountered in the development of future mobile communication systems. With multiple wirelessly communicating devices that cooperate with each other, a network of wireless nodes with virtual antenna arrays is created. This emulates a MIMO system and mimics most of its benefits. However bandwidth efficiency is a major issue in cooperative communication. Incremental-redundancy based techniques can be employed in cooperating nodes to minimize the bandwidth penalty but lacks error protection capability against unreliable decoding. Motivated by such shortcomings, a technique that combines the concept of incremental redundancy with space–time block coding (STBC) is proposed in this paper. The proposed scheme retains spatial diversity and bandwidth efficiency advantage offered by normal incremental redundancy based systems, in addition to offering guard against error propagation due to imperfect decoding at the relay. The theoretical framework is also developed to provide an understanding on the fundamental performance characteristics of the system. Two parameters such as Error Propagation Quotient (EPQ) and Spectral Efficiency Gain (SEG) are proposed to gauge the benefits offered by the proposed technique.     

The Haldane–Shastry spin chain and the topological basis realization

In this paper, based on the topological basis states, we investigate the Hamiltonian family {H₂,H₃,H₄}$\{H_2,H_3,H_4\}$ of a closed four-qubit Haldane–Shastry spin chain. Not only the two-qubit interaction form, but also the three-qubit interaction form and the four-qubit interaction form are presented in terms of spin operators. Meanwhile, we explore some particular properties of the topological basis states in these systems. With Yangian algebra, the symmetry of the systems and the transitions between the eigenstates have been investigated. We find a really useful effect of Y(sl(2))$Y\left(sl\left(2\right)\right)$ operators {J_±,J₃}$\{J_{\pm },J_3\}$, which is that they can describe the transitions between the spin single state and the spin triple states. Furthermore, we construct a new Hamiltonian, whose energy degeneracies can be changed by adjusting the strengths of the two-qubit interactions, three-qubit interactions, four-qubit interactions, and the external magnetic field.     

The envelope travelling wave solutions to the Gerdjikov–Ivanov model

Valence universal multireference coupled cluster (VUMRCC) method via eigenvalue independent partitioning has been applied to estimate the effect of three-body transformed Hamiltonian (\(\widetilde{{H}}_3\)) on ionisation potentials through full connected triple excitations \(S_{3}^{(1,0) }\). \(\widetilde{H}_3 \) is constructed using CCSDT1-A model of Bartlett et al for the ground-state calculation. Contribution of transformed Hamiltonian through full connected triples \(\overline{\widetilde{H}_3 S_3^{\left( {1,0} \right) }}\) involves huge amount of computational operations that is time-consuming. Investigation on \(\hbox {Cl}_{2}\) and \(\hbox {F}_{2}\) molecules using cc-pVDZ and cc-pVTZ basis sets shows that the above effect varies from 0.001 eV to around 0.5 eV, suggesting that inclusion of \(\overline{\widetilde{H} _3 S_3^{\left( {1,0} \right) } }\) is essential for highly accurate calculations.     

Photon wave function formalism for analysis of Mach–Zehnder interferometer and sum-frequency generation

Biakynicki-Birula introduced a photon wave function similar to the matter wave function that satisfies the Schrödinger equation. Its second quantization form can be applied to investigate nonlinear optics at nearly full quantum level. In this paper, we applied the photon wave function formalism to analyze both linear optical processes in the well-known Mach–Zehnder interferometer and nonlinear optical processes for sum-frequency generation in dispersive and lossless medium. Results by photon wave function formalism agree with the well-established Maxwell treatments and existing experimental verifications.