Wave functions of an elliptical cylinder and certain of their properties
Cylindrical elliptical waves, Mathieu functions, and addition theorems
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Atomic collisions in the presence of laser radiation - Time dependence and the asymptotic wave function
A time-dependent, wave-packet description of atomic collisions in the presence of laser radiation is extracted from the more conventional time-independent, stationary-state description. This approach resolves certain difficulties of interpretation in the time-independent approach which arise in the case of asymptotic near resonance. In the two-state model investigated, the approach predicts the existence of three spherically scattered waves in this asymptotically near-resonant case.
Devries, P. L.↗
New approach to folding with the Coulomb wave function
Due to the long-range character of the Coulomb interaction theoretical description of low-energy nuclear reactions with charged particles still remains a formidable task. One way of dealing with the problem in an integral-equation approach is to employ a screened Coulomb potential. A general approach without screening requires folding of kernels of the integral equations with the Coulomb wave. A new method of folding a function with the Coulomb partial waves is presented. The partial-wave Coulomb function both in the configuration and momentum representations is written in the form of separable series. Each term of the series is represented as a product of a factor depending only on the Coulomb parameter and a function depending on the spatial variable in the configuration space and the momentum variable if the momentum representation is used. Using a trial function, the method is demonstrated to be efficient and reliable.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
From Bessel beam to complex-source-point cylindrical wave-function
This investigation shows that a scalar Bessel beam can be transformed into the non-paraxial complex-source-point cylindrical wave (CSPCW). High-order CSPCW solutions, termed here high-order quasi-Gaussian cylindrical beams, which exactly satisfy the Helmholtz equation, are derived analytically. Moreover, partial-derivatives of the high-order CSPCW solutions satisfy the Helmholtz equation. In addition, the CSPCW solutions satisfy the nonrelativistic Schrödinger equation within standard quantum mechanics, thus, the results can be used in the description of elementary particle/matter motion and related applications in quantum scattering theory. Furthermore, the analysis is extended to the case of vector beams in which the components of the electromagnetic (EM) field are obtained based on different polarizations of the magnetic and electric vector potentials, which exactly satisfy Maxwell’s vectorial equations and Lorenz’ gauge condition. An attractive feature of the high-order solutions is the rigorous description of strongly focused (or strongly divergent) cylindrical wave-fields without any approximations, nor the need for numerical methods. Possible applications are in beam-forming design using high-aperture or collimated cylindrical laser/electron quasi-Gaussian beams in imaging microscopy, particle manipulation, optical tweezers, and the study of the scattering, and radiation forces on objects. - Highlights: • Bessel beam is transformed into the non-paraxial cylindrical complex-source-point. • Exact high-order tightly focused solutions are derived without any approximations. • The exact solutions also satisfy the nonrelativistic Schrödinger equation. • Electromagnetic beams are obtained as solutions of Maxwell’s vectorial equations. • Applications are in laser/electron beam imaging, tweezers, and radiation force.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Simple and Efficient Truncation of Virtual Spaces in Embedded Wave Functions via Concentric Localization
We present here a strategy to generate “concentrically local orbitals” for the purpose of decreasing the computational cost of wave function-in-density functional theory (WF-in-DFT) embedding. The concentric localization is performed for the virtual orbitals by first projecting the virtual space onto atomic orbitals centered on the embedded atoms. Using a one-particle operator, these projected orbitals are then taken as a starting point to iteratively span the virtual space, recursively creating virtual orbital “shells” with consecutively decreasing correlation energy recovery at each iteration. This process can be repeated to convergence, allowing for tunable accuracy. Furthermore, assessment of the proposed scheme is performed by application to the potential energy diagram of the Menshutkin reaction of chloromethane and ammonia inside a segment of a carbon nanotube and the torsional potential of a simplified version of the retinal chromophore.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Unveiling the Redox Noninnocence of Metallocorroles: Exploring K-Edge X-ray Absorption Near-Edge Spectroscopy with a Multiconfigurational Wave Function Approach
X-ray absorption near-edge spectroscopy (XANES) is an advanced technique for probing the local electronic structure of catalysts, effectively identifying the noninnocent nature of ligands in transition-metal complexes. Metallocorroles with noninnocent corrole rings exhibit unusual electronic structures that challenge traditional density functional theory (DFT) methods, necessitating more rigorous approaches to describe electron correlation accurately. We explored K-edge XANES spectra of Fe, Mn, and Co metallocorroles using TDDFT and wave function-based methods. This is the first investigation employing multireference methods, specifically RASSCF, RASPT2, and MC-PDFT, to analyze the redox noninnocent nature of metallocorroles reflected in their XANES spectra. We quantified the noninnocent character of the corrole and the oxidation states of the metals, capturing more than singly excited excitations responsible for the pre-edge peak. Our findings demonstrate the importance of these advanced computational techniques for accurately predicting XANES spectra, providing a reliable understanding of the electronic properties of such complexes. In conclusion, this study offers a new strategy for investigating ligand redox noninnocence via integrated experimental and computational XANES.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
An SYK-inspired model with density–density interactions: Spectral & wave function statistics, Green’s function and phase diagram
The Sachdev–Ye–Kitaev (SYK) model is a rare example of a strongly-interacting system that is analytically tractable. Tractability arises because the model is largely structureless by design and therefore artificial: while the interaction is restricted to two-body terms, interaction matrix elements are “randomized” and therefore the corresponding interaction operator does not commute with the local density. Unlike conventional density–density-type interactions, the SYK-interaction is, in this sense, not integrable. We here investigate a variant of the (complex) SYK model, which restores this integrability. It features a randomized single-body term and a density–density-type interaction. We present numerical investigations suggesting that the model exhibits two integrable phases separated by several intermediate phases including a chaotic one. The chaotic phase carries several characteristic SYK-signatures including in the spectral statistics and the frequency scaling of the Green’s function and therefore should be adiabatically connected to the non-Fermi liquid phase of the original SYK model. Thus, our model Hamiltonian provides a bridge from the SYK-model towards microscopic realism.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Wave functions and mass spectrum for a system of two relativistic spinor quarks coupled by a chromodynamical interaction
Exact solutions of relativistic quasipotential equations in the configuration representation were found for a system of two spin-1/2 quarks interacting via a Coulomb-like chromodynamical potential. Quantization conditions were found for the pseudoscalar, pseudovector, and vector cases. The present analysis was performed within the Hamiltonian formulation of quantum field theory via a transition to the relativistic configuration representation for the case of two relativistic spin-1/2 quarks of equal mass.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Kinetic-energy matrix elements for atomic Hylleraas-CI wave functions
Hylleraas-CI is a superposition-of-configurations method in which each configuration is constructed from a Slater-type orbital (STO) product to which is appended (linearly) at most one interelectron distance r{sub ij}. Computations of the kinetic energy for atoms by this method have been difficult due to the lack of formulas expressing these matrix elements for general angular momentum in terms of overlap and potential-energy integrals. It is shown here that a strategic application of angular-momentum theory, including the use of vector spherical harmonics, enables the reduction of all atomic kinetic-energy integrals to overlap and potential-energy matrix elements. The new formulas are validated by showing that they yield correct results for a large number of integrals published by other investigators.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
A rotationally invariant approach based on Gutzwiller wave function for correlated electron systems
Here, we introduce a rotationally invariant approach combined with the Gutzwiller conjugate gradient minimization method to study correlated electron systems. In the approach, the Gutzwiller projector is parametrized based on the number of electrons occupying the onsite orbitals instead of the onsite configurations. The approach efficiently groups the onsite orbitals according to their symmetry and greatly reduces the computational complexity, which yields a speedup of $20 \sim 50 \times $ in the minimal basis energy calculation of dimers. The computationally efficient approach promotes more accurate calculations beyond the minimal basis that is inapplicable in the original approach. A large-basis energy calculation of F 2 demonstrates favorable agreements with standard quantum-chemical calculations Bytautas et al (2007 J. Chem. Phys. 127 164317).
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Gradient of molecular Hartree–Fock–Bogoliubov energy with a linear combination of atomic orbital quasiparticle wave functions
The analytical gradient for the atomic-orbital-based Hartree–Fock–Bogoliubov (HFB) energy functional, the modified form of which was proposed by Staroverov and Scuseria to account for the static electron correlation [J. Chem. Phys. 117, 11107 (2002)], is derived. Interestingly, the Pulay force for the HFB energy is expressed with the same formula as that for the Hartree–Fock method. The efficiency of the present HFB energy gradient is demonstrated in the geometry optimizations of conjugated and biradical systems. The geometries optimized by using the HFB method with the appropriate factor ζ, which controls the degree of static correlation included, are found to show good agreement with those obtained by using a complete active-space self-consistent field method, although they are significantly dependent on ζ.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Balance-equation method for simulating terahertz quantum-cascade lasers using a wave-function basis with reduced dipole moments of tunnel-coupled states
A model based on a system of balance equations for localised and continuum states is developed to calculate the current − voltage (I − V) and power characteristics of quantum-cascade lasers (QCLs) operating in the terahertz (THz) range. A method for modifying the eigenbasis of the Schrödinger equation by reducing the dipole moments of tunnel-coupled states is proposed to take into account the effect of dephasing on the carrier transport. The calculated and experimental data on the current − voltage characteristics and the dependence of the integrated radiation intensity on current for the THz QCLs lasing at 2.3 THz are compared. The calculated and measured values of the threshold current, lasing current range, and maximum operating temperature T{sub max} are found to be in good agreement. It is shown that T{sub max} can be increased by 25 % by reducing the thickness of the top contact layer n{sup +}-GaAs of the laser structure under study from 800 to 100 nm. (paper)
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Origin of structure: statistical characterization of the primordial density fluctuations and the collapse of the wave function
The statistical properties of the primordial density perturbations has been considered in the past decade as a powerful probe of the physical processes taking place in the early universe. Within the inflationary paradigm, the properties of the bispectrum are one of the keys that serves to discriminate among competing scenarios concerning the details of the origin of cosmological perturbations. However, all of the scenarios, based on the conventional approach to the so-called ''quantum-to-classical transition'' during inflation, lack the ability to point out the precise physical mechanism responsible for generating the inhomogeneity and anisotropy of our universe starting from and exactly homogeneous and isotropic vacuum state associated with the early inflationary regime. In past works, we have shown that the proposals involving a spontaneous dynamical reduction of the quantum state provide plausible explanations for the birth of said primordial inhomogeneities and anisotropies. In the present manuscript we show that, when considering within the context of such proposals, the characterization of the spectrum and bispectrum turn out to be quite different from those found in the traditional approach, and in particular, some of the statistical features, must be treated in a different way leading to some rather different conclusions.
79 ASTRONOMY AND ASTROPHYSICS↗
Wave-function engineering and absorption spectra in Si{sub 0.16}Ge{sub 0.84}/Ge{sub 0.94}Sn{sub 0.06}/Si{sub 0.16}Ge{sub 0.84} strained on relaxed Si{sub 0.10}Ge{sub 0.90} type I quantum well
We theoretically investigate germanium-tin alloy as a semiconductor for the design of near infrared optical modulators in which the Ge{sub 1−x}Sn{sub x} alloy is the active region. We have calculated the electronic band parameters for heterointerfaces between strained Ge{sub 1−x}Sn{sub x} and relaxed Si{sub 1−y}Ge{sub y}. Then, a type-I strain-compensated Si{sub 0.10}Ge{sub 0.90}/Si{sub 0.16}Ge{sub 0.84}/Ge{sub 0.94}Sn{sub 0.06} quantum well heterostructure optimized in terms of compositions and thicknesses is studied by solving Schrödinger equation without and under applied bias voltage. The strong absorption coefficient (>1.5 × 10{sup 4} cm{sup −1}) and the shift of the direct transition under large Stark effect at 3 V are useful characteristics for the design of optoelectronic devices based on compressively strained IV-IV heterostructures at near infrared wavelengths.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Quantum turbulence, superfluidity, non-Markovian dynamics, and wave function thermalization
While quantum turbulence has been addressed both experimentally (predominantly for superfluid He 4 and He 3 ) and theoretically, the dynamics of various ensembles of quantized vortices has been followed in time only until the vortices have decayed into phonons. How this “thermalization” is achieved is still an unaddressed and thus an unelucidated question. The unitary Fermi gas (UFG) is a unique quantum system, which has no classical counterpart and is of relevance to neutron stars, cold atoms, condensed-matter and nuclear many-body systems. The non-Markovian evolution of an isolated UFG is put in evidence and its entire nonequilibrium evolution can be studied theoretically within a unified theoretical framework. The initial lattice of quantum vortices and antivortices evolves through a couple of vortex tangles and excitation of Kelvin waves, where vortices cross and reconnect, until very slowly thermalization sets in. Published by the American Physical Society 2024
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Pair wave function symmetry in UTe2 from zero-energy surface state visualization
Although nodal spin-triplet topological superconductivity appears probable in uranium ditelluride (UTe 2 ), its superconductive order parameter Δ k remains unestablished. In theory, a distinctive identifier would be the existence of a superconductive topological surface band, which could facilitate zero-energy Andreev tunneling to an s-wave superconductor and also distinguish a chiral from a nonchiral Δ k through enhanced s-wave proximity. In this study, we used s-wave superconductive scan tips and detected intense zero-energy Andreev conductance at the UTe 2 (0-11) termination surface. Imaging revealed subgap quasiparticle scattering interference signatures with a-axis orientation. The observed zero-energy Andreev peak splitting with enhanced s-wave proximity signifies that Δ k of UTe 2 is a nonchiral state: B 1u , B 2u , or B 3u . However, if the quasiparticle scattering along the a axis is internodal, then a nonchiral B 3u state is the most consistent for UTe 2 .
Gu, Qiangqiang [Cornell Univ., Ithaca, NY (United ↗
Fast & accurate emulation of two-body scattering observables without wave functions
We combine Newton's variational method with ideas from eigenvector continuation to construct a fast & accurate emulator for two-body scattering observables. The emulator will facilitate the application of rigorous statistical methods for interactions that depend smoothly on a set of free parameters. Our approach begins with a trial K or T matrix constructed from a small number of exact solutions to the Lippmann–Schwinger equation. Subsequent emulation only requires operations on small matrices. We provide several applications to short-range potentials with and without the Coulomb interaction and partial-wave coupling. It is shown that the emulator can accurately extrapolate far from the support of the training data. When used to emulate the neutron-proton cross section with a modern chiral interaction as a function of 26 free parameters, it reproduces the exact calculation with negligible error and provides an over 300x improvement in CPU time.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Polarization-Modulated Angle-Resolved Photoemission Spectroscopy: Toward Circular Dichroism without Circular Photons and Bloch Wave-function Reconstruction
Not Available
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗