On the Mean Field and Classical Limits of Quantum Mechanics

The main result in this paper is a new inequality bearing on solutions of the N-body linear Schrödinger equation and of the mean field Hartree equation. This inequality implies that the mean field limit of the quantum mechanics of N identical particles is uniform in the classical limit and provides a quantitative estimate of the quality of the approximation. This result applies to the case of C^1,1 interaction potentials. The quantity measuring the approximation of the N-body quantum dynamics by its mean field limit is analogous to the Monge–Kantorovich (or Wasserstein) distance with exponent 2. The inequality satisfied by this quantity is reminiscent of the work of Dobrushin on the mean field limit in classical mechanics [Func. Anal. Appl. 13, 115–123, (1979)]. Our approach to this problem is based on a direct analysis of the N-particle Liouville equation, and avoids using techniques based on the BBGKY hierarchy or on second quantization.     

Entropic Leggett–Garg inequality in neutrinos and <Emphasis Type="Italic">B</Emphasis>(<Emphasis Type="Italic">K</Emphasis>) meson systems

Entropic Leggett–Garg inequality is studied in systems like neutrinos in the context of two and three flavor neutrino oscillations and in neutral \(B_d\), \(B_s\) and K mesons. The neutrino dynamics is described with the matter effect taken into consideration. For the decohering B / K meson systems, the effect of decoherence and CP violation have also been taken into account, using the techniques of open quantum systems. Enhancement in the violation with increase in the number of measurements has been found, in consistency with findings in spin-s systems. The effect of decoherence is found to bring the deficit parameter \(\mathscr {D}^{[n]}\) closer to its classical value zero, as expected. The violation of entropic Leggett–Garg inequality lasts for a much longer time in K meson system than in \(B_d\) and \(B_s\) systems.     

MHD mixed convection flow and heat transfer in a porous medium

The effects of a steady two-dimensional laminar MHD mixed convection flow and heat transfer against a heated vertical semi-infinite permeable surface in a porous medium are discussed. The coupled nonlinear partial differential equations describing the conservation of mass, momentum, and energy are solved by a perturbation technique. The results are presented to illustrate the influence of Hartmann number (M), Prandtl number (Pr), permeability parameter (K _p ), suction/blowing parameter (f _w ), heat generation/absorption coefficient (?), and mixed convection or buoyancy parameter (γ). The effects of different parameters on the velocity and temperature as well as the skin friction and wall heat transfer are discussed with the help of figures.     

The Hitchin Functionals and the Topological B-Model at One Loop

The quantization in quadratic order of the Hitchin functional, which defines by critical points a Calabi–Yau structure on a six-dimensional manifold, is performed. The conjectured relation between the topological B-model and the Hitchin functional is studied at one loop. It is found that the genus one free energy of the topological B-model disagrees with the one-loop free energy of the minimal Hitchin functional. However, the topological B-model does agree at one-loop order with the extended Hitchin functional, which also defines by critical points a generalized Calabi–Yau structure. The dependence of the one-loop result on a background metric is studied, and a gravitational anomaly is found for both the B-model and the extended Hitchin model. The anomaly reduces to a volume-dependent factor if one computes for only Ricci-flat Kähler metrics     

Atomic Rearrangements and Photoemission Processes at a <Emphasis Type="Italic">p</Emphasis>-GaN(Cs)–Vacuum Interface

Spontaneous changes in photoemission properties of a р-GaN(Cs)–vacuum interface with effective negative electronic affinity induced by rearrangements of its atomic structure have been studied for the first time. The optimum Сs coating that ensures both the maximum photoelectron escape probability and its stability has been found. A thermodynamic model has been proposed to escape the relation of the photoemission properties of the р-GaN(Cs)–vacuum interface to its free energy and entropy.     

Randall–Sundrum II model from small field inflation in light of planck data and reheating temperature

We focus on the behaviours of small field of an arctangent potential form, in Randall–Sundrum II braneworld. Within this framework, there is only one brane with positive tension while the second membrane is sent to infinity, and the configuration the model allows to localize the gravity on the curvature of the bulk. In that context, we found that inflationary observables (n _s, r, and dn _s/dlnk) depend only on the e-folding number N. From the power perturbation value P _R (k) given by the latest observational measurements, we evaluate the values of brane tension λ and the energy scale V ₀, and we have shown that the various inflationary perturbation parameters are widely consistent with the recent Planck data for a suitable choice of value of the number N. Concerning the reheating phase, we found a large value of the temperature T _re ～ 5 × 10¹⁴ GeV.     

Radiative transition probabilities in ions of the silver isoelectronic sequence

The wave functions of one-electron states above the 4d ¹⁰ core have been calculated within the relativistic perturbation theory with a zero-order model potential. The wavelengths and probabilities of electric dipole transitions in an Ag-like ion have been calculated for the 5s-5p, 5p-5d, 5d-5f, and 4f-5d transitions. The data obtained are compared with the results of calculations by the relativistic Hartree-Fock method and within the relativistic many-body perturbation theory. The theoretical results are compared with experimental data on the lifetimes of energy levels in Ag-like ions.     

Harmonic analysis of coefficients of free energy decomposition in the polarization of a Rb<Subscript>2</Subscript>ZnCl<Subscript>4</Subscript> crystal

Landau–Devonshire decomposition coefficients W_C in a series with respect to P_C are determined via harmonic analysis of experimental free energy coordinates W_C of a Rb₂ZnCl₄ crystal, depending on its polarization P_C. The number of terms needed in W_C decomposition is determined for quantitative evaluation of the measured data.     

Impact of pairing on the heat capacity of systems with an isolated level bunch near the Fermi surface

Canonical heat capacity vs. the temperature for systems with an isolated level bunch near the Fermi surface is calculated using exact eigenvalues of the effective Bardeen–Cooper–Schrieffer Hamiltonian (H _BCS). Two degenerate levels separated by energy spacing Δε in spherical systems can produce two maxima in C at low values of G/Δε, where G is the pairing strength of H _BCS. These two maxima become one as G/Δε grows and the system deforms.     

On-top density in the nonlinear metallic screening and its implication on the exchange-correlation energy functional

In comparison with the accurate data on the on-top electron density n(0) in the proton-embedded electron gas with the density parameter r_s in the range 1?12 obtained by diffusion Monte Carlo (DMC) simulations, we have successfully constructed an alternative form of the exchange-correlation energy functional in the density functional theory by imposing the constraint due to the cusp theorem on the well-known Perdew–Burke–Ernzerhof (PBE) functional. Although PBE does not, our functional, referred to as the cusp-corrected PBE (ccPBE), reproduces the DMC data on n(0) in the entire range of r_s.     

On the Choice of a Distributed Basis Set in Calculations of Transition-Dipole Moments in the One-Determinant Approximation

The so-called “asymptotic projection technique” developed in previous papers of the authors is applied to the calculation of electronic transition-dipole moments (TDMs) in the one-determinant approximation between states of the same spin and spatial symmetry. The basic equations of the method and specific features of their application to a TDM calculation are briefly discussed. The attention focusses on the choice of a finite one-particle basis set. For this purpose, two possible algorithms for constructing distributed basis sets are proposed. In the first of them, the construction is based on minimization of the Hartree–Fock energy (E_HF) with respect to nonlinear basis set parameters. In the second case, the parameters are determined by minimizing the functional E = E_HF + E_MP2, which includes the electron correlation through the second order of Møller–Plesset perturbation theory (Е_МР2). On the whole, the results of calculations in both basis sets are in agreement with high-accuracy calculations performed by configuration interaction methods. The basis set adapted for E = E_HF + E_MP2 significantly improves the accuracy as compared to the basis set of the first type.     

Charge-exchange resonances and restoration of Wigner’s supersymmetry in heavy and superheavy nuclei

Various facets of the question of whether Wigner’s supersymmetry [SU(4) symmetry] may be restored in heavy and superheavy nuclei are analyzed on the basis of a comparison of the results of calculations with experimental data. The energy difference between the giant Gamow–Teller resonance and the analog resonance (the difference of E _G and E _A) according to calculations based on the theory of finite Fermi systems is presented for the case of 33 nuclei for which experimental data are available. The calculated difference ΔE _G–A of E _G and E _A tends to zero in heavier nuclei, showing evidence of the restoration of Wigner’s SU(4) symmetry. Also, the isotopic dependence of the Coulomb energy difference between neighboring isobaric nuclei is analyzed within the SU(4) approach for more than 400 nuclei in the mass-number range of A = 5–244. The restoration of Wigner’s SU(4) symmetry in heavy nuclei is confirmed. It is shown that the restoration of SU(4) symmetry is compatible with the possible existence of the stability island in the region of superheavy nuclei.     

Threshold perturbations in current-carrying superconducting bridges with a finite length near the critical temperature

Near the critical temperature of a superconducting transition, the energy of the threshold perturbation δF_thr that transfers a superconducting bridge to a resistive state at a current below the critical current I_c has been determined. It has been shown that δF_thr increases with a decrease in the length of a bridge for short bridges with lengths L < ξ (where ξ is the coherence length) and is saturated for long bridges with L ? ξ. At certain geometrical parameters of banks and bridge, the function δF_thr(L) at the current I → 0 has a minimum at L ~ (2–3)ξ. These results indicate that the effect of fluctuations on Josephson junctions made in the form of short superconducting bridges is reduced and that the effect of fluctuations on bridges with lengths ~(2–3)ξ is enhanced.     

Ionization potential of a metal cluster containing vacancies

A consistent procedure for determining the ionization potential of a large metal cluster of radius R _{N, v} , consisting of N atoms and N _v vacancies, is proposed. The perturbation theory in small parameters R _v /R _{N, v} and L _v /R _v (Rv and L _v are average distance between vacancies and the length of electron scattering on vacancies, respectively) is constructed in the effective-medium approximation for the electron ground state energy. The effective vacancy potential profile, the electron scattering phase and length are calculated by the Kohn–Sham method for a macroscopic metal in the stable jelly model. The obtained analytical dependences can be useful to analyze the results of photoionization experiments and to determine the size dependence of the vacancy concentration, including that near the melting temperature.     

Effect of alloying on the stabilities and catalytic properties of Pt–Au bimetallic subnanoclusters: a theoretical investigation

Density functional theory (DFT) has been applied to study the geometrical and electronic structures and the catalytic properties for NO oxidation of pure Pt and PtAu clusters. The calculated results suggest that Pt₁₀ clusters shows the most stable structure among the pure Pt _n (n = 2–13) clusters with the local maximum Δ₂ E value. The doping of Au atoms reduces the stability of the clusters, and Pt₆Au₄ cluster has the most stable structure among Pt_10?n Au _n (n = 1–7) clusters, due to the closest band centers between Pt and Au atoms (0.83 eV) and the obvious s–p resonance peaks near the Fermi level. Pt₆Au₄ cluster displays the strongest activation of O₂ molecules among Pt_10?n Au _n (n = 0–7) clusters, owing to the clear overlap between O 2p and Pt 6 s and Au 6 s near the Fermi level, and the more positive d band center than the others. The interaction between NO and metals changes slightly in NO/Pt_10-nAu_n (n = 2–7) systems, which is weaker than that in NO/Pt₉Au system, as a result of the decreasing resonance peaks of sp hybridization near the Fermi level. Compared to pure Pt₁₀ cluster, the lower energy barriers and larger reaction energies on Pt₆Au₄ cluster suggest a higher catalytic activity of PtAu cluster for the O₂ dissociation and NO oxidation reactions. Our study provides atomic-scale insights into the nature of the interfacial effect that determines NO oxidation on PtAu cluster catalysts.     

Mechanical and Dynamic Stability of Complete and Nonstoichiometric 3<Emphasis Type="Italic">C</Emphasis>-Si<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>C<Subscript><Emphasis Type="Italic">y</Emphasis></Subscript> from Ab Initio Calculations

The energies of formation of vacancies in the carbon and silicon sublattices, the independent elastic constants, the all-round compression, shear and Young’s moduli, and the anisotropy coefficients are determined for the complete and nonstoichiometric cubic phases of 3C-Si_xC_y (x, y = 1.0–0.75) by ab initio methods of the band theory. In the formalism of the density functional perturbation theory (DFPT), the phonon dispersion dependences are obtained for these phases (the comparison with the experiment is given for the complete phase). It is shown that the mechanical characteristics of the phases become strongly anisotropic upon the transition from 3C-SiC_0.875 to 3C-SiC_0.75. It is established from the analysis of the phonon dispersion curves that the 3C-SiC_0.875 and 3C-SiC_0.75 phases, in contrast to the complete 3C-SiC phase, are dynamically unstable at T = 0 K.     

Monte Carlo determination of the low-energy constants for a two-dimensional spin-1 Heisenberg model with spatial anisotropy

The low-energy constants, namely the spin stiffness ρ _s , the staggered magnetization density ? _s per area, and the spinwave velocity c of the two-dimensional (2D) spin-1 Heisenberg model on the square and rectangular lattices are determined using the first principles Monte Carlo method. In particular, the studied models have different antiferromagnetic couplings J ₁ and J ₂ in the spatial 1- and 2-directions, respectively. For each considered J ₂∕J ₁, the aspect ratio of the corresponding linear box sizes L ₂∕L ₁ used in the simulations is adjusted so that the squares of the two spatial winding numbers take the same values. In addition, the relevant finite-volume and -temperature predictions from magnon chiral perturbation theory are employed in extracting the numerical values of these low-energy constants. Our results of ρ _s1 are in quantitative agreement with those obtained by the series expansion method over a broad range of J ₂∕J ₁. This in turn provides convincing numerical evidence for the quantitative correctness of our approach. The ? _s and c presented here for the spatially anisotropic models are new and can be used as benchmarks for future related studies.     

Nonlinear generation of vorticity in thin smectic films

The energy levels of the fermions bound to the vortex are considered for vortices in the superfluid/superconducting systems that contain the symmetry protected plane of zeroes in the gap function in bulk. The Caroli–de Gennes–Matricon branches with different approach zero energy level at p_z → 0. The density of states of the bound fermions diverges at zero energy giving rise to the \(\sqrt \Omega \) dependence of the density of states in the polar phase of superfluid ³He rotating with the angular velocity Ω and to the \(\sqrt B \) dependence of the density of states for superconductors in the (d_xz + id_yz)-wave pairing state.     

Two-dimensional aluminum monoxide nanosheets: A computational study

By means of density functional theory (DFT) computations and particle-swarm optimization (PSO) structure searches, we herein predict five low-lying energy structures of two-dimensional (2D) aluminum monoxide (AlO) nanosheets. Their high cohesive energy, absence of imaginary phonon dispersion, and good thermal stability make them feasible targets for experimental realization. These monolayers exhibit diverse structural topologies, for instance, PmA- and Pmm-AlO possess buckled four- and six-membered AlO rings, whereas P62-, PmB-, and P6m-AlO have pores of varied sizes. Interestingly, the most energetically preferred monolayers, PmA- and Pmm-AlO, feature wide band gaps (2.45 and 5.13 eV, respectively), which are promising for green and blue light-emitting devices (LEDs) and photodetectors.     

Generalised model for anisotropic compact stars

In the present investigation an exact generalised model for anisotropic compact stars of embedding class 1 is sought with a general relativistic background. The generic solutions are verified by exploring different physical aspects, viz. energy conditions, mass–radius relation, stability of the models, in connection to their validity. It is observed that the model presented here for compact stars is compatible with all these physical tests and thus physically acceptable as far as the compact star candidates RXJ 1856-37, SAX J 1808.4-3658 (SS1) and SAX J 1808.4-3658 (SS2) are concerned.