On adiabatic N-soliton interactions and trace identities

We compare the Hamiltonian properties of the N-soliton solutions of the NLSE in the adiabatic approximation and show how it matches the Hamiltonian formulation for the complex Toda chain which describes the adiabatic N-soliton interactions. Received 21 October 2001 Published online 2 October 2002 RID="a" ID="a"e-mail: gerjikov@inrne.bas.bg     

Exciton localization at islands in quantum-well structures

Exciton localization at islands of cylindrical shape in quantum-well structures has been studied theoretically. It is shown that an exciton localizes at such islands, as a rule, as a whole. The validity regions of the adiabatic approximation in factorization of the exciton wave function have been established. The variation in the character of localization with increasing quantum-well barrier height is analyzed. Fiz. Tverd. Tela (St. Petersburg) 39, 1871–1874 (October 1997)     

Quantum dynamics in a thin film,I. Propagation of localized perturbations

In the one-particle approximation, the quantum behavior of a (quasi-)particle is studied in a thin waveguide having the form of a thin curvilinear film (in three-dimensional space) placed in external magnetic and electric fields. Objects of this type arise in the actively developing physics of nano-structures and, in particular, in the theory of ballistic transport of electrons. The corresponding quantum-mechanical equation is a Pauli-type equation with nonrelativistic Rashba spin-orbital interaction for a two-dimensional vector function. Asymptotic solutions of the Cauchy problem with special localized initial data and those of the spectral problem are obtained. The construction of asymptotic solutions is carried out in two stages. At the first stage, in the framework of the adiabatic approximation, using the “operator separation of variables” (the “generalized adiabatic principle”) for a rather broad class of quantum states, the original three-dimensional equation is reduced to a two-dimensional surface (the limit film), and then diverse solutions of this reduced equation are constructed. The first part of the paper is devoted to the reduction and the solutions of the Cauchy problem. Spectral problems will be treated in the second part. Dedicated to the memory of V. A. Geyler Supported by the RFBR grant no. 05-01-00968 and by the DFG-RAS project DFG 436 RUS 113/785.     

Quantum decoherence from adiabatic entanglement with external one or a few degrees of freedom

Based on the Born-Oppenhemer approximation, the concept of adiabatic quantum entanglement is introduced to account for quantum decoherence of a quantum system due to its interaction with a large system of one or a few degrees of freedom. In the adiabatic limit, it is shown that the wave function of the total system formed by the quantum system plus the large system can be factorized as an entangled state with correlation between adiabatic quantum states and quasi-classical motion configurations of the large system. In association with a novel viewpoint about quantum measurement, which has been directly verified by most recent experiments [e.g., S. Durr et al., Nature 33, 359 (1998)], it is shown that the adiabatic entanglement is indeed responsible for the quantum decoherence and thus can be regarded as a “clean” quantum measurement when the large system behaves as a classical object. By taking the large system respectively to be a macroscopically distinguishable spatial variable, a high spin system and a harmonic oscillator with a coherent initial state, three illustrations are presented with their explicit solutions in this paper. Received 26 February 2000 and Received in final form 14 July 2000     

Absence of Transport Under a Slowly Varying Potential in Disordered Systems

In the tight-binding random Hamiltonian on Z ^d , we consider the charge transport induced by an electric potential which varies sufficiently slowly in time, and prove that it is almost surely equal to zero at high disorder. In order to compute the charge transport, we adopt the adiabatic approximation and prove a weak form of adiabatic theorem while there is no spectral gap at the Fermi energy.     

Numerical investigation of cross-flow separation in three-dimensional supersonic flows around circular cones

The problem of supersonic three-dimensional flow over sharp cones is solved using the system of Navier-Stokes equations in a locally conical approximation. Numerical solutions are found using an implicit finite-difference scheme with second-order exponential approximation of the equations with respect to the cross-flow coordinate. The appearance and development of cross-flow separation on the leeward side of the cones in a laminar regime of gas flow in the shock layer are investigated. Zh. Tekh. Fiz. 68, 20–26 (October 1998)     

Theoretical studies of inelastic atomic collisions in a two-state model problem

A two-state scattering problem in which two non-crossing Morse curves are coupled by an exponential potential is discussed theoretically in both the diabatic and adiabatic approximations. Inelastic cross sections are estimated by various approximate analytical formulas, which are expressed in terms of the distorted wave matrix elements. The Landau (steepest descent) method is applied to estimate the distorted wave matrix element. The previously proposed separable potential approximation in the adiabatic method is found to be best among others by comparing with the exact numerical results. Transition probability as a function of l (angular momentum of relative motion) is well reproduced by this approximation. A glory effect in the velocity dependence of the cross section is found in the low energy region, and the adiabatic approximation reproduces this undulation phenomenon well.     

Spectral series of the Schrödinger operator in a thin waveguide with a periodic structure. 2. Closed three-dimensional waveguide in a magnetic field

In the paper, which is the second part of the paper by J. Brüning, S. Dobrokhotov, S. Sekerzh-Zenkovich, T. Tudorovskiy, “Spectral series of the Schrödinger operator in thin waveguides with a periodic structure. 1,” Russ. J. Math. Phys. 13 (4), 401–420 (2006), using the adiabatic approximation, diverse quantum states of the stationary Schrödinger equation for a particle in a thin waveguide in a magnetic field are constructed. The problems of “destruction” of the adiabatic approximation as the value of energy increases and of replacing this approximation by the approximation of V. P. Maslov’s theory of complex germ (the complex WKB method) are studied.     

Hyperspherical approach to description of electron correlation in negative ion of exciton

The binding energy of excitonium negative ion for the ground^1,3S-states in bulk semiconductors GaAs and ZnO in the hyperspherical coordinate method was found. Angular and radial correlations between electrons in gerade and ungerade states were taken into account by channel functions, that are the eigenfunctions of Hamiltonian on the surface of the sphere in the three-dimensional configuration space. Energy values were calculated using the adiabatic and Born-Oppenheimer approximations. The obtained energy values are in agreement with those obtained using variational method.     

Theoretical study of the LiNa molecule beyond the Born–Oppenheimer approximation: adiabatic and diabatic potential energy curves,radial coupling,adiabatic correction,dipole moments and vibrational levels

ABSTRACT

The adiabatic potential energy curves for ground and many excited states of ^{1, 3}Σ⁺, ^1,3Π, ^1,3Δ symmetries of the LiNa molecule have been performed. We have used an ab initio approach based on non-empirical pseudopotentials, parameterised l-dependent polarisation potentials and full configuration interaction calculations. In addition, the adiabatic potential energy curves determined in our previous work [Mabrouk and Berriche, J. Phys. B: At. Mol. Opt. Phys. 41, 155101 (2008).] are corrected by using a diabatisation procedure, based on the effective Hamiltonian theory and an effective metric. The diabatic permanent moments for first 10 ¹Σ⁺ electronic states show linear behaviours, especially at intermediate and large distance. The transition dipole moment between neighbour states has revealed many peaks located around the avoided crossing positions. The radial coupling between the adiabatic states was calculated using the Hellmann-Feynman formula and numerical differentiation of the rotation matrix. The first and the second derivatives revealed many peaks, associated to neutral-neutral and ionic-neutral crossings. Furthermore, the radial coupling is used to evaluate the adiabatic correction, which is found to be of an order of tens and hundreds of cm^?1, especially of higher excited states. In addition, we have determined the vibrational level spacing for all studied states.     

Minimal perimeter for N identical bubbles in two dimensions: Calculations and simulations

The minimal perimeter enclosing N planar regions, each being simply connected and of the same area, is an open problem, solved only for a few values of N . The problems of how to construct the configuration with the smallest possible perimeter E ( N ) and how to estimate the value of E ( N ) are considered. Defect-free configurations are classified and we start with the naïve approximation that the configuration is close to a circular portion of a honeycomb lattice. Numerical simulations and analysis that show excellent agreement to within one free parameter are presented; this significantly extends the range of values of N for which good candidates for the minimal perimeter have been found. We provide some intuitive insight into this problem in the hope that it will help the improvement in future numerical simulations and the derivation of exact results.     

Modelling nongrey gas-phase and soot radiation in luminous turbulent nonpremixed jet flames

Much progress has been made in radiative heat transfer modelling with respect to the treatment of nongrey radiation from both gas-phase species and soot particles, while radiation modelling in turbulent flame simulations is still in its infancy. Aiming at reducing this gap, this paper introduces state-of-the-art models of gas-phase and soot radiation to turbulent flame simulations. The full-spectrum k-distribution method (M.F. Modest, 2003, Journal of Quantitative Spectroscopy & Radiative Transfer, 76, 69–83) is implemented into a three-dimensional unstructured computational fluid dynamics (CFD) code for nongrey radiation modelling. The mixture full-spectrum k-distributions including nongrey absorbing soot particles are constructed from a narrow-band k-distribution database created for individual gas-phase species, and an efficient scheme is employed for their construction in CFD simulations. A detailed reaction mechanism including NO _x and soot kinetics is used to predict flame structure, and a detailed soot model using a method of moments is employed to determine soot particle size distributions. A spherical harmonic P₁ approximation is invoked to solve the radiative transfer equation. An oxygen-enriched, turbulent, nonpremixed jet flame is simulated, which features large concentrations of gas-phase radiating species and soot particles. Nongrey soot modelling is shown to be of greater importance than nongrey gas modelling in sooty flame simulations, with grey soot models producing large errors. The nongrey treatment of soot strongly influences flame temperatures in the upstream and the flame-tip region and is essential for accurate predictions of NO. The nongrey treatment of gases, however, weakly influences upstream flame temperatures and, therefore, has only a small effect on NO predictions. The effect of nongrey soot radiation on flame temperature is also substantial in downstream regions where the soot concentration is small. Limitations of the P₁ approximation are discussed for the jet flame configuration; the P₁ approximation yields large errors in the spatial distribution of the computed radiative heat flux for highly anisotropic radiation fields such as those in flames with localized, near-opaque soot regions.     

The Lagrangian Structure of Long-Time Torsional Dynamics Leading to RNA Folding

Within the context of biopolymer renaturation in vitro, a principle of maximization in the economy of the folding process has been previously formulated as the principle of sequential or stepwise minimization of conformational entropy loss (SMEL). When specialized to the RNA folding context, this principle leads to a predictive folding algorithm under the assumption that an adiabatic approximation is valid. This approximation requires that conformational microstates be lumped up into base-pairing patterns (BPPs) which are treated as quasiequilibrium states, while folding pathways are coarsely represented as sequences of BPP transitions. In this work, we develop a semiempirical microscopic treatment aimed at validating the adiabatic approximation and its underlying SMEL principle. We start by coarse-graining the conformation torsional space X = 3N-torus, with N = length of the chain, representing it as the lattice (Z ₂)^3N , where Z ₂ = integers modulo 2. This is done so that each point in the lattice represents a complete set of local torsional isomeric states coarsely specifying the chain conformation. Then, a coarse Lagrangian governing the long-time dynamics of chain torsions is identified as the variational counterpart of the SMEL principle. To prove this statement, the Lagrangian computation of the coarse Shannon information entropy associated to the specific partition of X into BPPs is performed at different times and contrasted with the adiabatic computation, revealing (a) the subordination of torsional microstate dynamics to BPP transitions within time scales relevant to folding and (b) the coincidence of both plots in the range of folding time scales.     

Ab initio investigation of the electronic and vibrational properties for the (CaLi)+ ionic molecule

A wide adiabatic study has been performed for numerous electronic states of CaLi⁺ molecular ion. The adiabatic potential energy curves and their spectroscopic constants (R_e, D_e, ω_e and T_e) have been calculated using an ab initio approach including a nonempirical pseudo-potential for the Ca and Li cores with the core polarisation potentials operator through full configuration interaction (FCI). Thereafter, the energies of vibrational levels and their spacing for all these states have been reported. In addition, the electric dipole moment curves have been investigated for the (1-19) Σ, (1-12) Π and (1-8) Δ electric states. Moreover it lets us check the extreme transition dipole moments (TDM). These behaviours of TDM are more accustomed to estimate the radiative lifetimes for all vibrational levels in 2¹Σ⁺ and 3¹Σ⁺ states. Also, the bound-bound and the bound-free contribution have been calculated precisely and by employing a Franck–Condon (FC) approximation.     

New intensity magneto-optical effect in materials exhibiting giant magnetoresistance

The change in the reflectivity of a metallic magnetic multilayer that exhibits giant magnetoresistance for a monochromatic electromagnetic plane wave with polarization along the magnetization (s polarization) in response to a change from the antiferromagnetic magnetic configuration of the multilayer to the ferromagnetic configuration is investigated. This magneto-optical effect is treated in the effective-medium approximation, in which the dielectric constant needed is found analytically with consideration of the interface roughness scattering of electrons. It is shown in the example of an Fe/Cu multilayer that the effect amounts to ∼0.7%. The representation found for the complex conductivity is convenient in a special case for investigating the magnetoresistive effect. Zh. éksp. Teor. Fiz. 114, 1101–1114 (September 1998)     

Continuum-discretized coupled-channels calculations for three-body models of deuteron-nucleus reactions

The formalism and results of truncated coupled channels evaluations of three-body models of deutron-induced nuclear reactions are reviewed. Emphasis is placed on breakup, elastic scattering and stripping. The relations of the coupled channels method to the Faddeev method, the adiabatic approximation and the distorted wave Born approximation are discussed extensively. Although the adiabatic approximation is seen to be excellent for the wavefunction in the elastic channel, it significantly underestimates the contributions of breakup states in stripping. Significant effects are associated with coupling to relative l = 2 breakup states.