Search

Using adiabatic and one-electron approximations, the rate of multiphonon relaxation of the 1s(T2) triplet of neutral magnesium donors in silicon is estimated. The dominant scattering processes associated with interaction with LO and LA phonons are taken into account. According to calculations, the rate of multiphonon relaxation at zero temperature is of the order of 1011 s–1. [ABSTRACT FROM AUTHOR]

Let O (3) denote the group of orthogonal 3 × 3 real matrices, and M the 5-dimensional real vector space of all 3 × 3 real symmetric matrices with trace zero. Let λ 1 (A) ≤ λ 2 (A) ≤ λ 3 (A) be the eigenvalues of A ∈ M and Ξ - = { A ∈ M ∣ λ 1 (A) = λ 2 (A) } . M is an inner product space with the inner product ⟨ A , B ⟩ = trace (A B) . Let G 3 (M) be the set of all 3-dimensional subspaces of M , a 6-dimensional Grassman manifold. O (3) acts on M on the left by conjugation via inner product preserving linear isomorphisms, which map any 3-dimensional subspace into another 3-dimensional subspace; thus G 3 (M) also has a left action of O (3) . G 3 (M) becomes a category, an action groupoid, with morphisms (V , M , W) ∈ G 3 (M) × O (3) × G 3 (M) , where W = M V M T . Composition of morphisms is (V 1 , N , V 2) ∘ (V 0 , M , V 1) = (V 0 , N M , V 2) . Let C be a category whose objects (V, S) consist of a real inner product space V and S ⊂ V , and whose arrows (V , S) → (W , T) consist of f : V → W , an inner product preserving real linear mapping such that f (S) ⊂ T . We have the functor V ↓ (V , M , W) W G 3 (M) ⟶ F - (V , Ξ - ∩ V) ↓ F - (M) (W , Ξ - ∩ W) C where F - (M) : V → W : A ↦ M A M T . Suppose further that S 3 denotes the group of permutations of { 1 , 2 , 3 } , and ρ : S 3 → O (3) denotes a group homomorphism which is isomorphic as a group representation to the natural representation of S 3 on R 3 (which permutes the coordinates). Let Obj (L S) denote the set of all V ∈ G 3 (M) whose isotropy subgroup contains S = ρ (S 3) as a subgroup. This paper completely describes the full subcategory L S of G 3 (M) with object set Obj (L S) , as well as the details of the above functor restricted to L S . Thus all the members V ∈ Obj (L S) are determined, as well as the smooth manifold structure on Obj (L S) ; it is embedded as a one-dimensional submanifold of G 3 (M) . The isotropy subgroups of all V ∈ Obj (L S) are computed and all pairs V , W ∈ Obj (L S) which are isomorphic via some M ∈ O (3) are determined. The sets Ξ - ∩ V are all determined, and the functorial mappings on morphism sets are computed. However, L S is not a Lie groupoid. The image of Obj (L S) under the functor π 1 F - is the collection of fibres of the smooth manifold ∐ V ∈ Obj (L S) V , which is the total space of the canonical vector bundle over the base manifold Obj (L S) . The bifurcation points of the family of subsets Ξ - ∩ V as V ranges over Obj (L S) (within this total space) are seen to be the points of Obj (L S) with infinite isotropy subgroups. We also show how this mathematical problem arises naturally from a problem in mathematical chemistry. Hence certain features of numerical calculations of energy eigenvalue intersection patterns of the simple chemical system H3 are rationalized through linearization about the triple intersection point. [ABSTRACT FROM AUTHOR]

At present, much attention is paid to the dielectric engineering of the material of the surrounding matrix and low-dimensional structures, which makes it possible to purposefully change their properties and optimize the characteristics of semiconductor devices. The aim of this work is a theoretical study of the influence of the pair interaction of quantum dots (QDs), as well as their interaction with the surrounding matrix through 2D dissipative tunneling, on the photodielectric effect (PDE) associated with the excitation of an impurity complex A+ + e in a QD system in an external electric field. Interaction of an electron with a hole in an impurity complex A+ + e in a QD has been considered in the adiabatic approximation. The dispersion equations for a hole in an impurity complex A+ + e in the presence of an external electric field and 2D dissipative tunneling for the s- and p-states of an electron in a QD are obtained within the framework of the zero-range potential model in the effective mass approximation. The influence of the electric field on the ground state of an electron in a QD has been taken into account in the second order of the perturbation theory. The probability of 2D dissipative tunneling is calculated in the one-instanton semiclassical approximation. The relative change in dielectric permittivity has been calculated in the dipole approximation. PDE field-dependence curves have been plotted for InSb QDs. It is shown that the PDE field dependence at a certain value of the strength of an external electric field and the parameters of 2D dissipative tunneling has a characteristic kink associated with the effect of 2D bifurcation, when, under the action of an electric field, the double-well oscillatory potential simulating the "QD–surrounding matrix" system is transformed and the tunnel transfer mode changes from synchronous to asynchronous. It has been established that there are irregular oscillations on the PDE curves in the vicinity of the 2D bifurcation point, which are associated with the regime of quantum beats. It is shown that the amplitude of the oscillations increases with increasing phonon mode frequency and temperature, while the break point shifts towards weaker fields. It has been found that an increase in the constant of interaction with the contact medium, as well as with the constant of the pair interaction of QDs, leads to the suppression of the PDE. [ABSTRACT FROM AUTHOR]

Quantum dots (QDs) have unique optical properties that are widely used in optoelectronics, biology, and medicine. The problem of controlling the spectral and luminescent properties of QDs has initiated studies of the mechanisms by which QDs interact with each other and with the surrounding matrix. Such interactions can, under certain conditions, significantly modify the radiative properties of QDs, which will affect the characteristics of laser structures and biosensors based on them. The aim of this work is a theoretical study of the 2D dissipative tunneling effect in the "QD–surrounding matrix" system, as well as the pair electrostatic interaction of QDs with A++ e impurity complexes, on recombination radiation associated with the optical transition of an electron from the QD ground state to the quasi-stationary A+ state in an external electric field. The interaction of an electron, which is in the ground state of a QD, and a hole that is localized at the A+ center has been considered within the framework of the adiabatic approximation. The dispersion equations that determine dependence of the hole binding energy in the A++ e impurity complex in a spherically symmetric QD on the external electric field and dissipative tunneling parameters have been obtained within the zero range potential model, in the effective mass approximation. Calculation of the spectral intensity of recombination radiation (SIRR) in QDs with an A++e impurity complex in an external electric field has been performed in the dipole approximation. Influence of the electric field on the ground state of an electron in a QD has been taken into account in the second order of the perturbation theory. Numerical calculations and plotting were carried out for a semiconductor quantum dot based on InSb using the symbolic mathematics of Mathcad 14 and Wolfram Mathematica 9. The 2D dissipative tunneling probability has been calculated with exponential accuracy for the 2D oscillatory potential model at a finite temperature, taking into account the linear interaction with the phonon modes of the environment media (or a heat bath) in the one-instanton semiclassical approximation. It is shown that the field dependence of the binding energy for the quasi-stationary A+ state has an oscillating character, associated with quantum beats that occur during parallel 2D tunneling transfer. It is found that the SIRR curves have a characteristic kink corresponding to the 2D bifurcation point that occurs when the tunneling regimes in the interacting pair of QDs change from synchronous to asynchronous. It has been established that, in the vicinity of the 2D bifurcation point, there are irregular oscillations in the SIRR associated with the modes of quantum beats, in the course of which competing trajectories of tunneling appear. It is found that the parameters of dissipative tunneling—the temperature, frequency of the phonon mode, constant of interaction with the contact medium, constant of the QDs interaction—have a significant effect on the amplitude of quantum beats and the position of the 2D bifurcation point in the SIRR. Taking into account the interaction of the QD with the surrounding matrix leads to a significant modification of the SIRR, which manifests itself in the form of bifurcation points and quantum beats that depend on the dissipative tunneling parameters. Accounting for the pairwise interaction of QDs with each other via hole repulsion in A++ e complexes leads to suppression of recombination radiation with an increase in the interaction constant. [ABSTRACT FROM AUTHOR]

In this paper, we consider a system driven by a controlled Schrödinger equation with two external control inputs. Motivated by applications to the control of quantum systems having conical or semi-conical eigenvalue intersections, we propose to study the singularities and the parametric bifurcations of the associated non-mixing field, along whose integral curves in the space of controls the adiabatic approximation holds with higher precision. Our results can be applied to optimize the adiabatic control strategies of well known quantum systems such as Qubit systems, Stirap Processes and Eberly-Law models. [ABSTRACT FROM AUTHOR]

Within the framework of the available theories, the initiation of plastic shear and nucleation cracks in perfect crystals is possible only at a deforming stress close to the theoretical strength. It is shown that a perfect crystal, treated as an open system of nuclei and electrons, loses its stability at applied stresses that are orders of magnitude smaller than the theoretical strength. This helps avoiding the use of the concept of various types of defects present in the bulk and in the surface layer of the crystal. The physical reason for the instability is the excitation of dynamic displacements determined by nonadiabatic transitions of Landau-Zener atoms between the intersecting potential energy surfaces in open nonequilibrium systems. A qualitative explanation of the experimentally observed results is given. [ABSTRACT FROM AUTHOR]

Electronic and excitonic states in an InSb strongly flattened ellipsoidal quantum dot (QD) with complicated dispersion law are theoretically investigated within the framework of the geometric adiabatic approximation in the strong, intermediate, and weak quantum confinement regimes. For the lower levels of the spectrum, the square root dependence of energy on QD sizes is revealed in the case of Kane's dispersion law. The obtained results are compared to the case of a parabolic (standard) dispersion law of charge carriers. The possibility of the accidental exciton instability is revealed for the intermediate quantum confinement regime. For the weak quantum confinement regime, the motion of the exciton's center-of-gravity is quantized, which leads to the appearance of additional Coulomb-like sub-levels. It is revealed that in the case of the Kane dispersion law, the Coulomb levels shift into the depth of the forbidden band gap, moving away from the quantum confined level, whereas in the case of the parabolic dispersion law, the opposite picture is observed. The corresponding selection rules of quantum transitions for the interband absorption of light are obtained. New selection rules of quantum transitions between levels conditioned by 2D exciton center of mass vertical motion quantization in a QD are revealed. The absorption threshold behavior characteristics depending on the QDs geometrical sizes are also revealed. [ABSTRACT FROM AUTHOR]

Semiconductor quantum dots, due to their unique optical properties, are promising materials for the design of optoelectronic devices. At the same time, the parameters of instruments significantly depend both on the band structure and the impurity energy levels in quantum dots. In this regard, the electron–phonon interaction acts as the most important mechanism of temperature shift in energy levels. The aim of the present work was to theoretically study how the electron–phonon interaction influences the temperature dependence of radiative recombination in an impurity complex in a semiconductor quasi-zero-dimensional structure. The effect of temperature on the energy levels in a semiconductor quantum dot was theoretically considered by the statistics method assuming that the electron–phonon interaction makes the main contribution to the temperature dependence. The dispersion equation defining the hole binding energy in the impurity complex in a spherically symmetric quantum dot was obtained in terms of the adiabatic approximation in the zero-range potential model. The spectral intensity of recombination radiation in the quasi-zero-dimensional structure with impurity complexes was calculated in the dipole approximation taking into account the radius dispersion of quantum dots. Temperature curves were plotted for the case of InSb-based quantum dots. The temperature dependence of the binding energy in the complex was calculated for different values of the quantum-dot radius. The hole binding energy was shown to decrease with an increase in temperature, which was due to a temperature spreading of the wave function of a quasi-steady A+ state under the conditions of electron–phonon and hole–phonon interactions. The bond energy of the A+ state was found to increase with a decrease in the quantum-dot radius due to an increase in the ground state energy of the adiabatic electron potential. The spectral intensity of recombination radiation was calculated as a function of the transition energy for different temperature values. It was found that, with an increase in temperature, the threshold transition energy shifts to the short-wave spectral region and thermal quenching of the recombination radiation occurs. This was due to a decrease in the overlap integral of the wave functions of initial and final electron states because of the transition energy increase. The effect of the electron–phonon interaction on recombination processes in the impurity complex in spherically symmetric quantum dot is manifested in temperature quenching of the recombination radiation spectral intensity. The effect of coming to a plateau appears to be common for different mechanisms of photoluminescence. [ABSTRACT FROM AUTHOR]

There has been an increasing interest in the study of the effect of electric field on the properties of semiconductor quantum dots. This is due to the fact that such systems provide a high degree of freedom in the control of the band structure and the binding energy of impurity states, which is important for instrumental applications. Of particular interest is the study of the effect of electric field on the A+ impurity states, which can form long-lived complexes with nonequilibrium electrons. Variations in the magnitude of the external electric field can be used to control the binding energy of the A+ state, concentration of charge carriers, and optical properties of quasi-zero-dimensional structures. The purpose of this work is to theoretically study the effect of external electric field on the binding energy of a hole in the impurity complex in a spherically symmetric quantum dot. The interaction of an electron in the ground state of a quantum dot and a hole localized at the A+ center is considered in the framework of the adiabatic approximation. The dispersion relation that determines the dependence of the binding energy of a hole in the impurity complex in a spherically symmetric quantum dot on the magnitude of the external electric field is obtained in the model of the zero-radius potential in the approximation of effective mass. All curves are plotted for quantum dots based on InSb. An analytical solution of the problem of bound states of a hole in the complex in a spherically symmetric quantum dot is obtained in the presence of an external electric field in the zero-radius-potential model in the adiabatic approximation. The centered and uncentered locations of the A+ center in a quantum dot are considered. It is shown that the curve of the field dependence of the binding energy of the A+ center has a characteristic maximum, the position of which is related to the dynamics of the adiabatic potential in the presence of an external electric field. It is shown that there is a threshold value of the external electric field at which the existence of the bound A+ state becomes impossible. The monotonic behavior of the dependence of the binding energy of the A+ state on the radius of the QD is violated for the uncentered A+ center. For certain values of the QD radius, the binding energy reaches maximum, which is due to coincidence of the position of the center and the minimum of the adiabatic potential. [ABSTRACT FROM AUTHOR]

The existence in the Born–Oppenheimer approximation of a fundamentally new type of broadening of the spectral line of the electronic vibrational–rotational (rovibronic) transition in a molecule, caused by zero-point vibrations and thermal fluctuations of atomic nuclei near their equilibrium positions during vibrational–rotational motion inside the molecule, is discovered. A quantitative description in the harmonic approximation is obtained to describe the shape and width of the electron transition line corresponding to this type of broadening, which is called parametric, since the energy of any rovibronic level and transition between levels depends parametrically on the current instantaneous position of nuclei, which move much more slowly than electrons. To take this effect into account, Franck-Condon diagrams with oblique (bent) levels of vibrational energy are proposed. From the point of view of the Copenhagen interpretation of quantum mechanics, the parametric broadening exists due to the difference between an open (i.e. experimentally measured) quantum system from an isolated (unobservable) one. The magnitude of this broadening is estimated on the example of the 0–0 transition in a series of polymethine dye monomers. The estimate showed that the magnitude of the parametric broadening of the indicated zero-phonon line is comparable with the broadening observed in the experiment. The existing quantum chemical methods for calculating molecular spectra do not take into account the parametric broadening. They smooth the quasi-continuum of closely spaced rovibronic transitions, approximately calculating their common envelope, but do not consider the broadening of a single transition. The creation of a theory of parametric broadening will contribute to the development of intramolecular converters of energy from nuclei to electrons and vice versa, sensing nanoprobes, and quantum radio, photoacoustic and acousto-optic, and transceiving or converting devices of molecular size. [ABSTRACT FROM AUTHOR]

We consider a multichannel scattering problem in an adiabatic representation. We assume that the nonadiabatic coupling matrix has a nontrivial value at large internuclear separations, and we construct asymptotic solutions at large internuclear distances. We show that these solutions up to the first order of the perturbation theory are identical to the asymptotic solutions of the reprojection approach, which was previously proposed as a means for solving the electron translation problem in the context of the Born-Oppenheimer method. [ABSTRACT FROM AUTHOR]

We discuss an adiabatic approximation for the evolution generated by an A-uniformly pseudo-Hermitian Hamiltonian H(t). Such a Hamiltonian is a time-dependent operator H(t) similar to a time-dependent Hermitian Hamiltonian G(t) under a time-independent invertible operator A. Using the relation between the solutions of the evolution equations H(t) and G(t), we prove that H(t) and H (t) have the same real eigenvalues and the corresponding eigenvectors form two biorthogonal Riesz bases for the state space. For the adiabatic approximate solution in case of the minimum eigenvalue and the ground state of the operator H(t), we prove that this solution coincides with the system state at every instant if and only if the ground eigenvector is time-independent. We also find two upper bounds for the adiabatic approximation error in terms of the norm distance and in terms of the generalized fidelity. We illustrate the obtained results with several examples. [ABSTRACT FROM AUTHOR]

We consider the three-dimensional bounded motion of a test particle around razor-thin disk configurations, by focusing on the adiabatic invariance of the vertical action associated with disk-crossing orbits. We find that it leads to an approximate third integral of motion predicting envelopes of the form $$Z(R)\propto [\varSigma (R)]^{-1/3}$$ , where R is the radial galactocentric coordinate, Z is the z-amplitude (vertical amplitude) of the orbit and $$\varSigma $$ represents the surface mass density of the thin disk. This third integral, which was previously formulated for the case of flattened 3D configurations, is tested for a variety of trajectories in different thin-disk models. [ABSTRACT FROM AUTHOR]

A mathematical model of the combustion of a thin iron rod in the atmosphere of oxygen with no forced air flow around it has been constructed. This model includes an adjustment parameter that relates the rate of combustion of the rod with its diameter and the content of oxygen. The problem on the combustion of a thin iron rod in oxygen was solved analytically in the adiabatic approximation. The results of calculations were compared with the corresponding experimental data. [ABSTRACT FROM AUTHOR]

For a given Hermitian Hamiltonian H( s) ( s ∈ [0, 1]) with eigenvalues E( s) and the corresponding eigenstates | E( s)〉 (1 ⩽ k ⩽ N), adiabatic evolution described by the dilated Hamiltonian H( t):= H( t/ T) ( t ∈ [0, T]) starting from any fixed eigenstate | E(0)〉 is discussed in this paper. Under the gap-condition that | E( s) − E( s)| ⩾ λ > 0 for all s ∈ [0, 1] and all k ≠ n, computable upper bounds for the adiabatic approximation errors between the exact solution | ψ( t)〉 and the adiabatic approximation solution | ψ ( t)〉 to the schrödinger equation $$i\left| {\dot \psi _T \left. {(t)} \right\rangle = H_T (t)} \right|\left. {\psi _T (t)} \right\rangle$$ with the initial condition | ψ (0)〉 = | E(0)〉 are given in terms of fidelity and distance, respectively. as an application, it is proved that when the total evolving time t goes to infinity, || ψ( t)〉 − | ψ ( t)〉| converges uniformly to zero, which implies that | ψ( t)〉 ≈ | ψ( t)〉 for all t ∈ [0, T] provided that T is large enough. [ABSTRACT FROM AUTHOR]

In this paper, we present a quantitative sufficient condition for adiabatic approximation in PT-symmetric quantum mechanics, which yields that a state of the PT-symmetric quantum system at any time will remain approximately in the m-th eigenstate up to a multiplicative phase factor whenever it is initially in the m-th eigenstate of the Hamiltonian. In addition, we estimate the approximation errors by the distance and the fidelity between the exact solution and the adiabatic approximate solution to the time evolution equation, respectively. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the adiabatic approximation of general Hamiltonians by splitting it into two parts, with one part a Hamiltonian that has at least one time-independent eigenstate up to a phase factor. We first develop the method of finding this kind of Hamiltonians. Then the relationship between adiabatic approximation and these Hamiltonians is discussed. Applying this to a general case, we give both a necessary condition and a sufficient condition for adiabatic approximation, followed by a spin-half example to illustrate. [ABSTRACT FROM AUTHOR]

The system of equations of gravity surface waves is considered in the case where the basin's bottom is given by a rapidly oscillating function against a background of slow variations of the bottom. Under the assumption that the lengths of the waves under study are greater than the characteristic length of the basin bottom's oscillations but can be much less than the characteristic dimensions of the domain where these waves propagate, the adiabatic approximation is used to pass to a reduced homogenized equation of wave equation type or to the linearized Boussinesq equation with dispersion that is 'anomalous' in the theory of surface waves (equations of wave equation type with added fourth derivatives). The rapidly varying solutions of the reduced equation can be found (and they were also found in the authors' works) by asymptotic methods, for example, by the WKB method, and in the case of focal points, by the Maslov canonical operator and its generalizations. [ABSTRACT FROM AUTHOR]

In the framework of the adiabatic approximation for a subsystem of nuclei with the average distance between them significantly exceeding the dimensions of the initial atom, we consider a nonrelativistic Coulomb system consisting of electrons and nuclei of one type for the temperature range where we can restrict ourself to using the ground state to describe the electron subsystem. We show that the equilibrium properties of such a system are equivalent to the thermodynamic properties of the one-component system of initial atoms interacting between themselves via a short-range potential that is the effective potential of the nucleus-nucleus interaction. In the framework of the applicability of Boltzmann statistics, we present quantum group expansions for the thermodynamic properties of a chemically reacting rarified gas that correspond to the method of initial atoms. [ABSTRACT FROM AUTHOR]

In this paper, we derive an upper bound for the adiabatic approximation error, which is the distance between the exact solution to a Schrödinger equation and the adiabatic approximation solution. As an application, we obtain an upper bound for 1 minus the fidelity of the exact solution and the adiabatic approximation solution to a Schrödinger equation. [ABSTRACT FROM AUTHOR]

A symmetric two-species competition system under the action of multiplicative noise, additive noise and periodic signal has been analytically studied by using two-state theory. The results indicate that signal-to-noise ratio of the system state variables exhibits a peak with multiplicative and additive noise intensities, i.e., a stochastic resonance phenomenon. [ABSTRACT FROM AUTHOR]

Semi-empirical adiabatic potential energy curves of highly excited states of the KRb molecule are calculated as a function of the internuclear distance R over a wide range from 3 to 150 a0. The diatomic molecule is treated as an effective two-electron system by using the large core pseudopotentials and core polarization potentials. All calculations are performed by using the nonrelativistic CASSCF/MRCI method with accurate basis set functions. The spectroscopic constants of the calculated electronic states agree well with experimental data, including the recent ones from Lee et al., and with available theoretical results. [ABSTRACT FROM AUTHOR]

Two linear In this letter, we prove the following conclusions by introducing a function F( t): (1) If a quantum system S with a time-dependent non-degenerate Hamiltonian H( t) is initially in the n-th eigenstate of H(0), then the state of the system at time t will remain in the n-th eigenstate of H( t) up to a multiplicative phase factor if and only if the values F( t) for all t are always on the circle centered at 1 with radius 1; (2) If a quantum system S with a time-dependent Hamiltonian H( t) is initially in the n-th eigenstate of H(0), then the state of the system at time t will remain ɛ-uniformly approximately in the n-th eigenstate of H( t) up to a multiplicative phase factor if and only if the values F( t) for all t are always outside of the circle centered at 1 with radius 1− ɛ. Moreover, some quantitative sufficient conditions for the state of the system at time t to remain ɛ-uniformly approximately in the n-th eigenstate of H( t) up to a multiplicative phase factor are established. Lastly, our results are illustrated by a spin-half particle in a rotating magnetic field. [ABSTRACT FROM AUTHOR]

We analyze the low-lying energy levels of a charge transfer exciton at vertically coupled coaxial nanorings in the presence of the external magnetic field applied along the axis. In order to assess the experimentally relevant domain of parameters, we adopt a model of a narrow ring for which the 3D wave equation can be reduced in the adiabatic approximation to a simpler 1D model describing a circular rotation of particles with renormalized parameters depending on the morphology of the actual heterostructure. The energies as functions of the threaded magnetic field are calculated and the effect of the nanoring's morphology and dimension on the Aharonov-Bohm (AB) oscillations, related to the difference between the electron and the hole masses, is analyzed. [ABSTRACT FROM AUTHOR]

In this section of Resonance, we invite readers to pose questions likely to be raised in a classroom situation. We may suggest strategies for dealing with them, or invite responses, or both. 'Classroom' is equally a forum for raising broader issues and sharing personal experiences and viewpoints on matters related to teaching and learning science. [ABSTRACT FROM AUTHOR]

In this paper, we considered four two-level atoms coupled with a microwave cavity via stimulated Raman adiabatic passage in quadrapod linkage pattern. Engineering Rabi frequencies of a system with suitable pulse orders, results in entangled W states of four atoms. We also compared the theoretical results with the numerical solutions of the Schrödinger equation in the adiabatic limit which shows the creation of W states at the end of dynamics. [ABSTRACT FROM AUTHOR]

The increasing number and variety of extrasolar planets illustrates the importance of characterizing planetary perturbations. Planetary orbits are typically described by physically intuitive orbital elements. Here, we explicitly express the equations of motion of the unaveraged perturbed two-body problem in terms of planetary orbital elements by using a generalized form of Gauss' equations. We consider a varied set of position and velocity-dependent perturbations, and also derive relevant specific cases of the equations: when they are averaged over fast variables (the 'adiabatic' approximation), and in the prograde and retrograde planar cases. In each instance, we delineate the properties of the equations. As brief demonstrations of potential applications, we consider the effect of Galactic tides. We measure the effect on the widest-known exoplanet orbit, Sedna-like objects, and distant scattered disk objects, particularly with regard to where the adiabatic approximation breaks down. The Mathematica code which can help derive the equations of motion for a user-defined perturbation is freely available upon request. [ABSTRACT FROM AUTHOR]

The problem of proton-antiproton motion in the H- $\bar H$ system is investigated by means of the variational method. We introduce a modified nuclear interaction through mass-scaling of the Born-Oppenheimer potential. This improved treatment of the interaction includes the nondivergent part of the otherwise divergent adiabatic correction and shows the correct threshold behaviour. Using this potential we calculate the vibrational energy levels with angular momentum 0 and 1 and the corresponding nuclear wave functions, as well as the S-wave scattering length. We obtain a full set of all bound states together with a large number of discretized continuum states that might be utilized in variational four-body calculations. The results of our calculations gives an indication of resonance states in the hydrogen-antihydrogen system. [ABSTRACT FROM AUTHOR]

In the framework of adiabatic approximation the energy spectrum and wave functions of two impenetrable particles in an infinitely deep potential well are considered for two cases of approximation of the effective confining potential of the 'slow' subsystem. In case of the quadraticterm approximation the obtained energy spectrum is equidistant. The probability distribution in the range of 'fast' particle has a symmetric shape while that in the range of the 'slow' particle is asymmetric and the peak of localization of the system in its ground state is shifted towards the 'fast' particle. In the first excited state the center of the probability distribution of the 'slow' particle is shifted towards the impenetrable wall. [ABSTRACT FROM AUTHOR]

An example of Schrödinger and Klein-Gordon equations with fast oscillating coefficients is used to show that they can be averaged by an adiabatic approximation based on V. P. Maslov's operator method. [ABSTRACT FROM AUTHOR]

Numerical simulation is carried out to study frequency shifts of a low-frequency sound field maxima under the effect of solitary internal waves (solitons) propagating along an acoustic track in the presence of mode coupling. The frequency shifts are measured by the correlation method. Simulation data obtained with allowance for mode coupling and data obtained in the adiabatic approximation are compared and analyzed. [ABSTRACT FROM AUTHOR]

Polymorphisms are a class of multivalued measure-preserving self-maps of Lebesgue spaces. Specifically, polymorphisms can be used to describe the change in the adiabatic invariant due to separatrix crossing. In this case, it consists of smooth functions mapping the unit interval into itself. In addition, there are some conditions these functions must satisfy in a typical case, namely, that their endpoints form rigid structures that persist under small perturbations. Here we will describe these conditions. [ABSTRACT FROM AUTHOR]

We show that the Foldy-Wouthuysen transformation and its generalizations are simplified if the methods of pseudodifferential operators are used, which also allow estimating the exactness of the transition from the Dirac equation to the reduced equations for electrons and positrons. The methods and techniques used can be useful not only in studying asymptotic solutions of the Dirac equation but also in other problems. [ABSTRACT FROM AUTHOR]

The melting of an ultrathin lubricating film during the friction of two solid atomically smooth surfaces is studied within the limits of the Lorentz model that approximates a viscoelastic medium, the deformation effect of the shear modulus being taken into account. It is shown that the action of a random force representing additive non-correlated noise results in the sustained oscillation mode that corresponds to stickslip friction. The numerical modeling of the process yields the ratios between the relaxation times at which the stick-slip mode is characterized by a high amplitude. The amplitude of stick-slip transitions is found to decrease as the shear modulus of the lubricant increases. [ABSTRACT FROM AUTHOR]

We consider a periodic Schrödinger operator in a constant magnetic field with vector potential A( x). A version of adiabatic approximation for quantum mechanical equations with rapidly varying electric potentials and weak magnetic fields is the Peierls substitution which, in appropriate dimensionless variables, permits writing the pseudodifferential equation for the new auxiliary function: [Figure not available: see fulltext.], where [Figure not available: see fulltext.] is the corresponding energy level of some auxiliary Schrödinger operator, assumed to be nondegenerate, and µ is a small parameter. In the present paper, we use V. P. Maslov’s operator method to show that, in the case of a constant magnetic field, such a reduction in any perturbation order leads to the equation [Figure not available: see fulltext.] with the operator [Figure not available: see fulltext.] represented as a function depending only on the operators of kinetic momenta $$ \hat P_j = - i\mu \partial _{x_j } + A_j \left( x \right) $$. [ABSTRACT FROM AUTHOR]

A method of controlling amplitude of a soliton of magnetization in an easy-axis magnet based on the phenomenon of autoresonance is proposed. Equations have been obtained that describe the temporal evolution of the soliton parameters under the effect of external variable fields. Configurations of pumping fields and conditions for the soliton-phase locking necessary for controlling field configurations have been found. [ABSTRACT FROM AUTHOR]

Presence of energy bands in quantum energy spectra of molecules reflects the existence of “slow” and “fast” motions in corresponding classical problem. Generic qualitative modifications of energy bands under the variation of some strict or approximate integrals or motion considered as control parameters are analyzed within purely quantum description, within semi-quantum one (slow dynamical variables are classical; fast variables are quantum) and within purely classical one. In quantum approach the reorganization of bands is seen from the redistribution of energy levels between bands. In semi-quantum approach the system of bands is represented by a complex vector bundle with the base space being the classical phase space for slow variables. The topological invariants (Chern classes) of the bundle are related to the number of states in bands through Fedosov deformation quantization. In purely classical description the reorganization of energy bands is manifested through the presence of Hamiltonian monodromy. [ABSTRACT FROM AUTHOR]

The concept of the adiabatic approximation is introduced from a few new standpoints, and the conditions are refined under which we can assume that the total energy of an electronic-vibrational (vibronic) state is the sum of the energies of the “electronic” and the “nuclear” problems and the wave function is represented as the product of the corresponding functions. An expression exactly corresponding to such an approximation is considered for the optical transition matrix element, and its individual terms are analyzed for any change in the geometric structure of the molecule upon optical excitation. [ABSTRACT FROM AUTHOR]

We consider equations of nonrelativistic quantum mechanics in thin three-dimensional tubes (nanotubes). We suggest a version of the adiabatic approximation that permits reducing the original three-dimensional equations to one-dimensional equations for a wide range of energies of longitudinal motion. The suggested reduction method (the operator method for separating the variables) is based on the Maslov operator method. We classify the solutions of the reduced one-dimensional equation. In Part I of this paper, we deal with the reduction problem, consider the main ideas of the operator separation of variables (in the adiabatic approximation), and derive the reduced equations. In Part II, we will discuss various asymptotic solutions and several effects described by these solutions. [ABSTRACT FROM AUTHOR]

We have upgraded a Self-consistent-field – Hartree–Fock routine to include a finite nuclear mass correction for molecules developed in our laboratory. The new routine can handle isotopomers without calculating any nuclear kinetic energy matrix element. Tests on H2, LiH, HF, F2, and H2O isotopomers indicate the equivalence of our correction to the standard diagonal adiabatic correction. A further original application to C2H6 illustrates the usefulness of the method for polyatomic molecules. The resulting molecular orbitals carry the nuclear mass signature, exemplified with Koopmans’ ionization potentials. [ABSTRACT FROM AUTHOR]

The vibrational-rotational ( v-J) energies of HD in the electronic ground state (1sσ) are calculated in the 'adiabatic' approximation. The accurate wave functions and energies calculated in the approximation, where the nuclei are 'infinitely heavy', are used as the basis for the calculation, and thus the ( v-J) energies are believed to be better. Furthermore, meticulous attention has been paid to the numerical evaluation of the ( v-J) energies, ensuring that the possible numerical truncations, at each stage, are reduced to a minimum, thus enhancing the credence that the energy eigenvalues within the limits of the approximation, are better than the ones reported earlier. [ABSTRACT FROM AUTHOR]