Adiabatic Perturbation Theory Research Articles

Stabilizing a breather in the damped nonlinear Schrödinger equation driven by two frequencies

In the framework of adiabatic perturbation theory and energy balance conditions, we analyze the possbility of stabilizing a breatherlike state (a bound state of two solitons with coinciding centers) in the damped (1+1)-dimensional cubic nonlinear Schroedinger equation by a two-frequency ac drive. The analytic predictions for the threshold of driving strengths above which a stable breather exists are in good agreement with those measured in numerical simulations.

Adiabatic Perturbation Theory. Semiclassical Limit of the Reflection Coefficient on a Potential Barrier

Using methods of Adiabatic Perturbation Theory, the asymptotic behaviour in the semiclassical limit of the reflection coefficient for one dimensional collisions in quantum mechanics is studied rigorously. In this limit we give a recursive method for an exact calculation to all orders. In contrast to other methods (which fail), our method still works when the energy is near or equal to the top of the potential. First we derive the coefficient for a specific potential. Then we give the coefficient to first three orders for an arbitrary potential depending only on the potential's behaviour around its maximum. We point out that each term needs to be analysed to “all orders”.

Hyperradiance from soliton oscillators synchronized by capacitive or inductive coupling

The output power from coupled Josephson oscillators is investigated when the junctions are operated in their single fluxon mode. We demonstrate that both inductive and capacitive coupling mechanisms can give rise to hyperradiance when the power is coupled out through a boundary resistor. Analytical expressions are derived from adiabatic perturbation theory and excellent agreement is found between the analytical expression and numerical simulations.

Tests of an adiabatic perturbation theory for symmetric charge exchange

A recently developed adiabatic perturbation theory for symmetric molecular charge exchange is tested against accurate calculations over a range of energies from 0.5 to 32 eV. Good agreement is found over the whole energy range, and the discrepancies are roughly the same at all energies so that an adiabatic basis set should be good even at high energies. The total charge exchange cross section is calculated for specific initial vibrational states. It depends strongly on the initial state, and it oscillates as a function of energy, so that this cross section may be a useful way to fit a potential to experimental data

About enhancement of infrared absorption by molecules adsorbed on rough surfaces

On the base of the adiabatic perturbation theory, using the results obtained by the author in the SERS theory, a theory of enhancement of infrared absorption by molecules adsorbed on rough surfaces is developed. The expressions for the infrared absorption cross section in free space and in a surface electromagnetic field with the dipole and quadrupole light-molecule interactions taken into account are obtained. It is shown that the absorption process may be more complex than it was considered earlier. The corresponding estimations demonstrate that the cross section can increase due to the growth of both the dipole and quadrupole light-electron and light-nuclear interactions.

Adiabatic Perturbation Theory on Reactions Induced by Weakly Bound Particles at Higher Incident Energies

We develop an adiabatic perturbation theory to clarify the relation of the adiabatic approxima­ tion of-Johnson and Soper to the method of continuum discretized coupled-channels (CDCC). The theory presents a systematic way of evaluating corrections to the adiabatic approximation. It is proven on the basis of the adiabatic theorem that the corrections vanish in the adiabatic limit of motions of nucleons in the projectile nucleus, or in the limit of high incident energies. The correc· tions do not include any geometrical quantity such as Berry's phase, because of no diabolic point in the .parameter space. 4 ),5) for reactions induced by weakly bound particles at higher incident energies. These approximations are performed with the following common procedure. First the total system is considered to be composed of slow and fast subsystems interacting through a coupling between them. The total Hamiltonian H is then separated into a sub-Hamiltonian Hs of the slow subsystem and the remainder Hf describing motions of the fast subsystem interacting with the slow one through the coupling. The coupling in Hf depends on intrinsic coordinates r of the slow subsys­ tem, but the coordinates work only as parameters in Hf, since Hf does not include any kinetic energy operator on r. So the fast subsystem is assumed to be in an eigenstate I())m(r» of H f, with a common quantum number ni at each r. The eigenstate has different energies Em(r) at each r in the cases of (a) and (b). In (c), the energy is an incident energy E po of the projectile independently of r, and then the quantum number m represents an incident momentum of the projectile. Next His approximated into Hs+ Em(r) by replacing Hf by Em(r), and the slow subsystem is considered to be in an eigenstate ¢(r) of Hs+ Em(r). Eventually the total wave function 1Jf is given approx­ imately by 1JfAD= ¢(r)1 ())m(r». The separation of H is often called the adiabatic separation approximation. In (c), 1JfAD satisfies the equation, (Hf - Ep,) 1JfAD=O, i.e., (Hf + eo-E) 1JfAD=O, since the total energy Eis the sum of Epo and the eigenvalue eo of Hs in its ground state. This indicates that the adiabatic Hamiltonian, Hf+eo, can be simply defined from H by replacing Hs by eo. So far the approximation (c) was defined with the replace-

Adiabatic Perturbation Theory on Reactions Induced by Weakly Bound Particles at Higher Incident Energies

Adiabatic Perturbation Theory on Reactions Induced by Weakly Bound Particles at Higher Incident Energies

Adiabatic approach for the low-temperature conductivity in one-dimentional disordered metals

An adiabatic perturbation theory for Green functions of electrons moving in slowly varying external fields is derived. This approach is applied to calculate the conductivity of 1d disordered metals at a temperature small compared with the localized electrons' intrinsic frequency which involves the phonon renormalization of the electron mass (polaron effect). The result obtained on the basis of the presented theory gives evidence for the violation of the well-known Mott law for temperature-dependent conductivity of 1d localized electrons.

Initial- versus final-state effects in the narrow-band spectra of heavy-fermion systems.

The {ital f}-electron spectral density of heavy-fermion systems, as observed by x-ray photoelectron spectroscopy (XPS) and bremsstrahlung isochromat spectroscopy (BIS), is discussed in terms of initial- and final-state effects. The properties of the initial state, described by the periodic Anderson model, are obtained from the adiabatic perturbation theory, with the on-site correlation {ital U}{sub {ital f}{ital f}} taken as the expansion parameter. In the final state the transient effects following the sudden ionization of the system in XPS or BIS are discussed by using the time-dependent perturbation expansion. The overall spectral shapes, as would be observed experimentally, turn out to be given as a convolution of the adiabatic spectral function, which reflects the many-body interactions in the initial state, and the shape function, which accounts for the nonadiabatic effects following the destruction of the charge neutrality in XPS and BIS. Our treatment allows us to explain the position and the shape of the {ital f}-derived peaks in the XPS spectra of actinide intermetallics and to remove the conceptual difficulty in understanding the data acquired independently from thermodynamic (low-energy) and spectroscopic (high-energy) measurements of heavy fermions within a unified framework.

Divergences in the iterative and perturbative methods for computing Hannay's angle.

A classical analog is obtained for Berry's nonperturbative scheme of adiabatic iteration which computes corrections to Berry's phase (or Hannay's angle) for finite values of the adiabatic parameter \ensuremath{\epsilon}. The iterative method is compared to the Lie version of adiabatic perturbation theory. Both approaches show a divergence of k!${\mathrm{\ensuremath{\epsilon}}}^{\mathit{k}}$, where k is the order of iteration. It is argued that the divergences are a mathematical artifact of the asymptotic methods used, not related to the physical effect of transitions, nor to the nonconservation of the action variables.

About the SERS Phenomenon I. The Cross‐Section in Adiabatic Perturbation Theory

AbstractThe theory of SERS (surface enhanced Raman scattering) is developed. First the light interaction with molecules is considered. The wave functions of the molecule are received in the first order of the adiabatic perturbation theory. Then the cross‐section of Raman scattering with the dipole and quadrupole light interaction with a molecule taken into account is obtained.

A perturbation theory for the solitary-drift-vortex solutions of the Hasegawa-Mima equation

A multiple-scales adiabatic perturbation theory is presented describing the adiabatic dissipation of the solitary vortex-pair solutions of the Hasegawa-Mima equation. The vortex parameter transport equations are derived as solvability conditions for the asymptotic expansion and are identical with the transport equations previously derived by Aburdzhaniya et al. (1987) using an energy- and enstrophy-conservation balance procedure. The theoretical results are compared with high-resolution numerical simulations. Global properties such as the decay in the enstrophy and energy are accurately reproduced. Local properties such as the position of the centre of the vortex pair, decay of the extrema in the vorticity and stream-function fields, and the dilation of the vortex dipole are also in good agreement. In addition, time series of vorticity–stream-function scatter diagrams for the numerical simulations are presented to verify the adiabatic ansatz.

Adiabatic perturbation theory for the degenerate case. III. Adiabatic formalism by Gell‐Mann and low with an arbitrary switching function

AbstractAn adiabatic formalism in the degenerate or quasidegenerate subspaces, which does not depend on the particular form of the switching function g(α, t), is outlined. A general factorization theorem for the dynamic operator Sα(t, t0 | g) is proved. This theorem enables one to formulate the perturbation expansion for the effective Hamiltonian and the wave operator which is free from the adiabatic divergencies.

Polarization and binding effects in K-shell ionization by 16O and 32S ions.

The theoretical model of Montenegro and Sigaud is used for the description of the experimental total K-shell ionization cross sections for 2.2-MeV/u /sup 16/O and /sup 32/S on 24 targets from /sub 21/Sc to /sub 83/Bi obtained by Seidel et al. The predictions of the model, which considers both binding and static polarization effects within the framework of adiabatic perturbation theory, are very good for the majority of the measured data in the region of validity of the model. The electron-capture process that can contribute in the region of the largest values of relative velocity xi/sub K/ is also analyzed.

1s sigma molecular orbital ionisation in asymmetric ion-atom collisions by direct Coulomb interaction

Adiabatic perturbation theory is applied to the ionisation of the 1s sigma molecular orbital (MO) and extended to less adiabatic collisions by imposing an asymptotic matching with the semiclassical approximation. The transient molecular state wavefunction is modelled using the concept of an 'effective' charge for the colliding system. Through this procedure the transition amplitudes are evaluated simulating both the relaxation of the passive electrons and the modification of the active electron wavefunction, as well as their connection with the motion of the centre of charge during the collision. The direct Coulomb ionisation of the 1s sigma MO is calculated for projectiles following hyperbolic paths, in terms of this 'effective' charge, using the current-vector formalism. Comparison is made with a large amount of experimental data and good agreement is found.

Saturation behavior of a far-wing satellite

We use a saddle point method to derive an asymptotic approximation to the adiabatic perturbation theory transition amplitude. This result is used to discuss the saturation of an ‘‘optical’’ collision when the field is resonant at an extremum of the potential energy difference. We point out that although the onset of saturation in this satellite occurs for lower field strengths than those needed to saturate a linear crossing, the satellite saturates more slowly than a linear crossing as the field strength is increased.

A new type of cluster expansion and time-dependent adiabatic perturbation theory on finite and infinite lattices

A new type of cluster expansion is proposed, which is used to calculate the properties of the lower part of the spectrum of a general lattice Hamiltonian. The method does not involve power series in the number of lattice sites. Surface effects are easily incorporated into the theory in a natural way. Application to the 1-d Ising model in a transverse magnetic field demonstrates that good results can be obtained with moderate computational effort.

The adiabatic semiclassical perturbation theory for vibrationally inelastic scattering. III. Morse oscillators

We have modified our previous adiabatic theory for vibrationally inelastic scattering [J. Chem. Phys. 71, 1426 (1979)]. A perturbation calculation is done using a partially adiabatic basis set. The result is exponentiated to give the full scattering matrix. Several improvements were made in the theory for collinear scattering from harmonic oscillators. The accuracy is much better than the previous version, and the computation time is less. The theory has been adapted for the Morse oscillator, and the accuracy is as good or better than for the harmonic oscillator except for the system He+HBr. The poor accuracy in the case of He+HBr seems to be due to the large perturbation involved as well as the mass combinations of the various atoms involved in the collision.

Tunnel Electrode I. Electron Transfer Process at Highly Doped SnO2 Electrode with Ce4+ in High Overvoltage Region

Abstract Electron transfer theory at tunnel semiconductor electrode was derived from the double adiabatic perturbation theory. The cathodic current of Ce4+ with very positive redox potential was measured at highly doped SnO2 electrode. The rearrangement energy of 0.65 eV for Ce4+ was estimated from the relationship of transfer coefficient vs. electrode potential. Large electron transfer rate in the high overvoltage region can be explained in terms of the contribution of excited vibrational states in the first coordination sphere into electron transfer.

Tunnel electrode: Part II. Electron-transfer theory at an n-type semiconductor tunnel electrode

The formula for the cathodic tunnel current at an n-type semiconductor tunnel electrode was derived from the double adiabatic perturbation theory considering the vibration in the first coordination sphere. In the low-temperature limiting case, the apparent difference between the normal and the abnormal regions was observed in both the transfer coefficient α and the activation energy E* as a function of potential. It was concluded that the semiconductor tunnel electrode has advantageous characteristics for investigation of the electron-transfer mechanism at high overvoltage.