Radiation conditions and scattering theory forN-particle Hamiltonians

The correct form of the angular part of radiation conditions is found in scattering problem forN-particle quantum systems. The estimates obtained allow us to give an elementary proof of asymptotic completeness for such systems in the framework of the theory of smooth perturbations.     

Determination of some scattering factors for the case of mixed scattering of charge carriers

The method of determining the Fermi energy and some scattering factors in the case of mixed scattering of charge carriers is described under the presumption that the relaxation time is given by the following equation: = Cx ^s.     

The time dependent amplitude equation for the Swift-Hohenberg problem

Precise estimates for the validity of the amplitude approximation for the swift-Hohenberg equation are given, in a fully time dependent framework. It is shown that small solutions of orderO() which are modulated like stationary solutions have an evolution which is well described in the amplitude approximation for a time of orderO(^-2). For the proofs, we use techniques for nonlinear semigroups and oscillatory integrals.Dedicated to Res Jost and Arthur Wightman     

Two-body collisions and time dependent Hartree-Fock theory

The time-dependent Hartree-Fock (TDHF) theory is generalized in order to include the effect of two-body collisions (i.e. the residual interaction). This is achieved by adding a collision integral into the TDHF equations, similar to the one ordinarily used in the Boltzmann equation. It is shown, that two-body collisions arise from the imaginary part of the effective interaction between two nucleons whereas the Hartree-Fock field is associated to the real part of the same interaction. There is thus no double counting when the collisions are added to a single particle field. Various approximations for the collision integral are discussed and their accuracy evaluated. Special effort is made in order to obtain conserving approximations. It is shown that for discrete fields, energy as well as momentum conservation is achieved by off-shell scattering processes. In the light of a previous paper, it is argued that two-body collisions should dominate the irreversible processes above some critical energy (roughly 200 MeV per nucleon). Below this energy the irreversible effects due to the single particle field and the collisions are expected to be of the same order of magnitude.     

Raman scattering from the molecular charge transfer crystal anthracene-PMDA

The Raman spectrum of the mixed stack charge transfer (CT) crystal anthracene-PMDA, has been measured in the wavelength region near the lowest CT transition at 5458 Å. Six low frequency modes are observed below 140 cm^?1, the mode at 130 cm^?1 showing strong resonance enhancement. These modes are assigned as librational motion of the anthracene and PMDA molecules by rigid body analysis of X-ray structural data.     

Relaxation time for a charge carrier due to its scattering from other charge carriers in superlattices

A calculation of relaxation time for (i) electron–electron scattering in a modulation-doped superlattice of type-I and (ii) electron–electron, hole–hole and electron–hole scattering processes in a compositional superlattice of type-II has been performed, using Fermi's golden rule. As compared to a two-dimensional electron gas system, both intralayer and interlayer interactions, between charge carriers in a superlattice, contribute to relaxation time. It is found that scattering processes at all possible value of momentum transfer contribute to relaxation time, for a given value of temperature and carrier density. We further find interlayer interactions in a superlattice make a significant contribution to relaxation time. Relaxation time is found to decrease on increasing temperature, carrier density and single particle energy, in a superlattice. The computed relaxation time for an electron (hole) in a superlattice enhances on increasing the width of layer consisting of electrons (holes). The electron–hole (hole–electron) scattering process in a type-II superlattice yields maximum contribution to the relaxation time when a hole layer lies exactly in between two consecutive electron layers.     

A multi-channel model of weak scattering of leptons

A multi-channel model of weak scattering is developed, based on the four-fermion theory of weak interactions using the Bethe-Salpeter equation. It leads to several relations among the crosssections of different weak scattering processes. In the low energy limit the cross-section of all included reactions are expressed with the help of a single constant.     

Quantal friction,nonlinear Hamiltonians,and information theory

Information theory ideas together with entropy dynamical properties are combined in order to formulate a new algorithm for the treatment of non-linear Hamiltonians, whether time dependent or not. The approach is illustrated with reference to Kostin's Hamiltonian and the General Friction one.     

Action-angle maps and scattering theory for some finite-dimensional integrable systems

We construct an action-angle transformation for the Calogero-Moser systems with repulsive potentials, and for relativistic generalizations thereof. This map is shown to be closely related to the wave transformations for a large classl of Hamiltonians, and is shown to have remarkable duality properties. All dynamics inl lead to the same scattering transformation, which is obtained explicitly and exhibits a soliton structure. An auxiliary result concerns the spectral asymptotics of matrices of the formM exp(tD) ast→∞. It pertains to diagonal matricesD whose diagonal elements have pairwise different real parts and to matricesM for which certain principal minors are non-zero.     

Adiabatic theory,Liapunov exponents,and rotation number for quadratic Hamiltonians

We consider the adiabatic problem for general time-dependent quadratic Hamiltonians and develop a method quite different from WKB. In particular, we apply our results to the Schrödinger equation in a strip. We show that there exists a first regular step (avoiding resonance problems) providing one adiabatic invariant, bounds on the Liapunov exponents, and estimates on the rotation number at any order of the perturbation theory. The further step is shown to be equivalent to a quantum adiabatic problem, which, by the usual adiabatic techniques, provides the other possible adiabatic invariants. In the special case of the Schrödinger equation our method is simpler and more powerful than the WKB techniques.     

A note on the inverse scattering problem in quantum field theory

We study the set of local fields describing the dynamics of a scalar, massless particle. It turns out that these fields are relatively local to the free, massless, scalar fieldA if the massless particle does not interact. This leads to a simple algebraic characterisation of interacting fields in the above framework.     

Solution of an inverse problem in scattering theory

Hoyt (1939) and Firsov devised methods in classical mechanics to deduce a central scattering potential from a measured differential effective cross-section in the nonrelativistic case. These methods are here extended to the relativistic case. A detailed analysis of the applicability of all methods has been undertaken for potentials of the form V(r) = ±r^–k for sufficiently high energies of the colliding particles. It is found that Hoyt's method is inapplicable in the relativistic case only when the potential represents attraction. A relatively simple method is given for deducing the parameters and k for a monotonic attraction potential that can be approximated by V(r) = –r^–k. The method is based on simple arguments concerning the dimensions of the cross-section. It is sufficient to know only two values of the integral cross-section in the same range of angles but at different energies to determine the parameters.     

Compton scattering and charge transfer in Er substituted DyAl2

A unique applicability of Compton spectroscopy in probing the electronic states of rare earth aluminides using high energy (662 keV) γ-rays is reported. We have measured first-ever Compton profiles of Dy_1-xEr_xAl₂ (x=0, 0.2) using 20Ci ¹³⁷Cs Compton spectrometer. The charge reorganization in Dy_1−xEr_xAl₂ (x=0, 0.2), on the formation of compound, has been discussed using the valence band Compton profile data. The experimental Compton profile data unambiguously establish charge transfer from Al to Dy (Dy and Er) on formation of x=0.0 (0.2) compound, which is in tune with spin polarized relativistic Korringa–Kohn–Rostoker (SPR-KKR) calculations. A reasonable agreement between SPR-KKR based Compton profiles and the experimental data show applicability of the Green function method in predicting the electronic properties of rare earth compounds.     

A resolution of some orthogonality and expansion-set problems in many-body scattering theory

A modification to the coupled channel equations for many-body scattering is introduced, based on the evaluation of the discontinuity equation for the matrix of transition operators. The resulting (modified) equations are shown to be in a form which resolves some problems associated with continuum states in an analysis of rearrangement collisions using the eigenstate expansion method.     

Non-adiabatic effects in the time dependent level crossing problem

We discuss the exact solution of the time-dependent Schrödinger equation for a system of two crossing levels with a residual interaction. In contrast to the familiar Landau-Zener (LZ) solution used in most applications, we allow for more general boundary conditions; in particular we treat explicitly the case of afinite interval around the crossing point. The exact jumping probability is shown to be extremely sensitive to these boundary conditions; in many realistic cases it is found to be smaller than the LZ value by several orders of magnitude. We also compare the exact excitation energy to the one obtained in the usual cranking approach.