K. Dietz

Selective excitation of molecular vibrations by interference of Floquet states

The authors develop a mechanism for the selective excitation of molecular vibrational states by short strong laser pulses. This mechanism is based on constructive interference of Floquet states. A phase functional is constructed which allows the theoretical prediction of the parameters of optimal pulses. The role of anharmonicities of the molecular binding potential and their effect on the structure of the instantaneous Floquet states is clarified.

The acceleration of convergence of many-body perturbation theory: unlinked-graph shift in Møller-Plesset perturbation theory

Abstract We recently proposed (parts I and II of this series of publications) a new method of infinite subsummation in the Moller-Plesset perturbation series with the objective of “effecting convergence of otherwise divergent series”. In the present work we undertake to study the importance of a shift of unlinked graphs in the Moller-Plesset renormalization term. We demonstrate that this modification of many-body perturbation theory presents a viable starting point for new approximations devised to obtain a substantial fraction of the correlation energy at low order. We present an explicit investigation of the excited states of LiH in a suitable full-CI model space, using our method to calculate the correlation energy and monitoring convergence up to tenth order.

Generalized Bloch spheres for m-qubit states

m-qubit states are embedded in Clifford algebras. Their probability spectrum then depends on O(2m)- or O(2m + 1)-invariants, respectively. Parameter domains for O(2m(+1))-vector and -tensor configurations, generalizing the notion of a Bloch sphere, are derived.

Systematic construction of efficient many‐body perturbation series

A new procedure for the splitting of many‐body Hamiltonians into ‘‘free’’ and ‘‘interaction’’ parts is proposed which leads to a rapidly converging perturbation expansion. The efficiency of this method is shown for the case of small molecules: Already first and second order perturbations turn out to produce very reasonable results even for excited states; higher terms rapidly converge to zero. An important point to notice is that our method allows for a priori estimates of the convergence (or divergence) behavior.

Strong laser fields interacting with matter I

We discuss non-perturbative aspects of the Floquet picture for the interaction of single mode strong laser fields with electrons. In numerical studies we show that this system stays adiabatic to a surprising degree: for smooth pulses, adiabaticity holds even for very short pulse-length (down to the order of 10 cycles) except for transitions at avoided crossings sharply located in time. The latter are seen to act as interferometers, a non-adiabatic pumping mechanism is proposed. Non-perturbative aspects of multi-photon transitions are clarified.

Critical Higgs Mass for the (2+1)-dimensional Georgi-glashow Model

Abstract The ground state of a (2+1) dimensional Georgi-Glashow model is discussed in a dilute monopole gas approximation. In addition to the Coulomb interaction of the latter, we include a Higgs force which is attractive irrespective of the sign of monopole charges. For (Higgs masses) −1 comparable to the mean free distance of monopoles we find a phase transition which is presumably of first order. Strings of monopoles dominate the clustering behaviour near the critical Higgs mass.

On the classical dynamics of strongly driven anharmonic oscillators

Abstract We investigate the dynamics of periodically driven anharmonic oscillators. In particular, we consider values of the coupling strength which are orders of magnitude higher than those required for the overlap of primary resonances. We observe a division of phase space into a regular and a stochastic region. Both regions are separated by a sharp chaos border which sets an upper limit to the stochastic heating of particles; its dependence on the coupling strength is studied. We construct perpetual adiabatic invariants governing regular motion. A bifurcation mechanism leading to the annihilation of resonances is explained.

Optimised mean fields for atoms. II. Numerical studies

For pt.I see ibid., vol.15, no.23, p.4293 (1982). The one-parameter non-uniqueness of stationary electron configurations in atoms can be used to single out a mean-field equation yielding the exact total energy. This equation is Hartree-like and contains exchange terms with a strength parametrising electron correlations, radiative corrections and further perturbative contributions. A numerical study of this equation is presented for the relativistic case.

Explicit construction of a convergent MBPT series for the 1Δ state of C2 and the H2 ground state at large bond distance

We explicitly construct a convergent perturbation series for intrinsically divergent Moller—Plesset cases. The means to accomplish this goal is an explicit reduction of the size of the perturbation. This is achieved by means of a Λ transformation and an unlinked-graph shift. Generic multi-reference cases are treated by single-reference methods after a simple and feasible transformation of the Hamiltonian matrix to a basis comprising a suitable reference zero-order vector. This effectively solves the intruder-state problem. We present the 1Δ state of C2 and the H2 ground state at large bond distance as typical examples.

Single particle orbitals for configuration interaction derived from quantum electrodynamics

By explicitly introducing degrees of freedom for the electromagnetic field into the Hamiltonian for an N-electron system, we propose a variational procedure leading to mean fields different from the Hartree-Fock field. We show that g-Hartree equations result if the electromagnetic field is assumed to be in a coherent state. Since the solutions of these equations, the g-Hartree orbitals, are derived from a variational ansatz more general than the Hartree-Fock functional, we expect them to be particularly suitable to furnish a single-particle basis set for fast converging configuration interaction (CI) calculations. We report configuration interaction studies on the water molecule in a double zeta basis set employing various single-particle basis set transformations for the construction of the configuration state functions and investigate the convergence behaviour of the CI expansion explicitly. We find that the expansion in terms of g-Hartree orbitals receives substantially larger fractions of the total correlation energy in the case considered, if single excitations with respect to the mean field configuration are retained in the CI procedure.