The hierarchicalφ 4-trajectory by perturbation theory in a running coupling and its logarithmby perturbation theory in a running coupling and its logarithm

We compute the hierarchical ⁴- in terms of perturbation theory in a running coupling. In the three-dimensional case we resolve a singularity due to resonance of power counting factors in terms of logarithms of the running coupling. Numerical data are presented and the limits of validity explored. We also compute moving eigenvalues and eigenvectors on the trajectory as well as their fusion rules.     

Monotonicity and concavity in Coulomb systems

The eigenvalues ofH()=H ₀+H ^*, whereH ^* is an arbitrary Coulomb potential, decrease with increasing 0. Linear and parabolic bounds for the ground-state energy are presented. These bounds are applied to the biexciton and the exciton at a neutral donor.     

On the connection between the one-dimensionalS=1/2 Heisenberg chain and Haldane-Shastry model

Extra integrals of motion and the Lax representation are found for interacting spin systems with the HamiltonianH = (J/2) _{j, k=1,j k} ^N P(j – k) _{j k} , where one of the periods of the WeierstrassP function is equal toN. The Heisenberg and Haldane-Shastry chains appear as limiting cases of these systems at some values of the second period. The simplest eigenvectors and eigenvalues ofH corresponding to the scattering of two spin waves are presented explicitly for these finite-dimensional systems and for their infinite-dimensional version.     

Mössbauer-NMR double resonance: A completely quantized quasi-static approach

We have introduced the concept dressed nucleus in order to describe the interaction of a nucleus (in a static magnetic field) with a radiation field havingn photons of a certain mode. The idea is to consider the global system as one quantum system in the Schrödinger representation. The number of eigenvalues of the global system is (2I+1)² withI the spin of the free nuclear state. Taking into account the form of the corresponding eigenvectors and the relevant selection rules, the total number of -transitions for the nuclear M1 transition 3/2^–1/2^– is 24. If a Mössbauer effect experiment is set up with a single line absorber, the source being an ensemble of dressed nuclei, we would expect a spectrum showing 24 lines, the relative positions and intensities of which are calculated.     

Two-Dimensional Coulomb Systems in a Disk with Ideal Dielectric Boundaries

We study two-dimensional Coulomb systems confined in a disk with ideal dielectric boundaries. In particular we consider the two-component plasma in detail. When the coulombic coupling constant =2 the model is exactly solvable. We compute the grand potential, densities and correlations. We show that the grand potential has a universal logarithmic finite-size correction as predicted in previous works. This logarithmic finite-size correction is also found in the free energy of another solvable model: the one-component plasma.     

Relativistic point interaction

A four-parameter family of all self-adjoint operators corresponding to the one-dimensional Dirac Hamiltonian with point interaction is characterized in terms of boundary conditions. The spectrum and eigenvectors, and the scattering parameters are calculated. It is shown that the nonrelativistic limit reproduces (in the norm resolvent sense) the four-parameter family of Schrödinger operators with point interaction, their eigenvalues and scattering parameters.Graduiertenkolleg Geometrie und mathematische Physik.Alexander von Humboldt fellow. On leave of absence from SISSA, Trieste, Italy.     

Exact hierarchical solution of the damped oscillator problem

As a alternative to other exact approaches we present a procedure, in which the eigenvectors of a coupled oscillatory system are calculated in a hierarchically exact (N) manner. In the system a single oscillator is coupled to a dense sequence of background oscillators, which among themselves are not mutually coupled (Oscillatory Fano problem). The eigenvectors beeing known, all decay laws become computable. Two of them are given. It is strongly emphasized thatquite different decay laws evolve fordifferent initial conditions.Dedicated to B. Mühlschlegel on the occasion of his 60th birthday     

Three-body treatment of Coulomb effects in the problem of long-range effective interactions

The problem of Coulomb scattering of a charged particle by a two-particle bound system, consisting of a charged and a neutral particle, is investigated in the integral-equation approach of rigorous three-body theory. The bound state of the two particles is provided by a short-range interaction chosen in the simplest form using anS-wave separable potential. The integral equation defining the effective potential of the interaction of the charged particle with the two-particle bound system is formulated. It is shown that the multiple Coulomb scattering of the involved charged particles generates a sequence of long-range terms in the effective potential. It turns out that the long-range effects of Coulomb scattering are partly cancelled. As a result the polarization potential does not contain the longest-ranged terms which decrease at large distances as ^–2 and ^–3.     

Bremsstrahlung of Debye plasma

The effect of Debye screening on the bremsstrahlung spectrum and total bremsstrahlung intensity of plasma is calculated. As compared with the Coulomb field approximation (infinitely large Debye radiusL) an additional density and temperature dependence of the radiation intensity is found. Results are expressed in terms of a dimensionless parameter=²/2mL ² kT, wherem is the rest mass of an electron and other symbols have their standard meaning. Deviations from the Coulomb field approximation become significant for the values 10^–3.I am grateful to Dr. J.Horáek and Dr. J.Obdrálek for their help in performing the numerical calculations.