The anomalous chiral Schwinger model and its quantization

We solve the anomalous chiral Schwinger model in the hamiltonian formulation implementing the Faddeev proposal. We diagonalize the hamiltonian by functional techniques and construct the eigenfunctionals of the quantized system. The spectrum is non Lorentz invariant since the Poincarè algebra is not closed. We point out that, relinquishing the Faddeev condition, there would be an infinite degeneration of the hamiltonian. Among the degenerate 1-particle eigenfunctionals it is possible to find a state with relativistic spectrum. We also examine the meaning of a non local modification of the hamiltonian which restores Lorentz invariance.     

Theorie der Elektron-Phonon-Wechselwirkung in paramagnetischen Salzen

The electron-phonon hamiltonian of paramagnetic ions, derived from the assumption of a deformable potential of the surrounding ligands, is given as a function of the static crystalline field. With that it is possible to reduce the spin-lattice relaxation time to the coefficients of the expansion of the crystalline potential in terms of spherical harmonics, present in the treatment of energy splitting by the crystalline field. The anisotropy of the matrix elements of the electron-phonon hamiltonian relative to the propagation vector of lattice vibrations is discussed.     

Nuclear hyperfine interactions in non-linear semi-rigid molecules

From the expression for the hamiltonian in molecular coordinates we obtained previously, the computation of an effective hamiltonian for a nondegenerate electronic state is performed to second order in degenerate perturbation theory. We thus obtain explicitly all dominant parameters for the spin-vibration and spin-rotation interactions; in addition, the parameters associated with the interactions between the magnetic moment induced by the molecular motion and an external magnetic field are computed. The vibrational dependence of these parameters is studied and the hamiltonian is written in a form adapted to the computation of an effective hamiltonian for an arbitrary vibrational state.     

The geometric content of the interacting boson model for molecular spectra: A testground for the nuclear IBM

The recently proposed algebraic model for collective spectra of diatomic molecules is analysed in terms of conventional geometrical degrees of freedom. We present a mapping of the algebraic hamiltonian onto an exactly solvable geometrical hamiltonian with the Morse potential. This mapping explains the success of the algebraic model in reproducing the low-lying part of molecular spectra. At the same time the mapping shows that the expression for the dipole transition operators in terms of boson operators differs from the simplest IBM expression and in general must include many-body boson terms. The study also provides an insight into the problem of possible interpretations of the bosons in the nuclear IBM.     

Stability in bihamiltonian systems and multidimensional rigid body

The presence of two compatible hamiltonian structures is known to be one of the main, and the most natural, mechanisms of integrability. For every pair of hamiltonian structures, there are associated conservation laws (first integrals). Another approach is to consider the second hamiltonian structure on its own as a tensor conservation law. The latter is more intrinsic as compared to scalar conservation laws derived from it and, as a rule, it is “simpler”. Thus it is natural to ask: can the dynamics of a bihamiltonian system be understood by studying its hamiltonian pair, without studying the associated first integrals?     

Polaron formalism applied to donor-acceptor pairs in semiconductors

The effective hamiltonian for the electronic states of a donor-acceptor pair in a polar semiconductor is formulated as a Fröhlich hamiltonian generalized to an electron and a positive hole interacting in the field of the positive donor and negative acceptor cores. The polarization of the lattice by the ion cores is simplified by a Platzman transformation; that by the electron and positive hole, by a further unitary transformation in the adiabatic approximation. The total effective hamiltonian including the lattice polarization energy is then considered for application of the variational principle to determine the parameters of the electron and positive hole effective mass functions. The Inglis-Williams analysis of the zero-phonon luminescent spactra of pairs is reconciled with the present theory by determining what single effective hamiltonian for the excited electronic state is consistent with their theoretical spactra. Within the approximations of their analysis, which are clarified, it is found to be the total effective hamiltonian. Finally, a more general and rigorously-derived effective hamiltonian is presented for the direct theoretical determination of the zero-phonon radiative transition energies of donor-acceptor pairs in compound semiconductors.     

Site representation for charge transfer excitations in molecular crystals

A phenomenological site hamiltonian is constructed for molecular crystals whose lowest electronic excitations involve an electron transfer, as in many donor-acceptor and free-radical crystals. When only the lowest chargetransfer states are retained, a fermion representation of the site hamiltonian is obtained which leads to a typical many-body problem. The model reduces in special cases to the Hubbard and the Pariser-Parr-Pople models. However, instead of a one-electron, frozen core model, the site representation includes core rearrangements and polarization.     

E.S.R. Study of copper and silver N,N-dialkyldiselenocarbamates

Single crystal E.S.R. studies of Cu(II) and Ag(II) dialkyldiselenocarbamates, diluted in the corresponding Ni(II) complexes, are reported. A method has been developed which removes the necessity to measure the spectra on the same single crystal and in three mutually orthogonal planes. Equations have been derived for the resonance fields and the transition probabilities, taking into account the full spin hamiltonian and without assuming coinciding tensor axes. Applying these equations the g tensor and the metal hyperfine and quadrupole coupling tensors are obtained in high precision. In contrast to the situation in the corresponding dithiocarbamates, it was found for all diselenocarbamates studied that the axes of the g and metal hyperfine tensor do not coincide and that the relative orientation depends on the central metal ion and on the molecular symmetry. The highest g value was always found in the molecular plane, whereas in the dithiocarbamates the highest value is found perpendicular to the molecular plane. The spectra reveal the presence of two sets of two equivalent Se atoms, so that the molecule has inversion symmetry. Especially from the measured ⁷⁷Se hyperfine splittings it could be concluded that the built in guest molecule accepts the structure of the host crystal. Also measurements are reported on powders, glasses and liquid solutions. Evidence has been obtained that in the latter two media the g and metal hyperfine principal axes coincide.     

Magnetic multipole moments

Literature definitions of magnetic multipole moment operators are shown to be at variance, and new definitions are formulated which are consistent with a general multipole interaction hamiltonian and with the radiation field of a dynamic charge distribution. The applicability of traceless multipole moments is examined.

The multipole hamiltonian is used to derive expressions for some magnetic quadrupole distortion tensors. For those describing the quadrupole moment induced by a magnetic field and by a field gradient the number of independent components for various molecular symmetries is evaluated.     

13C contact shifts of diamagnetic solvent molecules

In order to study the hyperfine effects induced by molecular vibration, we expand the expression given by Moss [5] for the molecular hamiltonian, in order to include all relevant interaction terms involving nuclear magnetic moments. The transformation from space-fixed coordinates to molecular coordinates is done directly.     

Effective hamiltonians

Non-linear equations, generalizing those determining Bloch's transformation to an effective hamiltonian, are set up in a very simple way. It is shown how they immediately determine the results of Van Vleck, Bloch and Soliverez. Treating the Foldy-Wouthuysen transformation as a special case of the Van Vleck transformation, sixth-order expressions are obtained by means of the non-linear equations. The transformations of Soliverez, Roussy and Kvasnicka are shown to be strictly identical—because they all have a simple property which is proven to be unique for that of Soliverez. Kvasnicka relates his transformation to that of Primas'. We shall see that it is also very closely related to that of Van Vleck's. A certain non-hermitian effective hamiltonian also given by Roussy is proven to be identical to that of Bloch's. Primas' level shift transformation gives an effective hamiltonian for each level in zeroth order. This effective hamiltonian is seen to be identical to that of Soliverez's up to and including third order—and to all orders if one makes a simple change in ‘normalization’. Computer treatment of finite matrices is discussed. The sixth-order Van Vleck hamiltonian recently given by Jørgensen and Pedersen in terms of commutators is derived in a more simple way.     

Verbesserung der Kubo-Theorie für die lineare und lokale Suszeptibilität

We use the Kubo-Theory to derive a correlation-function formula for the local susceptibility of a dielectric with regard to the internal fluctuating electro-magnetic fields in matter. The hamiltonian of the coupled system of field and matter is rewritten into a form, that it includes only operators which relate to volume elements with many atoms. The interaction between different volume elements and with it spatial dispersion is neglected. The possible energy levels in each volume element are approximated by an Oszillator model. The difference between the local susceptibility and the response function to an external field, which is calculated in the usual Kubo-Theory, is shown.     

Secondary Quantum Hamiltonian Reductions

Recently, it has been shown how to perform the quantum hamiltonian reduction in the case of general embeddings into Lie (super)algebras, and in the case of general embeddings into Lie superalgebras. In another development it has been shown that when and are both subalgebras of a Lie algebra with , then classically the algebra can be obtained by performing a secondary hamiltonian reduction on . In this paper we show that the corresponding statement is true also for quantum hamiltonian reduction when the simple roots of can be chosen as a subset of the simple roots of . As an application, we show that the quantum secondary reductions provide a natural framework to study and explain the linearization of the algebras, as well as a great number of new realizations of algebras. Received: 18 May 1995 / Accepted: 16 January 1996     

Boundary conditions on current carrying states and the implications for observations of bloch oscillations

The problem of the precise form (together with the associated boundary conditions) of a one-dimensional hamiltonian describing a particle of variable mass is addressed. It is shown that although hermiticity may be a necessary condition, it is not sufficient to specify uniquely the hamiltonian. In particular one form of the latter that is widely employed in the literature is shown to lead to a violation of the Heisenberg Uncertainty Principle. However imposition of the additional demand that any singular terms arising from the kinetic energy can be transformed away does lead to a unique specification of the hamiltonian. Finally the implications of the latter with regard to the standard probability interpretation of the wavefunction and for the observation of Bloch oscillations in quantum well structures is described.     

A laser-like model of vibrational condensation

A trilinear hamiltonian describing the interaction of three vibrational modes is proposed as a possible simplified version able to describe a nonequilibrium vibrational condensation of the Fröhlich type.     

Collision hamiltonian for non-linear molecules

A model hamiltonian which describes the non-reactive collision of two non-linear molecules has been constructed. This hamiltonian gives insight into the character of the complex translational, vibrational and rotational motions. The main features of the isolated molecule case are essentially disturbed by the non-adiabatic interaction between the macroscopic molecular motions and the vibrations. The usual angular momentum expressions are found to be the asymptotic limits of the true angular momenta in the case when these non-adiabaticities are switched off.     

Microscopic analysis of nuclear collective motions in terms of the boson expansion theory: (I). Formulation

A normal-ordered linked-cluster boson expansion theory, previously worked out by one of the authors (T.K.) and Tamura, has been developed further by reformulating it in a “physical” quasiparticle subspace which contains no spurious particle-number excitation modes. The expansion coefficients of the collective hamiltonian for low-lying quadrupole motions are determined starting from a microscopic fermion hamiltonian including self-consistent higher-order (many-body) interactions derived in our previous work. The contributions from the non-collective states with all possible non-collective one-boson excitations having I^π = 0⁺− 4⁺, which can directly couple to the collective states with one or two phonons, are taken into account in a systematic and compact way.