On the interaction of collective degrees of freedom in nuclei

The structure of the interaction of giant dipole and giant quadrupole oscillations with nuclear surface vibrations is established. The various coupling parameters are calculated in the hydrodynamic model. The significance of the interaction terms is discussed.     

On the partial trace over collective spin degrees of freedom

We derive analytical properties for the degeneracy ν(N,j) occurring in the decomposition of the state space C2⊗N. We also investigate the dynamics of two qubits coupled via Ising interactions to separate spin baths, and we study the thermodynamic limit.     

On pionic degrees of freedom in atomic nuclei

The possibility of explicit pionic degrees of freedom in atomic nuclei and their association with pionic reactions involving fragment emission is discussed. Although no present direct evidence for such degrees of freedom is available they could be searched for in doorway states — other than the anticipated N¹ doorway — in the excitation function in the pion-induced partial reaction cross sections. Such a search is underway. A framework is discussed in terms of which such new pion doorways might be described.     

Sp(4, R) symmetry in light nuclei

A classification of nuclear states according to the non-compact Lie algebra Sp(4, R) is investigated. This model strikes a compromise between the Sp(6, R) and Sp(2, R) models and furnishes a practical, yet algebraically simple means for selecting those shell-model core excitations which are needed for the development of quadrupole collectivity in rotational bands of deformed nuclei. Applications to rotational bands in ²⁴Mg and ¹⁶O, including shell-model excitations with excitation energies up to 10?ω, show that the core excitations needed to fit observed E2 rates in these nuclei are too large to be treated by perturbation theory. Despite this, a definite symplectic band structure emerges. The nature of the core excitations is very simple, so that it may be feasible to incorporate such symplectic excitation structures into more detailed shell-model calculations.     

Interaction of the single-particle and collective degrees of freedom in non-magic nuclei: The role of phonon tadpole terms

A method of consistent treatment of phonon contributions to the self-energy and gap terms in non-magic nuclei is developed in so-called g ² approximation, where g is the creation amplitude of a low-lying phonon. The method simultaneously takes into account both usual non-local and local phonon tadpole terms. Relations that allow the tadpoles to be calculated without introduction of new parameters are derived. As an application of the method, the effect of the phonon tadpoles on the single-particle strength distribution, single-particle energies and gap values is considered. Hypothesis of the surface nature of pairing correlations is discussed in the light of the tadpole effect.     

Coupling between spin and orbital degrees of freedom in KCuF3

We present the results of resonant x-ray scattering experiments on KCuF3. Structurally forbidden reflections, corresponding to magnetic and 3d-orbital long-range order, have been observed. Integrated intensities have been measured as a function of incident energy, polarization, azimuthal angle, and temperature. The results give evidence for a strong coupling between orbital and spin degrees of freedom. The interplay between magnetic and orbital order parameters is revealed by the temperature dependence of the intensity of orbital Bragg peaks.     

Interrelation of the spin,orbital, and charge degrees of freedom in half-doped manganites

Based on the double-exchange model in the tight-binding approximation, self-consistent energy-band-structure calculations are carried out for the first time for the orbital and charge ordering in La_0.5Ca_0.5MnO₃-type manganites with 16 Mn ions in the unit cell under the assumption of a linear dependence of the Jahn-Teller splitting of the e _g level on the occupancy of each ion. The equilibrium magnetic and orbital configurations are determined by minimizing the total energy with respect to the direction of the local magnetic moments and the orbital states of the Mn ions. The dependence of the splitting on the occupancy favors the stabilization of phases with charge separation. This separation is an important factor determining the magnetic structure of the ground state. The ground state can be an insulating antiferromagnetic structure of the CE or G type or a new ferrimagnetic structure with a magnetization lower than that of a saturated ferromagnet by a factor of 2. The existence and the width of the bandgap in the electronic energy spectrum of the CE phase depend on the ratio between the values of the Hund exchange and the splitting. When the splitting is sufficiently large, the Jahn-Teller effect stabilizes the insulating state. The finite value of the Hund coupling also favors the stabilization of the CE phase for the realistic values of the interionic exchange and the hopping integral of itinerant electrons.     

Coupling between internal spin dynamics and external degrees of freedom in the presence of colored noise

We observe asymmetric transition rates between Zeeman levels (spin flips) of magnetically trapped atoms. The asymmetry strongly depends on the spectral shape of an applied noise. This effect follows from the interplay between the internal states of the atoms and their external degrees of freedom, where different trapped levels experience different potentials. Such insight may prove useful for controlling atomic states by the introduction of noise, as well as provide a better understanding of the effect of noise on the coherent operation of quantum systems.     

Separation of charge and spin degrees of freedom in the Hubbard model

The representation of the electron field operators separating charge from spin and providing transmutations between spin and isospin quantum numbers has been derived for any dimension. In this representation the interaction term in the Hubbard model is expressed in a bilinear form of quasiparticle field operators. The quasiparticles are spinless fermions with the electron electric charge. The consequence of this representation is that superconductivity in the strong coupling Hubbard model is due to odd wave pairings of electrons.The author expresses his sincere gratitude to Professor S. Stenholm for discussions and for the warm hospitality at the Research Institute for Theoretical Physics, University of Helsinki where this work has began. He would especially like to thank Professor C. Cronström who played an important role in the early and final stages of this work. Professor Anderson is acknowledged for providing the author with two chapters of his book (not yet published) quoted in the Discussion.     

Mesonic degrees of freedom in nuclei and the definition of meson-exchange currents

We describe the nucleus by a meson-nucleon system. Starting from a covariant field theoretical Hamiltonian we derive an effective Schrödinger equation for the nucleonic components. The meson-exchange currents are then defined unarbitrarily by an effective operator (current) in the space of the nucleonic components. The advantage over theS-matrix method [1] is discussed. In the nonrelativistic limit the meson-current as well as the seagull (pair) current agrees with theS-matrix result. Recoil and wavefunction orthogonalization cancels completely in this limit.     

Bose-Einstein condensation of S = 1 nickel spin degrees of freedom in NiCl2-4SC(NH2)2

It has recently been suggested that the organic compound NiCl2-4SC(NH2)2 (DTN) undergoes field-induced Bose-Einstein condensation (BEC) of the Ni spin degrees of freedom. The Ni S = 1 spins exhibit three-dimensional XY antiferromagnetism above a critical field H(c1) approximately 2 T. The spin fluid can be described as a gas of hard-core bosons where the field-induced antiferromagnetic transition corresponds to Bose-Einstein condensation. We have determined the spin Hamiltonian of DTN using inelastic neutron diffraction measurements, and we have studied the high-field phase diagram by means of specific heat and magnetocaloric effect measurements. Our results show that the field-temperature phase boundary approaches a power-law H - H(c1) proportional variant T(alpha)(c) near the quantum critical point, with an exponent that is consistent with the 3D BEC universal value of alpha = 1.5.     

The Clebsch-Gordan coefficients ofsl(2,R) in the parabolic basis

We realize the Lie algebra sl(2,R) in terms of second-order differential operators defined on a dense common domain of square-integrable functions on a two-chart space, where the self-adjoint extension(s) (families) lead to all (and only) self-adjoint irreducible representations of the algebra, single- as well as multi-valued over the group. This allows for a rather straight-forward evaluation of the Clebsch-Gordan coefficients of sl(2,R) in the parabolic subalgebra basis.Invited talk presented at the International Symposium Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 14–19, 1981.I would like to thank the hospitality of Prof. J. A. de Azcárraga, at the Instituto de Fí'sica Teórica, Universidad de Valencia, where this review was written.     

Mesonic degrees of freedom in nuclei and retardation effects in meson-exchange currents

In the present paper we give a brief review of a consistent calculation of meson-exchange effects. For the charge density these currents are calculated up to the order of $\text{O(}\text{1}\text{M}{}^3\text{)}$ for π, ρ- and ω-exchange. The retardation currents arising from the recoil and wave function reorthonormalization currents are derived. A quantitative discussion of the retardation currents is done for the example of the deuteron form factors. As for the quadrupole form factor the retardation contribution is shown to be important. In the case of the charge form factor these effects are unimportant for our choice of deuteron wave functions.     

On the connection between spin glasses and gauge field theories

A simple connection between Ising spin glasses and the Z₂ lattice gauge theory, at negative plaquette temperatures, is presented. It is first shown that annealed models give useful lower bounds on the free energy and ground-state energy of spin glasses. However, they have unphysical low temperature properties (e.g. a negative entropy), which are related to a temperature dependence of the frustration. A restricted annealing scheme is presented which remedies this deficiency through the introduction of a pure gauge coupling counterterm. The possible phase diagrams of the lattice gauge system and their relevance to spin glass transitions are discussed.     

The role of mesonic degrees of freedom in deep inelastic structure functions of nuclei

We show that with light mesons (pions) carrying a few percent (1–5%) of the totalP ₊ of a nucleus, the SLAC data on nuclear structure functions can be explained. We stress the importance of these mesons for the region 0.3<x<0.7.     

Relaxation and decoherence of orbital and spin degrees of freedom in quantum dots

The phonon induced mechanisms of relaxation/decoherence in quantum dots are analysed. A non-perturbative technique - a modification of the Davydov transformation appropriate to the localised particles is applied for solving the electron-phonon eigenvalue problem in a quantum dot at magnetic field presence. The decay rates for polaron relaxation via the anharmonicity induced channel are analysed in details. In particular, it is indicated that previous, of perturbative type, estimations of the anharminicity induced relaxation rates were too severe and after including the coherence effects they are of, at least, one order longer. The process of exciton dressing with phonons is also analysed as the unavoidable source of picosecond scale decoherence in optically driven nanostructures. A break-down of an instant Pauli spin blocking mechanism and a large enhancement of the Fröhlich constant for confined electrons are also addressed.