H. J. W. Müller-Kirsten

A modified Mottola-Wipf model with sphaleron and instanton fields

Abstract We modify the Mottola-Wipf O(3) sigma model by extending it with a Skyrme term. The resulting model supports a localised instanton solution, as well as sphaleron solution in the static limit.

Dynamic properties of proton transfer in hydrogen-bonded molecular systems

The mechanism of the formation of ionic and bonding defects and the interaction between protons and heavy ions in hydrogen-bonded molecular systems is investigated and a new model is constructed. This model considers two coupled sublattices corresponding to those of protons and heavy ions in order to study the dynamic properties resulting from deformation and local fluctuation of the heavy ion sublattice due to the protonic displacements. As compared with other models, the model emphasizes, in particular, the collective effect of the motion and the mutual correlation between the two sublattices. The equations of motion admit analytic soliton solutions of different types corresponding to two different defects. The combined effect of the two defects and the proton transfer in the system are described by means of these solutions, and the appropriate conditions associated with actual physical processes. Finally, we discuss in detail the characteristics of the proton transfer and the advantages of the model.

Solitons, bounces and sphalerons on a circle

Abstract A recent study of φ 4 -solutons on a circle is extended to φ 4 -bounces and sine-Gordon-solitons. In each case the static solutions are derived. It is then shown that the equations of small fluctuations about these solutions are Lame equations whose discrete, polynomial solutions and eigenvalues are known. Using these, the classical stability of the static solutions can be investigated. Sphalerons and bounces appear as unstable configurations.

FIRST-ORDER PHASE TRANSITIONS IN QUANTUM-MECHANICAL TUNNELING MODELS

A criterion is derived for the determination of parameter domains of first-order phase transitions in quantum-mechanical tunneling models. The criterion is tested by application to various models, in particular to some that have been used recently to explore spin tunneling in macroscopic particles. In each case agreement is found with previously heuristically determined domains.

Gross-Ooguri phase transition at zero and finite temperature: two circular Wilson loop case

In the context of AdS/CFT correspondence the two Wilson loop correlator is examined at both zero and finite temperatures. On the basis of an entirely analytical approach we have found for Nambu-Goto strings the functional relation dSc(Reg)/dL = 2πk between Euclidean action Sc and loop separation L with integration constant k, which corresponds to the analogous formula for point-particles. The physical implications of this relation are explored in particular for the Gross-Ooguri phase transition at finite temperature.

Quantum phase interference for quantum tunneling in spin systems

The point-particle-like Hamiltonian of a biaxial spin particle with external magnetic field along the hard axis is obtained in terms of the potential field description of spin systems with exact spin-coordinate correspondence. The Zeeman energy term turns out to be an effective gauge potential which leads to a nonintegrable phase of the Euclidean Feynman propagator. The phase interference between clockwise and anticlockwise under barrier propagations is recognized explicitly as the Aharonov-Bohm effect. An additional phase which is significant for quantum phase interference is discovered with the quantum theory of spin systems in addition to the known phase obtained with the semiclassical treatment of spin. We also show the energy dependence of the effect and obtain the tunneling splitting at excited states with the help of periodic instantons.

Chiral bosons in noncommutative spacetime

Underlying a general noncommutative algebra with both noncommutative coordinates and noncommutative momenta in a (1+1)-dimensional spacetime, a chiral boson lagrangian with manifest Lorentz covariance is proposed by linearly imposing a generalized self-duality condition on a noncommutative generalization of massless real scalar fields. A significant property uncovered for noncommutative chiral bosons is that the left- and right-moving chiral scalars cannot be distinguished from each other, which originates from the noncommutativity of coordinates and momenta. An interesting result is that Diracs method can be consistently applied to the constrained system whose lagrangian explicitly contains space and time. The self-duality of the noncommutative chiral boson action does not exist.

Explicit solution of the wave equation for arbitrary power potentials with application to charmonium spectroscopy

We present an explicit and almost complete series solution of the Schrodinger equation for an arbitrary quark‐confining power potential with or without a weak Coulomb component or other corrections. In particular, we derive two pairs of high‐energy asymptotic expansions of the bound‐state eigenfunctions together with a corresponding expansion of the eigenvalue determined by the secular equation. We also obtain a pair of uniformly convergent expansions and discuss other types of solutions. Various properties of the solutions and eigenvalues are examined including the scattering problem of the cutoff potential and the behavior of Regge trajectories. Finally, the relevance of these investigations to the spectroscopy of heavy quark composites is discussed. In particular, we derive approximate expressions for leptonic decay rates. Examples are given to demonstrate the usefulness of these results for theoretical discussion and as alternatives for numerical integration techniques. A subsequent paper will deal wi...

Quantum Tunneling and Phase Transitions in Spin Systems with an Applied Magnetic Field

Transitions from classical to quantum behaviour in a spin system with two degenerate ground states separated by twin energy barriers which are asymmetric due to an applied magnetic field are investigated. It is shown that these transitions can be interpreted as first- or second-order phase transitions depending on the anisotropy and magnetic parameters defining the system in an effective Lagrangian description.

Particle with torsion on 3d null-curves

We consider a (2+1)-dimensional mechanical system with the Lagrangian linear in the torsion of a light-like curve. We give Hamiltonian formulation of this system and show that its mass and spin spectra are defined by one-dimensional nonrelativistic mechanics with a cubic potential. Consequently, this system possesses the properties typical of resonance-like particles.Abstract We consider a (2 + 1)-dimensional mechanical system with the Lagrangian linear in the torsion of a light-like curve. We give Hamiltonian formulation of this system and show that its mass and spin spectra are defined by one-dimensional nonrelativistic mechanics with a cubic potential. Consequently, this system possesses the properties typical of resonance-like particles.