F. Zimmerschied

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.

ENHANCEMENT OF QUANTUM TUNNELING FOR EXCITED STATES IN FERROMAGNETIC PARTICLES

A formula suitable for a quantitative evaluation of the tunneling effect in a ferromagnetic particle is derived with the help of the instanton method. The tunneling between nth degenerate states of neighboring wells is dominated by a periodic pseudoparticle configuration. The low-lying level-splitting previously obtained with the Lehmann-Symanzik-Zimmermann method in field theory in which the tunneling is viewed as the transition of n bosons induced by the usual (vacuum) instanton is recovered. The observation made with our result is that the tunneling effect increases at excited states. The results should be useful in analyzing results of experimental tests of macroscopic quantum coherence in ferromagnetic particles.

Quantum tunneling of spin particles in periodic potentials with asymmetric twin barriers

Abstract The tunneling effect of a periodic potential with an asymmetric twin barrier per period is calculated using the instanton method. The model is derived from the Hamiltonian of a small ferromagnetic particle in an external magnetic field using the spin-coherent-state path integral. The instantons in two neighbouring barriers differ and lead to different level shifts Δϵ1, Δϵ2. Using Bloch theory we derive the energy spectrum which has formally the structure of an energy band. The spectrum depends on both level shifts. The removal of Kramers degeneracy by an external magnetic field is discussed. In addition we find a new kind of quenching of macroscopic quantum coherence which is irrelevant to Kramers degeneracy.

Calculation of Spin Tunneling Effects in the Presence of an Applied Magnetic Field

Abstract The tunneling splitting of the energy levels of a ferromagnetic particle in the presence of an applied magnetic field - previously derived only for the ground state with the path integral method — is obtained in a simple way from Schrodinger theory. The origin of the factors entering the result is clearly understood, in particular the effect of the asymmetry of the barriers of the potential. The method should appeal particularly to experimentalists searching for evidence of macroscopic spin tunneling.

BRST-Invariant Approach to Quantum Mechanical Tunneling

Abstract A new approach with BRST invariance is suggested to cure the degeneracy problem of ill defined path integrals in the path-integral calculation of quantum mechanical tunneling effects in which the problem arises due to the occurrence of zero modes. The Faddeev-Popov procedure is avoided and the integral over the zero mode is transformed in a systematic way into a well defined integral over instanton positions. No special procedure has to be adopted as in the Faddeev-Popov method in calculating the Jacobian of the transformation. The quantum mechanical tunneling for the sine-Gordon potential is used as a test of the method and the width of the lowest energy band is obtained in exact agreement with that of WKB calculations.

A new look at the RST model

The RST model is augmented by the addition of a scalar field and a boundary term so that it is well-posed and local. Expressing the RST action in terms of the ADM formulation, the constraint structure can be analyzed completely. It is shown that from the viewpoint of local field theories, there exists a hidden dynamical field ψ1 in the RST model. Due to the presence of this hidden dynamical field, we can reconstruct the closed algebra of the constraints which guarantee the general invariance of the RST action. The resulting stress tensors T±± are recovered to be true tensor quantities. In particular, the part of the stress tensors for the hidden dynamical field ψ1 gives the precise expression for t±. At the quantum level, the cancellation condition for the total central charge is re-examined. Finally, with the help of the hidden dynamical field ψ1, the fact that the semiclassical static solution of the RST model has two independent parameters (P, M), whereas for the classical CGHS model there is only one, can be explained.

On the stability equation of Skyrme-like solitons

Abstract We compare the derivations of the stability equations for classical static solutions given by the time-dependent Euler-Lagrange equation and the static energy functional. Considering Skyrme-like models in d =1,2 and 3 space dimensions, we show that the two stability eigenvalue problems are equivalent if one chooses a specific measure in the space of eigenfunctions.

Dilute instanton gas of an O(3) Skyrme model

The pure-Skyrme limit of a scale-breaking Skyrmed O(3) sigma model in 1+1 dimensions is employed to study the effect of the Skyrme term on the semiclassical analysis of a field theory with instantons. The instantons of this model are self-dual and can be evaluated explicitly. They are also localised to an absolute scale, and their fluctuation action can be reduced to a scalar subsystem. This permits the explicit calculation of the fluctuation determinant and the shift in vacuum energy due to instantons. The model also illustrates the semiclassical quantisation of a Skyrmed field theory.

SIGNIFICANCE OF ZERO MODES IN PATH INTEGRAL QUANTIZATION OF SOLITONIC THEORIES WITH BRST INVARIANCE

The significance of zero modes in the path integral quantization of some solitonic models is investigated. In particular a Skyrme-like theory with topological vortices in 1 + 2 dimensions is studied, and with a BRST-invariant gauge fixing a well-defined transition amplitude is obtained in the one-loop approximation. We also present an alternative method which does not necessitate evoking the time dependence in the functional integral, but is equivalent to the original one in dealing with the quantization in the background of the static classical solution of the nonlinear field equations. The considerations given here are particularly useful in — but also limited to — the one-loop approximation.

Non-self-dual solutions to scale breaking Skyrme-like models in every dimension

Non-self-dual solutions to the scale breaking Skyrme-like models in Rd are constructed by replacing the self-duality equation with another first-integral of the field equation. This is carried out explicitly for the class of potentials V = 12(1−|o|2d)2.