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Abstract: Winding number transitions from quantum to classical behavior are studied in the case of the 1+1 dimensional Mottola-Wipf model with the space coordinate on a circle for exploring the possibility of obtaining transitions of second order. The model is also studied as a prototype theory which demonstrates the procedure of such investigations. In the model at hand we find that even on a circle the transitions remain those of first order.
Abstract: Following our earlier investigations we examine the quantum-classical winding number transition in the Abelian-Higgs system. It is demonstrated that the winding number transition in this system is of the smooth second order type in the full range of parameter space. Comparison of the action of classical vortices with that of the sphaleron supports our finding.
Abstract: The calculation of absorption cross sections for minimal scalars in supergravity backgrounds is an important aspect of the investigation of AdS/CFT correspondence and requires a matching of appropriate wave functions. The low energy case has attracted particular attention. In the following the dependence of the cross section on the matching point is investigated. It is shown that the low energy limit is independent of the matching point and hence exhibits universality. In the high energy limit the independence is not maintained, but the result is believed to possess the correct energy dependence.
Abstract: A Born-Infeld theory describing a D2-brane coupled to a 4-form RR field strength is considered, and the general solutions of the static and Euclidean time equations are derived and discussed. The period of the bounce solutions is shown to allow a consideration of tunneling and quantum-classical transitions in the sphaleron region. The order of such transitions, depending on the strength of the RR field strength, is determined. A criterion is then derived to confirm these findings.
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.
Abstract: 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 besides 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.
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 Schr"odinger 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.
Abstract: The periodic bounce configurations responsible for quantum tunneling are obtained explicitly and are extended to the finite energy case for minisuperspace models of the Universe. As a common feature of the tunneling models at finite energy considered here we observe that the period of the bounce increases with energy monotonically. The periodic bounces do not have bifurcations and make no contribution to the nucleation rate except the one with zero energy. The sharp first order phase transition from quantum tunneling to thermal activation is verified with the general criterions.
Abstract: The transition from the quantum to the classical regime of the nucleation of the closed Robertson-Walker Universe with spacially homogeneous matter fields is investigated with a perturbation expansion around the sphaleron configuration. A criterion is derived for the occurrence of a first-order type transition, and the related phase diagram for scalar and vector fields is obtained. For scalar fields both the first and second order transitions can occur depending on the shape of the potential barrier. For a vector field, here that of an O (3) nonlinear o-model, the transition is seen to be only of the first order. PACS numbers: 11.15.Kc, 03.65Sq, 05.70.Fh, 98.80.Cq