D. K. Park

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.

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.

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.

D-Branes and their Absorptivity in Born-Infeld Theory

Abstract: Standard methods of nonlinear dynamics are used to investigate the stability of particles, branes and D-branes of abelian Born-Infeld theory. In particular the equation of small fluctuations about the D-brane is derived and converted into a modified Mathieu equation and - complementing earlier low-energy investigations in the case of the dilaton-axion system - studied in the high-energy domain. Explicit expressions are derived for the S-matrix and absorption and reflection amplitudes of the scalar fluctuation in the presence of the D-brane. The results confirm physical expectations and numerical studies of others. With the derivation and use of the (hitherto practically unknown) high energy expansion of the Floquet exponent our considerations also close a gap in earlier treatments of the Mathieu equation.

Tunneling of Born-Infeld strings to D2-branes

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.

Universality or non-universality of absorption cross sections for extended objects

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.

General criterion for the existence of supertube and BIon in curved target space

The supertube and BIon spike solutions are examined in a general curved target space. The criteria for the existence of these solutions are explicitly derived. Also the equation which the general BIon solution should satisfy is derived.

Winding number transitions in the Mottola–Wipf model on a circle

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.

Macroscopic quantum phase interference in antiferromagnetic particles

The tunnel splitting in biaxial antiferromagnetic particles is studied with a magnetic field applied along the hard anisotropy axis. We observe the oscillation of tunnel splitting as a function of the magnetic field due to the quantum phase interference of two tunnelling paths of opposite windings. The oscillation is similar to the recent experimental result with Fe8 molecular clusters.

Functional relation of interquark potential with interquark distance

Abstract The functional relation between interquark potential and interquark distance is explicitly derived by considering the Nambu–Goto action in the AdS 5 × S 5 background. It is also shown that a similar relation holds in a general background. The implications of this relation for confinement are briefly discussed.