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Ohne Zusammenfassung     

On condensation of extended structures

Solitons and vortices may condense if the coupling is of order one.     

Random paths and random surfaces on a digital computer

We describe a local stochastic process that generates statistical ensembles of paths (or surfaces) with a Boltzmann probabilistic weight. The method is expected to be applicable to Monte Carlo simulations of field theories that contain fermions, to the roughening transition and to a reformulation of gauge theories in terms of random surfaces.     

o-Diacetylbenzol aus 1,4-Dimethyl-naphthalin

Ohne Zusammenfassung20. Mitt. der Reihe Acylderivate cyclischer Verbindungen; 19. Mitt., Mh. Chem.92, 1191 (1961).     

Quantum phase transitions in Bose-Einstein condensates from a Bethe ansatz perspective

We investigate two solvable models for Bose-Einstein condensates and extract physical information by studying the structure of the solutions of their Bethe ansatz equations. A careful observation of these solutions for the ground state of both models, as we vary some parameters of the Hamiltonian, suggests a connection between the behavior of the roots of the Bethe ansatz equations and the physical behavior of the models. Then, by the use of standard techniques for approaching quantum phase transition - gap, entanglement and fidelity - we find that the change in the scenery in the roots of the Bethe ansatz equations is directly related to a quantum phase transition, thus providing an alternative method for its detection.     

Magnetization plateau and quantum phase transitions in a spin-orbital model

A spin-orbital chain with different Landé g factors and one-ion anisotropy is studied in the context of the thermodynamical Bethe ansatz. It is found that there exists a magnetization plateau resulting from the different Landé g factors. Detailed phase diagram in the presence of an external magnetic field is presented both numerically and analytically. For some values of the anisotropy, the four-component system undergoes five consecutive quantum phase transitions when the magnetic field varies. We also study the magnetization in various cases, especially its behaviors in the vicinity of the critical points. For the SU(4) spin-orbital model, explicit analytical expressions for the critical fields are derived, with excellent accuracy compared with numerics.Received: 8 January 2004, Published online: 8 June 2004PACS: 75.30.Kz Magnetic phase boundaries (including magnetic transitions, metamagnetism, etc.) - 71.27. + a Strongly correlated electron systems; heavy fermions - 75.10.Jm Quantized spin models     

A neighboring optimal feedback control scheme for systems using discontinuous control

The calculation and implementation of the neighboring optimal feedback control law for multiinput, nonlinear dynamical systems, using discontinuous control, is the subject of this paper. The concept of neighboring optimal feedback control of systems with continuous, unbounded control functions has been investigated by others. The differentiating features between this class of problems and that considered here are the control discontinuities and the inherent system uncontrollability during the latter stages of the control-law operating time.The neighboring control law is determined by minimizing the second-order terms in the expansion of the performance index about an optimal nominal path. The resulting gains are a function of the states associated with the nominal trajectory. The development of a feedback control scheme utilizing these gains requires a technique for choosing the gains appropriate for each neighboring state. Such a technique is described in this paper. The technique combines abootstrap algorithm for determining the number of neighboring switch times and the initial and final controls with a scheme based ontime-to-go along the nominal and neighboring paths until the next predicted switch time or the predicted final time. This scheme requires that the nominal state, which is used to specify the feedback gains, be chosen such that the predicted time-to-go from the neighboring state be identical to the time-to-go from the nominal state. This technique for choosing feedback gains possesses minimal storage requirements and readily leads to a real-time feedback implementation of the neighboring control law.The optimal feedback control scheme described in this paper is utilized to solve the minimum-time satellite attitude-acquisition problem. The action of the neighboring control scheme when applied to states which do not lie in an immediate neighborhood of the nominal path is investigated. For this particular problem, the neighboring control scheme performs quite well despite the fact that, when the state perturbations are finite, the terminal constraints can never be satisfied exactly.This research was sponsored by the National Aeronautics and Space Administration under Research Grant No. NGL-05-020-007 and is a condensed version of the investigation described in Ref. 1. The authors are indebted to Professor Arthur E. Bryson, Jr., for suggesting the topic and providing stimulating discussions.