## Fachbereich Physik

- Holographic Trace Anomaly and Cocycle of Weyl Group (2001)
- Abstract: The behavior of the divergent part of the bulk AdS/CFT effective action is considered with respect to the special finite diffeomorphism transformations acting on the boundary as a Weyl transformation of the boundary metric. The resulting 1-cocycle of the Weyl group is in full agreement with the 1-cocycle of the Weyl group obtained from the cohomological consideration of the effective action of the corresponding CFT.

- Wannier-Stark Resonances in optical and semiconductor superlattices (2001)
- In this work, we discuss the resonance states of a quantum particle in a periodic potential plus static force. Originally this problem was formulated for a crystalline electron subject to the static electric field and is known nowadays as the Wannier-Stark problem. We describe a novel approach to the Wannier-Stark problem developed in recent years. This approach allows to compute the complex energy spectrum of a Wannier-Stark system as the poles of a rigorously constructed scattering matrix and, in this sense, solves the Wannier-Stark problem without any approximation. The suggested method is very efficient from the numerical point of view and has proven to be a powerful analytic tool for Wannier-Stark resonances appearing in different physical systems like optical or semiconductor superlattices.

- Quantum-field-theoretical techniques for stochastic representation of quantum problems (2001)
- Abstract: We describe quantum-field-theoretical (QFT) techniques for mapping quantum problems onto c-number stochastic problems. This approach yields results which are identical to phase-space techniques [C.W. Gardiner, Quantum Noise (1991)] when the latter result in a Fokker-Planck equation for a corresponding pseudo-probability distribution. If phase-space techniques do not result in a Fokker-Planck equation and hence fail to produce a stochastic representation, the QFT techniques nevertheless yield stochastic di erence equations in discretised time.

- Gross-Ooguri Phase Transition at Zero and Finite Temperature: Two Circular Wilson Loop Case (2001)
- Abstract: 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 = 2*pi*k 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.

- Semiclassical Approximations in Phase Space with Coherent States (2001)
- We present a complete derivation of the semiclassical limit of the coherent state propagator in one dimension, starting from path integrals in phase space. We show that the arbitrariness in the path integral representation, which follows from the overcompleteness of the coherent states, results in many different semiclassical limits. We explicitly derive two possible semiclassical formulae for the propagator, we suggest a third one, and we discuss their relationships. We also derive an initial value representation for the semiclassical propagator, based on an initial gaussian wavepacket. It turns out to be related to, but different from, Heller's thawed gaussian approximation. It is very different from the Herman - Kluk formula, which is not a correct semiclassical limit. We point out errors in two derivations of the latter. Finally we show how the semiclassical coherent state propagators lead to WKB-type quantization rules and to approximations for the Husimi distributions of stationary states.

- Conformal partial wave analysis of AdS amplitudes for dilaton-axion four-point functions (2001)
- Abstract: Operator product expansions are applied to dilaton-axion four-point functions. In the expansions of the bilocal fields "doubble Phi", CC and "Phi"C, the conformal fields which are symmetric traceless tensors of rank l and have dimensions "delta" = 2+l or 8+l+ "eta"(l) and "eta"(l) = O(N ^ -2) are identified. The unidentified field have dimension "delta" = "lambda"+l+eta(l) with "lambda" >= 10. The anomalous dimensions eta(l) are calculated at order O(N ^ -2) for both 2 ^ -1/2(-"doubble Phi" + CC) and 2 ^ -1/2(-"Phi"C + C"Phi") and are found to be the same, proving U(1)_Y symmetry. The relevant coupling constants are given at order O(1).

- Wannier-Stark resonances in semiconductor superlattices (2001)
- Wannier-Stark states for semiconductor superlattices in strong static fields, where the interband Landau-Zener tunneling cannot be neglected, are rigorously calculated. The lifetime of these metastable states was found to show multiscale oscillations as a function of the static field, which is explained by an interaction with above-barrier resonances. An equation, expressing the absorption spectrum of semiconductor superlattices in terms of the resonance Wannier-Stark states is obtained and used to calculate the absorption spectrum in the region of high static fields.

- Dipole Blockade and Quantum Information Processing in Mesoscopic Atomic Ensembles (2000)
- Abstract: We describe a technique for manipulating quantum information stored in collective states of mesoscopic ensembles. Quantum processing is accomplished by optical excitation into states with strong dipole-dipole interactions. The resulting "dipole blockade" can be used to inhibit transitions into all but singly excited collective states. This can be employed for a controlled generation of collective atomic spin states as well as non-classical photonic states and for scalable quantum logic gates. An example involving a cold Rydberg gas is analyzed.

- Universality or Non-Universality of Absorption Cross Sections for Extended Objects (2000)
- 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.

- Instanton-Sphaleron transition in the d = 2 Abelian-Higgs model on a Circle (2000)
- Abstract: The transition from the instanton-dominated quantum regime to the sphaleron-dominated classical regime is studied in the d = 2 abelian-Higgs model when the spatial coordinate is compactified to S1. Contrary to the noncompactified case, this model allows both sharp first-order and smooth second-order transitions depending on the size of the circle. This finding may make the model a useful toy model for the analysis of baryon number violating processes.