Seminar ``Aktuelle Probleme der Theoretischen Physik''

 

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Alexander Albus
Zur Statistik wechselwirkender Bosonen und Fermionen

Wir geben eine Einfuehrung in die Beschreibung von Vielteilchensystemen. Die Ununterscheidbarkeit von identischen Teilchen fuehrt auf die zwei moeglichen Quantenstatistiken: Bosonen und Fermionen. Es wird angegeben, wie der Grundzustand eines Systems von N Teilchen ohne Wechselwirkung aussieht. Eine Teilchen-Teilchen-Wechselwirkung kann stoerungstheoretisch behandelt werden. Wir zeigen, wie die entsprechende Reihe mit Hilfe von Feynman-Diagrammen dargestellt werden und naeherungsweise ausgewertet werden kann. Konkret interessieren wir uns fuer die Grundzustandsenergie eines Boson-Fermion-Gemisches.

Ernest Montbrio
Small Worlds

It is believed that almost any pair of people in the world can be connected to one another by a short chain of intermediate acquaintances, of typical length about six. This "small world" phenomenon has been the subject of considerable interest within the physics community recently. The talk provides a short review of the topic with a special emphasis to ecological implications.

Horst Hohberger
Rainbows, Caustics, and Semiclassics

We consider the scattering of a wave from a compact potential in the semiclassical limit (short-wavelength asymptotics). Using the rays for the corresponding geometrical optics problem, we construct an asymptotic expression for the far-field scattering amplitude. In the geometrical optics limit, this amplitude shows unphysical divergences when the scattering angle shows a maximum as a function of the impact parameter. These divergences are smoothed in our approach, being replaced by standard integrals known from catastrophe theory. A key argument in our proof is the fact that the far-field angles and angular momenta form a Lagrangian manifold, that the initial impact parameters are mapped upon in a diffeomorphic way. This allows us to find suitable phase space coordinates that avoid the singularities.

Samuel Morgan
Finite T Excitations of BECs in Spherical Traps

We present numerical results from a gapless theory of excitations in atomic Bose-Einstein condensates (BECs). Our theory takes account of both finite temperature and finite size effects, which can be important for spherically symmetric traps. We show that while the simple picture of a decay rate (corresponding to a Lorentzian excitation spectrum) can describe some modes, finite size effects can lead to interesting non-Lorentzian lineshapes and anomalously large shifts. These effects should be observable in current experimental configurations.

Crispin Gardiner
1S-2S Spectroscopy of cold Hydrogen

The atomic hydrogen BEC is of a rather different kind from those prevalent in the now almost ubiquitous alkali-metal vapor condensates. The characteristic features of the hydrogen system are:

1. The condensate fraction is rather low, typically about 5%. However, the number of atoms in the condensate is nevertheless very large, about 10⁹, compared to about 10⁶ for Na condensates and about 10⁵ for Rb condensates.
2. The hydrogen condensate at MIT is a `hot' condensate, formed at 44 µK.
3. Because of the rather small scattering length of hydrogen, the condensate density is very much higher than in the alkali-metal condensates. It is experimentally measured spectroscopically using the cold-collision frequency shift for the 1S-2S two-photon transition. The measured condensate frequency shift does not appear to exhibit the expected reduction of a factor of two (due to quantum statistics) compared with that of a non-condensed vapor of the same density.

By taking into account the quasiparticle dynamics of this `hot' condensate, we show that the cold collision frequency shift formula in the experimentally observed situation is substantially different from both the fully condensed situation and the uncondensed situation, and can only be described by a spatially dependent factor which can vary between 3 and 1.

D. L. Shepelyansky
Quantum computers: facing chaos

A study of a generic model of a quantum computer, composed of many qubits coupled by a short-range interaction, is presented. Above a critical interqubit coupling strength, quantum chaos sets in, leading to quantum ergodicity of the computer eigenstates. In this regime the noninteracting qubit structure disappears, the eigenstates become complex and the operability of the computer is destroyed. Despite the fact that the spacing between multi-qubit states drops exponentially with the number of qubits n it is shown that the quantum chaos border decreases only linearly with n. This opens a broad parameter region where the efficient operation of a quantum computer can be realized. The links with the emergence of quantum chaos in complex atoms, nuclei, quantum dots and spin glass shards are also discussed. It is shown that new developed algorithms allow to simulate accurately and with exponential efficiency certain problems of quantum and classical chaos.

Enrique Solano
Mesoscopic quantum state manipulation in cavity QED and with trapped ions

Conditional large Fock state preparation and field state reconstruction in Cavity QED
We propose the conditional preparation of large Fock states by means of the implementation of a selective interaction in CQED. We show this scheme is suitable for an efficient reconstruction of the Wigner function of the field without the necessity of Ramsey interferometry.

Mesoscopic superpositions of vibronic collective states of N trapped ions
We propose the use of a resonant bichromatic beam homogeneously illuminating N cold ions in a row for generating, in a fast and efficient way, different kinds of Schr–dinger cat states in the vibronic degrees of freedom of the composed system.