5 research outputs found

### Detecting an exciton crystal by statistical means

We investigate an ensemble of excitons in a coupled quantum well excited via
an applied laser field. Using an effective disordered quantum Ising model, we
perform a numerical simulation of the experimental procedure and calculate the
probability distribution function $P(M)$ to create $M$ excitons as well as
their correlation function. It shows clear evidence of the existence of two
phases corresponding to a liquid and a crystal phase. We demonstrate that not
only the correlation function but also the distribution $P(M)$ is very well
suited to monitor this transition.Comment: 5 pages, 5 figure

### FCS for superconducting quantum point contacts

The calculation of the full counting statistics (FCS) for quantum mechanical systems has attracted much attention in recent years. In this thesis the FCS for superconducting quantum point contacts have been calculated. Such quantum point contacts frequently occur in modern microelectronic devices, which exploit the special features of superconductors. The FCS for normal metal-superconductor and superconductor-superconductor contacts have been
calculated using a generalized Keldysh formalism and the results have been compared to both experimental and theoretical results. The calculation of the FCS allows a precise understanding of the physical nature of charge transfer. Particularly doubled shot noise due to Andreev reflections was explained and the behaviour of the Josephson current for long measurement times was calculated. The obtained results are also valuable for the
understanding of transport through quantum dots with superconducting leads

### Min Cost Flow in balancierten Netzwerken mit konvexer Kostenfunktion

Standard matching problems can be stated in terms of skew symmetric networks. On skew symmetric networks matching problems can be solved using network flow techniques. We consider the problem of minimizing a separable convex objective function over a skew-symmetric network with a balanced flow. We call this problem the Convex Balanced Min Cost Flow (Convex BMCF) problem.
We start with 2 examples of Convex BMCF problems. The first problem is a problem from condensed matter physics: We want to simulate a so called super-rough phase using methods from graph-theory. This problem has previously been studied by Blasum, Hochstaettler, Rieger a and Moll. The second problem is a typical example for the minconvex-problems previously studied by Apollonio and Sebo and Berger and Hochstaettler [9].
We review the results for skew-symmetric networks by Jungnickel and Fremuth-Paeger and Kocay and Stone. Using these results we present several algorithms to solve the Convex BMCF problem. We present the first complete version
of the Primal-Dual algorithm previously studied by Fremuth-Paeger and Jungnickel. However, we only consider the case of positive costs. We also show how to apply this algorithm to the Convex BMCF problem. Then we extend the Shortest Admissible Path Approach of Jungnickel and Fremuth-Paeger [23, p. 12] to a complete algorithm for linear as well as convex cost problems on skew symmetric networks. In
the same manner we show how to adapt the Capacity Scaling algorithm by Ahuja and Orlin to skew symmetric networks and
balanced flows. The capacity scaling algorithm is weakly polynomial.
Another possibility for a weakly polynomial algorithm is the Balanced Out-of-Kilter algorithm. This algorithm is based on Fulkersonâ€™s Out-of-Kilter algorithm and Minouxâ€™s adaptation of the algorithm for convex costs. We show that augmentation on valid paths is not always necessary and introduce the idea of slightly different networks. Using the same ideas for the Balanced Capacity Scaling we
obtain an Enhanced Capacity Scaling algorithm. The Enhanced Capacity Scaling algorithm as well as the Balanced Out-of-Kilter algorithm are the fastest algorithms presented here with a complexity of roughly O(m2log2U).
Finally we show how to solve the problem from condensed matter physics using the new idea of anti-balanced flows on skew-symmetric networks. Using the Balanced Successive Shortest Path algorithm we also obtain a new complexity limit for the minconvex problem. This improves the complexity bound of Berger [8] by a factor of m in the case of separable convex costs with positive slope.
In the appendix of this thesis we consider dual approaches for the Convex BMCF problem. The Balanced Relaxation algorithm, based on the Relaxation algorithm by Bertsekas [13], does not determine a balanced flow as the resulting flow will not necessarily be integral. This way we only determine fractional matchings. As the algorithm is also slow this algorithm is probably of limited use. A better ansatz seems to be the Cancel and Tighten method by Karzanov and McCormick. We review their results and end with some ideas on how to implement a balanced version of this algorithm