Affine crystal structure on rigged configurations of type D_n^(1)

Extending the work arXiv:math/0508107, we introduce the affine crystal action on rigged configurations which is isomorphic to the Kirillov-Reshetikhin crystal B^{r,s} of type D_n^(1) for any r,s. We also introduce a representation of B^{r,s} (r not equal to n-1,n) in terms of tableaux of rectangular shape r x s, which we coin Kirillov-Reshetikhin tableaux (using a non-trivial analogue of the type A column splitting procedure) to construct a bijection between elements of a tensor product of Kirillov-Reshetikhin crystals and rigged configurations.Comment: 26 pages, 3 figures. (v3) corrections in the proof reading. (v2) 26 pages; examples added; introduction revised; final version. (v1) 24 page

Sequencing Chess

We analyze the structure of the state space of chess by means of transition path sampling Monte Carlo simulation. Based on the typical number of moves required to transpose a given configuration of chess pieces into another, we conclude that the state space consists of several pockets between which transitions are rare. Skilled players explore an even smaller subset of positions that populate some of these pockets only very sparsely. These results suggest that the usual measures to estimate both, the size of the state space and the size of the tree of legal moves, are not unique indicators of the complexity of the game, but that topological considerations are equally important

Experimental tests for macroscopic phase coherence in magnetic-quasiparticle condensates of insulating spin systems

For most kinds of already known Bose-Einstein condensates experimental evidence for the existence of a macroscopic coherent quantum state has been provided, e.g., from the observation of interference phenomena, the formation vortices, the detection of Josephson effects, or even by the manifestation of superfluid behaviour. However, none of these hallmarks for a true, macroscopic phase-coherent state has ever been reported for any insulating spin system in a solid in which magnetic bosonic quasiparticles are thought to condense close to a quantum critical point. We describe an attempt to detect superfluid behaviour in TlCuCl3, and discuss in more detail a proposal for an experiment in which the a.c. Josephson effect can be probed by using a device composed of two weakly coupled magnetic insulators with different critical fields. We conclude that the detection of the a.c. Josephson effect is feasible for a proper choice of compounds with realistic material parameters.Comment: 6 pages, 2 figure

The fraction of Bose-Einstein condensed triplons in TlCuCl3 from magnetization M(T,H)-data

In this study we calculate the fraction of condensed magnetic quasiparticles of TlCuCl3 from magnetization M(T,H)-data. It is independent of the direction of the magnetic field and slightly decreases with increasing magnetic field.Comment: 8 pages, 10 figure