12,188 research outputs found
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
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