The exactly solvable spin Sutherland model of B_N type and its related spin chain

We compute the spectrum of the su(m) spin Sutherland model of B_N type, including the exact degeneracy of all energy levels. By studying the large coupling constant limit of this model and of its scalar counterpart, we evaluate the partition function of their associated spin chain of Haldane-Shastry type in closed form. With the help of the formula for the partition function thus obtained we study the chain's spectrum, showing that it cannot be obtained as a limiting case of its BC_N counterpart. The structure of the partition function also suggests that the spectrum of the Haldane-Shastry spin chain of B_N type is equivalent to that of a suitable vertex model, as is the case for its A_{N-1} counterpart, and that the density of its eigenvalues is normally distributed when the number of sites N tends to infinity. We analyze this last conjecture numerically using again the explicit formula for the partition function, and check its validity for several values of N and m.Comment: Typeset in LaTeX (24 pages, 4 figures). arXiv admin note: text overlap with arXiv:0909.296

Rational quantum integrable systems of D_N type with polarized spin reversal operators

We study the spin Calogero model of D_N type with polarized spin reversal operators, as well as its associated spin chain of Haldane-Shastry type, both in the antiferromagnetic and ferromagnetic cases. We compute the spectrum and the partition function of the former model in closed form, from which we derive an exact formula for the chain's partition function in terms of products of partition functions of Polychronakos-Frahm spin chains of type A. Using a recursion relation for the latter partition functions that we derive in the paper, we are able to numerically evaluate the partition function, and thus the spectrum, of the D_N-type spin chain for relatively high values of the number of spins N. We analyze several global properties of the chain's spectrum, such as the asymptotic level density, the distribution of consecutive spacings of the unfolded spectrum, and the average degeneracy. In particular, our results suggest that this chain is invariant under a suitable Yangian group, and that its spectrum coincides with that of a Yangian-invariant vertex model with linear energy function and dispersion relation.Comment: 26 pages, 5 figures, typeset in LaTe

Response of a marine-terminating Greenland outlet glacier to abrupt cooling 8200 and 9300 years ago

Long-term records of Greenland outlet-glacier change extending beyond the satellite era can inform future predictions of Greenland Ice Sheet behavior. Of particular relevance is elucidating the Greenland Ice Sheet's response to decadal- and centennial-scale climate change. Here, we reconstruct the early Holocene history of Jakobshavn Isbræ, Greenland's largest outlet glacier, using 10Be surface exposure ages and 14C-dated lake sediments. Our chronology of ice-margin change demonstrates that Jakobshavn Isbræ advanced to deposit moraines in response to abrupt cooling recorded in central Greenland ice cores ca. 8,200 and 9,300 years ago. While the rapid, dynamically aided retreat of many Greenland outlet glaciers in response to warming is well documented, these results indicate that marine-terminating outlet glaciers are also able to respond quickly to cooling. We suggest that short lag times of high ice flux margins enable a greater magnitude response of marine-terminating outlets to abrupt climate change compared to their land-terminating counterparts

1/fα1/f^\alpha noise and integrable systems

An innovative test for detecting quantum chaos based on the analysis of the spectral fluctuations regarded as a time series has been recently proposed. According to this test, the fluctuations of a fully chaotic system should exhibit 1/f noise, whereas for an integrable system this noise should obey the 1/f^2 power law. In this letter, we show that there is a family of well-known integrable systems, namely spin chains of Haldane-Shastry type, whose spectral fluctuations decay instead as 1/f^4. We present a simple theoretical justification of this fact, and propose an alternative characterization of quantum chaos versus integrability formulated directly in terms of the power spectrum of the spacings of the unfolded spectrum.Comment: 5 pages, 3 figures, RevTe

Public Perceptions of Regulatory Costs, Their Uncertainty and Interindividual Distribution

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/122430/1/risa12532.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/122430/2/risa12532_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/122430/3/risa12532-sup-0001-SupMat.pd

Convex Hull of Arithmetic Automata

Arithmetic automata recognize infinite words of digits denoting decompositions of real and integer vectors. These automata are known expressive and efficient enough to represent the whole set of solutions of complex linear constraints combining both integral and real variables. In this paper, the closed convex hull of arithmetic automata is proved rational polyhedral. Moreover an algorithm computing the linear constraints defining these convex set is provided. Such an algorithm is useful for effectively extracting geometrical properties of the whole set of solutions of complex constraints symbolically represented by arithmetic automata