Cohomology of the minimal nilpotent orbit

We compute the integral cohomology of the minimal non-trivial nilpotent orbit in a complex simple (or quasi-simple) Lie algebra. We find by a uniform approach that the middle cohomology group is isomorphic to the fundamental group of the sub-root system generated by the long simple roots. The modulo $\ell$ reduction of the Springer correspondent representation involves the sign representation exactly when $\ell$ divides the order of this cohomology group. The primes dividing the torsion of the rest of the cohomology are bad primes.Comment: 29 pages, v2 : Leray-Serre spectral sequence replaced by Gysin sequence only, corrected typo

Noiseless Quantum Circuits for the Peres Separability Criterion

In this Letter we give a method for constructing sets of simple circuits that can determine the spectrum of a partially transposed density matrix, without requiring either a tomographically complete POVM or the addition of noise to make the spectrum non-negative. These circuits depend only on the dimension of the Hilbert space and are otherwise independent of the state.Comment: 4 pages RevTeX, 7 figures encapsulated postscript. v5: title changed slightly, more-or-less equivalent to the published versio

Complexified sigma model and duality

We show that the equations of motion associated with a complexified sigma-model action do not admit manifest dual SO(n,n) symmetry. In the process we discover new type of numbers which we called `complexoids' in order to emphasize their close relation with both complex numbers and matroids. It turns out that the complexoids allow to consider the analogue of the complexified sigma-model action but with (1+1)-worldsheet metric, instead of Euclidean-worldsheet metric. Our observations can be useful for further developments of complexified quantum mechanics.Comment: 15 pages, Latex, improved versio

Local invariants of stabilizer codes

In [Phys. Rev. A 58, 1833 (1998)] a family of polynomial invariants which separate the orbits of multi-qubit density operators $\rho$ under the action of the local unitary group was presented. We consider this family of invariants for the class of those $\rho$ which are the projection operators describing stabilizer codes and give a complete translation of these invariants into the binary framework in which stabilizer codes are usually described. Such an investigation of local invariants of quantum codes is of natural importance in quantum coding theory, since locally equivalent codes have the same error-correcting capabilities and local invariants are powerful tools to explore their structure. Moreover, the present result is relevant in the context of multipartite entanglement and the development of the measurement-based model of quantum computation known as the one-way quantum computer.Comment: 10 pages, 1 figure. Minor changes. Accepted in Phys. Rev.

Roots of the affine Cremona group

Let k[x_1,...,x_n] be the polynomial algebra in n variables and let A^n=Spec k[x_1,...,x_n]. In this note we show that the root vectors of the affine Cremona group Aut(A^n) with respect to the diagonal torus are exactly the locally nilpotent derivations x^a\times d/dx_i, where x^a is any monomial not depending on x_i. This answers a question due to Popov.Comment: 4 page

The eclipsing post-common envelope binary CSS21055: a white dwarf with a probable brown-dwarf companion

We report photometric observations of the eclipsing close binary CSS21055 (SDSS J141126+200911) that strongly suggest that the companion to the carbon-oxygen white dwarf is a brown dwarf with a mass between 0.030 and 0.074 Msun. The measured orbital period is 121.73min and the totality of the eclipse lasts 125s. If confirmed, CSS21055 would be the first detached eclipsing WD+BD binary. Spectroscopy in the eclipse could provide information about the companion's evolutionary state and atmospheric structure.Comment: 6 pages, 5 figure

Rolling balls and Octonions

In this semi-expository paper we disclose hidden symmetries of a classical nonholonomic kinematic model and try to explain geometric meaning of basic invariants of vector distributions

Black holes admitting a Freudenthal dual

The quantised charges x of four dimensional stringy black holes may be assigned to elements of an integral Freudenthal triple system whose automorphism group is the corresponding U-duality and whose U-invariant quartic norm Delta(x) determines the lowest order entropy. Here we introduce a Freudenthal duality x -> \tilde{x}, for which \tilde{\tilde{x}}=-x. Although distinct from U-duality it nevertheless leaves Delta(x) invariant. However, the requirement that \tilde{x} be integer restricts us to the subset of black holes for which Delta(x) is necessarily a perfect square. The issue of higher-order corrections remains open as some, but not all, of the discrete U-duality invariants are Freudenthal invariant. Similarly, the quantised charges A of five dimensional black holes and strings may be assigned to elements of an integral Jordan algebra, whose cubic norm N(A) determines the lowest order entropy. We introduce an analogous Jordan dual A*, with N(A) necessarily a perfect cube, for which A**=A and which leaves N(A) invariant. The two dualities are related by a 4D/5D lift.Comment: 32 pages revtex, 10 tables; minor corrections, references adde

Dryland river restoration via carnivore reintroduction: Nonnative fauna dominate diets of river otters reintroduced to the Upper Rio Grande

Dryland rivers often harbor abundant populations of nonnative species that threaten native fauna and negatively alter ecosystem structure and function. Native semiaquatic carnivores, such as river otters (Lontra canadensis), that could predate nonnative fauna have been extirpated from many dryland rivers. During 2008–2010, river otters were reintroduced to the Upper Rio Grande (URG), a principal dryland river in the arid southwestern USA that has been colonized by dozens of nonnative fish and invertebrates. We conducted a scat-based food habits study and investigated whether otter reintroduction could be useful for managing nonnative aquatic fauna via predation. Across seasons, nonnative crayfish and fish were the dominant prey items in otter scats; crayfish frequency of occurrence was highest (61–95%), followed by nonnative suckers (7–26%) and trout (3–28%). After accounting for heterogeneous sampling effort between seasons, multi-level models estimated 0.77–0.93 probabilities that scats contained crayfish, compared to 0.05–0.21 and 0.03–0.14 probabilities for suckers and trout, respectively. Reintroducing river otters, and possibly other semiaquatic carnivores, to degraded dryland rivers might be an effective conservation action for controlling nonnative faunal populations within the biomic approach to river restoration, which could reestablish trophic cascades that improve ecosystem structure and function