We present a method using Feynman-like diagrams to calculate the statistical properties of random many-body potentials. This method provides a promising alternative to existing techniques typically applied to this class of problems, such as the metho
d of supersymmetry and the eigenvector expansion technique pioneered in [1]. We use it here to calculate the fourth, sixth and eighth moments of the average level density for systems with $m$ bosons or fermions that interact through a random $k$-body Hermitian potential ($k le m$); the ensemble of such potentials with a Gaussian weight is known as the embedded Gaussian Unitary Ensemble (eGUE) [2]. Our results apply in the limit where the number $l$ of available single-particle states is taken to infinity. A key advantage of the method is that it provides an efficient way to identify only those expressions which will stay relevant in this limit. It also provides a general argument for why these terms have to be the same for bosons and fermions. The moments are obtained as sums over ratios of binomial expressions, with a transition from moments associated to a semi-circular level density for $m < 2k$ to Gaussian moments in the dilute limit $k ll m ll l$. Regarding the form of this transition, we see that as $m$ is increased, more and more diagrams become relevant, with new contributions starting from each of the points $m = 2k, 3k, ldots, nk$ for the $2n$-th moment.
We present a new method which uses Feynman-like diagrams to calculate the statistical quantities of embedded many-body random matrix problems. The method provides a promising alternative to existing techniques and offers many important simplification
s. We use it here to find the fourth, sixth and eighth moments of the level density for k fermions or bosons interacting through a random hermitian potential in the limit where the number of possible single-particle states is taken to infinity. All share the same transition, starting immediately after 2k = m, from moments arising from a semi-circular level density to gaussian moments. The results also reveal a striking feature; the domain of the 2nth moment is naturally divided into n subdomains specified by the points 2k = m, 3k = m, ..., nk = m.
We report on a series of outbursts of the high mass X-ray binary XTE J1946+274 in 2010/2011 as observed with INTEGRAL, RXTE, and Swift. We discuss possible mechanisms resulting in the extraordinary outburst behavior of this source. The X-ray spectra
can be described by standard phenomenological models, enhanced by an absorption feature of unknown origin at about 10 keV and a narrow iron K alpha fluorescence line at 6.4 keV, which are variable in flux and pulse phase. We find possible evidence for the presence of a cyclotron resonance scattering feature at about 25 keV at the 93% level. The presence of a strong cyclotron line at 35 keV seen in data from the sources 1998 outburst and confirmed by a reanalysis of these data can be excluded. This result indicates that the cyclotron line feature in XTE J1946+274 is variable between individual outbursts.
We study survival of nearest-neighbour branching random walks in random environment (BRWRE) on ${mathbb Z}$. A priori there are three different regimes of survival: global survival, local survival, and strong local survival. We show that local and st
rong local survival regimes coincide for BRWRE and that they can be characterized with the spectral radius of the first moment matrix of the process. These results are generalizations of the classification of BRWRE in recurrent and transient regimes. Our main result is a characterization of global survival that is given in terms of Lyapunov exponents of an infinite product of i.i.d. $2times 2$ random matrices.
