Hyperbola-generator for location of aperiodic events

Plotting device, when used in conjunction with three or more detectors and local receiver and recorder, can quickly pinpoint location of any aperiodic event. Operation requires minimal training and is readily adapted to the field. Mechanical error in device prototype is less than or equal to 3 percent

A Special Case Of A Conjecture By Widom With Implications To Fermionic Entanglement Entropy

We prove a special case of a conjecture in asymptotic analysis by Harold Widom. More precisely, we establish the leading and next-to-leading term of a semi-classical expansion of the trace of the square of certain integral operators on the Hilbert space $L^2(\R^d)$. As already observed by Gioev and Klich, this implies that the bi-partite entanglement entropy of the free Fermi gas in its ground state grows at least as fast as the surface area of the spatially bounded part times a logarithmic enhancement.Comment: 20 pages, 3 figures, improvement of the presentation, some references added or updated, proof of Theorem 12 (formerly Lemma 11) adde

Dark matter in natural supersymmetric extensions of the Standard Model

We explore the dark matter sector in extensions of the Minimal Supersymmetric Standard Model (MSSM) that can provide a good fit to the PAMELA cosmic ray positron excess, while at the same time addressing the little hierarchy problem of the MSSM. Adding a singlet Higgs superfield, S, can account for the observed positron excess, as recently discussed in the literature, but we point out that it requires a fine-tuned choice for the parameters of the model. We find that including an additional singlet allows both a reduction of the weak-scale fine-tuning, and an interpretation of the cosmic ray observations in terms of dark matter annihilations in the galactic halo. Our setup contains a light axion, but does not require light CP-even scalars in the spectrum.Comment: 26 pages, 8 figures, references adde

Conformal field theory correlations in the Abelian sandpile mode

We calculate all multipoint correlation functions of all local bond modifications in the two-dimensional Abelian sandpile model, both at the critical point, and in the model with dissipation. The set of local bond modifications includes, as the most physically interesting case, all weakly allowed cluster variables. The correlation functions show that all local bond modifications have scaling dimension two, and can be written as linear combinations of operators in the central charge -2 logarithmic conformal field theory, in agreement with a form conjectured earlier by Mahieu and Ruelle in Phys. Rev. E 64, 066130 (2001). We find closed form expressions for the coefficients of the operators, and describe methods that allow their rapid calculation. We determine the fields associated with adding or removing bonds, both in the bulk, and along open and closed boundaries; some bond defects have scaling dimension two, while others have scaling dimension four. We also determine the corrections to bulk probabilities for local bond modifications near open and closed boundaries.Comment: 13 pages, 5 figures; referee comments incorporated; Accepted by Phys. Rev.

Lifetimes of tidally limited star clusters with different radii

We study the escape rate, dN/dt, from clusters with different radii in a tidal field using analytical predictions and direct N-body simulations. We find that dN/dt depends on the ratio R=r_h/r_j, where r_h is the half-mass radius and r_j the radius of the zero-velocity surface. For R>0.05, the "tidal regime", there is almost no dependence of dN/dt on R. To first order this is because the fraction of escapers per relaxation time, t_rh, scales approximately as R^1.5, which cancels out the r_h^1.5 term in t_rh. For R<0.05, the "isolated regime", dN/dt scales as R^-1.5. Clusters that start with their initial R, Ri, in the tidal regime dissolve completely in this regime and their t_dis is insensitive to the initial r_h. We predicts that clusters that start with Ri<0.05 always expand to the tidal regime before final dissolution. Their t_dis has a shallower dependence on Ri than what would be expected when t_dis is a constant times t_rh. For realistic values of Ri, the lifetime varies by less than a factor of 1.5 due to changes in Ri. This implies that the "survival" diagram for globular clusters should allow for more small clusters to survive. We note that with our result it is impossible to explain the universal peaked mass function of globular cluster systems by dynamical evolution from a power-law initial mass function, since the peak will be at lower masses in the outer parts of galaxies. Our results finally show that in the tidal regime t_dis scales as N^0.65/w, with w the angular frequency of the cluster in the host galaxy. [ABRIDGED

Dispersion processes

We study a synchronous dispersion process in which $M$ particles are initially placed at a distinguished origin vertex of a graph $G$. At each time step, at each vertex $v$ occupied by more than one particle at the beginning of this step, each of these particles moves to a neighbour of $v$ chosen independently and uniformly at random. The dispersion process ends once the particles have all stopped moving, i.e. at the first step at which each vertex is occupied by at most one particle. For the complete graph $K_n$ and star graph $S_n$, we show that for any constant $\delta>1$, with high probability, if $M \le n/2(1-\delta)$, then the process finishes in $O(\log n)$ steps, whereas if $M \ge n/2(1+\delta)$, then the process needs $e^{\Omega(n)}$ steps to complete (if ever). We also show that an analogous lazy variant of the process exhibits the same behaviour but for higher thresholds, allowing faster dispersion of more particles. For paths, trees, grids, hypercubes and Cayley graphs of large enough sizes (in terms of $M$) we give bounds on the time to finish and the maximum distance traveled from the origin as a function of the number of particles $M$

Trace formulas for Wiener-Hopf operators with applications to entropies of free fermionic equilibrium states

We consider non-smooth functions of (truncated) Wiener–Hopf type operators on the Hilbert space L2(Rd) . Our main results are uniform estimates for trace norms ( d≥1 ) and quasiclassical asymptotic formulas for traces of the resulting operators ( d=1 ). Here, we follow Harold Widom's seminal ideas, who proved such formulas for smooth functions decades ago. The extension to non-smooth functions and the uniformity of the estimates in various (physical) parameters rest on recent advances by one of the authors (AVS). We use our results to obtain the large-scale behaviour of the local entropy and the spatially bipartite entanglement entropy (EE) of thermal equilibrium states of non-interacting fermions in position space Rd ( d≥1 ) at positive temperature, T>0 . In particular, our definition of the thermal EE leads to estimates that are simultaneously sharp for small T and large scaling parameter α>0 provided that the product Tα remains bounded from below. Here α is the reciprocal quasiclassical parameter. For d=1 we obtain for the thermal EE an asymptotic formula which is consistent with the large-scale behaviour of the ground-state EE (at T=0 ), previously established by the authors for d≥1

Asymptotic Growth of the Local Ground-State Entropy of the Ideal Fermi Gas in a Constant Magnetic Field

We consider the ideal Fermi gas of indistinguishable particles without spin but with electric charge, confined to a Euclidean plane R2 perpendicular to an external constant magnetic field of strength B>0. We assume this (infinite) quantum gas to be in thermal equilibrium at zero temperature, that is, in its ground state with chemical potential μ≥B (in suitable physical units). For this (pure) state we define its local entropy S(Λ) associated with a bounded (sub)region Λ⊂R2 as the von Neumann entropy of the (mixed) local substate obtained by reducing the infinite-area ground state to this region Λ of finite area |Λ|. In this setting we prove that the leading asymptotic growth of S(LΛ), as the dimensionless scaling parameter L>0 tends to infinity, has the form LB−−√|∂Λ| up to a precisely given (positive multiplicative) coefficient which is independent of Λ and dependent on B and μ only through the integer part of (μ/B−1)/2. Here we have assumed the boundary curve ∂Λ of Λ to be sufficiently smooth which, in particular, ensures that its arc length |∂Λ| is well-defined. This result is in agreement with a so-called area-law scaling (for two spatial dimensions). It contrasts the zero-field case B=0, where an additional logarithmic factor ln(L) is known to be present. We also have a similar result, with a slightly more explicit coefficient, for the simpler situation where the underlying single-particle Hamiltonian, known as the Landau Hamiltonian, is restricted from its natural Hilbert space L2(R2) to the eigenspace of a single but arbitrary Landau level. Both results extend to the whole one-parameter family of quantum Rényi entropies. As opposed to the case B=0, the corresponding asymptotic coefficients depend on the Rényi index in a non-trivial way

Time-Dependent Models for Dark Matter at the Galactic Center

The prospects of indirect detection of dark matter at the galactic center depend sensitively on the mass profile within the inner parsec. We calculate the distribution of dark matter on sub-parsec scales by integrating the time-dependent Fokker-Planck equation, including the effects of self-annihilations, scattering of dark matter particles by stars, and capture in the supermassive black hole. We consider a variety of initial dark matter distributions, including models with very high densities ("spikes") near the black hole, and models with "adiabatic compression" of the baryons. The annihilation signal after 10 Gyr is found to be substantially reduced from its initial value, but in dark matter models with an initial spike, order-of-magnitude enhancements can persist compared with the rate in spike-free models, with important implications for indirect dark matter searches with GLAST and Air Cherenkov Telescopes like HESS and CANGAROO.Comment: Four page