Quantum dislocations: the fate of multiple vacancies in two dimensional solid 4He

Defects are believed to play a fundamental role in the supersolid state of 4He. We have studied solid 4He in two dimensions (2D) as function of the number of vacancies n_v, up to 30, inserted in the initial configuration at rho = 0.0765 A^-2, close to the melting density, with the exact zero temperature Shadow Path Integral Ground State method. The crystalline order is found to be stable also in presence of many vacancies and we observe two completely different regimes. For small n_v, up to about 6, vacancies form a bound state and cause a decrease of the crystalline order. At larger n_v, the formation energy of an extra vacancy at fixed density decreases by one order of magnitude to about 0.6 K. In the equilibrated state it is no more possible to recognize vacancies because they mainly transform into quantum dislocations and crystalline order is found almost independent on how many vacancies have been inserted in the initial configuration. The one--body density matrix in this latter regime shows a non decaying large distance tail: dislocations, that in 2D are point defects, turn out to be mobile, their number is fluctuating, and they are able to induce exchanges of particles across the system mainly triggered by the dislocation cores. These results indicate that the notion of incommensurate versus commensurate state loses meaning for solid 4He in 2D, because the number of lattice sites becomes ill defined when the system is not commensurate. Crystalline order is found to be stable also in 3D in presence of up to 100 vacancies

Lower and upper bounds for the first eigenvalue of nonlocal diffusion problems in the whole space

We find lower and upper bounds for the first eigenvalue of a nonlocal diffusion operator of the form T(u) = - \int_{\rr^d} K(x,y) (u(y)-u(x)) \, dy. Here we consider a kernel $K(x,y)=\psi (y-a(x))+\psi(x-a(y))$ where $\psi$ is a bounded, nonnegative function supported in the unit ball and $a$ means a diffeomorphism on \rr^d. A simple example being a linear function $a(x)= Ax$. The upper and lower bounds that we obtain are given in terms of the Jacobian of $a$ and the integral of $\psi$. Indeed, in the linear case $a(x) = Ax$ we obtain an explicit expression for the first eigenvalue in the whole \rr^d and it is positive when the the determinant of the matrix $A$ is different from one. As an application of our results, we observe that, when the first eigenvalue is positive, there is an exponential decay for the solutions to the associated evolution problem. As a tool to obtain the result, we also study the behaviour of the principal eigenvalue of the nonlocal Dirichlet problem in the ball $B_R$ and prove that it converges to the first eigenvalue in the whole space as $R\to \infty$

On the Quasi-Hopf structure of deformed double Yangians

We construct universal twists connecting the centrally extended double Yangian DY(sl(2))_c with deformed double Yangians DY_r(sl(2))_c, thereby establishing the quasi-Hopf structures of the latter.Comment: 11 page

An optimal mass transport approach for limits of eigenvalue problems for the fractional pp-Laplacian

We find interpretation using optimal mass transport theory for eigenvalue problems obtained as limits of the eigenvalue problems for the fractional $p-$Laplacian operators as $p\to +\infty$. We deal both with Dirichlet and Neumann boundary conditions.Comment: 20 page

Exact ground state Monte Carlo method for Bosons without importance sampling

Generally ``exact'' Quantum Monte Carlo computations for the ground state of many Bosons make use of importance sampling. The importance sampling is based, either on a guiding function or on an initial variational wave function. Here we investigate the need of importance sampling in the case of Path Integral Ground State (PIGS) Monte Carlo. PIGS is based on a discrete imaginary time evolution of an initial wave function with a non zero overlap with the ground state, that gives rise to a discrete path which is sampled via a Metropolis like algorithm. In principle the exact ground state is reached in the limit of an infinite imaginary time evolution, but actual computations are based on finite time evolutions and the question is whether such computations give unbiased exact results. We have studied bulk liquid and solid 4He with PIGS by considering as initial wave function a constant, i.e. the ground state of an ideal Bose gas. This implies that the evolution toward the ground state is driven only by the imaginary time propagator, i.e. there is no importance sampling. For both the phases we obtain results converging to those obtained by considering the best available variational wave function (the Shadow wave function) as initial wave function. Moreover we obtain the same results even by considering wave functions with the wrong correlations, for instance a wave function of a strongly localized Einstein crystal for the liquid phase. This convergence is true not only for diagonal properties such as the energy, the radial distribution function and the static structure factor, but also for off-diagonal ones, such as the one--body density matrix. From this analysis we conclude that zero temperature PIGS calculations can be as unbiased as those of finite temperature Path Integral Monte Carlo.Comment: 11 pages, 10 figure

Mars Observer Radar Altimeter Radiometer (MORAR)

The Mars Observer Project will permit the advancement of the state of the topographic and hypsometric knowledge of Mars to a level of 10 m or better over the surface of the planet Mars, the measurement of microwave surface brightness temperature of Mars with an accuracy of 15 to 20 K over 24 hours, and the measurement, globally, of surface returned power related to radar cross section with an accuracy of 1 dB and a repeatability of .5 dB. The MORAR Hardware Development, Ground Data Processing, and the Mission Operations will allow the accomplishment of these scientific objectives to define globally the topography of Mars at sufficient vertical resolution and spatial scale to address both large-scale geophysical and small-scale geologic problems, and to obtain global surface electrical and scattering properties of the upper several centimeters of the Martian surface for assessment of the composition, physical state, and volatile distribution of the surface

A Double Hurdle Model of Preferences for a Proposed Capacity Reduction Program in the Atlantic Shark Fishery

The Atlantic shark fishery is considered to be overcapitalized. One approach to capacity management is the purchase and permanent retirement of fishing vessels, fishing permits, or both under voluntary buyback programs. Representatives of the commercial shark fishery have proposed such an approach to manage the overcapacity in their fishery in the Gulf of Mexico and Atlantic regions. This program would allow owners to submit willingness-to-accept (WTA) bids for their permits and vessels. This study uses econometric modeling to explain the potential participation and bid amounts from a survey of permit owners.Resource /Energy Economics and Policy,