Area distribution of two-dimensional random walks on a square lattice

The algebraic area probability distribution of closed planar random walks of length N on a square lattice is considered. The generating function for the distribution satisfies a recurrence relation in which the combinatorics is encoded. A particular case generalizes the q-binomial theorem to the case of three addends. The distribution fits the L\'evy probability distribution for Brownian curves with its first-order 1/N correction quite well, even for N rather small.Comment: 8 pages, LaTeX 2e. Reformulated in terms of q-commutator

Input-output theory for fermions in an atom cavity

We generalize the quantum optical input-output theory developed for optical cavities to ultracold fermionic atoms confined in a trapping potential, which forms an "atom cavity". In order to account for the Pauli exclusion principle, quantum Langevin equations for all cavity modes are derived. The dissipative part of these multi-mode Langevin equations includes a coupling between cavity modes. We also derive a set of boundary conditions for the Fermi field that relate the output fields to the input fields and the field radiated by the cavity. Starting from a constant uniform current of fermions incident on one side of the cavity, we use the boundary conditions to calculate the occupation numbers and current density for the fermions that are reflected and transmitted by the cavity

Interference of a Tonks-Girardeau Gas on a Ring

We study the quantum dynamics of a one-dimensional gas of impenetrable bosons on a ring, and investigate the interference that results when an initially trapped gas localized on one side of the ring is released, split via an optical-dipole grating, and recombined on the other side of the ring. Large visibility interference fringes arise when the wavevector of the optical dipole grating is larger than the effective Fermi wavevector of the initial gas.Comment: 7 pages, 3 figure

Some flows in shape optimization

Geometric flows related to shape optimization problems of Bernoulli type are investigated. The evolution law is the sum of a curvature term and a nonlocal term of Hele-Shaw type. We introduce generalized set solutions, the definition of which is widely inspired by viscosity solutions. The main result is an inclusion preservation principle for generalized solutions. As a consequence, we obtain existence, uniqueness and stability of solutions. Asymptotic behavior for the flow is discussed: we prove that the solutions converge to a generalized Bernoulli exterior free boundary problem

Information transfer through disordered media by diffuse waves

We consider the information content h of a scalar multiple-scattered, diffuse wave field $\psi(\vec{r})$ and the information capacity C of a communication channel that employs diffuse waves to transfer the information through a disordered medium. Both h and C are shown to be directly related to the mesoscopic correlations between the values of $\psi(\vec{r})$ at different positions $\vec{r}$ in space, arising due to the coherent nature of the wave. For the particular case of a communication channel between two identical linear arrays of $n \gg 1$ equally-spaced transmitters/receivers (receiver spacing a), we show that the average capacity $\propto n$ and obtain explicit analytic expressions for $/n$ in the limit of $n \to \infty$ and $k \ell \to \infty$, where $k= 2\pi/ \lambda$, $\lambda$ is the wavelength, and $\ell$ is the mean free path. Modification of the above results in the case of finite but large n and $k \ell$ is discussed as well.Comment: REVTeX 4, 12 pages, 7 figure

Asymptotics and zeros of Sobolev orthogonal polynomials on unbounded supports

In this paper we present a survey about analytic properties of polynomials orthogonal with respect to a weighted Sobolev inner product such that the vector of measures has an unbounded support. In particular, we are focused in the study of the asymptotic behaviour of such polynomials as well as in the distribution of their zeros. Some open problems as well as some new directions for a future research are formulated.Comment: Changed content; 34 pages, 41 reference

Semiparametric theory and empirical processes in causal inference

In this paper we review important aspects of semiparametric theory and empirical processes that arise in causal inference problems. We begin with a brief introduction to the general problem of causal inference, and go on to discuss estimation and inference for causal effects under semiparametric models, which allow parts of the data-generating process to be unrestricted if they are not of particular interest (i.e., nuisance functions). These models are very useful in causal problems because the outcome process is often complex and difficult to model, and there may only be information available about the treatment process (at best). Semiparametric theory gives a framework for benchmarking efficiency and constructing estimators in such settings. In the second part of the paper we discuss empirical process theory, which provides powerful tools for understanding the asymptotic behavior of semiparametric estimators that depend on flexible nonparametric estimators of nuisance functions. These tools are crucial for incorporating machine learning and other modern methods into causal inference analyses. We conclude by examining related extensions and future directions for work in semiparametric causal inference

The nomenclature and application of the names Euphorbia candelabrum Welw. and Euphorbia ingens in tropical Africa

During the last 40 years, one of the most widespread and conspicuous succulent trees in East and north‐east Africa has been referred to as Euphorbia candelabrum Kotschy or as E. candelabrum Trémaux ex Kotschy. This name is a later homonym of E. candelabrum Welw., and consequently it is illegitimate. The species to which the name E. candelabrum Kotschy has been widely applied is shown to be conspecific with E. ingens, which occurs from southern Ethiopia to subtropical South Africa.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/152821/1/tax12091_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/152821/2/tax12091.pd

Spinor condensates and light scattering from Bose-Einstein condensates

These notes discuss two aspects of the physics of atomic Bose-Einstein condensates: optical properties and spinor condensates. The first topic includes light scattering experiments which probe the excitations of a condensate in both the free-particle and phonon regime. At higher light intensity, a new form of superradiance and phase-coherent matter wave amplification were observed. We also discuss properties of spinor condensates and describe studies of ground--state spin domain structures and dynamical studies which revealed metastable excited states and quantum tunneling.Comment: 58 pages, 33 figures, to appear in Proceedings of Les Houches 1999 Summer School, Session LXXI

Quantification of CO2 removal in a large-scale enhanced weathering field trial on an oil palm plantation in Sabah, Malaysia

Modeling studies show that large-scale deployment of enhanced rock weathering on croplands has the potential to reduce levels of atmospheric carbon dioxide by the end of the century. There is, however, a pressing need to verify model predictions through long-term field trials. Here we report results from the first 3 years of an ongoing enhanced weathering field trial, carried out on an oil palm plantation in Sabah, Malaysia. Crushed silicate rock was applied to three hydrologically isolated catchments, and three adjacent (paired) reference catchments were left untreated. The drawdown of atmospheric CO2 was quantified via the export of alkalinity in stream waters and changes in soil carbonate content. The amended and reference catchments were found to have a similar extent of CO2 drawdown via alkalinity export [respectively, 3.8 ± 0.8 (1 SD) and 3.7 ± 0.6 (1 SD) tCO2 ha−1] when all catchments were averaged over the study period (October 2018 to July 2021). However, differences were observed between the different catchment pairs (plots): two of the plots displayed a similar extent of CO2 removal for both the amended and reference catchments, but the third amended catchment had a higher extent of CO2 removal of ~1 tCO2 ha−1 relative to its adjacent reference catchment. The difference in CO2 removal rates determined for this plot can likely be attributed to increased weathering of silicate minerals in the amended catchment. Soil carbonate concentrations were on average < 0.2 wt% CaCO3, but we report a small increase of ~0.03 wt% CaCO3 in the top 30 cm of soil in the amended soils relative to the reference catchments. The magnitude of CO2 drawdown via alkalinity export determined for these agricultural catchments is around an order of magnitude higher than in natural forested catchments in Sabah and similar to that of basaltic catchments. We show that these high weathering rates are primarily driven by weathering of carbonate fertilizers. The data presented from this field trial provide vital contextual information on the real-world efficacy and practicalities associated with the implementation of enhanced weathering for atmospheric CO2 removal that will help to inform further trials as well as wider-scale deployment