Critical wetting, first-order wetting and prewetting phase transitions in binary mixtures of Bose-Einstein condensates

An ultralow-temperature binary mixture of Bose-Einstein condensates adsorbed at an optical wall can undergo a wetting phase transition in which one of the species excludes the other from contact with the wall. Interestingly, while hard-wall boundary conditions entail the wetting transition to be of first order, using Gross-Pitaevskii theory we show that first-order wetting as well as critical wetting can occur when a realistic exponential optical wall potential (evanescent wave) with a finite turn-on length $\lambda$ is assumed. The relevant surface excess energies are computed in an expansion in $\lambda/\xi_i$, where $\xi_i$ is the healing length of condensate $i$. Experimentally, the wetting transition may best be approached by varying the interspecies scattering length $a_{12}$ using Feshbach resonances. In the hard-wall limit, $\lambda \rightarrow 0$, exact results are derived for the prewetting and first-order wetting phase boundaries.Comment: 18 pages, 15 figure

Collective Excitations of Harmonically Trapped Ideal Gases

We theoretically study the collective excitations of an ideal gas confined in an isotropic harmonic trap. We give an exact solution to the Boltzmann-Vlasov equation; as expected for a single-component system, the associated mode frequencies are integer multiples of the trapping frequency. We show that the expressions found by the scaling ansatz method are a special case of our solution. Our findings, however, are most useful in case the trap contains more than one phase: we demonstrate how to obtain the oscillation frequencies in case an interface is present between the ideal gas and a different phase.Comment: 4 pages, submitted to special issue of Eur. Phys. J. B "Novel Quantum Phases and Mesoscopic Physics in Quantum Gases

Post-processing through linear regression

Various post-processing techniques are compared for both deterministic and ensemble forecasts, all based on linear regression between forecast data and observations. In order to evaluate the quality of the regression methods, three criteria are proposed, related to the effective correction of forecast error, the optimal variability of the corrected forecast and multicollinearity. The regression schemes under consideration include the ordinary least-square (OLS) method, a new time-dependent Tikhonov regularization (TDTR) method, the total least-square method, a new geometric-mean regression (GM), a recently introduced error-in-variables (EVMOS) method and, finally, a "best member" OLS method. The advantages and drawbacks of each method are clarified. These techniques are applied in the context of the 63 Lorenz system, whose model version is affected by both initial condition and model errors. For short forecast lead times, the number and choice of predictors plays an important role. Contrarily to the other techniques, GM degrades when the number of predictors increases. At intermediate lead times, linear regression is unable to provide corrections to the forecast and can sometimes degrade the performance (GM and the best member OLS with noise). At long lead times the regression schemes (EVMOS, TDTR) which yield the correct variability and the largest correlation between ensemble error and spread, should be preferred

Static interfacial properties of Bose-Einstein condensate mixtures

Interfacial profiles and interfacial tensions of phase-separated binary mixtures of Bose-Einstein condensates are studied theoretically. The two condensates are characterized by their respective healing lengths $\xi_1$ and $\xi_2$ and by the inter-species repulsive interaction $K$. An exact solution to the Gross-Pitaevskii (GP) equations is obtained for the special case $\xi_2/\xi_1 = 1/2$ and $K = 3/2$. Furthermore, applying a double-parabola approximation (DPA) to the energy density featured in GP theory allows us to define a DPA model, which is much simpler to handle than GP theory but nevertheless still captures the main physics. In particular, a compact analytic expression for the interfacial tension is derived that is useful for all $\xi_1, \xi_2$ and $K$. An application to wetting phenomena is presented for condensates adsorbed at an optical wall. The wetting phase boundary obtained within the DPA model nearly coincides with the exact one in GP theory.Comment: 24 pages, 6 figure

Normal-Superfluid Interface for Polarized Fermion Gases

Recent experiments on imbalanced fermion gases have proved the existence of a sharp interface between a superfluid and a normal phase. We show that, at the lowest experimental temperatures, a temperature difference between N and SF phase can appear as a consequence of the blocking of energy transfer across the interface. Such blocking is a consequence of the existence of a SF gap, which causes low-energy normal particles to be reflected from the N-SF interface. Our quantitative analysis is based on the Hartree-Fock-Bogoliubov-de Gennes formalism, which allows us to give analytical expressions for the thermodynamic properties and characterize the possible interface scattering regimes, including the case of unequal masses. Our central result is that the thermal conductivity is exponentially small at the lowest experimental temperatures.Comment: 11 pages, 5 figure

Weakly Interacting Bose Mixtures at Finite Temperature

Motivated by the recent experiments on Bose-Einstein mixtures with tunable interactions we study repulsive weakly interacting Bose mixtures at finite temperature. We obtain phase diagrams using Hartree-Fock theory which are directly applicable to experimentally trapped systems. Almost all features of the diagrams can be characterized using simple physical insights. Our work reveals two surprising effects which are dissimilar to a system at zero temperature. First of all, no pure phases exist, that is, at each point in the trap, particles of both species are always present. Second, even for very weak interspecies repulsion when full mixing is expected, condensate particles of both species may be present in a trap without them being mixed.Comment: 4 pages, 2 figure

Climate sensitivity to land use changes over the City of Brussels

Prompted with the ongoing and projected climate change, a wide range of cities have committed, not only to mitigate greenhouse gas emissions but also to implement different climate change adaptation measures. These measures serve to ensure the wellbeing of the urban population. In practice, however, the planning of realistic adaptation measures is a complex process. Prior to starting such endeavor, it may therefore be useful to explore the maximum potential benefit that can be gained through adaptation measures. In this work, simple, extreme yet realistic adaptation measures are proposed in terms of changes in albedo and vegetation fraction. The impact of these land-use scenarios is explored by use of the land surface model SURFEX on the summer climate in terms of heat waves and the urban heat island for the city of Brussels. This is done for different periods in the future using the greenhouse gas scenario RCP8.5