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-spec
ies 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.
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.
We present a simple model of network growth and solve it by writing down the dynamic equations for its macroscopic characteristics like the degree distribution and degree correlations. This allows us to study carefully the percolation transition usin
g a generating functions theory. The model considers a network with a fixed number of nodes wherein links are introduced using degree-dependent linking probabilities $p_k$. To illustrate the techniques and support our findings using Monte-Carlo simulations, we introduce the exemplary linking rule $p_k$ proportional to $k^{-alpha}$, with $alpha$ between -1 and plus infinity. This parameter may be used to interpolate between different regimes. For negative $alpha$, links are most likely attached to high-degree nodes. On the other hand, in case $alpha>0$, nodes with low degrees are connected and the model asymptotically approaches a process undergoing explosive percolation.
Recent studies introduced biased (degree-dependent) edge percolation as a model for failures in real-life systems. In this work, such process is applied to networks consisting of two types of nodes with edges running only between nodes of unlike type
. Such bipartite graphs appear in many social networks, for instance in affiliation networks and in sexual contact networks in which both types of nodes show the scale-free characteristic for the degree distribution. During the depreciation process, an edge between nodes with degrees k and q is retained with probability proportional to (kq)^(-alpha), where alpha is positive so that links between hubs are more prone to failure. The removal process is studied analytically by introducing a generating functions theory. We deduce exact self-consistent equations describing the system at a macroscopic level and discuss the percolation transition. Critical exponents are obtained by exploiting the Fortuin-Kasteleyn construction which provides a link between our model and a limit of the Potts model.
We study population imbalanced Fermi mixtures under quasi-two-dimensional confinement at zero temperature. Using mean-field theory and the local-density approximation, we study the ground state configuration throughout the BEC-BCS crossover. We find
the trapped system to be either fully normal or to consist of a superfluid core surrounded by a normal shell, which is itself either fully or partially polarized. Upon changing the trap imbalance, the trap configuration may undergo continuous transitions between the different ground states. Finally, we argue that thermal equilibration throughout the trap will be considerably slowed down at low temperatures when a superfluid phase is present.
Biased (degree-dependent) percolation was recently shown to provide new strategies for turning robust networks fragile and vice versa. Here we present more detailed results for biased edge percolation on scale-free networks. We assume a network in wh
ich the probability for an edge between nodes $i$ and $j$ to be retained is proportional to $(k_ik_j)^{-alpha}$ with $k_i$ and $k_j$ the degrees of the nodes. We discuss two methods of network reconstruction, sequential and simultaneous, and investigate their properties by analytical and numerical means. The system is examined away from the percolation transition, where the size of the giant cluster is obtained, and close to the transition, where nonuniversal critical exponents are extracted using the generating functions method. The theory is found to agree quite well with simulations. By introducing an extension of the Fortuin-Kasteleyn construction, we find that biased percolation is well described by the $qto 1$ limit of the $q$-state Potts model with inhomogeneous couplings.
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 a
s 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.
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 exp
erimentally 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.
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 integ
er 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.
Motivated by recent observations of phase-segregated binary Bose-Einstein condensates, we propose a method to calculate the excess energy due to the interface tension of a trapped configuration. By this method one should be able to numerically reprod
uce the experimental data by means of a simple Thomas-Fermi approximation, combined with interface excess terms and the Laplace equation. Using the Gross-Pitaevskii theory, we find expressions for the interface excesses which are accurate in a very broad range of the interspecies and intraspecies interaction parameters. We also present finite-temperature corrections to the interface tension which, aside from the regime of weak segregation, turn out to be small.
