Condensates of p-wave pairs are exact solutions for rotating two-component Bose gases

We derive exact analytical results for the wave functions and energies of harmonically trapped two-component Bose-Einstein condensates with weakly repulsive interactions under rotation. The isospin symmetric wave functions are universal and do not depend on the matrix elements of the two-body interaction. The comparison with the results from numerical diagonalization shows that the ground state and low-lying excitations consists of condensates of p-wave pairs for repulsive contact interactions, Coulomb interactions, and the repulsive interactions between aligned dipoles.Comment: 4 pages, 1 figure; revised version explains exact solutions in terms of isospin symmetry and Hund's rul

Mixtures of Bose gases confined in concentrically coupled annular traps

A two-component Bose-Einstein condensate confined in an axially-symmetric potential with two local minima, resembling two concentric annular traps, is investigated. The system shows a number of quantum phase transitions that result from the competition between phase coexistence, and radial/azimuthal phase separation. The ground-state phase diagram, as well as the rotational properties, including the (meta)stability of currents in this system, are analysed.Comment: 6 pages, 5 figures, minor revision

Optimal evaluation of single-molecule force spectroscopy experiments

The forced rupture of single chemical bonds under external load is addressed. A general framework is put forward to optimally utilize the experimentally observed rupture force data for estimating the parameters of a theoretical model. As an application we explore to what extent a distinction between several recently proposed models is feasible on the basis of realistic experimental data sets.Comment: 4 pages, 3 figures, accepted for publication in Phys. Rev.

Phase transitions in optimal unsupervised learning

We determine the optimal performance of learning the orientation of the symmetry axis of a set of P = alpha N points that are uniformly distributed in all the directions but one on the N-dimensional sphere. The components along the symmetry breaking direction, of unitary vector B, are sampled from a mixture of two gaussians of variable separation and width. The typical optimal performance is measured through the overlap Ropt=B.J* where J* is the optimal guess of the symmetry breaking direction. Within this general scenario, the learning curves Ropt(alpha) may present first order transitions if the clusters are narrow enough. Close to these transitions, high performance states can be obtained through the minimization of the corresponding optimal potential, although these solutions are metastable, and therefore not learnable, within the usual bayesian scenario.Comment: 9 pages, 8 figures, submitted to PRE, This new version of the paper contains one new section, Bayesian versus optimal solutions, where we explain in detail the results supporting our claim that bayesian learning may not be optimal. Figures 4 of the first submission was difficult to understand. We replaced it by two new figures (Figs. 4 and 5 in this new version) containing more detail

Size distribution of sputtered particles from Au nanoislands due to MeV self-ion bombardment

Nanoisland gold films, deposited by vacuum evaporation of gold onto Si(100) substrates, were irradiated with 1.5 MeV Au$^{2+}$ ions up to a fluence of $5\times 10^{14}$ ions cm$^{-2}$ and at incidence angles up to $60^{\circ}$ with respect to the surface normal. The sputtered particles were collected on carbon coated grids (catcher grid) during ion irradiation and were analyzed with transmission electron microscopy and Rutherford backscattering spectrometry. The average sputtered particle size and the areal coverage are determined from transmission electron microscopy measurements, whereas the amount of gold on the substrate is found by Rutherford backscattering spectrometry. The size distributions of larger particles (number of atoms/particle, $n$ $\ge$ 1,000) show an inverse power-law with an exponent of $\sim$ -1 in broad agreement with a molecular dynamics simulation of ion impact on cluster targets.Comment: 13 pages, 8 figures, Submitted for publication in JA

A Quantum Analogue of the Jarzynski Equality

A quantum analogue of the Jarzynski equality is constructed. This equality connects an ensemble average of exponentiated work with the Helmholtz free-energy difference in a nonequilibrium switching process subject to a thermal heat bath. To confirm its validity in a practical situation, we also investigate an open quantum system that is a spin 1/2 system with a scanning magnetic field interacting with a thermal heat bath. As a result, we find that the quantum analogue functions well.Comment: 7 pages, 1 figure; to appear in J. Phys. Soc. Jpn. 69 (2000

Finite sampling effects on generalized fluctuation-dissipation relations for steady states

We study the effects of the finite number of experimental data on the computation of a generalized fluctuation-dissipation relation around a nonequilibrium steady state of a Brownian particle in a toroidal optical trap. We show that the finite sampling has two different effects, which can give rise to a poor estimate of the linear response function. The first concerns the accessibility of the generalized fluctuation-dissipation relation due to the finite number of actual perturbations imposed to the control parameter. The second concerns the propagation of the error made at the initial sampling of the external perturbation of the system. This can be highly enhanced by introducing an estimator which corrects the error of the initial sampled condition. When these two effects are taken into account in the data analysis, the generalized fluctuation-dissipation relation is verified experimentally

Correlation in the velocity of a Brownian particle induced by frictional anisotropy and magnetic field

We study the motion of charged Brownian particles in an external magnetic field. It is found that a correlation appears between the components of particle velocity in the case of anisotropic friction, approaching asymptotically zero in the stationary limit. If magnetic field is smaller compared to the critical value, determined by frictional anisotropy, the relaxation of the correlation is non-oscillating in time. However, in a larger magnetic field this relaxation becomes oscillating. The phenomenon is related to the statistical dependence of the components of transformed random force caused by the simultaneous influence of magnetic field and anisotropic dissipation.Comment: 7 pages, 2 figure

Density Functional Theory of Multicomponent Quantum Dots

Quantum dots with conduction electrons or holes originating from several bands are considered. We assume the particles are confined in a harmonic potential and assume the electrons (or holes) belonging to different bands to be different types of fermions with isotropic effective masses. The density functional method with the local density approximation is used. The increased number of internal (Kohn-Sham) states leads to a generalisation of Hund's first rule at high densities. At low densitites the formation of Wigner molecules is favored by the increased internal freedom.Comment: 11 pages, 5 figure