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Within Density Functional Theory, we have investigated the coalescence dynamics of two superfluid helium nanodroplets hosting vortex lines in different relative orientations, which are drawn towards each other by the Van der Waals mutual attraction. We have found a rich phenomenology depending on how the vortex lines are oriented. In particular, when a vortex and anti-vortex lines are present in the merging droplets, a dark soliton develops at the droplet contact region, which eventually decays into vortex rings. Reconnection events are observed between the vortex lines or rings, leading to the creation of more vortices. Our simulations show the interplay between vortex creation and reconnections, as well as the effect of the droplet surface which pins the vortex ends and, by reflecting short-wavelength excitations produced by the interactions between vortices, strongly affects the droplet final state. Additional vorticity is nucleated in the proximity of surface indentations produced in the course of the dynamics, which in turn interact with other vortices present in the droplets. These effects, obviously absent in the case of bulk liquid helium, show that the droplet surface may act as a multiplier of vortex reconnections. The analysis of the energy spectrum shows that vortex-antivortex ring annihilation, as well as vortex-antivortex reconnections, yields roton bursts of different intensity., Comment: 11 pages, 11 figures + Supplemental Material

Within Density Functional Theory, we have studied the interplay between vortex arrays and capillary waves in spinning prolate He-4 droplets made of several thousands of helium atoms. Surface capillary waves are ubiquitous in prolate superfluid He-4 droplets and, depending on the size and angular momentum of the droplet, they may coexist with vortex arrays. We have found that the equilibrium configuration of small prolate droplets is vortex-free, evolving towards vortex-hosting as the droplet size increases. This result is in agreement with a recent experiment [S.M. O'Connell et al., Phys. Rev. Lett. 124, 215301 (2020)], where it has been disclosed that vortex arrays and capillary waves coexist in the equilibrium configuration of very large drops. Contrarily to viscous droplets executing rigid body rotation, the stability phase diagram of spinning He-4 droplets cannot be universally described in terms of dimensionless angular momentum and angular velocity variables: instead, the rotational properties of superfluid helium droplets display a clear dependence on the droplet size and the number of vortices they host., Comment: 11 pages, 6 figures

When weakly-bound complexes are multiply excited by intense electromagnetic radiation, energy can be exchanged between neighboring atoms through a type of resonant interatomic Coulombic decay (ICD). This decay mechanism due to multiple excitations has been predicted to be relatively slow, typically lasting tens to hundreds of picoseconds. Here, we directly measure the ICD timescale in resonantly excited helium droplets using a high resolution, tunable, extreme ultraviolet free electron laser. Over an extensive range of droplet sizes and laser intensities, we discover the decay to be surprisingly fast, with decay times as fast as 400 femtoseconds, and to only present a weak dependence on the density of the excited states. Using a combination of time dependent density functional theory and ab initio quantum chemistry calculations, we elucidate the mechanisms of this ultrafast decay process where pairs of excited helium atoms in one droplet strongly attract each other and form merging void bubbles which drastically accelerates ICD.

Some discrepancies between experimental results on quantum droplets made of a mixture of $^{39}$K atoms in different hyperfine states and their analysis within extended Gross-Pitaevskii theory (which incorporates beyond mean-field corrections) have been recently solved by introducing finite-range effects into the theory. Here, we study the influence of these effects on the monopole and quadrupole excitation spectrum of extremely dilute quantum droplets using a density functional built from first-principles quantum Monte Carlo calculations, which can be easily introduced in the existing Gross-Pitaevskii numerical solvers. Our results show differences of up to $20\%$ with those obtained within the extended Gross-Pitaevskii theory, likely providing another way to observe finite-range effects in mixed quantum droplets by measuring their lowest excitation frequencies.

The relaxation of photoexcited nanosystems is a fundamental process of light-matter interaction. Depending on the couplings of the internal degrees of freedom, relaxation can be ultrafast, converting electronic energy in a few fs, or slow, if the energy is trapped in a metastable state that decouples from its environment. Here, helium nanodroplets are resonantly excited by femtosecond extreme-ultraviolet (XUV) pulses from a seeded free-electron laser. Despite their superfluid nature, we find that helium nanodroplets in the lowest electronically excited states undergo ultrafast relaxation. By comparing experimental photoelectron spectra with time-dependent density functional theory simulations, we unravel the full relaxation pathway: Following an ultrafast interband transition, a void nanometer-sized bubble forms around the localized excitation (He*) within 1 ps. Subsequently, the bubble collapses and releases metastable He* at the droplet surface. This study highlights the high level of detail achievable in probing the photodynamics of nanosystems using tunable XUV pulses.

We present a combined ion imaging and density functional theory study of the dynamics of the desorption process of rubidium and cesium atoms off the surface of helium nanodroplets upon excitation of the perturbed $6s$ and $7s$ states, respectively. Both experimental and theoretical results are well represented by the pseudodiatomic model for effective masses of the helium droplet in the desorption reaction of m_eff/m_He~10 (Rb) and 13 (Cs). Deviations from this model are found for Rb excited to the 6p state. Photoelectron spectra indicate that the dopant-droplet interaction induces relaxation into low-lying electronic states of the desorbed atoms in the course of the ejection process., Comment: in press, J. Phys. Chem. A (2014)

We investigate long-range effects of the dipolar interaction in Bose-Einstein condensates by solving the time-dependent 3D Gross-Pitaevskii equation. We study the propagation of excitations between non-overlapping condensates when a collective mode is excited in one of the condensates. We obtain the frequency shifts due to the long-range character of the dipolar coupling for the bilayer and also the trilayer system when the dipolar mode is excited in one condensate. The propagation of the monopolar and quadrupolar modes are also investigated. The coupled-pendulum model is proposed to qualitatively explain the long range effects of the dipolar coupling., Comment: 10 pages, 8 figures

A dipolar condensate confined in a toroidal trap constitutes a self-induced Josepshon junction when the dipoles are oriented perpendicularly to the trap symmetry axis and the s-wave scattering length is small enough. The ring-shaped double-well potential coming from the anisotropic character of the mean-field dipolar interaction is robust enough to sustain self-trapping dynamics, which takes place when the initial population imbalance between the two wells is large. We show that in this system the self-trapping regime is directly related to a vortex-induced phase-slip dynamics. A vortex and antivortex are spontaneously nucleated in the low density regions, before a minimum of the population imbalance is reached, and then cross the toroidal section in opposite directions through the junctions.This vortex dynamics yields a phase slip between the two weakly linked condensates causing an inversion of the particle flux., Comment: 4 pages

A finite-temperature density functional approach to describe the properties of parahydrogen in the liquid-vapor coexistence region is presented. The first proposed functional is zero-range, where the density-gradient term is adjusted so as to reproduce the surface tension of the liquid-vapor interface at low temperature. The second functional is finite-range and, while it is fitted to reproduce bulk pH2 properties only, it is shown to yield surface properties in good agreement with experiments. These functionals are used to study the surface thickness of the liquid-vapor interface, the wetting transition of parahydrogen on a planar Rb model surface, and homogeneous cavitation in bulk liquid pH2., Comment: 24 pages and 8 figures

We propose a new scheme for observing Josephson oscillations and macroscopic quantum self-trapping phenomena in a toroidally confined Bose-Einstein condensate: a dipolar self-induced Josephson junction. Polarizing the atoms perpendicularly to the trap symmetry axis, an effective ring-shaped, double-well potential is achieved which is induced by the dipolar interaction. By numerically solving the three-dimensional time-dependent Gross-Pitaevskii equation we show that coherent tunneling phenomena such as Josephson oscillations and quantum self-trapping can take place. The dynamics in the self-induced junction can be qualitatively described by a two-mode model taking into account both s-wave and dipolar interactions., Comment: Major changes. Accepted for publication in EPL

We study a Bose-Einstein condensate of 52Cr atoms confined in a toroidal trap with a variable strength of s-wave contact interactions. We analyze the effects of the anisotropic nature of the dipolar interaction by considering the magnetization axis to be perpendicular to the trap symmetry axis. In the absence of a central repulsive barrier, when the trap is purely harmonic, the effect of reducing the scattering length is a tuning of the geometry of the system: from a pancake-shaped condensate when it is large, to a cigar-shaped condensate for small scattering lengths. For a condensate in a toroidal trap, the interaction in combination with the central repulsive Gaussian barrier produces an azimuthal dependence of the particle density for a fixed radial distance. We find that along the magnetization direction the density decreases as the scattering length is reduced but presents two symmetric density peaks in the perpendicular axis. For even lower values of the scattering length we observe that the system undergoes a dipolar-induced symmetry breaking phenomenon. The whole density becomes concentrated in one of the peaks, resembling an origin-displaced cigar-shaped condensate. In this context we also analyze stationary vortex states and their associated velocity field, finding that this latter also shows a strong azimuthal dependence for small scattering lengths. The expectation value of the angular momentum along the z direction provides a qualitative measure of the difference between the velocity in the different density peaks., Comment: 9 pages, 12 figures

We consider singly-quantized vortex states in a condensate of 52Cr atoms in a pancake trap. We obtain the vortex solutions by numerically solving the Gross-Pitaevskii equation in the rotating frame with no further approximations. The behavior of the condensate is studied under three different situations concerning the interactions: only s-wave, s-wave plus dipolar and only dipolar. The energy barrier for the nucleation of a vortex is calculated as a function of the vortex displacement from the rotation axis in the three cases. These results are compared to those obtained for contact interaction condensates in the Thomas-Fermi approximation, and to a pseudo-analytical model, showing this latter a very good agreement with the numerical calculation., Comment: Submitted to Laser Physics

We present full three-dimensional numerical calculations of single vortex states in rotating dipolar condensates. We consider a Bose-Einstein condensate of 52Cr atoms with dipole-dipole and s-wave contact interactions confined in an axially symmetric harmonic trap. We obtain the vortex states by numerically solving the Gross-Pitaevskii equation in the rotating frame with no further approximations. We investigate the properties of a single vortex and calculate the critical angular velocity for different values of the s-wave scattering length. We show that, whereas the standard variational approach breaks down in the limit of pure dipolar interactions, exact solutions of the Gross-Pitaevskii equation can be obtained for values of the s-wave scattering length down to zero. The energy barrier for the nucleation of a vortex is calculated as a function of the vortex displacement from the rotation axis for different values of the angular velocity of the rotating trap., Comment: 10 pages with 9 figures

Vertically coupled double quantum rings submitted to a perpendicular magnetic field $B$ are addressed within the local spin-density functional theory. We describe the structure of quantum ring molecules containing up to 40 electrons considering different inter-ring distances and intensities of the applied magnetic field. When the rings are quantum mechanically strongly coupled, only bonding states are occupied and the addition spectrum of the artificial molecules resembles that of a single quantum ring, with some small differences appearing as an effect of the magnetic field. Despite the latter has the tendency to flatten the spectra, in the strong coupling limit some clear peaks are still found even when $B\neq 0$ that can be interpretated from the single-particle energy levels analogously as at zero applied field, namely in terms of closed-shell and Hund's-rule configurations. Increasing the inter-ring distance, the occupation of the first antibonding orbitals washes out such structures and the addition spectra become flatter and irregular. In the weak coupling regime, numerous isospin oscillations are found as a function of $B$., Comment: 27 pages, 11 figures. To be published in Phys. Rev. B

We present systematic results, based on density functional calculations, for the structure and energetics of $^3$He and $^4$He nanodroplets doped with alkaline earth atoms. We predict that alkaline earth atoms from Mg to Ba go to the center of $^3$He drops, whereas Ca, Sr, and Ba reside in a deep dimple at the surface of $^4$He drops, and Mg is at their center. For Ca and Sr, the structure of the dimples is shown to be very sensitive to the He-alkaline earth pair potentials used in the calculations. The $5s5p\leftarrow5s^2$ transition of strontium atoms attached to helium nanodroplets of either isotope has been probed in absorption experiments. The spectra show that strontium is solvated inside $^3$He nanodroplets, supporting the calculations. In the light of our findings, we emphasize the relevance of the heavier alkaline earth atoms for analyzing mixed $^3$He-$^4$He nanodroplets, and in particular, we suggest their use to experimentally probe the $^3$He-$^4$He interface., Comment: Typeset using Revtex, 20 pages and 8 Postscript files

The ground state structure of few-electron concentric double quantum rings is investigated within the local spin density approximation. Signatures of inter-ring coupling in the addition energy spectrum are identified and discussed. We show that the electronic configurations in these structures can be greatly modulated by the inter-ring distance: At short and long distances the low-lying electron states localize in the inner and outer rings, respectively, and the energy structure is essentially that of an isolated single quantum ring. However, at intermediate distances the electron states localized in the inner and the outer ring become quasi-degenerate and a rather entangled, strongly-correlated system is formed., Comment: 16 pages (preprint format), 6 figures

Using mean field theory, we have studied Bose-Fermi mixtures in a one-dimensional optical lattice in the case of an attractive boson-fermion interaction. We consider that the fermions are in the degenerate regime and that the laser intensities are such that quantum coherence across the condensate is ensured. We discuss the effect of the optical lattice on the critical rotational frequency for vortex line creation in the Bose-Einstein condensate, as well as how it affects the stability of the boson-fermion mixture. A reduction of the critical frequency for nucleating a vortex is observed as the strength of the applied laser is increased. The onset of instability of the mixture occurs for a sizeably lower number of fermions in the presence of a deep optical lattice., Comment: 7 pages, 6 figures, revtex4, 14th International Laser Physics Workshop (LPHYS'05)

We investigate within mean-field theory the influence of a one-dimensional optical lattice and of trapped degenerate fermions on the critical rotational frequency for vortex line creation in a Bose-Einstein condensate. We consider laser intensities of the lattice such that quantum coherence across the condensate is ensured. We find a sizable decrease of the thermodynamic critical frequency for vortex nucleation with increasing applied laser strength and suggest suitable parameters for experimental observation. Since 87Rb-40K mixtures may undergo collapse, we analyze the related question of how the optical lattice affects the mechanical stability of the system., Comment: 5 pages, 4 figures, revtex4

We show that, at high densities, fully variational solutions of solid-like type can be obtained from a density functional formalism originally designed for liquid 4He. Motivated by this finding, we propose an extension of the method that accurately describes the solid phase and the freezing transition of liquid 4He at zero temperature. The density profile of the interface between liquid and the (0001) surface of the 4He crystal is also investigated, and its surface energy evaluated. The interfacial tension is found to be in semiquantitative agreement with experiments and with other microscopic calculations. This opens the possibility to use unbiased DF methods to study highly non-homogeneous systems, like 4He interacting with strongly attractive impurities/substrates, or the nucleation of the solid phase in the metastable liquid., Comment: 5 pages, 4 figures, submitted to Phys. Rev. B

Recent magneto-transport experiments of holes in InGaAs quantum dots [D. Reuter, P. Kailuweit, A.D. Wieck, U. Zeitler, O. Wibbelhoff, C. Meier, A. Lorke, and J.C. Maan, Phys. Rev. Lett. 94, 026808 (2005)] are interpreted by employing a multi-band kp Hamiltonian, which considers the interaction between heavy hole and light hole subbands explicitely. No need of invoking an incomplete energy shell filling is required within this model. The crucial role we ascribe to the heavy hole-light hole interaction is further supported by one-band local-spin-density functional calculations, which show that Coulomb interactions do not induce any incomplete hole shell filling and therefore cannot account for the experimental magnetic field dispersion., Comment: 5 pages with 3 figures and one table. The paper has been submitted to Phys.Rev.B

We have used a Hartree-type electron-helium potential together with a density functional description of liquid $^4$He and $^3$He to study the explosion of electron bubbles submitted to a negative pressure. The critical pressure at which bubbles explode has been determined as a function of temperature. It has been found that this critical pressure is very close to the pressure at which liquid helium becomes globally unstable in the presence of electrons. It is shown that at high temperatures the capillary model overestimates the critical pressures. We have checked that a commonly used and rather simple electron-helium interaction yields results very similar to those obtained using the more accurate Hartree-type interaction. We have estimated that the crossover temperature for thermal to quantum nucleation of electron bubbles is very low, of the order of 6 mK for $^4$He., Comment: 22 pages, 9 figures

We have experimentally studied the electronic $3p-> 3s$ excitation of Na atoms attached to $^3$He droplets by means of laser-induced fluorescence as well as beam depletion spectroscopy. From the similarities of the spectra (width/shift of absorption lines) with these of Na on $^4$He droplets, we conclude that sodium atoms reside in a ``dimple'' on the droplet surface and that superfluid-related effects are negligible. The experimental results are supported by Density Functional calculations at zero temperature, which confirm the surface location of Na, K and Rb atoms on $^3$He droplets. In the case of Na, the calculated shift of the excitation spectra for the two isotopes is in good agreement with the experimental data., Comment: 6 pages, 3 figures, sent to JLTP

We have experimentally studied the electronic $3p\leftarrow 3s$ excitation of Na atoms attached to $^3$He droplets by means of laser-induced fluorescence as well as beam depletion spectroscopy. From the similarities of the spectra (width/shift of absorption lines) with these of Na on $^4$He droplets, we conclude that sodium atoms reside in a ``dimple'' on the droplet surface and that superfluid-related effects are negligible. The experimental results are supported by Density Functional calculations at zero temperature, which confirm the surface location of sodium on $^3$He droplets, and provide a detailed description of the ``dimple'' structure. The calculated shift of the excitation spectra for the two isotopes is in good agreement with the experimental data., Comment: 5pages, 5 figures. Sent to PRB

We study a confined mixture of bosons and fermions in the quantal degeneracy regime with attractive boson-fermion interaction. We discuss the effect that the presence of vortical states and the displacement of the trapping potentials may have on mixtures near collapse, and investigate the phase stability diagram of the K-Rb mixture in the mean field approximation supposing in one case that the trapping potentials felt by bosons and fermions are shifted from each other, as it happens in the presence of a gravitational sag, and in another case, assuming that the Bose condensate sustains a vortex state. In both cases, we have obtained an analytical expression for the fermion effective potential when the Bose condensate is in the Thomas-Fermi regime, that can be used to determine the maxima of the fermionic density. We have numerically checked that the values one obtains for the location of these maxima using the analytical formulas remain valid up to the critical boson and fermion numbers, above which the mixture collapses., Comment: Submitted to Phys. Rev. A (on May 2004), 15 pages with 3 figures

We have experimentally studied the electronic $3p\leftarrow 3s$ excitation of Na atoms attached to $^3$He droplets by means of laser-induced fluorescence as well as beam depletion spectroscopy. From the similarities of the spectra (width/shift of absorption lines) with these of Na on $^4$He droplets, we conclude that sodium atoms reside in a ``dimple'' on the droplet surface. The experimental results are supported by Density Functional calculations at zero temperature, which confirm the surface location of sodium on $^3$He droplets, and provide a microscopic description of the ``dimple'' structure., Comment: 4 pages, 5 figures

We investigate the behavior of mixed 3He-4He droplets on alkali surfaces at zero temperature, within the frame of Finite Range Density Functional theory. The properties of one single 3He atom on 4He_N4 droplets on different alkali surfaces are addressed, and the energetics and structure of 4He_N4+3He_N3 systems on Cs surfaces, for nanoscopic 4He drops, are analyzed through the solutions of the mean field equations for varying number N3 of 3He atoms. We discuss the size effects on the single particle spectrum of 3He atoms and on the shapes of both helium distributions., Comment: 12 pages, and 12 figures (PNG format)

We investigate the spreading of 4He droplets on alkali surfaces at zero temperature, within the frame of Finite Range Density Functional theory. The equilibrium configurations of several 4He_N clusters and their asymptotic trend with increasing particle number N, which can be traced to the wetting behavior of the quantum fluid, are examined for nanoscopic droplets. We discuss the size effects, inferring that the asymptotic properties of large droplets correspond to those of the prewetting film.

We show that small amounts of 3He atoms, added to a 4He drop deposited on a flat cesium surface at zero temperature, populate bound states localized at the contact line. These edge states show up for drops large enough to develop well defined surface and bulk regions together with a contact line, and they are structurally different from the well-known Andreev states that appear at the free surface and at the liquid-solid interface of films. We illustrate the one-body density of 3He in a drop with 1000 4He atoms, and show that for sufficiently large number of impurities, the density profiles spread beyond the edge, coating both the curved drop surface and its flat base and eventually isolating it from the substrate., Comment: 10 pages and 7 figures. Submitted to PRL

We present experimental results for the ground state electrochemical potentials of a few electron semiconductor artificial molecule made by vertically coupling two quantum dots, in the intermediate coupling regime, in perpendicular and parallel magnetic fields up to 5 T. We perform a quantitative analysis based on local-spin density functional theory. The agreement between theoretical and experimental results is good, and the phase transitions are well reproduced., Comment: Typeset using Revtex, 13 pages and 8 Postscript figures

We present a numerical method for generating vortex rings in Bose-Einstein condensates confined in axially symmetric traps. The vortex ring is generated using the line-source approximation for the vorticity, i.e., the rotational of the superfluid velocity field is different from zero only on a circumference of given radius located on a plane perpendicular to the symmetry axis and coaxial with it. The particle density is obtained by solving a modified Gross-Pitaevskii equation that incorporates the effect of the velocity field. We discuss the appearance of density profiles, the vortex core structure and the vortex nucleation energy, i.e., the energy difference between vortical and ground-state configurations. This is used to present a qualitative description of the vortex dynamics., Comment: Accepted for publication in Phys. Rev. A

We present a systematic study of ground state and spectroscopic properties of many-electron nanoscopic quantum rings. Addition energies at zero magnetic field (B) and electro-chemical potentials as a function of $B$ are given for a ring hosting up to 24 electrons. We find discontinuities in the excitation energies of multipole spin and charge density modes, and a coupling between the charge and spin density responses that allow to identify the formation of ferromagnetic ground states in narrow magnetic field regions. These effects can be observed in Raman experiments, and are related to the fractional Aharonov-Bohm oscillations of the energy and of the persistent current in the ring., Comment: Accepted for publication in Phys. Rev. B

We investigate the dissociation of few-electron circular vertical semiconductor double quantum dot artificial molecules at 0 T as a function of interdot distance. Slight mismatch introduced in the fabrication of the artificial molecules from nominally identical constituent quantum wells induces localization by offsetting the energy levels in the quantum dots by up to 2 meV, and this plays a crucial role in the appearance of the addition energy spectra as a function of coupling strength particularly in the weak coupling limit., Comment: Accepted for publication in Phys. Rev. Lett

We have investigated the far-infrared dipole modes of a quantum antidot submitted to a perpendicularly applied magnetic field B. The ground state of the antidot is described within local spin-density functional theory, and the spectrum within time-dependent local spin-density functional theory. The results are compared with those corresponding to a quantum dot of similar electronic surface density. The method is able to reproduce two of the more salient experimental features, namely that main bulk and edge modes have the same circular polarization, and that the negative B dispersion edge branch oscillates, having minima at the B values corresponding to fully occupied Landau levels. It fails, however, to yield the unique feature of short-period antidot lattices that the energy of the edge magnetoplasmon approaches the cyclotron frequency for small B. The existence of anticyclotron polarized bulk modes is discussed, and a detailed account of the dipole spin mode is presented., Comment: Typeset using Revtex, 20 pages with 10 Postscript figures included

We present a study of phase separation from supersaturated 3He-4He liquid mixtures at low temperatures addressing both the degree of critical supersaturation Dx and the thermal-to-quantum crossover temperature T* for the nucleation process. Two different nucleation seeds are investigated, namely 3He droplets and 4He vortex lines with cores filled with 3He. We have found that the experimental T* is reproduced when we consider that nucleation proceeds from 3He droplets, whereas Dx is reproduced when we consider 4He vortex lines filled with 3He. However, neither nucleation configuration is able to simultaneously reproduce the current experimental information on Dx and T*., Comment: To appear in J. of Low Temp. Physics

We have carried out a systematic analysis of the transverse dipole spin response of a large size quantum dot within time-dependent current density functional theory. Results for magnetic fields corresponding to integer filling factors are reported, as well as a comparison with the longitudinal dipole spin response. As in the two dimensional electron gas, the spin response at high spin magnetization is dominated by a low energy transverse mode., Comment: Typeset using Revtex, 14 pages and 8 Postscript figures

We have employed time-dependent local-spin density theory to analyze the multipole spin and charge density excitations recently found in GaAs-AlGaAs quatum dots [C. Sch\"uller et al, Phys. Rev. Lett {\bf 80}, 2673 (1998)]. The overall agreement between theory and experiment is good, identifying the angular momentum of the modes observed in the experiment. We have found that high multipolarity spin density edge modes originate from interband transitions instead that from intraband transitions, as it happens in the dipole case., Comment: Typeset using Revtex, 7 pages and 5 Postscript figures

We have studied the structure and dipole charge density response of nanorings as a function of the magnetic field using local-spin density functional theory. Two small rings consisting of 12 and 22 electrons confined by a positively charged background are used to represent the cases of a narrow and a wide ring. The results are qualitatively compared with experimental data existing on microrings and on antidots. A smaller ring containing 5 electrons is also analyzed to allow for a closer comparison with a recent experiment on a two electron quantum ring., Comment: Typeset using Revtex, 13 pages and 11 Postscript figures

The longitudinal dipole response of a quantum dot has been calculated in the far-infrared regime using local spin density functional theory. We have studied the coupling between the collective spin and density modes as a function of the magnetic field. We have found that the spin dipole mode and single particle excitations have a sizeable overlap, and that the magnetoplasmon modes can be excited by the dipole spin operator if the dot is spin polarized. The frequency of the dipole spin edge mode presents an oscillation which is clearly filling factor ($\nu$) related. We have found that the spin dipole mode is especially soft for even $\nu$ values, becoming unstable for magnetic fields in the region $1 < \nu \leq 2$. Results for selected number of electrons and confining potentials are discussed. An analytical model which reproduces the main features of the microscopic spectra has been developed., Comment: We have added some new references and minor changes on the mnuscript have been made

The effect of ring vortices on the destabilization of supersaturated liquid helium mixtures at very low temperatures is investigated as a function of pressure. We have found that large ring vortices trigger the segregation of 3He at smaller values of the concentration than small ring vortices. Our calculations indicate that the existence of ring vortices in the mixture is a possible mechanism to understand the rather small degree of critical supersaturation found in the experiments., Comment: Typeset using Revtex, 11 pages and 10 Postscript figures

We have investigated edge modes of different multipolarity sustained by quantum dots submitted to external magnetic fields. We present a microscopic description based on a variational solution of the equation of motion for any axially symmetric confining potential and multipole mode. Numerical results for dots with different number of electrons whose ground-state is described within a local Current Density Functional Theory are discussed. Two sum rules, which are exact within this theory, are derived. In the limit of a large neutral dot at B=0, we have shown that the classical hydrodynamic dispersion law for edge waves \omega(q) \sim \sqrt{q \ln (q_0/q)} holds when quantum and finite size effects are taken into account., Comment: We have changed some figures as well as a part of the text

At low temperatures and 3He concentrations below 6.6 %, there is experimental evidence about the existence in liquid helium mixtures, of stable vortices with 3He-rich cores. When the system is either supersaturated or submitted to a tensile strength, vortices lose stability becoming metastable and eventually completely unstable, so that their cores freely expand. Within a density functional approach, we have determined the pressure-3He concentration curve along which this instability appears at zero temperature., Comment: Typeset using Revtex, 9 pages and 5 Postscript figures

We have investigated the quantum-to-thermal crossover temperature T* for cavitation in liquid helium mixtures up to 0.05 3He concentrations. With respect to the pure 4He case, T* is sizeably reduced, to a value below 50 mK for 3He concentrations above 0.02. As in pure 4He, the homogeneous cavitation pressure is systematically found close to the spinodal pressure., Comment: Typeset using Revtex, 9 pages and 4 figures

Using a functional-integral approach, we have determined the temperature below which cavitation in liquid helium is driven by thermally assisted quantum tunneling. For both helium isotopes, we have obtained the crossover temperature in the whole range of allowed negative p essures. Our results are compatible with recent experimental results on 4He., Comment: Typeset using Revtex, 10 pages and 2 figures, Phys. Rev B (1996)