Resonances in a trapped 3D Bose-Einstein condensate under periodically varying atomic scattering length

Nonlinear oscillations of a 3D radial symmetric Bose-Einstein condensate under periodic variation in time of the atomic scattering length have been studied analytically and numerically. The time-dependent variational approach is used for the analysis of the characteristics of nonlinear resonances in the oscillations of the condensate. The bistability in oscillations of the BEC width is invistigated. The dependence of the BEC collapse threshold on the drive amplitude and parameters of the condensate and trap is found. Predictions of the theory are confirmed by numerical simulations of the full Gross-Pitaevski equation.Comment: 17 pages, 10 figures, submitted to Journal of Physics

Propagation of ultra-short, resonant, ionizing laser pulses in rubidium vapor

We investigate the propagation of ultra-short laser pulses in atomic rubidium vapor. The pulses are intensive enough to ionize the atoms and are directly resonant with the 780 nm $D_2$ line. We derive a relatively simple theory for computing the nonlinear optical response of atoms and investigate the competing effects of strong resonant nonlinearity and ionization in the medium using computer simulations. A nonlinear self-channeling of pulse energy is found to produce a continuous plasma channel with complete ionization. We evaluate the length, width and homogeneity of the resulting plasma channel for various values of pulse energy and initial focusing to identify regimes optimal for applications in plasma-wave accelerator devices such as that being built by the AWAKE collaboration at CERN. Similarities and differences with laser pulse filamentation in atmospheric gases are discussed.Comment: 8 figure

Transient shear banding in the nematic dumbbell model of liquid crystalline polymers

In the shear flow of liquid crystalline polymers (LCPs) the nematic director orientation can align with the flow direction for some materials, but continuously tumble in others. The nematic dumbbell (ND) model was originally developed to describe the rheology of flow-aligning semi-flexible LCPs, and flow-aligning LCPs are the focus in this paper. In the shear flow of monodomain LCPs it is usually assumed that the spatial distribution of the velocity is uniform. This is in contrast to polymer solutions, where highly non-uniform spatial velocity profiles have been observed in experiments. We analyse the ND model, with an additional gradient term in the constitutive model, using a linear stability analysis. We investigate the separate cases of constant applied shear stress, and constant applied shear rate. We find that the ND model has a transient flow instability to the formation of a spatially inhomogeneous flow velocity for certain starting orientations of the director. We calculate the spatially resolved flow profile in both constant applied stress and constant applied shear rate in start up from rest, using a model with one spatial dimension to illustrate the flow behaviour of the fluid. For low shear rates flow reversal can be seen as the director realigns with the flow direction, whereas for high shear rates the director reorientation occurs simultaneously across the gap. Experimentally, this inhomogeneous flow is predicted to be observed in flow reversal experiments in LCPs.Comment: 16 pages, 15 figure

Theory of inelastic lifetimes of low-energy electrons in metals

Electron dynamics in the bulk and at the surface of solid materials are well known to play a key role in a variety of physical and chemical phenomena. In this article we describe the main aspects of the interaction of low-energy electrons with solids, and report extensive calculations of inelastic lifetimes of both low-energy electrons in bulk materials and image-potential states at metal surfaces. New calculations of inelastic lifetimes in a homogeneous electron gas are presented, by using various well-known representations of the electronic response of the medium. Band-structure calculations, which have been recently carried out by the authors and collaborators, are reviewed, and future work is addressed.Comment: 28 pages, 18 figures, to appear in Chem. Phy

Nonlinear response theory for Markov processes: Simple models for glassy relaxation

The theory of nonlinear response for Markov processes obeying a master equation is formulated in terms of time-dependent perturbation theory for the Green's functions and general expressions for the response functions up to third order in the external field are given. The nonlinear response is calculated for a model of dipole reorientations in an asymmetric double well potential, a standard model in the field of dielectric spectroscopy. The static nonlinear response is finite with the exception of a certain temperature $T_0$ determined by the value of the asymmetry. In a narrow temperature range around $T_0$, the modulus of the frequency-dependent cubic response shows a peak at a frequency on the order of the relaxation rate and it vanishes for both, low frequencies and high frequencies. At temperatures at which the static response is finite (lower and higher than $T_0$), the modulus is found to decay monotonously from the static limit to zero at high frequencies. In addition, results of calculations for a trap model with a Gaussian density of states are presented. In this case, the cubic response depends on the specific dynamical variable considered and also on the way the external field is coupled to the kinetics of the model. In particular, a set of different dynamical variables is considered that gives rise to identical shapes of the linear susceptibility and only to different temperature dependencies of the relaxation times. It is found that the frequency dependence of the nonlinear response functions, however, strongly depends on the particular choice of the variables. The results are discussed in the context of recent theoretical and experimental findings regarding the nonlinear response of supercooled liquids and glasses.Comment: 23 pages, 10 figure

Density Functional Theory of doped superfluid liquid helium and nanodroplets

During the last decade, density function theory (DFT) in its static and dynamic time dependent forms, has emerged as a powerful tool to describe the structure and dynamics of doped liquid helium and droplets. In this review, we summarize the activity carried out in this field within the DFT framework since the publication of the previous review article on this subject [M. Barranco et al., J. Low Temp. Phys. 142, 1 (2006)]. Furthermore, a comprehensive presentation of the actual implementations of helium DFT is given, which have not been discussed in the individual articles or are scattered in the existing literature. This is an Accepted Manuscript of an article published on August 2, 2017 by Taylor & Francis Group in Int. Rev. Phys. Chem. 36, 621 (2017), available online: http://dx.doi.org/10.1080/0144235X.2017.1351672Comment: 113 pages, 42 figure

The Thermal Evolution of the Donors in AM CVn Binaries

(Abridged) We calculate the full stellar-structural evolution of donors in AM CVn systems formed through the WD channel coupled to the binary's evolution. Contrary to assumptions made in prior modelling, these donors are not fully convective over much of the AM CVn phase and do not evolve adiabatically under mass loss indefinitely. Instead, we identify three distinct phases of evolution: a mass transfer turn-on phase (during which the orbital period continues to decrease even after contact, the donor contracts, and the mass transfer rate accelerates to its maximum), a phase in which the donor expands adiabatically in response to mass loss, and a cooling phase beginning at orbital periods of approximately 45--55 minutes during which the donor contracts. The physics that determines the behaviour in the first and third phases, both of which are new outcomes of this study, are discussed in some detail. We find the overall duration of the turn-on phase to be between $\sim 10^4$-$10^6$ yrs, significantly longer than prior estimates. We predict the donor's luminosity and effective temperature. During the adiabatic expansion phase (ignoring irradiation effects), the luminosity is approximately $10^{-6}$--$10^{-4} L_\odot$ and the effective temperature is approximately 1000--1800 K. However, the flux generated in the accretion flow dominates the donor's intrinsic light at all times. The impact of irradiation on the donor extends the phase of adiabatic expansion to longer orbital periods and alters the donor's observational characteristics. Irradiated donors during the adiabatic phase can attain a surface luminosity of up to $\approx10^{-2} L_\odot$. We argue that the turn-on and cooling phases both will leave significant imprints on the AM CVn population's orbital period distribution.Comment: (20 pages, 20 figures, accepted to the Monthly Notices of the Royal Astronomical Society

The Migration and Growth of Protoplanets in Protostellar Discs

We investigate the gravitational interaction of a Jovian mass protoplanet with a gaseous disc with aspect ratio and kinematic viscosity expected for the protoplanetary disc from which it formed. Different disc surface density distributions have been investigated. We focus on the tidal interaction with the disc with the consequent gap formation and orbital migration of the protoplanet. Nonlinear hydrodynamic simulations are employed using three independent numerical codes. A principal result is that the direction of the orbital migration is always inwards and such that the protoplanet reaches the central star in a near circular orbit after a characteristic viscous time scale of approximately 10,000 initial orbital periods. This was found to be independent of whether the protoplanet was allowed to accrete mass or not. Inward migration is helped through the disappearance of the inner disc, and therefore the positive torque it would exert, because of accretion onto the central star.Our results indicate that a realistic upper limit for the masses of closely orbiting giant planets is approximately 5 Jupiter masses, because of the reduced accretion rates obtained for planets of increasing mass. Assuming some process such as termination of the inner disc through a magnetospheric cavity stops the migration, the range of masses estimated for a number of close orbiting giant planets (Marcy, Cochran, & Mayor 1999; Marcy & Butler 1998) as well as their inward orbital migration can be accounted for by consideration of disc--protoplanet interactions during the late stages of giant planet formation. Maximally accreting protoplanets reached about four Jovian masses on reaching the neighbourhood of the central star.Comment: 19 pages, 16 figures, submitted to MNRAS. A version of this paper that includes high resolution figures may be obtained from http://www.maths.qmw.ac.uk/~rpn/preprint.htm

Spin-orbit final state interaction in the framework of Glauber theory for (e,e'p) reactions

We investigate the reactions D(e,e'p)n and D(\vec e,e'p)n at GeV energies and discuss the opportunities to distinguish between different models for the nuclear ground state by measuring the response functions. In calculating the final-state interaction (FSI) we employ Glauber theory, and we also include relativistic effects in the electromagnetic current. We include not only the central FSI, but also the spin-orbit FSI which is usually neglected in (e,e'p) calculations within the Glauber framework and we show that this contribution plays a crucial role for the fifth response function. All of the methods developed here can be applied to any target nucleus.Comment: 20 pages, 12 figures, minor change in figures 3 and 4 (changed beam energy), correction of error in figure 4 in the previous replacemen

The onset of instability in unsteady boundary-layer separation

The process of unsteady two-dimensional boundary-layer separation at high Reynolds number is considered. Solutions of the unsteady non-interactive boundary-layer equations are known to develop a generic separation singularity in regions where the pressure gradient is prescribed and adverse. As the boundary layer starts to separate from the surface, however, the external pressure distribution is altered through viscous-inviscid interaction just prior to the formation of the separation singularity; hitherto this has been referred to as the first interactive stage. A numerical solution of this stage is obtained here in Lagrangian coordinates. The solution is shown to exhibit a high-frequency inviscid instability resulting in an immediate finite-time breakdown of this stage. The presence of the instability is confirmed through a linear stability analysis. The implications for the theoretical description of unsteady boundary-layer separation are discussed, and it is suggested that the onset of interaction may occur much sooner than previously thought