Improved numerical approach for time-independent Gross-Pitaevskii nonlinear Schroedinger equation

In the present work, we improve a numerical method, developed to solve the Gross-Pitaevkii nonlinear Schroedinger equation. A particular scaling is used in the equation, which permits to evaluate the wave-function normalization after the numerical solution. We have a two point boundary value problem, where the second point is taken at infinity. The differential equation is solved using the shooting method and Runge-Kutta integration method, requiring that the asymptotic constants, for the function and its derivative, are equal for large distances. In order to obtain fast convergence, the secant method is used.Comment: 2 figure

Ab initio Quantum and ab initio Molecular Dynamics of the Dissociative Adsorption of Hydrogen on Pd(100)

The dissociative adsorption of hydrogen on Pd(100) has been studied by ab initio quantum dynamics and ab initio molecular dynamics calculations. Treating all hydrogen degrees of freedom as dynamical coordinates implies a high dimensionality and requires statistical averages over thousands of trajectories. An efficient and accurate treatment of such extensive statistics is achieved in two steps: In a first step we evaluate the ab initio potential energy surface (PES) and determine an analytical representation. Then, in an independent second step dynamical calculations are performed on the analytical representation of the PES. Thus the dissociation dynamics is investigated without any crucial assumption except for the Born-Oppenheimer approximation which is anyhow employed when density-functional theory calculations are performed. The ab initio molecular dynamics is compared to detailed quantum dynamical calculations on exactly the same ab initio PES. The occurence of quantum oscillations in the sticking probability as a function of kinetic energy is addressed. They turn out to be very sensitive to the symmetry of the initial conditions. At low kinetic energies sticking is dominated by the steering effect which is illustrated using classical trajectories. The steering effects depends on the kinetic energy, but not on the mass of the molecules. Zero-point effects lead to strong differences between quantum and classical calculations of the sticking probability. The dependence of the sticking probability on the angle of incidence is analysed; it is found to be in good agreement with experimental data. The results show that the determination of the potential energy surface combined with high-dimensional dynamical calculations, in which all relevant degrees of freedon are taken into account, leads to a detailed understanding of the dissociation dynamics of hydrogen at a transition metal surface.Comment: 15 pages, 9 figures, subm. to Phys. Rev.

Free expansion of Bose-Einstein condensates with quantized vortices

The expansion of Bose-Einstein condensates with quantized vortices is studied by solving numerically the time-dependent Gross-Pitaevskii equation at zero temperature. For a condensate initially trapped in a spherical harmonic potential, we confirm previous results obtained by means of variational methods showing that, after releasing the trap, the vortex core expands faster than the radius of the atomic cloud. This could make the detection of vortices feasible, by observing the depletion of the density along the axis of rotation. We find that this effect is significantly enhanced in the case of anisotropic disc-shaped traps. The results obtained as a function of the anisotropy of the initial configuration are compared with the analytic solution for a noninteracting gas in 3D as well as with the scaling law predicted for an interacting gas in 2D.Comment: 5 pages, 6 postscript figure

Preparation of decoherence-free, subradiant states in a cavity

The cause of decoherence in a quantum system can be traced back to the interaction with the environment. As it has been pointed out first by Dicke, in a system of N two-level atoms where each of the atoms is individually dipole coupled to the environment, there are collective, subradiant states, that have no dipole coupling to photon modes, and therefore they are expected to decay slower. This property also implies that these type of states, which form an N-1 dimensional subspace of the atomic subsytem, also decohere slower. We propose a scheme which will create such states. First the two-level atoms are placed in a strongly detuned cavity and one of the atoms, called the control atom is excited. The time evolution of the coupled atom-cavity system leads to an appropriately entangled state of the atoms. By applying subsequent laser pulses at a well defined time instant, it is possible to drive the atomic state into the subradiant, i. e., decoherence free subspace. Up to a certain average number of the photons, the result is independent of the state of the cavity. The analysis of the conditions shows that this scheme is feasible with present day techniques achieved in atom cavity interaction experiments.Comment: 5 page

Abelian Higgs Hair for Electrically Charged Dilaton Black Holes

It is argued that an electronically charged dilaton black hole can support a long range field of a Nielsen-Olesen string. Combining both numerical and perturbative techniques we examine the properties of an Abelian-Higgs vortex in the presence of the black hole under consideration. Allowing the black hole to approach extremality we found that all fields of the vortex are expelled from the extreme black hole. In the thin string limit we obtained the metric of a conical electrically charged dilaton black hole. The effect of the vortex can be measured from infinity justifying its characterization as black hole hair.Comment: 13 pages, 14 figures, Revtex, to appear in Phys.Rev.D1

Relativistic instant-form approach to the structure of two-body composite systems

A new approach to the electroweak properties of two-particle composite systems is developed. The approach is based on the use of the instant form of relativistic Hamiltonian dynamics. The main novel feature of this approach is the new method of construction of the matrix element of the electroweak current operator. The electroweak current matrix element satisfies the relativistic covariance conditions and in the case of the electromagnetic current also the conservation law automatically. The properties of the system as well as the approximations are formulated in terms of form factors. The approach makes it possible to formulate relativistic impulse approximation in such a way that the Lorentz-covariance of the current is ensured. In the electromagnetic case the current conservation law is ensured, too. The results of the calculations are unambiguous: they do not depend on the choice of the coordinate frame and on the choice of "good" components of the current as it takes place in the standard form of light--front dynamics. Our approach gives good results for the pion electromagnetic form factor in the whole range of momentum transfers available for experiments at present time, as well as for lepton decay constant of pion.Comment: 26 pages, Revtex, 5 figure

Intersubband spin-density excitations in quantum wells with Rashba spin splitting

In inversion-asymmetric semiconductors, spin-orbit coupling induces a k-dependent spin splitting of valence and conduction bands, which is a well-known cause for spin decoherence in bulk and heterostructures. Manipulating nonequilibrium spin coherence in device applications thus requires understanding how valence and conduction band spin splitting affects carrier spin dynamics. This paper studies the relevance of this decoherence mechanism for collective intersubband spin-density excitations (SDEs) in quantum wells. A density-functional formalism for the linear spin-density matrix response is presented that describes SDEs in the conduction band of quantum wells with subbands that may be non-parabolic and spin-split due to bulk or structural inversion asymmetry (Rashba effect). As an example, we consider a 40 nm GaAs/AlGaAs quantum well, including Rashba spin splitting of the conduction subbands. We find a coupling and wavevector-dependent splitting of the longitudinal and transverse SDEs. However, decoherence of the SDEs is not determined by subband spin splitting, due to collective effects arising from dynamical exchange and correlation.Comment: 10 pages, 4 figure

Spin fluctuations in nearly magnetic metals from ab-initio dynamical spin susceptibility calculations:application to Pd and Cr95V5

We describe our theoretical formalism and computational scheme for making ab-initio calculations of the dynamic paramagnetic spin susceptibilities of metals and alloys at finite temperatures. Its basis is Time-Dependent Density Functional Theory within an electronic multiple scattering, imaginary time Green function formalism. Results receive a natural interpretation in terms of overdamped oscillator systems making them suitable for incorporation into spin fluctuation theories. For illustration we apply our method to the nearly ferromagnetic metal Pd and the nearly antiferromagnetic chromium alloy Cr95V5. We compare and contrast the spin dynamics of these two metals and in each case identify those fluctuations with relaxation times much longer than typical electronic `hopping times'Comment: 21 pages, 9 figures. To appear in Physical Review B (July 2000

The (LATTICE) QCD Potential and Running Coupling: How to Accurately Interpolate between Multi-Loop QCD and the String Picture

We present a simple parameterization of a running coupling constant, defined via the static potential, that interpolates between 2-loop QCD in the UV and the string prediction in the IR. Besides the usual \Lam-parameter and the string tension, the coupling depends on one dimensionless parameter, determining how fast the crossover from UV to IR behavior occurs (in principle we know how to take into account any number of loops by adding more parameters). Using a new Ansatz for the LATTICE potential in terms of the continuum coupling, we can fit quenched and unquenched Monte Carlo results for the potential down to ONE lattice spacing, and at the same time extract the running coupling to high precision. We compare our Ansatz with 1-loop results for the lattice potential, and use the coupling from our fits to quantitatively check the accuracy of 2-loop evolution, compare with the Lepage-Mackenzie estimate of the coupling extracted from the plaquette, and determine Sommer's scale $r_0$ much more accurately than previously possible. For pure SU(3) we find that the coupling scales on the percent level for $\beta\geq 6$.Comment: 47 pages, incl. 4 figures in LaTeX [Added remarks on correlated vs. uncorrelated fits in sect. 4; corrected misprints; updated references.