Ground-state coherence induced oscillations in a three-level system

The interaction of a three-level atomic medium with two degenerate sublevels in the ground-state with a coherent radiation field in a ring cavity is investigated. We pay specific attention to atomic coherence within the ground-state doublet, considering separate decay rates for the ground-state coherence and the population difference. In a previous paper we presented the stationary solutions and here we report on self-pulsing solutions. At critical intensities of the input field, the partially stable symmetry-breaking branches give rise to Hopf bifurcations. Furthermore, we observe in a limiting case of the limit cycles solitary solutions. The associated diverging periods show an interesting power law behaviour.Work supported by the Swiss National Science Foundation     

Relationship between spectral properties and spatial coherence properties in one-dimensional free fields

Some consequences of a recently derived relationship between the spectral properties and the spatial coherence properties of a stationary optical field are studied for the case when the field is one-dimensional. It is found that the spectrum may be determined from the knowledge of the spatial coherence of the field at all pairs of points that lie within an interval whose length is at least as great as the coherence length of the light.     

Synchrotron beam coherence: a spatially resolved measurement

We report a precise and spatially resolved measurement of the complex degree of coherence of a one-dimensional 1.5-keV beam produced by a third-generation synchrotron source. The method of phase-space tomography is used, which requires only measurements of the x-ray intensity. We find that the field is statistically stationary to within experimental error, the correlations are very well approximated by a Gaussian distribution, and the measured coherence length is in excellent agreement with expectations.     

Perturbative Treatment for Stationary State of Local Master Equation

The local approach to construct master equation for a composite open system with a weak internal coupling is simple and seems reasonable. However, it is thermodynamic consistent only when the subsystems are resonantly coupled. Efforts are being made to understand the inconsistency and test the validity of the local master equation. We present a perturbative method to solve the steady-state solutions of linear local master equations, which are demonstrated by two simple models. The solving process shows the stationary state as the result of competition between incoherent operations and the unitary creating quantum coherence, and consequently relate quantum coherence with thermodynamic consistency.     

The physics of vortex superconductivity. II

The effect of charge on a vortex world-sheet is examined. The relationship between world-sheet charge, winding number, and the flow of momentum along the vortex is illuminated. Full solutions for bosonic field and current profiles are obtained numerically. Both the string energy per unit length and tension are calculated. As an application stationary circular string solutions are studied. We find that except possibly for extreme cases rings stabilized by winding number alone do not exist. The role of angular momentum in stabilizing a ring is then discussed, emphasizing its model independent nature, and it is shown that in this case stationary spinning ring solutions, called vortons, are easily found. In a cosmological setting this can lead to a massive overdensity of vortons equivalent to a monopole problem.     

Perturbative Treatment for Stationary State of Local Master Equation

The local approach to construct master equation for a composite open system with a weak internal coupling is simple and seems reasonable. However, it is thermodynamic consistent only when the subsystems are resonantly coupled. Efforts are being made to understand the inconsistency and test the validity of the local master equation. We present a perturbative method to solve the steady-state solutions of linear local master equations, which are demonstrated by two simple models. The solving process shows the stationary state as the result of competition between incoherent operations and the unitary creating quantum coherence, and consequently relate quantum coherence with thermodynamic consistency.     

Boundary Value Problems for the Stationary Axisymmetric Einstein Equations: A Disk Rotating Around a Black Hole

We solve a class of boundary value problems for the stationary axisymmetric Einstein equations involving a disk rotating around a central black hole. The solutions are given explicitly in terms of theta functions on a family of hyperelliptic Riemann surfaces of genus 4. In the absence of a disk, they reduce to the Kerr black hole. In the absence of a black hole, they reduce to the Neugebauer-Meinel disk.     

Bifurcation phenomena in a convection problem with temperature dependent viscosity at low aspect ratio

In this paper we analyse convective solutions of a two dimensional fluid layer in which viscosity depends exponentially on temperature. This problem takes in features of mantle convection, since large viscosity variations are to be expected in the Earth’s interior. These solutions are compared with solutions obtained at constant viscosity. Special attention is paid to the influence of the aspect ratio in the solutions presented. The analysis is assisted by bifurcation techniques such as branch continuation, which has proven to be a useful, systematic method for gaining insight into the possible stationary solutions satisfied by the basic equations. One feature presented by the fluid with non constant viscosity is the presence of pitchfork and saddle-node subcritical bifurcations and the presence of convective solutions below the linear critical threshold. The analysis also provides limits of existence of stationary solutions and draws the boundaries for time dependent convection.     

Excess resistance in the superconducting transition of a mesoscopic Al disk

We report resistance measurements on a mesoscopic Al disk whose size is comparable to the superconducting coherence length. As the magnetic field increases, resistance peaks successively appear and some of the peak resistances are larger than the normal state value R_N. These peaks are ascribed to the transitions between different vortex states in the superconducting Al disk. The experimental results suggest that some anomalous energy dissipation is caused by the dynamics of the vortices in the confined geometry.     

FREE VIBRATION ANALYSIS OF A SPINNING FLEXIBLE DISK-SPINDLE SYSTEM SUPPORTED BY BALL BEARING AND FLEXIBLE SHAFT USING THE FINITE ELEMENT METHOD AND SUBSTRUCTURE SYNTHESIS

Free vibration of a spinning flexible disk-spindle system supported by ball bearing and flexible shaft is analyzed by using Hamilton's principle, FEM and substructure synthesis. The spinning disk is described by using the Kirchhoff plate theory and von Karman non-linear strain. The rotating spindle and stationary shaft are modelled by Rayleigh beam and Euler beam respectively. Using Hamilton's principle and including the rigid body translation and tilting motion, partial differential equations of motion of the spinning flexible disk and spindle are derived consistently to satisfy the geometric compatibility in the internal boundary between substructures. FEM is used to discretize the derived governing equations, and substructure synthesis is introduced to assemble each component of the disk-spindle-bearing-shaft system. The developed method is applied to the spindle system of a computer hard disk drive with three disks, and modal testing is performed to verify the simulation results. The simulation result agrees very well with the experimental one. This research investigates critical design parameters in an HDD spindle system, i.e., the non-linearity of a spinning disk and the flexibility and boundary condition of a stationary shaft, to predict the free vibration characteristics accurately. The proposed method may be effectively applied to predict the vibration characteristics of a spinning flexible disk-spindle system supported by ball bearing and flexible shaft in the various forms of computer storage device, i.e., FDD, CD, HDD and DVD.     

On the role of the boundary conditions in the Ginzburg-Landau theory

The effect of the boundary conditions for solutions on the Ginzburg-Landau (GL) equations for superconducting plates in the vortex-free limit is studied by numerical methods. Based on the self-consistent solution of the system of GL equations, the dependence of the critical current I _c on the external magnetic field and the distribution of the order parameter over the plate thickness are determined. When solving the equations with general boundary conditions, it was found that the critical temperature and critical current density decreased in comparison with those obtained by solving equations with ordinary boundary conditions. According to the results of this study, the use of general boundary conditions leads to a number of interesting results which were not observed when using ordinary boundary conditions. The range of the applicability of the vortex-free limit for the films of thickness of the order of the coherence length ξ are discussed. The effect of boundary conditions on the applicability of this limit is analyzed.     

Phase and vortex correlations in superconducting Josephson-junction arrays at irrational magnetic frustration

Phase coherence and vortex order in a Josephson-junction array at irrational frustration are studied by extensive Monte Carlo simulations using the parallel-tempering method. A scaling analysis of the correlation length of phase variables in the full equilibrated system shows that the critical temperature vanishes with a power-law divergent correlation length and critical exponent nuph, in agreement with recent results from resistivity scaling analysis. A similar scaling analysis for vortex variables reveals a different critical exponent nuv, suggesting that there are two distinct correlation lengths associated with a decoupled zero-temperature phase transition.     

Collapse mechanism of the condensate wavefunction in the Bose-Fermi mixture with attraction between the components

The ground state of the mixture of degenerate Bose and Fermi atoms in a trap has been analyzed on the basis of the effective Hamiltonian. The two types of the solutions of the modified Gross-Pitaevskii equation that correspond to the stationary and unstable states of the Bose gas have been found numerically. The chemical potential and energy are found as functions of the number of bosons for these two types of the solutions. The manyvalued character of these functions has been analyzed and the critical number of bosons at which the system collapse occurs has been determined.     

Length dependence of critical current in thin superconductors

The critical current and its dependence on the length of a thin superconducting wire between two normal metals and the voltage difference across the wire at the critical current is calcualted. The latter arises from the conversion of the normal current into supercurrent and vice versa at the contacts. It is found that the critical current is zero when the length of the wire is π coherence lengths or smaller.     

Cross-diffusive effects on the onset of double-diffusive convection in a horizontal saturated porous fluid layer heated and salted from above

Double-diffusive stationary and oscillatory instabilities at the marginal state in a saturated porous horizontal fluid layer heated and salted from above are investigated theoretically under the Darcy's framework for a porous medium. The contributions of Soret and Dufour coefficients are taken into account in the analysis. Linear stability analysis shows that the critical value of the Darcy-Rayleigh number depends on cross-diffusive parameters at marginally stationary convection, while the marginal state characterized by oscillatory convection does not depend on the cross-diffusion terms even if the condition and frequency of oscillatory convection depends on the cross-diffusive parameters. The critical value of the Darcy-Rayleigh number increases with increasing value of the solutal Darcy-Rayleigh number in the absence of cross-diffusive parameters. The critical Darcy-Rayleigh number decreases with increasing Soret number, resulting in destabilization of the system, while its value increases with increasing Dufour number, resulting in stabilization of the system at the marginal state characterized by stationary convection. The analysis reveals that the Dufour and Soret parameters as well as the porosity parameter play an important role in deciding the type of instability at the onset. This analysis also indicates that the stationary convection is followed by the oscillatory convection for certain fluid mixtures. It is interesting to note that the roles of cross-diffusive parameters on the double-diffusive system heated and salted from above are reciprocal to the double-diffusive system heated and salted from below.     

Finite-temperature scaling of quantum coherence near criticality in a spin chain

We explore quantum coherence, inherited from Wigner-Yanase skew information, to analyzequantum criticality in the anisotropic XY chain model at finite temperature. Based on theexact solutions of the Hamiltonian, the quantum coherence contained in a nearest-neighborspin pairs reduced density matrix ρ is obtained. The first-order derivative of thequantum coherence is non-analytic around the critical point at sufficient low temperature.The finite-temperature scaling behavior and the universality are verified numerically. Inparticular, the quantum coherence can also detect the factorization transition in such amodel at sufficient low temperature. We also show that quantum coherence contained indistant spin pairs can characterize quantum criticality and factorization phenomena atfinite temperature. Our results imply that quantum coherence can serve as an efficientindicator of quantum criticality in such a model and shed considerable light on therelationships between quantum phase transitions and quantum information theory at finitetemperature.     

Coherence properties of an amplified spontaneous emission laser: experiments on a 10 Hz vacuum–ultraviolet H2-laser

Spatial coherence properties of a mirrorless laser, namely a 10 Hz Lyman-band molecular hydrogen laser pumped by femtosecond pulses of only 200 mJ, are studied. Assuming a Gaussian Schell-model source and using the generalized van Cittert–Zernike theorem we are able to measure both the coherence length arising from free-space propagation and the coherence length at the source plane. This analysis is particularly suitable to the study of the coherence properties of lasers operating in the amplified spontaneous emission regime and is particularly indicated for x-ray lasers. Measurements at various target lengths show a monotonic increase in the degree of spatial coherence and decrease in the source size versus length of the gain column. As a consequence, a monotonic decrease in the number of sustained transverse modes with length of the gain medium is observed, demonstrating the effects of gain guiding and refractive antiguiding.     

Colloidal dipolar interactions in 2D smectic-C films

We use a two-dimensional (2D) elastic free energy to calculate the effective interaction between two circular disks immersed in smectic-C films. For strong homeotropic anchoring, the distortion of the director field caused by the disks generates topological defects that induce an effective interaction between the disks. We use finite elements, with adaptive meshing, to minimize the 2D elastic free energy. The method is shown to be accurate and efficient for inhomogeneities on the length scales set by the disks and the defects, that differ by up to 3 orders of magnitude. We compute the effective interaction between two disk-defect pairs in a simple (linear) configuration. For large disk separations, D, the elastic free energy scales as ∼D ^-2, confirming the dipolar character of the long-range effective interaction. For small D the energy exhibits a pronounced minimum. The lowest energy corresponds to a symmetrical configuration of the disk-defect pairs, with the inner defect at the mid-point between the disks. The disks are separated by a distance that is twice the distance of the outer defect from the nearest disk. The latter is identical to the equilibrium distance of a defect nucleated by an isolated disk. Received 26 October 2001 and Received in final form 14 December 2001     

The spatial coherence properties of the spontaneous emission in the one-dimensional strong random system with gain

By using the finite difference time domain method, the spatial coherence properties of the spontaneous emission in the one-dimensional strong random system with gain are investigated in detail. Results show that the coherence properties improve slowly with the increase of the system length at low pump rates. And at high pump rates the coherence properties obviously become better after a certain system length. While at very high pump rates it is a non-monotonic function of the system length, there exists the best coherence at a certain system length. These behaviors are explained by Lamb theory and scaling theory. Our study may be helpful to the designing of random lasers.