Asymptotically exact mean field theory for the Anderson model including double occupancy

The Anderson impurity model for finite values of the Coulomb repulsion $U$ is studied using a slave boson representation for the empty and doubly occupied $f$-level. In order to avoid well known problems with a naive mean field theory for the boson fields, we use the coherent state path integral representation to first integrate out the double occupancy slave bosons. The resulting effective action is linearized using {\bf two-time} auxiliary fields. After integration over the fermionic degrees of freedom one obtains an effective action suitable for a $1/N_f$-expansion. Concerning the constraint the same problem remains as in the infinite $U$ case. For $T \rightarrow 0$ and $N_f \rightarrow \infty$ exact results for the ground state properties are recovered in the saddle point approximation. Numerical solutions of the saddle point equations show that even in the spindegenerate case $N_f = 2$ the results are quite good.Comment: 19, RevTeX, cond-mat/930502

Model study of the sign problem in the mean-field approximation

We argue the sign problem of the fermion determinant at finite density. It is unavoidable not only in Monte-Carlo simulations on the lattice but in the mean-field approximation as well. A simple model deriving from Quantum Chromodynamics (QCD) in the double limit of large quark mass and large quark chemical potential exemplifies how the sign problem arises in the Polyakov loop dynamics at finite temperature and density. In the color SU(2) case our mean-field estimate is in excellent agreement with the lattice simulation. We combine the mean-field approximation with a simple phase reweighting technique to circumvent the complex action encountered in the color SU(3) case. We also investigate the mean-field free energy, from the saddle-point of which we can estimate the expectation value of the Polyakov loop.Comment: 14 page, 18 figures, typos corrected, references added, some clarification in sec.I

Classical and quantum-mechanical treatments of nonsequential double ionization with few-cycle laser pulses

We address nonsequential double ionization induced by strong, linearly polarized laser fields of only a few cycles, considering a physical mechanism in which the second electron is dislodged by the inelastic collision of the first electron with its parent ion. The problem is treated classically, using an ensemble model, and quantum-mechanically, within the strong-field and uniform saddle-point approximations. In the latter case, the results are interpreted in terms of "quantum orbits", which can be related to the trajectories of a classical electron in an electric field. We obtain highly asymmetric electron momentum distributions, which strongly depend on the absolute phase, i.e., on the phase difference between the pulse envelope and its carrier frequency. Around a particular value of this parameter, the distributions shift from the region of positive to that of negative momenta, or vice-versa, in a radical fashion. This behavior is investigated in detail for several driving-field parameters, and provides a very efficient method for measuring the absolute phase. Both models yield very similar distributions, which share the same physical explanation. There exist, however, minor discrepancies due to the fact that, beyond the region for which electron-impact ionization is classically allowed, the yields from the quantum mechanical computation decay exponentially, whereas their classical counterparts vanish.Comment: 12 pages revtex, 12 figures (eps files

Flow in a double-film-fed fluid bead between contra-rotating rolls, Part 1: equilibrium flow structure

In multiple-roll coaters thin liquid films are transferred from roll to roll by means of liquid ‘beads’ which occupy the small gaps between adjacent rolls. Double-Film-Fed (DFF) beads are those which feature two ingoing films instead of the usual one, and arise in the intermediate stages of certain types of roll coater. One of the ingoing films, h1, is supplied from the previous inter-roll gap while the other, h2, ‘returns’ from the subsequent gap. Such a flow is investigated here under the conditions of low flow rate, small capillary number and negligible gravity and inertia, using lubrication theory and finite element analysis. The thickness of film h1 is fixed independently, while that of h2 is specified as a fraction, [zeta], of the film output on the same roll. This simple approach allows a degree of feedback between the output and input of the bead, and enables one to simulate different conditions in the subsequent gap. Predictions of outgoing film thicknesses made using the two models agree extremely well and show that, for each value of [zeta] < 1, one outgoing film thickness decreases monotonically with speed ratio, S, while the other features a maximum. Good agreement is also seen in the pressure profiles, which are entirely sub-ambient in keeping with the small capillary number conditions. The finite element solutions reveal that in the ‘zero-flux’ case (when [zeta] = 1) the flow structures are very similar to those seen in an idealized cavity problem. In the more general ([zeta] < 1) situation, as in single-film-fed meniscus roll coating, several liquid transfer-jets occur by which liquid is conveyed through the bead from one roll to the other. The lubrication model is used to calculate several critical flow rates at which the flow is transformed, and it is shown that when the total dimensionless flow rate through the bead exceeds 1/3, the downstream flow structure is independent of the relative sizes of the ingoing films

Small aspect ratio Taylor-Couette flow: onset of a very-low-frequency three-torus state

The nonlinear dynamics of Taylor-Couette flow in a small aspect ratio annulus (where the length of the cylinders is half of the annular gap between them) is investigated by numerically solving the full three-dimensional Navier-Stokes equations. The system is invariant to arbitrary rotations about the annulus axis and to a reflection about the annulus half-height, so that the symmetry group is SO(2)×Z2. In this paper, we systematically investigate primary and subsequent bifurcations of the basic state, concentrating on a parameter regime where the basic state becomes unstable via Hopf bifurcations. We derive the four distinct cases for the symmetries of the bifurcated orbit, and numerically find two of these. In the parameter regime considered, we also locate the codimension-two double Hopf bifurcation where these two Hopf bifurcations coincide. Secondary Hopf bifurcations (Neimark-Sacker bifurcations), leading to modulated rotating waves, are subsequently found and a saddle-node-infinite-period bifurcation between a stable (node) and an unstable (saddle) modulated rotating wave is located, which gives rise to a very-low-frequency three-torus. This paper provides the computed example of such a state, along with a comprehensive bifurcation sequence leading to its onset.Postprint (published version

A Scaling Theory of Bifurcations in the Symmetric Weak-Noise Escape Problem

We consider the overdamped limit of two-dimensional double well systems perturbed by weak noise. In the weak noise limit the most probable fluctuational path leading from either point attractor to the separatrix (the most probable escape path, or MPEP) must terminate on the saddle between the two wells. However, as the parameters of a symmetric double well system are varied, a unique MPEP may bifurcate into two equally likely MPEP's. At the bifurcation point in parameter space, the activation kinetics of the system become non-Arrhenius. In this paper we quantify the non-Arrhenius behavior of a system at the bifurcation point, by using the Maslov-WKB method to construct an approximation to the quasistationary probability distribution of the system that is valid in a boundary layer near the separatrix. The approximation is a formal asymptotic solution of the Smoluchowski equation. Our analysis relies on the development of a new scaling theory, which yields `critical exponents' describing weak-noise behavior near the saddle, at the bifurcation point.Comment: LaTeX, 60 pages, 24 Postscript figures. Uses epsf macros to include the figures. A file in `uufiles' format containing the figures is separately available at ftp://platinum.math.arizona.edu/pub/papers-rsm/paperF/figures.uu and a Postscript version of the whole paper (figures included) is available at ftp://platinum.math.arizona.edu/pub/papers-rsm/paperF/paperF.p