Path representation of maximal parabolic Kazhdan-Lusztig polynomials

We provide simple rules for the computation of Kazhdan--Lusztig polynomials in the maximal parabolic case. They are obtained by filling regions delimited by paths with "Dyck strips" obeying certain rules. We compare our results with those of Lascoux and Sch\"utzenberger.Comment: v3: fixed proof of lemma

The transition temperature of the dilute interacting Bose gas for NN internal degrees of freedom

We calculate explicitly the variation $\delta T_c$ of the Bose-Einstein condensation temperature $T_c$ induced by weak repulsive two-body interactions to leading order in the interaction strength. As shown earlier by general arguments, $\delta T_c/T_c$ is linear in the dimensionless product $an^{1/3}$ to leading order, where $n$ is the density and $a$ the scattering length. This result is non-perturbative, and a direct perturbative calculation of the amplitude is impossible due to infrared divergences familiar from the study of the superfluid helium lambda transition. Therefore we introduce here another standard expansion scheme, generalizing the initial model which depends on one complex field to one depending on $N$ real fields, and calculating the temperature shift at leading order for large $N$. The result is explicit and finite. The reliability of the result depends on the relevance of the large $N$ expansion to the situation N=2, which can in principle be checked by systematic higher order calculations. The large $N$ result agrees remarkably well with recent numerical simulations.Comment: 10 pages, Revtex, submitted to Europhysics Letter

Enhancement of field renormalization in scalar theories via functional renormalization group

The flow equations of the Functional Renormalization Group are applied to the O(N)-symmetric scalar theory, for N=1 and N=4, in four Euclidean dimensions, d=4, to determine the effective potential and the renormalization function of the field in the broken phase. In our numerical analysis, the infrared limit, corresponding to the vanishing of the running momentum scale in the equations, is approached to obtain the physical values of the parameters by extrapolation. In the N=4 theory a non-perturbatively large value of the physical renormalization of the longitudinal component of the field is observed. The dependence of the field renormalization on the UV cut-off and on the bare coupling is also investigated.Comment: 20 pages, 7 figures. To appear in Physical Review

Application of finite element techniques in predicting the acoustic properties of turbofan inlets

An analytical technique was developed for predicting the acoustic performance of turbofan inlets carrying a subsonic axisymmetric steady flow. The finite element method combined with the method of weighted residuals is used in predicting the acoustic properties of variable area, annular ducts with or without acoustic treatments along their walls. An approximate solution for the steady inviscid flow field is obtained using an integral method for calculating the incompressible potential flow field in the inlet with a correction to account for compressibility effects. The accuracy of the finite element technique was assessed by comparison with available analytical solutions for the problems of plane and spinning wave propagation through a hard walled annular cylinder with a constant mean flow

Acoustic properties of turbofan inlets

The acoustic field within a duct containing a nonuniform steady flow was predicted. This analysis used the finite element method to calculate the velocity potential within the duct

Mean-Motion Resonances of High Order in Extrasolar Planetary Systems

Many multi-planet systems have been discovered in recent years. Some of them are in mean-motion resonances (MMR). Planet formation theory was successful in explaining the formation of 2:1, 3:1 and other low resonances as a result of convergent migration. However, higher order resonances require high initial orbital eccentricities in order to be formed by this process and these are in general unexpected in a dissipative disk. We present a way of generating large initial eccentricities using additional planets. This procedure allows us to form high order MMRs and predict new planets using a genetic N-body code.Comment: To appear in Proceedings: Extrasolar Planets in Multi-body Systems: Theory and Observations; Editors K. Gozdziewski, A. Niedzielski and J. Schneider; 5 pages, 2 figures

Condensation temperature of interacting Bose gases with and without disorder

The momentum-shell renormalization group (RG) is used to study the condensation of interacting Bose gases without and with disorder. First of all, for the homogeneous disorder-free Bose gas the interaction-induced shifts in the critical temperature and chemical potential are determined up to second order in the scattering length. The approach does not make use of dimensional reduction and is thus independent of previous derivations. Secondly, the RG is used together with the replica method to study the interacting Bose gas with delta-correlated disorder. The flow equations are derived and found to reduce, in the high-temperature limit, to the RG equations of the classical Landau-Ginzburg model with random-exchange defects. The random fixed point is used to calculate the condensation temperature under the combined influence of particle interactions and disorder.Comment: 7 pages, 2 figure

Quantum phase transition in an atomic Bose gas near a Feshbach resonance

We study the quantum phase transition in an atomic Bose gas near a Feshbach resonance in terms of the renormalization group. This quantum phase transition is characterized by an Ising order parameter. We show that in the low temperature regime where the quantum fluctuations dominate the low-energy physics this phase transition is of first order because of the coupling between the Ising order parameter and the Goldstone mode existing in the bosonic superfluid. However, when the thermal fluctuations become important, the phase transition turns into the second order one, which belongs to the three-dimensional Ising universality class. We also calculate the damping rate of the collective mode in the phase with only a molecular Bose-Einstein condensate near the second-order transition line, which can serve as an experimental signature of the second-order transition.Comment: 8 pages, 2 figures, published version in Phys. Rev.

Quantum critical scaling behavior of deconfined spinons

We perform a renormalization group analysis of some important effective field theoretic models for deconfined spinons. We show that deconfined spinons are critical for an isotropic SU(N) Heisenberg antiferromagnet, if $N$ is large enough. We argue that nonperturbatively this result should persist down to N=2 and provide further evidence for the so called deconfined quantum criticality scenario. Deconfined spinons are also shown to be critical for the case describing a transition between quantum spin nematic and dimerized phases. On the other hand, the deconfined quantum criticality scenario is shown to fail for a class of easy-plane models. For the cases where deconfined quantum criticality occurs, we calculate the critical exponent $\eta$ for the decay of the two-spin correlation function to first-order in $\epsilon=4-d$. We also note the scaling relation $\eta=d+2(1-\phi/\nu)$ connecting the exponent $\eta$ for the decay to the correlation length exponent $\nu$ and the crossover exponent $\phi$.Comment: 4.1 pages, no figures, references added; Version accepted for publication in PRB (RC

Bose-Einstein Condensation Temperature of Homogenous Weakly Interacting Bose Gas in Variational Perturbation Theory Through Seven Loops

The shift of the Bose-Einstein condensation temperature for a homogenous weakly interacting Bose gas in leading order in the scattering length `a' is computed for given particle density `n.' Variational perturbation theory is used to resum the corresponding perturbative series for Delta/Nu in a classical three-dimensional scalar field theory with coupling `u' and where the physical case of N=2 field components is generalized to arbitrary N. Our results for N=1,2,4 are in agreement with recent Monte-Carlo simulations; for N=2, we obtain Delta T_c/T_c = 1.27 +/- 0.11 a n^(1/3). We use seven-loop perturbative coefficients, extending earlier work by one loop order.Comment: 8 pages; typos and errors of presentation fixed; beautifications; results unchange