4,090 research outputs found
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 internal degrees of freedom
We calculate explicitly the variation of the Bose-Einstein
condensation temperature induced by weak repulsive two-body interactions
to leading order in the interaction strength. As shown earlier by general
arguments, is linear in the dimensionless product
to leading order, where is the density and 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 real fields, and calculating the
temperature shift at leading order for large . The result is explicit and
finite. The reliability of the result depends on the relevance of the large
expansion to the situation N=2, which can in principle be checked by systematic
higher order calculations. The large 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 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 for the decay of
the two-spin correlation function to first-order in . We also
note the scaling relation connecting the exponent
for the decay to the correlation length exponent and the crossover
exponent .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
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