Planar Harmonic Polynomials of Type B

The hyperoctahedral group is the Weyl group of type B and is associated with a two-parameter family of differential-difference operators T_i, i=1,..,N (the dimension of the underlying Euclidean space). These operators are analogous to partial derivative operators. This paper finds all the polynomials in N variables which are annihilated by the sum of the squares (T_1)^2+(T_2)^2 and by all T_i for i>2 (harmonic). They are given explicitly in terms of a novel basis of polynomials, defined by generating functions. The harmonic polynomials can be used to find wave functions for the quantum many-body spin Calogero model.Comment: 17 pages, LaTe

Dynamics of the excitations of a quantum dot in a microcavity

We study the dynamics of a quantum dot embedded in a three-dimensional microcavity in the strong coupling regime in which the quantum dot exciton has an energy close to the frequency of a confined cavity mode. Under the continuous pumping of the system, confined electron and hole can recombine either by spontaneous emission through a leaky mode or by stimulated emission of a cavity mode that can escape from the cavity. The numerical integration of a master equation including all these effects gives the dynamics of the density matrix. By using the quantum regression theorem, we compute the first and second order coherence functions required to calculate the photon statistics and the spectrum of the emitted light. Our main result is the determination of a range of parameters in which a state of cavity modes with poissonian or sub-poissonian (non-classical) statistics can be built up within the microcavity. Depending on the relative values of pumping and rate of stimulated emission, either one or two peaks close to the excitation energy of the dot and/or to the natural frequency of the cavity are observed in the emission spectrum. The physics behind these results is discussed

Electrostatic control of quantum dot entanglement induced by coupling to external reservoirs

We propose a quantum transport experiment to prepare and measure charge-entanglement between two electrostatically defined quantum dots. Coherent population trapping, as realized in cavity quantum electrodynamics, can be carried out by using a third quantum dot to play the role of the optical cavity. In our proposal, a pumping which is quantum mechanically indistinguishable for the quantum dots drives the system into a state with a high degree of entanglement. The whole effect can be switched on and off by means of a gate potential allowing both state preparation and entanglement detection by simply measuring the total current.Comment: 5 pages, 4 figures, Latex2e with EPL macros, to appear in Europhysics Letter

Hot Quark Matter with an Axial Chemical Potential

We analyze the phase diagram of hot quark matter in presence of an axial chemical potential, $\mu_5$. The latter is introduced to mimic the chirality transitions induced, in hot Quantum Chromodynamics, by the strong sphaleron configurations. In particular, we study the curvature of the critical line at small $\mu_5$, the effects of a finite quark mass and of a vector interaction. Moreover, we build the mixed phase at the first order phase transition line, and draw the phase diagram in the chiral density and temperature plane. We finally compute the full topological susceptibility in presence of a background of topological charge.Comment: 12 pages, 7 figures. Few references added, short discussion included. Final version appearing on Phys. Rev.

Statistical properties of an ideal subgrid-scale correction for Lagrangian particle tracking in turbulent channel flow

One issue associated with the use of Large-Eddy Simulation (LES) to investigate the dispersion of small inertial particles in turbulent flows is the accuracy with which particle statistics and concentration can be reproduced. The motion of particles in LES fields may differ significantly from that observed in experiments or direct numerical simulation (DNS) because the force acting on the particles is not accurately estimated, due to the availability of the only filtered fluid velocity, and because errors accumulate in time leading to a progressive divergence of the trajectories. This may lead to different degrees of inaccuracy in the prediction of statistics and concentration. We identify herein an ideal subgrid correction of the a-priori LES fluid velocity seen by the particles in turbulent channel flow. This correction is computed by imposing that the trajectories of individual particles moving in filtered DNS fields exactly coincide with the particle trajectories in a DNS. In this way the errors introduced by filtering into the particle motion equations can be singled out and analyzed separately from those due to the progressive divergence of the trajectories. The subgrid correction term, and therefore the filtering error, is characterized in the present paper in terms of statistical moments. The effects of the particle inertia and of the filter type and width on the properties of the correction term are investigated.Comment: 15 pages,24 figures. Submitted to Journal of Physics: Conference Serie

Elementary Excitations of Heisenberg Ferrimagnetic Spin Chains

We numerically investigate elementary excitations of the Heisenberg alternating-spin chains with two kinds of spins 1 and 1/2 antiferromagnetically coupled to each other. Employing a recently developed efficient Monte Carlo technique as well as an exact diagonalization method, we verify the spin-wave argument that the model exhibits two distinct excitations from the ground state which are gapless and gapped. The gapless branch shows a quadratic dispersion in the small-momentum region, which is of ferromagnetic type. With the intention of elucidating the physical mechanism of both excitations, we make a perturbation approach from the decoupled-dimer limit. The gapless branch is directly related to spin 1's, while the gapped branch originates from cooperation of the two kinds of spins.Comment: 7 pages, 7 Postscript figures, RevTe

Dynamics of Quasi-ordered Structure in a Regio-regulated pi-Conjugated Polymer:Poly(4-methylthiazole-2,5-diyl)

Dynamics of regio-regulated Poly(4-methylthiazole-2,5-diyl) [HH-P4MeTz] was inves tigated by solid-state 1H, 2D, 13C NMR spectroscopies, and differential scanning calorimetry(DSC) measurements. DSC, 2D quadrupolar echo NMR, 13C cross-polarization and magic-angle spinning(CPMAS) NMR, and 2D spin-echo(2DSE) CPMAS NMR spectroscopy suggest existence of a quasi-ordered phase in which backbone twists take place with weakened pi-stackings. Two-dimensional exchange 2D NMR(2DEX) detected slow dynamics with a rate of an order of 10^2Hz for the CD_3 group in d_3-HH-P4MeTz at 288K. The frequency dependence of proton longitudinal relaxation rate at 288K shows a omega^-1/2 dependence, which is due to the one-dimensional diffusion-like motion of backbone conformational modulation waves. The diffusion rate was estimated as 3+/-2 GHz, which was approximately 10^7 times larger than that estimated by 2DEX NMR measurements. These results suggest that there exists anomalous dispersion of modulation waves in HH-P4MeTz. The one-dimensional group velocity of the wave packet is responsible for the behavior of proton longitudinal relaxation time. On the other hand, the 2DEX NMR is sensitive to phase velocity of the nutation of methyl groups that is associated with backbone twists. From proton T_1 and T_2 measurements, the activation energy was estimated as 2.9 and 3.4 kcal/mol, respectively. These were in agreement with 3.0 kcal/mol determined by Moller-Plesset(MP2) molecular orbital(MO) calculation. We also performed chemical shielding calculation of the methyl-carbon in order to understand chemical shift tensor behavior, leading to the fact that a quasi-ordered phase coexist with the crystalline phase.Comment: 14 pages, 11 figures, to appear in Phys.Rev.

Laboratory experiments on two coalescing axisymmetric turbulent plumes in a rotating fluid

Author Posting. © The Author(s), 2011. This is the author's version of the work. It is posted here by permission of American Institute of Physics for personal use, not for redistribution. The definitive version was published in Physics of Fluids 23 (2011): 056601, doi:10.1063/1.3584134.We investigate the early-time coalescence of two co-flowing axisymmetric turbulent plumes and the later-time flow of the induced vortices in a rotating, homogeneous fluid using laboratory experiments. The experiments demonstrate the critical importance of the rotation period Tf = 2π/f, where f is the Coriolis parameter of the background rotation. We find that if the plumes’ sources are sufficiently “close” for the plumes to merge initially at an “early time” tm≲tr = 3Tf/4, the experimentally observed merging height zme agrees well with the non-rotating theoretical relationship of zmt ≈ (0.44/α)x0tr, however, the flow dynamics are substantially more complicated, as the flow becomes significantly affected by rotation. The propagation and entrainment of the plumes becomes strongly affected by the vortices induced by the entrainment flow in a rotating environment. Also, the plume fluid itself starts to interact with these vortices. If the plumes have already initially merged by the time t = tr, a single vortex (initially located at the midpoint of the line connecting the two plume sources) develops, which both advects and modifies the geometry of the merging plumes. Coupled with the various suppressing effects of rotation on the radial plume entrainment, the “apparent” observed height of merger can vary substantially from its initial value. Conversely, for more widely separated “distant” plumes, where x0>xc = (25α/2)F01/4f-3/4, the plumes do not merge before the critical time tr when rotation becomes significant in the flow dynamics and two vortices are observed, each located over a plume source. The combined effect of these vortices with the associated suppression of entrainment by rotation thus significantly further delays the merger of the two plumes, which apparently becomes possible only through the merger of the induced vortices.This work was supported by the Center for Planetary Science