Peaks and Troughs in Helioseismology: The Power Spectrum of Solar Oscillations

I present a matched-wave asymptotic analysis of the driving of solar oscillations by a general localised source. The analysis provides a simple mathematical description of the asymmetric peaks in the power spectrum in terms of the relative locations of eigenmodes and troughs in the spectral response. It is suggested that the difference in measured phase function between the modes and the troughs in the spectrum will provide a key diagnostic of the source of the oscillations. I also suggest a form for the asymmetric line profiles to be used in the fitting of solar power spectra. Finally I present a comparison between the numerical and asymptotic descriptions of the oscillations. The numerical results bear out the qualitative features suggested by the asymptotic analysis but suggest that numerical calculations of the locations of the troughs will be necessary for a quantitative comparison with the observations.Comment: 18 pages + 8 separate figures. To appear in Ap

Improved bounds and new techniques for Davenport-Schinzel sequences and their generalizations

Let lambda_s(n) denote the maximum length of a Davenport-Schinzel sequence of order s on n symbols. For s=3 it is known that lambda_3(n) = Theta(n alpha(n)) (Hart and Sharir, 1986). For general s>=4 there are almost-tight upper and lower bounds, both of the form n * 2^poly(alpha(n)) (Agarwal, Sharir, and Shor, 1989). Our first result is an improvement of the upper-bound technique of Agarwal et al. We obtain improved upper bounds for s>=6, which are tight for even s up to lower-order terms in the exponent. More importantly, we also present a new technique for deriving upper bounds for lambda_s(n). With this new technique we: (1) re-derive the upper bound of lambda_3(n) <= 2n alpha(n) + O(n sqrt alpha(n)) (first shown by Klazar, 1999); (2) re-derive our own new upper bounds for general s; and (3) obtain improved upper bounds for the generalized Davenport-Schinzel sequences considered by Adamec, Klazar, and Valtr (1992). Regarding lower bounds, we show that lambda_3(n) >= 2n alpha(n) - O(n), and therefore, the coefficient 2 is tight. We also present a simpler version of the construction of Agarwal, Sharir, and Shor that achieves the known lower bounds for even s>=4.Comment: To appear in Journal of the ACM. 48 pages, 3 figure

Understanding the Heavy Fermion Phenomenology from Microscopic Model

We solve the 3D periodic Anderson model via two impurity DMFT. We obtain the temperature v.s. hybridization phase diagram. In approaching the quantum critical point (QCP) both the Neel and lattice Kondo temperatures decrease and they do not cross at the lowest temperature we reached. While strong ferromagnetic spin fluctuation on the Kondo side is observed, our result indicates the critical static spin susceptibility is local in space at the QCP. We observe in the crossover region logarithmic temperature dependence in the specific heat coefficient and spin susceptibility

Screening of charged spheroidal colloidal particles

We study the effective screened electrostatic potential created by a spheroidal colloidal particle immersed in an electrolyte, within the mean field approximation, using Poisson--Botzmann equation in its linear and nonlinear forms, and also beyond the mean field by means of Monte Carlo computer simulation. The anisotropic shape of the particle has a strong effect on the screened potential, even at large distances (compared to the Debye length) from it. To quantify this anisotropy effect, we focus our study on the dependence of the potential on the position of the observation point with respect with the orientation of the spheroidal particle. For several different boundary conditions (constant potential, or constant surface charge) we find that, at large distance, the potential is higher in the direction of the large axis of the spheroidal particle

Monoids, Embedding Functors and Quantum Groups

We show that the left regular representation \pi_l of a discrete quantum group (A,\Delta) has the absorbing property and forms a monoid (\pi_l,\tilde{m},\tilde{\eta}) in the representation category Rep(A,\Delta). Next we show that an absorbing monoid in an abstract tensor *-category C gives rise to an embedding functor E:C->Vect_C, and we identify conditions on the monoid, satisfied by (\pi_l,\tilde{m},\tilde{\eta}), implying that E is *-preserving. As is well-known, from an embedding functor E: C->\mathrm{Hilb} the generalized Tannaka theorem produces a discrete quantum group (A,\Delta) such that C is equivalent to Rep_f(A,\Delta). Thus, for a C^*-tensor category C with conjugates and irreducible unit the following are equivalent: (1) C is equivalent to the representation category of a discrete quantum group (A,\Delta), (2) C admits an absorbing monoid, (3) there exists a *-preserving embedding functor E: C->\mathrm{Hilb}.Comment: Final version, to appear in Int. Journ. Math. (Added some references and Subsection 1.2.) Latex2e, 21 page

Two-component plasma in a gravitational field: Thermodynamics

We revisit the model of the two-component plasma in a gravitational field, which mimics charged colloidal suspensions. We concentrate on the computation of the grand potential of the system. Also, a special sum rule for this model is presented.Comment: 7 pages, LaTeX2

An efficient sampling algorithm for Variational Monte Carlo

We propose a new algorithm for sampling the $N$-body density $|\Psi({\bf R})|^2/\int_{\mathbb{R}^{3N}} |\Psi|^2$ in the Variational Monte Carlo (VMC) framework. This algorithm is based upon a modified Ricci-Ciccotti discretization of the Langevin dynamics in the phase space $({\bf R},{\bf P})$ improved by a Metropolis acceptation/rejection step. We show through some representative numerical examples (Lithium, Fluorine and Copper atoms, and phenol molecule), that this algorithm is superior to the standard sampling algorithm based on the biased random walk (importance sampling).Comment: 23 page

Electric field control and optical signature of entanglement in quantum dot molecules

The degree of entanglement of an electron with a hole in a vertically coupled self-assembled dot molecule is shown to be tunable by an external electric field. Using atomistic pseudopotential calculations followed by a configuration interaction many-body treatment of correlations, we calculate the electronic states, degree of entanglement and optical absorption. We offer a novel way to spectroscopically detect the magnitude of electric field needed to maximize the entanglement.Comment: 4 pages, 6 figure

A New Test of the Einstein Equivalence Principle and the Isotropy of Space

Recent research has established that nonsymmetric gravitation theories like Moffat's NGT predict that a gravitational field singles out an orthogonal pair of polarization states of light that propagate with different phase velocities. We show that a much wider class of nonmetric theories encompassed by the $\chi g$ formalism predict such violations of the Einstein equivalence principle. This gravity-induced birefringence of space implies that propagation through a gravitational field can alter the polarization of light. We use data from polarization measurements of extragalactic sources to constrain birefringence induced by the field of the Galaxy. Our new constraint is $10^8$ times sharper than previous ones.Comment: 21 pages, Latex, 3 Postscript figure

Optimal molecular alignment and orientation through rotational ladder climbing

We study the control by electromagnetic fields of molecular alignment and orientation, in a linear, rigid rotor model. With the help of a monotonically convergent algorithm, we find that the optimal field is in the microwave part of the spectrum and acts by resonantly exciting the rotation of the molecule progressively from the ground state, i.e., by rotational ladder climbing. This mechanism is present not only when maximizing orientation or alignment, but also when using prescribed target states that simultaneously optimize the efficiency of orientation/alignment and its duration. The extension of the optimization method to consider a finite rotational temperature is also presented.Comment: 14 pages, 12 figure